PART I
Devices and
Basic Circuits
CHAPTER 1
Signals and Amplifiers 4
CHAPTER 2
Operational Amplifiers 52
CHAPTER 3
Semiconductors 124
CHAPTER 4
Diodes 164
CHAPTER 5
MOS Field-Effect Transistors (MOSFETs) 230
CHAPTER 6
Bipolar Junction Transistors (BJTs) 350
P
art I, Devices and Basic Circuits, includes the most fundamental and essential topics
for the study of electronic circuits. At the same time, it constitutes a complete package for a first course on the subject.
The heart of Part I is the study of the three basic semiconductor devices: the diode
(Chapter 4); the MOS transistor (Chapter 5); and the bipolar transistor (Chapter 6). In each
case, we study the device operation, its characterization, and its basic circuit applications.
For those who have not had a prior course on device physics, Chapter 3 provides an overview of semiconductor concepts at a level sufficient for the study of electronic circuits. A
review of Chapter 3 should prove useful even for those with prior knowledge of semiconductors.
Since the purpose of electronic circuits is the processing of signals, an understanding
is essential of signals, their characterization in the time and frequency domains, and their
analog and digital representations. This is provided in Chapter 1, which also introduces
the most common signal-processing function, amplification, and the characterization
and types of amplifiers.
Besides diodes and transistors, the basic electronic devices, the op amp is studied in
Part I. Although not an electronic device in the most fundamental sense, the op amp is
commercially available as an integrated circuit (IC) package and has well-defined terminal characteristics. Thus, despite the fact that the op amp’s internal circuit is complex, typically incorporating 20 or more transistors, its almost-ideal terminal behavior makes it
possible to treat the op amp as a circuit element and to use it in the design of powerful
circuits, as we do in Chapter 2, without any knowledge of its internal construction. We
should mention, however, that the study of op amps can be delayed to a later point, and
Chapter 2 can be skipped with no loss of continuity.
The foundation of this book, and of any electronics course, is the study of the two
transistor types in use today: the MOS transistor in Chapter 5 and the bipolar transistor
in Chapter 6. These two chapters have been written to be completely independent of one
another and thus can be studied in either order as desired. Furthermore, the two chapters have the same structure, making it easier and faster to study the second device, as
well as to draw comparisons between the two device types.
After the study of Part I, the reader will be fully prepared to undertake the study of
either integrated-circuit amplifiers in Part II or digital integrated circuits in Part III.
3
CHAPTER 1
Signals
and Amplifiers
Introduction 5
1.5
Circuit Models for Amplifiers 21
1.1
Signals 6
1.6
Frequency Response of Amplifiers 30
1.2
Frequency Spectrum of Signals 9
Summary 41
1.3
Analog and Digital Signals 11
Problems 42
1.4 Amplifiers 14
IN THIS CHAPTER YOU WILL LEARN
1. That electronic circuits process signals, and thus understanding electrical signals is essential to appreciating the material in this book.
2. The Thévenin and Norton representations of signal sources.
3. The representation of a signal as the sum of sine waves.
4. The analog and digital representations of a signal.
5. The most basic and pervasive signal-processing function: signal amplification, and correspondingly, the signal amplifier.
6. How amplifiers are characterized (modeled) as circuit building blocks
independent of their internal circuitry.
7. How the frequency response of an amplifier is measured, and how it is
calculated, especially in the simple but common case of a single-timeconstant (STC) type response.
Introduction
!"#$%&'(#)*$+,$*"-%$'++.$-%$/+0#12$#3#)*1+2-)%4$5$,-#30$*"5*$"5%$)+/#$*+$'#$.2+62$5%$!"#$%&
'('#)$%*"#+7, -"#$%'('#)$%*"#+$ 1#,#1%$ *+$ *"#$ -2*#815*#09)-1)&-*$ :;<=$ *#)"2+3+8>$ *"5*$ 5*$ *"#
*-/#$ +,$ *"-%$ 61-*-28$ -%$ )5?5'3#$ +,$ ?1+0&)-28$ )-1)&-*%$ *"5*$ )+2*5-2$ "&201#0%$ +,$ /-33-+2%$ +,
)+/?+2#2*%$-2$5$%/533$?-#)#$+,$%-3-)+2$:.2+62$5%$5$+"("#%*,#."/=$6"+%#$51#5$-%$+2$*"#$+10#1
+,$@AA$//B7$C2#$%&)"$/-)1+#3#)*1+2-)$)-1)&-*4$,+1$#D5/?3#4$-%$5$)+/?3#*#$0-8-*53$)+/?&*#14
6"-)"$5))+10-283>$-%$.2+62$5%$5$!"#$%#%!/0)'$$+14$/+1#$8#2#1533>4$5$!"#$%/$%#'++%$7
;2$*"-%$'++.$6#$%"533$%*&0>$#3#)*1+2-)$0#E-)#%$*"5*$)52$'#$&%#0$%-283>$:-2$*"#$0#%-82$+,$1"+&
#$')', #"$#0")+=$ +1$ 5%$ )+/?+2#2*%$ +,$ 52$ "*)'2$3)'1&#"$#0")$ 4567$ )"-?7$ F#$ %"533$ %*&0>$ *"#
0#%-82$520$5253>%-%$+,$-2*#1)+22#)*-+2%$+,$*"#%#$0#E-)#%4$6"-)"$,+1/$0-%)1#*#$520$-2*#815*#0
)-1)&-*%$+,$E51>-28$)+/?3#D-*>$520$?#1,+1/$5$6-0#$E51-#*>$+,$,&2)*-+2%7$F#$%"533$53%+$3#512
5'+&*$5E5-35'3#$;<$)"-?%$520$*"#-1$5??3-)5*-+2$-2$*"#$0#%-82$+,$#3#)*1+2-)$%>%*#/%7
!"#$?&1?+%#$+,$*"-%$,-1%*$)"5?*#1$-%$*+$-2*1+0&)#$%+/#$'5%-)$)+2)#?*%$520$*#1/-2+3+8>7$;2
?51*-)&3514$6#$%"533$3#512$5'+&*$%-8253%$520$5'+&*$+2#$+,$*"#$/+%*$-/?+1*52*$%-82539?1+)#%%-28
,&2)*-+2%$#3#)*1+2-)$)-1)&-*%$51#$0#%-82#0$*+$?#1,+1/4$25/#3>4$%-8253$5/?3-,-)5*-+27$F#$%"533
*"#2$ 3++.$ 5*$ )-1)&-*$ 1#?1#%#2*5*-+2%$ +1$ /+0#3%$ ,+1$ 3-2#51$ 5/?3-,-#1%7$ !"#%#$ /+0#3%$ 6-33$ '#
#/?3+>#0$-2$%&'%#G&#2*$)"5?*#1%$-2$*"#$0#%-82$520$5253>%-%$+,$5)*&53$5/?3-,-#1$)-1)&-*%7
5
6 Chapter 1 Signals and Amplifiers
;2$500-*-+2$*+$/+*-E5*-28$*"#$%*&0>$+,$#3#)*1+2-)%4$*"-%$)"5?*#1$%#1E#%$5%$5$'1-08#$'#*6##2
*"#$%*&0>$+,$3-2#51$)-1)&-*%$520$*"5*$+,$*"#$%&'(#)*$+,$*"-%$'++.H$*"#$0#%-82$520$5253>%-%$+,
#3#)*1+2-)$)-1)&-*%7
1.1 Signals
I-8253%$)+2*5-2$-2,+1/5*-+2$5'+&*$5$E51-#*>$+,$*"-28%$520$5)*-E-*-#%$-2$+&1$?">%-)53$6+1307
JD5/?3#%$5'+&20H$;2,+1/5*-+2$5'+&*$*"#$6#5*"#1$-%$)+2*5-2#0$-2$%-8253%$*"5*$1#?1#%#2*$*"#
5-1$*#/?#15*&1#4$?1#%%&1#4$6-20$%?##04$#*)7$!"#$E+-)#$+,$5$150-+$522+&2)#1$1#50-28$*"#$2#6%
-2*+$5$/-)1+?"+2#$?1+E-0#%$52$5)+&%*-)$%-8253$*"5*$)+2*5-2%$-2,+1/5*-+2$5'+&*$6+130$5,,5-1%7
!+$/+2-*+1$*"#$%*5*&%$+,$5$2&)3#51$1#5)*+14$-2%*1&/#2*%$51#$&%#0$*+$/#5%&1#$5$/&3*-*&0#$+,
1#3#E52*$?515/#*#1%4$#5)"$-2%*1&/#2*$?1+0&)-28$5$%-82537
!+$ #D*15)*$ 1#G&-1#0$ -2,+1/5*-+2$ ,1+/$ 5$ %#*$ +,$ %-8253%4$ *"#$ +'%#1E#1$ :'#$ -*$ 5$ "&/52$ +1$ 5
/5)"-2#=$-2E51-5'3>$2##0%$*+$/$%#'++$*"#$%-8253%$-2$%+/#$?1#0#*#1/-2#0$/522#17$!"-%$+"2*3(
/$%#'++"*2$-%$&%&533>$/+%*$)+2E#2-#2*3>$?#1,+1/#0$'>$#3#)*1+2-)$%>%*#/%7$K+1$*"-%$*+$'#$?+%%-9
'3#4$"+6#E#14$*"#$%-8253$/&%*$,-1%*$'#$)+2E#1*#0$-2*+$52$#3#)*1-)53$%-82534$*"5*$-%4$5$E+3*58#$+1$5
)&11#2*7$!"-%$?1+)#%%$-%$5))+/?3-%"#0$'>$0#E-)#%$.2+62$5%$)$3*+10#'$+7,L$E51-#*>$+,$*152%9
0&)#1%$#D-%*4$#5)"$%&-*5'3#$,+1$+2#$+,$*"#$E51-+&%$,+1/%$+,$?">%-)53$%-8253%7$K+1$-2%*52)#4$*"#
%+&20$65E#%$8#2#15*#0$'>$5$"&/52$)52$'#$)+2E#1*#0$-2*+$#3#)*1-)53$%-8253%$'>$&%-28$5$/-)1+9
?"+2#4$6"-)"$-%$-2$#,,#)*$5$?1#%%&1#$*152%0&)#17$;*$-%$2+*$+&1$?&1?+%#$"#1#$*+$%*&0>$*152%0&)#1%M
15*"#14$6#$%"533$5%%&/#$*"5*$*"#$%-8253%$+,$-2*#1#%*$531#50>$#D-%*$-2$*"#$#3#)*1-)53$0+/5-2$520
1#?1#%#2*$*"#/$'>$+2#$+,$*"#$*6+$#G&-E53#2*$,+1/%$%"+62$-2$K-87$@7@7$;2$K-87$@7@:5=$*"#$%-8253$-%
1#?1#%#2*#0$'>$5$E+3*58#$%+&1)#$v!:"=$"5E-28$5$%+&1)#$1#%-%*52)#$#!7$;2$*"#$53*#125*#$1#?1#%#2*59
*-+2$+,$K-87$@7@:'=$*"#$%-8253$-%$1#?1#%#2*#0$'>$5$)&11#2*$%+&1)#$$!:"=$"5E-28$5$%+&1)#$1#%-%*52)#
#!7$L3*"+&8"$*"#$*6+$1#?1#%#2*5*-+2%$51#$#G&-E53#2*4$*"5*$-2$K-87$@7@:5=$:.2+62$5%$*"#$!"NE#2-2
,+1/=$ -%$ ?1#,#11#0$ 6"#2$ #!$ -%$ 3+67$ !"#$ 1#?1#%#2*5*-+2$ +,$ K-87$ @7@:'=$ :.2+62$ 5%$ *"#$ O+1*+2
,+1/=$-%$?1#,#11#0$6"#2$#!$-%$"-8"7$!"#$1#50#1$6-33$)+/#$*+$5??1#)-5*#$*"-%$?+-2*$35*#1$-2$*"-%
)"5?*#1$6"#2$6#$%*&0>$*"#$0-,,#1#2*$*>?#%$+,$5/?3-,-#1%7$K+1$*"#$*-/#$'#-284$-*$-%$-/?+1*52*$*+
'#$,5/-3-51$6-*"$!"NE#2-2P%$520$O+1*+2P%$*"#+1#/%$:,+1$5$'1-#,$1#E-#64$%##$L??#20-D$Q=$520$*+
2+*#$*"5*$,+1$*"#$*6+$1#?1#%#2*5*-+2%$-2$K-87$@7@$*+$'#$#G&-E53#2*4$*"#-1$?515/#*#1%$51#$1#35*#0$'>
v! ( " ) = #! $! ( " )
Rs
vs(t)
"
!
(a)
is(t)
Rs
(b)
Figure 1.1 !6+$53*#125*-E#$1#?1#%#2*5*-+2%$+,
5$%-8253$%+&1)#H,437$*"#$!"NE#2-2$,+1/M$487$*"#
O+1*+2$,+1/7
Example 1.1
!"#$+&*?&*$1#%-%*52)#$+,$5$%-8253$%+&1)#4$53*"+&8"$-2#E-*5'3#4$-%$52$-/?#1,#)*-+2$*"5*$3-/-*%$*"#$5'-3-*>$+,$*"#
%+&1)#$*+$0#3-E#1$-*%$,&33$%-8253$%*1#28*"$*+$5$(%317$!+$%##$*"-%$?+-2*$/+1#$)3#513>4$)+2%-0#1$*"#$%-8253$%+&1)#
6"#2$)+22#)*#0$*+$5$3+50$1#%-%*52)#$#%$5%$%"+62$-2$K-87$@7B7$K+1$*"#$)5%#$-2$6"-)"$*"#$%+&1)#$-%$1#?1#%#2*#0
1.1 Signals
'>$-*%$!"NE#2-2$#G&-E53#2*$,+1/4$,-20$*"#$E+3*58#$v&$*"5*$5??#51%$5)1+%%$#%4$520$"#2)#$*"#$)+20-*-+2$*"5*$#!
/&%*$%5*-%,>$,+1$ v&$*+$'#$)3+%#$*+$*"#$E53&#$+,$ v!7$R#?#5*$,+1$*"#$O+1*+291#?1#%#2*#0$%+&1)#M$-2$*"-%$)5%#
,-20-28$*"#$)&11#2*$$&$*"5*$,3+6%$*"1+&8"$#%$520$"#2)#$*"#$)+20-*-+2$*"5*$#!$/&%*$%5*-%,>$,+1$$&$*+$'#$)3+%#$*+
*"#$E53&#$+,$$!7
Rs
io
"
vs
"
!
RL
vo
is
Rs
RL
!
(a)
(b)
Figure 1.2 <-1)&-*%$ ,+1
JD5/?3#$@7@7
Solution
K+1$*"#$!"NE#2-291#?1#%#2*#0$%-8253$%+&1)#$%"+62$-2$K-87$@7B:5=4$*"#$+&*?&*$E+3*58#$ v&$*"5*$5??#51%$5)1+%%
*"#$3+50$1#%-%*52)#$#%$)52$'#$,+&20$,1+/$*"#$15*-+$+,$*"#$E+3*58#$0-E-0#1$,+1/#0$'>$#!$520$#%4
#%
9
v & " v ! 99999999999999999
#% ! #!
K1+/$*"-%$#G&5*-+2$6#$%##$*"5*$,+1
v& ! v!
*"#$%+&1)#$1#%-%*52)#$#!$/&%*$'#$/&)"$3+6#1$*"52$*"#$3+50$1#%-%*52)#$#%4$
#! # #%
!"&%4$,+1$5$%+&1)#$1#?1#%#2*#0$'>$-*%$!"NE#2-2$#G&-E53#2*4$-0#533>$#!$S$A4$520$5%$#!$-%$-2)1#5%#04$1#35*-E#$*+
*"#$3+50$1#%-%*52)#$#%$6-*"$6"-)"$*"-%$%+&1)#$-%$-2*#20#0$*+$+?#15*#4$*"#$E+3*58#$v&$*"5*$5??#51%$5)1+%%$*"#
3+50$'#)+/#%$%/533#14$2+*$5$0#%-15'3#$+&*)+/#7
O#D*4$6#$)+2%-0#1$*"#$O+1*+291#?1#%#2*#0$%-8253$%+&1)#$-2$K-87$@7B:'=7$!+$+'*5-2$*"#$)&11#2*$$&$*"5*$,3+6%
*"1+&8"$*"#$3+50$1#%-%*52)#$#%4$6#$&*-3-T#$*"#$15*-+$+,$*"#$)&11#2*$0-E-0#1$,+1/#0$'>$#!$520$#%4
#!
9
$ & $ " $ ! 99999999999999999
#! ! #%
K1+/$*"-%$1#35*-+2%"-?$6#$%##$*"5*$,+1
$& ! $!
*"#$%+&1)#$1#%-%*52)#$#!$/&%*$'#$/&)"$3518#1$*"5*$#%4
#! $ #%
!"&%$,+1$5$%-8253$%+&1)#$1#?1#%#2*#0$'>$-*%$O+1*+2$#G&-E53#2*4$-0#533>$#!$S$∞4$520$5%$#!$-%$1#0&)#04$1#35*-E#
*+$*"#$3+50$1#%-%*52)#$#%$6-*"$6"-)"$*"-%$%+&1)#$-%$-2*#20#0$*+$+?#15*#4$*"#$)&11#2*$$&$*"5*$,3+6%$*"1+&8"$*"#
3+50$'#)+/#%$%/533#14$2+*$5$0#%-15'3#$+&*)+/#7
K-2533>4$6#$2+*#$*"5*$53*"+&8"$)-1)&-*$0#%-82#1%$)522+*$&%&533>$0+$/&)"$5'+&*$*"#$E53&#$+,$ #!M$*"#>$/5>
"5E#$*+$0#E-%#$5$)-1)&-*$%+3&*-+2$*"5*$/-2-/-T#%$+1$#3-/-25*#%$*"#$3+%%$+,$%-8253$%*1#28*"$*"5*$1#%&3*%$6"#2
*"#$%+&1)#$-%$)+22#)*#0$*+$*"#$3+507
7
8 Chapter 1 Signals and Amplifiers
EXERCISES
1.1$ K+1$*"#$%-82539%+&1)#$1#?1#%#2*5*-+2%$%"+62$-2$K-8%7$@7@:5=$520$@7@:'=4$6"5*$51#$*"#$+?#29)-1)&-*
+&*?&*$E+3*58#%$*"5*$6+&30$'#$+'%#1E#0X$;,4$,+1$#5)"4$*"#$+&*?&*$*#1/-253%$51#$%"+1*9)-1)&-*#0$:-7#74
6-1#0$*+8#*"#1=4$6"5*$)&11#2*$6+&30$,3+6X$K+1$*"#$1#?1#%#2*5*-+2%$*+$'#$#G&-E53#2*4$6"5*$/&%*$*"#$1#9
35*-+2%"-?$'#$'#*6##2$v!4$$!4$520$#!X
Ans. K+1$:5=4$v&'$S$v!:"=M$,+1$:'=4$v&'$S$#!$!:"=M$,+1$:5=4$ $ !' = v ! ( " ) ⁄ # ! M$,+1$:'=4$$!'$S$$!:"=M$,+1$#G&-E53#2)>4
v!:"=$S$#!$!:"=
1.2 L$%-8253$%+&1)#$"5%$52$+?#29)-1)&-*$E+3*58#$+,$@A$/Y$520$5$%"+1*9)-1)&-*$)&11#2*$+,$@A$µL7$F"5*$-%$*"#
%+&1)#$1#%-%*52)#X
Ans. @$.Ω
1.3 L$%-8253$%+&1)#$*"5*$-%$/+%*$)+2E#2-#2*3>$1#?1#%#2*#0$'>$-*%$!"NE#2-2$#G&-E53#2*$"5%$v!$S$@A$/Y$520
#!$S$@$.Ω7$;,$*"#$%+&1)#$,##0%$5$3+50$1#%-%*52)#$#%4$,-20$*"#$E+3*58#$v&$*"5*$5??#51%$5)1+%%$*"#$3+50$,+1
#%$S$@AA$.Ω4$@A$.Ω4$@$.Ω4$520$@AA$Ω7$L3%+4$,-20$*"#$3+6#%*$?#1/-%%-'3#$E53&#$+,$ #%$,+1$6"-)"$*"#
+&*?&*$E+3*58#$-%$5*$3#5%*$ZA[$+,$*"#$%+&1)#$E+3*58#7
Ans. \7\$/YM$\7@$/YM$]$/YM$A7\$/YM$^$.Ω
1.4 L$%-8253$%+&1)#$*"5*$-%$/+%*$)+2E#2-#2*3>$1#?1#%#2*#0$'>$-*%$O+1*+2$#G&-E53#2*$,+1/$"5%$ $!$S$@A$µL
520$#!$S$@AA$.Ω7$;,$*"#$%+&1)#$,##0%$5$3+50$1#%-%*52)#$#%4$,-20$*"#$)&11#2*$$&$*"5*$,3+6%$*"1+&8"$*"#$3+50
,+1$#%$S$@$.Ω4$@A$.Ω4$@AA$.Ω4$520$@$_Ω7$L3%+4$,-20$*"#$3518#%*$?#1/-%%-'3#$E53&#$+,$#%$,+1$6"-)"$*"#
3+50$)&11#2*$-%$5*$3#5%*$ZA[$+,$*"#$%+&1)#$)&11#2*7
Ans. #$#%µ&'%#$(%µ&'%)%µ&'%*$#%µ&'%+)%,Ω
K1+/$*"#$0-%)&%%-+2$5'+E#4$-*$%"+&30$'#$5??51#2*$*"5*$5$%-8253$-%$5$*-/#9E51>-28$G&52*-*>$*"5*
)52$'#$1#?1#%#2*#0$'>$5$815?"$%&)"$5%$*"5*$%"+62$-2$K-87$@7U7$;2$,5)*4$*"#$-2,+1/5*-+2$)+2*#2*$+,
*"#$%-8253$-%$1#?1#%#2*#0$'>$*"#$)"528#%$-2$-*%$/582-*&0#$5%$*-/#$?1+81#%%#%M$*"5*$-%4$*"#$-2,+1/5*-+2
-%$)+2*5-2#0$-2$*"#$V6-883#%W$-2$*"#$%-8253$65E#,+1/7$;2$8#2#1534$%&)"$65E#,+1/%$51#$0-,,-)&3*$*+
)"515)*#1-T#$/5*"#/5*-)533>7$;2$+*"#1$6+10%4$-*$-%$2+*$#5%>$*+$0#%)1-'#$%&))-2)*3>$52$51'-*151>9
3++.-28$65E#,+1/$%&)"$5%$*"5*$+,$K-87$@7U7$C,$)+&1%#4$%&)"$5$0#%)1-?*-+2$-%$+,$81#5*$-/?+1*52)#$,+1
*"#$?&1?+%#$+,$0#%-82-28$5??1+?1-5*#$%-82539?1+)#%%-28$)-1)&-*%$*"5*$?#1,+1/$0#%-1#0$,&2)*-+2%$+2
*"#$8-E#2$%-82537$L2$#,,#)*-E#$5??1+5)"$*+$%-8253$)"515)*#1-T5*-+2$-%$%*&0-#0$-2$*"#$2#D*$%#)*-+27
Figure 1.3 L2$51'-*151>$E+3*58#$%-8253$v! :"=7
1.2 Frequency Spectrum of Signals 9
1.2 Frequency Spectrum of Signals
L2$#D*1#/#3>$&%#,&3$)"515)*#1-T5*-+2$+,$5$%-82534$520$,+1$*"5*$/5**#1$+,$52>$51'-*151>$,&2)*-+2
+,$ *-/#4$ -%$ -2$ *#1/%$ +,$ -*%$ 9$':0'*#;, +/'#)$0!7$ I&)"$ 5$ 0#%)1-?*-+2$ +,$ %-8253%$ -%$ +'*5-2#0
*"1+&8"$*"#$/5*"#/5*-)53$*++3%$+,$<%0$"'$,+'$"'+$520$<%0$"'$,)$3*+9%$!7@$F#$51#$2+*$-2*#19
#%*#0$"#1#$-2$*"#$0#*5-3%$+,$*"#%#$*152%,+1/5*-+2%M$%&,,-)#$-*$*+$%5>$*"5*$*"#>$?1+E-0#$*"#$/#52%
,+1$1#?1#%#2*-28$5$E+3*58#$%-8253$v!:"=$+1$5$)&11#2*$%-8253$$!:"=$5%$*"#$%&/$+,$%-2#965E#$%-8253%
+,$0-,,#1#2*$,1#G&#2)-#%$520$5/?3-*&0#%7$!"-%$/5.#%$*"#$%-2#$65E#$5$E#1>$-/?+1*52*$%-8253$-2
*"#$5253>%-%4$0#%-824$520$*#%*-28$+,$#3#)*1+2-)$)-1)&-*%7$!"#1#,+1#4$6#$%"533$'1-#,3>$1#E-#6$*"#
?1+?#1*-#%$+,$*"#$%-2&%+-07
K-8&1#$@7^$%"+6%$5$%-2#965E#$E+3*58#$%-8253$v(:"=4
v ( ( " ) = ) ( %-2 ω "
-($(.
6"#1#$)($0#2+*#%$*"#$?#5.$E53&#$+1$5/?3-*&0#$-2$E+3*%$520 ω 0#2+*#%$*"#$528&351$,1#G&#2)>$-2
150-52%$?#1$%#)+20M$*"5*$-%4$ ω = B π * 150`%4$6"#1#$*+$-%$*"#$,1#G&#2)>$-2$"#1*T4$ * S @`,$ aT4$520
,$-%$*"#$?#1-+0$-2$%#)+20%7
!"#$%-2#965E#$%-8253$-%$)+/?3#*#3>$)"515)*#1-T#0$'>$-*%$?#5.$E53&#$)( 4$-*%$,1#G&#2)>$ ω4
520$-*%$?"5%#$6-*"$1#%?#)*$*+$52$51'-*151>$1#,#1#2)#$*-/#7$;2$*"#$)5%#$0#?-)*#0$-2$K-87$@7^4$*"#
*-/#$+1-8-2$"5%$'##2$)"+%#2$%+$*"5*$*"#$?"5%#$5283#$-%$A7$;*$%"+&30$'#$/#2*-+2#0$*"5*$-*$-%$)+/9
/+2$*+$#D?1#%%$*"#$5/?3-*&0#$+,$5$%-2#965E#$%-8253$-2$*#1/%$+,$-*%$1++*9/#529%G&51#$:1/%=
E53&#4$6"-)"$-%$#G&53$*+$*"#$?#5.$E53&#$0-E-0#0$'>$ B7$!"&%$*"#$1/%$E53&#$+,$*"#$%-2&%+-0$v(:"=
+,$K-87$@7^$-%$)( ⁄ B7$K+1$-2%*52)#4$6"#2$6#$%?#5.$+,$*"#$6533$?+6#1$%&??3>$-2$+&1$"+/#%$5%
'#-28$@BA$Y4$6#$/#52$*"5*$-*$"5%$5$%-2#$65E#,+1/$+,$ @BA B $E+3*%$?#5.$E53&#7$
R#*&12-28$2+6$*+$*"#$1#?1#%#2*5*-+2$+,$%-8253%$5%$*"#$%&/$+,$%-2&%+-0%4$6#$2+*#$*"5*$*"#$K+&9
1-#1$%#1-#%$-%$&*-3-T#0$*+$5))+/?3-%"$*"-%$*5%.$,+1$*"#$%?#)-53$)5%#$+,$5$%-8253$*"5*$-%$5$?#1-+0-)$,&2)9
*-+2$+,$*-/#7$C2$*"#$+*"#1$"5204$*"#$K+&1-#1$*152%,+1/$-%$/+1#$8#2#153$520$)52$'#$&%#0$*+$+'*5-2
*"#$,1#G&#2)>$%?#)*1&/$+,$5$%-8253$6"+%#$65E#,+1/$-%$52$51'-*151>$,&2)*-+2$+, *-/#7
!"#$K+&1-#1$%#1-#%$533+6%$&%$*+$#D?1#%%$5$8-E#2$?#1-+0-)$,&2)*-+2$+,$*-/#$5%$*"#$%&/$+,$52
-2,-2-*#$2&/'#1$+,$%-2&%+-0%$6"+%#$,1#G&#2)-#%$51#$"51/+2-)533>$1#35*#07$K+1$-2%*52)#4$*"#
%>//#*1-)53$%G&51#965E#$%-8253$-2$K-87$@7]$)52$'#$#D?1#%%#0$5%$
^)
v ( " ) = 9999999 :%-2 ω A " + @99U9 %-2 U ω A " + @99]9 %-2 ] ω A " + 7$7$7 = $
π
-($+.
Figure 1.4 I-2#965E#$ E+3*58#$ %-8253$ +,
5/?3-*&0#$)($520$,1#G&#2)>$$* S @`, aT7$!"#
528&351$,1#G&#2)>$ ω " Bπ * $150`%7
@
!"#$1#50#1$6"+$"5%$2+*$>#*$%*&0-#0$*"#%#$*+?-)%$%"+&30$2+*$'#$5351/#07$O+$0#*5-3#0$5??3-)5*-+2$+,$*"-%$
/5*#1-53$6-33$'#$/50#$&2*-3$<"5?*#1$\7$O#E#1*"#3#%%4$5$8#2#153$&20#1%*520-28$+,$I#)*-+2$@7B$%"+&30$'#$
E#1>$"#3?,&3$-2$%*&0>-28$#513>$?51*%$+,$*"-%$'++.7
10 Chapter 1 Signals and Amplifiers
Figure 1.5 L$%>//#*1-)53$%G&51#965E#$%-8253$+,$5/?3-*&0#$)7
6"#1#$)$-%$*"#$5/?3-*&0#$+,$*"#$%G&51#$65E#$520$ω A $S$B π ⁄ , $:,$-%$*"#$?#1-+0$+,$*"#$%G&51#
65E#=$ -%$ )533#0$ *"#$ 90*13!'*)3(, 9$':0'*#;7$ O+*#$ *"5*$ '#)5&%#$ *"#$ 5/?3-*&0#%$ +,$ *"#
"51/+2-)%$ ?1+81#%%-E#3>$ 0#)1#5%#4$ *"#$ -2,-2-*#$ %#1-#%$ )52$ '#$ *1&2)5*#04$ 6-*"$ *"#$ *1&2)5*#0
%#1-#%$?1+E-0-28$52$5??1+D-/5*-+2$*+$*"#$%G&51#$65E#,+1/7
!"#$%-2&%+-053$)+/?+2#2*%$-2$*"#$%#1-#%$+,$JG7$:@7B=$)+2%*-*&*#$*"#$,1#G&#2)>$%?#)*1&/$+,
*"#$%G&51#965E#$%-82537$I&)"$5$%?#)*1&/$)52$'#$815?"-)533>$1#?1#%#2*#0$5%$-2$K-87$@7b4$6"#1#
*"#$"+1-T+2*53$5D-%$1#?1#%#2*%$*"#$528&351$,1#G&#2)>$ω$-2$150-52%$?#1$%#)+207$
!"#$ K+&1-#1$ *152%,+1/$ )52$ '#$ 5??3-#0$ *+$ 5$ 2+2?#1-+0-)$ ,&2)*-+2$ +,$ *-/#4$ %&)"$ 5%$ *"5*
0#?-)*#0$-2$K-87$@7U4$520$?1+E-0#%$-*%$,1#G&#2)>$%?#)*1&/$5%$5$)+2*-2&+&%$,&2)*-+2$+,$,1#9
G&#2)>4$5%$-20-)5*#0$-2$K-87$@7c7$d23-.#$*"#$)5%#$+,$?#1-+0-)$%-8253%4$6"#1#$*"#$%?#)*1&/$)+29
%-%*%$+,$0-%)1#*#$,1#G&#2)-#%$:5*$ ω A$520$-*%$"51/+2-)%=4$*"#$%?#)*1&/$+,$5$2+2?#1-+0-)$%-8253
)+2*5-2%$-2$8#2#153$533$?+%%-'3#$,1#G&#2)-#%7$O#E#1*"#3#%%4$*"#$#%%#2*-53$?51*%$+,$*"#$%?#)*15
+,$?15)*-)53$%-8253%$51#$&%&533>$)+2,-2#0$*+$1#35*-E#3>$%"+1*$%#8/#2*%$+,$*"#$,1#G&#2)>$ -ω.
5D-%e52$+'%#1E5*-+2$*"5*$-%$E#1>$&%#,&3$-2$*"#$?1+)#%%-28$+,$%&)"$%-8253%7$K+1$-2%*52)#4$*"#
%?#)*1&/$+,$5&0-'3#$%+&20%$%&)"$5%$%?##)"$520$ /&%-)$#D*#20%$,1+/$5'+&*$BA$aT$*+$5'+&*
BA .aTe5$,1#G&#2)>$1528#$.2+62$5%$*"#$301"%,83*17$a#1#$6#$%"+&30$2+*#$*"5*$53*"+&8"
%+/#$/&%-)53$*+2#%$"5E#$,1#G&#2)-#%$5'+E#$BA$.aT4$*"#$"&/52$#51$-%$-2)5?5'3#$+,$"#51-28
,1#G&#2)-#%$ *"5*$ 51#$ /&)"$ 5'+E#$ BA$ .aT7$ L%$ 52+*"#1$ #D5/?3#4$ 5253+8$ E-0#+$ %-8253%$ "5E#
*"#-1$%?#)*15$-2$*"#$1528#$+,$A$_aT$*+$^7]$_aT7$$$$
Figure 1.6 !"#$,1#G&#2)>$%?#)*1&/$:53%+$.2+62$5%$*"#$("*',+/'#)$0!=$+,$*"#$?#1-+0-)$
%G&51#$65E#$+,$K-87 @7]7
1.3 Analog and Digital Signals 11
Figure 1.7 !"#$ ,1#G&#2)>$ %?#)*1&/$ +,
52$51'-*151>$65E#,+1/$%&)"$5%$*"5*$-2$K-87
@7U7
F#$)+2)3&0#$*"-%$%#)*-+2$'>$2+*-28$*"5*$5$%-8253$)52$'#$1#?1#%#2*#0$#-*"#1$'>$*"#$/522#1$-2
6"-)"$-*%$65E#,+1/$E51-#%$6-*"$*-/#4$5%$,+1$*"#$E+3*58#$%-8253$ v(:"=$%"+62$-2$K-87$@7U4$+1$-2
*#1/%$+,$-*%$,1#G&#2)>$%?#)*1&/4$5%$-2$K-87$@7c7$!"#$*6+$53*#125*-E#$1#?1#%#2*5*-+2%$51#$.2+62
5%$*"#$*-/#90+/5-2$1#?1#%#2*5*-+2$520$*"#$,1#G&#2)>90+/5-2$1#?1#%#2*5*-+24$1#%?#)*-E#3>7$!"#
,1#G&#2)>90+/5-2$1#?1#%#2*5*-+2$+,$v(:"=$6-33$'#$0#2+*#0$'>$*"#$%>/'+3$)(:ω=7$
EXERCISES
1.5 K-20$*"#$,1#G&#2)-#%$*$520$ω$+,$5$%-2#965E#$%-8253$6-*"$5$?#1-+0$+,$@$/%7
U
Ans. *$= @AAA$aTM$ ω = B π × @A $150`%
1.6 F"5*$-%$*"#$?#1-+0$,$+,$%-2#$65E#,+1/%$)"515)*#1-T#0$'>$,1#G&#2)-#%$+,$:5=$*+=$bA$aTX$:'=$*+=$@A−U$aTX
:)=$*+=$@$_aTX$$
Ans. @b7c$/%M$@AAA$%M$@$µ%
1.7 !"#$daK$:&3*15$"-8"$,1#G&#2)>=$*#3#E-%-+2$'1+50)5%*$'520$'#8-2%$6-*"$)"522#3$@^$520$#D*#20%$,1+/
^cA$_aT$*+$ZAb$_aT7$;,$b$_aT$-%$533+)5*#0$,+1$#5)"$)"522#34$"+6$/52>$)"522#3%$)52$*"-%$'520
5))+//+05*#X
Ans. ]bM$)"522#3%$@^$*+$b\
1.8 F"#2$*"#$%G&51#965E#$%-8253$+,$K-87$@7]4$6"+%#$K+&1-#1$%#1-#%$-%$8-E#2$-2$JG7$:@7B=4$-%$5??3-#0$*+$5$1#%-%9
,
*+14$*"#$*+*53$?+6#1$0-%%-?5*#0$/5>$'#$)53)&35*#0$0-1#)*3>$&%-28$*"#$1#35*-+2%"-?$ - = @ ⁄ , A ( v B ⁄ # ) ."
+1$-20-1#)*3>$'>$%&//-28$*"#$)+2*1-'&*-+2$+,$#5)"$+,$*"#$"51/+2-)$)+/?+2#2*%4$*"5*$-%4$-$S$-@$f$-U$f
-] f$g4$6"-)"$/5>$'#$,+&20$0-1#)*3>$,1+/$1/%$E53&#%7$Y#1-,>$*"5*$*"#$*6+$5??1+5)"#%$51#$#G&-E53#2*7
F"5*$,15)*-+2$+,$*"#$#2#18>$+,$5$%G&51#$65E#$-%$-2$-*%$,&205/#2*53X$;2$-*%$,-1%*$,-E#$"51/+2-)%X$;2$-*%$,-1%*
%#E#2X$K-1%*$2-2#X$;2$6"5*$2&/'#1$+,$"51/+2-)%$-%$\A[$+,$*"#$#2#18>X$:O+*#$*"5*$-2$)+&2*-28$"51/+2-)%4
*"#$,&205/#2*53$5*$ω A$-%$*"#$,-1%*4$*"#$+2#$5*$Bω A$-%$*"#$%#)+204$#*)7=
Ans. A7Z@M$A7\UM$A7\]M$A7\bM$U
1.3 Analog and Digital Signals
!"#$E+3*58#$%-8253$0#?-)*#0$-2$K-87$@7U$-%$)533#0$52$3*3(%2,+"2*3(7$!"#$25/#$0#1-E#%$,1+/
*"#$,5)*$*"5*$%&)"$5$%-8253$-%$5253+8+&%$*+$*"#$?">%-)53$%-8253$*"5*$-*$1#?1#%#2*%7$!"#$/582-9
*&0#$+,$52$5253+8$%-8253$)52$*5.#$+2$52>$E53&#M$*"5*$-%4$*"#$5/?3-*&0#$+,$52$5253+8$%-8253
#D"-'-*%$5$)+2*-2&+&%$E51-5*-+2$+E#1$-*%$1528#$+,$5)*-E-*>7$!"#$E5%*$/5(+1-*>$+,$%-8253%$-2$*"#
12 Chapter 1 Signals and Amplifiers
6+130$51+&20$&%$51#$5253+87$J3#)*1+2-)$)-1)&-*%$*"5*$?1+)#%%$%&)"$%-8253%$51#$.2+62$5%$3*3&
(%2,#"$#0")+7$L$E51-#*>$+,$5253+8$)-1)&-*%$6-33$'#$%*&0-#0$-2$*"-%$'++.7
L2$53*#125*-E#$,+1/$+,$%-8253$1#?1#%#2*5*-+2$-%$*"5*$+,$5$%#G&#2)#$+,$2&/'#1%4$#5)"$2&/9
'#1$1#?1#%#2*-28$*"#$%-8253$/582-*&0#$5*$52$-2%*52*$+,$*-/#7$!"#$1#%&3*-28$%-8253$-%$)533#0$5
1"2")3(,+"2*3(7,!+$%##$"+6$5$%-8253$)52$'#$1#?1#%#2*#0$-2$*"-%$,+1/e*"5*$-%4$"+6$%-8253%$)52
'#$)+2E#1*#0$,1+/$5253+8$*+$0-8-*53$,+1/e)+2%-0#1$K-87$@7Z:5=7$a#1#$*"#$)&1E#$1#?1#%#2*%$5
E+3*58#$%-82534$-0#2*-)53$*+$*"5*$-2$K-87$@7U7$L*$#G&53$-2*#1E53%$53+28$*"#$*-/#$5D-%4$6#$"5E#
/51.#0$*"#$*-/#$-2%*52*%$"A4$"@4$"B4$520$%+$+27$L*$#5)"$+,$*"#%#$*-/#$-2%*52*%4$*"#$/582-*&0#$+,
*"#$%-8253$-%$/#5%&1#04$5$?1+)#%%$.2+62$5%$+3!/("*2$$K-8&1#$@7Z:'=$%"+6%$5$1#?1#%#2*5*-+2
+,$*"#$%-8253$+,$K-87$@7Z:5=$-2$*#1/%$+,$-*%,%5/?3#%7$!"#$%-8253$+,$K-87$@7Z:'=$-%$0#,-2#0$+23>$5*
*"#$%5/?3-28$-2%*52*%M$-*$2+$3+28#1$-%$5$)+2*-2&+&%$,&2)*-+2$+,$*-/#M$15*"#14$-*$-%$5$1"+#$')'&
)"!',+"2*3(7,a+6#E#14$%-2)#$*"#$/582-*&0#$+,$#5)"$%5/?3#$)52$*5.#$52>$E53&#$-2$5$)+2*-2&+&%
1528#4$*"#$%-8253$-2$K-87$@7Z:'=$-%$%*-33$52$5253+8$%-82537
O+6$-,$6#$1#?1#%#2*$*"#$/582-*&0#$+,$#5)"$+,$*"#$%-8253$%5/?3#%$-2$K-87$@7Z:'=$'>$5$2&/'#1
"5E-28$ 5$ ,-2-*#$ 2&/'#1$ +,$ 0-8-*%4$ *"#2$ *"#$ %-8253$ 5/?3-*&0#$ 6-33$ 2+$ 3+28#1$ '#$ )+2*-2&+&%M
15*"#14$-*$-%$%5-0$*+$'#$:03*)"='14,1"+#$')"='14,+1$1"2")"='17$!"#$1#%&3*-28$0-8-*53$%-8253$*"#2$-%
%-/?3>$5$%#G&#2)#$+,$2&/'#1%$*"5*$1#?1#%#2*$*"#$/582-*&0#%$+,$*"#$%&))#%%-E#$%-8253$%5/?3#%7
!"#$)"+-)#$+,$2&/'#1$%>%*#/$*+$1#?1#%#2*$*"#$%-8253$%5/?3#%$5,,#)*%$*"#$*>?#$+,$0-8-*53
%-8253$?1+0&)#04$520$"5%$5$?1+,+&20$#,,#)*$+2$*"#$)+/?3#D-*>$+,$*"#$0-8-*53$)-1)&-*%$1#G&-1#0
*+$?1+)#%%$*"#$%-8253%7$;*$*&12%$+&*$*"5*$*"#$8"*3$;$2&/'#1$%>%*#/$1#%&3*%$-2$*"#$%-/?3#%*$?+%9
%-'3#$0-8-*53$%-8253%$520$)-1)&-*%7$;2$5$'-251>$%>%*#/4$#5)"$0-8-*$-2$*"#$2&/'#1$*5.#%$+2$+2#$+,
(a)
Figure 1.8 I5/?3-28$*"#$)+2*-2&+&%9*-/#$5253+8$%-8253$-2$437$1#%&3*%$-2$*"#$0-%)1#*#9*-/#$%-8253$-2$487>
1.3 Analog and Digital Signals 13
v (t)
"5
Logic values
0
1
0
1
1
0
1
0
0
Time, t
Figure 1.9 Y51-5*-+2$+,$5$?51*-)&351$'-251>$0-8-*53$%-8253$6-*"$*-/#7
+23>$*6+$?+%%-'3#$E53&#%4$0#2+*#0$A$520$@7$<+11#%?+20-283>4$*"#$0-8-*53$%-8253%$-2$'-251>$%>%9
*#/%$2##0$"5E#$+23>$*6+$E+3*58#$3#E#3%4$6"-)"$)52$'#$35'#3#0$3+6$520$"-8"7$L%$52$#D5/?3#4$-2
%+/#$ +,$ *"#$ 0-8-*53$ )-1)&-*%$ %*&0-#0$ -2$ *"-%$ '++.4$ *"#$ 3#E#3%$ 51#$ A$ Y$ 520$ +]$ Y7$ K-8&1#$ @7\
%"+6%$*"#$*-/#$E51-5*-+2$+,$%&)"$5$0-8-*53$%-82537$C'%#1E#$*"5*$*"#$65E#,+1/$-%$5$?&3%#$*15-2
6-*"$A$Y$1#?1#%#2*-28$5$A$%-82534$+1$3+8-)$A4$520$+]$Y$1#?1#%#2*-28$3+8-)$@7
;,$6#$&%#$/$0-251>$0-8$"!$:'-*%=$*+$1#?1#%#2*$#5)"$%5/?3#$+,$*"#$5253+8$%-82534$*"#2$*"#$0-89
-*-T#0$%5/?3#$E53&#$)52$'#$#D?1#%%#0$5%$
1 = 0 A B + 0 @ B + 0 B B + …$f 0 /−@ B
A
@
B
/−@
-($/.
6"#1#$ 0A4$ 0@4$ g4$ 0/h@4$ 0#2+*#$ *"#$ /$ '-*%$ 520$ "5E#$ E53&#%$ +,$ A$ +1$ @7$ a#1#$ '-*$ 0A$ -%$ *"#$ ('3+)
+"2*"9"#3*),8"),:?@A=4$520$'-*$0/h@$-%$*"#$!%+),+"2*"9"#3*),8"),:-@A=7$<+2E#2*-+2533>4$*"-%$'-251>
2&/'#1$-%$61-**#2$5%$0/h@$0/hB$g+0A7$F#$+'%#1E#$*"5*$%&)"$5$1#?1#%#2*5*-+2$G&52*-T#%$*"#$5253+8
%5/?3#$-2*+$+2#$+,$B/$3#E#3%7$C'E-+&%3>$*"#$81#5*#1$*"#$2&/'#1$+,$'-*%$:-7#74$*"#$3518#1$*"#$/=4$*"#
)3+%#1$*"#$0-8-*53$6+10$1$5??1+D-/5*#%$*"#$/582-*&0#$+,$*"#$5253+8$%5/?3#7$!"5*$-%4$-2)1#5%-28
*"#$2&/'#1$+,$'-*%$1#0&)#%$*"#$23(4"$5("$&4+677&7$520$-2)1#5%#%$*"#$1#%+3&*-+2$+,$*"#$5253+89*+9
0-8-*53$)+2E#1%-+27$!"-%$-/?1+E#/#2*$-%4$"+6#E#14$&%&533>$+'*5-2#0$5*$*"#$#D?#2%#$+,$/+1#$)+/9
?3#D$520$"#2)#$/+1#$)+%*3>$)-1)&-*$-/?3#/#2*5*-+2%7$;*$-%$2+*$+&1$?&1?+%#$"#1#$*+$0#3E#$-2*+$*"-%
*+?-)$52>$0##?#1M$6#$/#1#3>$652*$*"#$1#50#1$*+$5??1#)-5*#$*"#$25*&1#$+,$5253+8$520$0-8-*53$%-8253%7
O#E#1*"#3#%%4$-*$-%$52$+??+1*&2#$*-/#$*+$-2*1+0&)#$5$E#1>$-/?+1*52*$)-1)&-*$'&-30-28$'3+).$+,$/+09
#12$#3#)*1+2-)$%>%*#/%H$*"#$3*3(%2&)%&1"2")3(,#%*B'$)'$$:CDE$+1$CE6=$%"+62$-2$'3+).$,+1/$-2
K-87$@7@A$!"#$LQ<$5))#?*%$5*$-*%$-2?&*$*"#$%5/?3#%$+,$52$5253+8$%-8253$520$?1+E-0#%$,+1$#5)"
-2?&*$%5/?3#$*"#$)+11#%?+20-28$/9'-*$0-8-*53$1#?1#%#2*5*-+2$:5))+10-28$*+$JG7$@7U=$5*$-*%$/$+&*?&*
*#1/-253%7$!"&%$53*"+&8"$*"#$E+3*58#$5*$*"#$-2?&*$/-8"*$'#4$%5>4$b7]@$Y4$5*$#5)"$+,$*"#$+&*?&*$*#19
/-253%$:%5>4$5*$*"#$$*"$*#1/-253=4$*"#$E+3*58#$6-33$'#$#-*"#1$3+6$:A$Y=$+1$"-8"$:] Y=$-,$0$$-%$%&??+%#0
Analog "
v
input A
!
A/D
converter
b0
b1
bN!1
Digital
output
Figure 1.10 i3+).90-5815/$1#?1#%#2*5*-+2$+,$*"#$5253+89*+90-8-*53$)+2E#1*#1$:LQ<=7
14 Chapter 1 Signals and Amplifiers
*+$'#$A$+1$@4$1#%?#)*-E#3>7$!"#$0&53$)-1)&-*$+,$*"#$LQ<$-%$*"#$1"2")3(&)%&3*3(%2,#%*B'$)'$$:EDC$+1
EC6=7$;*$)+2E#1*%$52$/9'-*$0-8-*53$-2?&*$*+$52$5253+8$+&*?&*$E+3*58#7
C2)#$*"#$%-8253$-%$-2$0-8-*53$,+1/4$-*$)52$'#$?1+)#%%#0$&%-28$1"2")3(,#"$#0")+>$C,$)+&1%#
0-8-*53$)-1)&-*%$)52$0#53$53%+$6-*"$%-8253%$*"5*$0+$2+*$"5E#$52$5253+8$+1-8-24$%&)"$5%$*"#$%-89
253%$*"5*$1#?1#%#2*$*"#$E51-+&%$-2%*1&)*-+2%$+,$5$0-8-*53$)+/?&*#17
I-2)#$0-8-*53$)-1)&-*%$0#53$#D)3&%-E#3>$6-*"$'-251>$%-8253%4$*"#-1$0#%-82$-%$%-/?3#1$*"52$*"5*$+,
5253+8$ )-1)&-*%7$ K&1*"#1/+1#4$ 0-8-*53$ %>%*#/%$ )52$ '#$ 0#%-82#0$ &%-28$ 5$ 1#35*-E#3>$ ,#6$ 0-,,#1#2*
.-20%$+,$0-8-*53$)-1)&-*$'3+).%7$a+6#E#14$5$3518#$2&/'#1$:#7874$"&201#0%$+,$*"+&%520%$+1$#E#2$/-39
3-+2%=$+,$#5)"$+,$*"#%#$'3+).%$51#$&%&533>$2##0#07$!"&%$*"#$0#%-82$+,$0-8-*53$)-1)&-*%$?+%#%$-*%$+62
%#*$+,$)"533#28#%$*+$*"#$0#%-82#1$'&*$?1+E-0#%$1#3-5'3#$520$#)+2+/-)$-/?3#/#2*5*-+2%$+,$5$81#5*
E51-#*>$+,$%-82539?1+)#%%-28$,&2)*-+2%4$/52>$+,$6"-)"$51#$2+*$?+%%-'3#$6-*"$5253+8$)-1)&-*%7$L*
*"#$?1#%#2*$*-/#4$/+1#$520$/+1#$+,$*"#$%-82539?1+)#%%-28$,&2)*-+2%$51#$'#-28$?#1,+1/#0$0-8-*533>7
JD5/?3#%$51+&20$&%$5'+&20H$,1+/$*"#$0-8-*53$65*)"$520$*"#$)53)&35*+1$*+$0-8-*53$5&0-+$%>%*#/%4
0-8-*53$)5/#15%$5204$/+1#$1#)#2*3>4$0-8-*53$*#3#E-%-+27$_+1#+E#14$%+/#$3+28%*520-28$5253+8$%>%9
*#/%$ %&)"$ 5%$ *"#$ *#3#?"+2#$ )+//&2-)5*-+2$ %>%*#/$ 51#$ 2+6$ 53/+%*$ #2*-1#3>$ 0-8-*537$ L20$ 6#
%"+&30$2+*$,+18#*$*"#$/+%*$-/?+1*52*$+,$533$0-8-*53$%>%*#/%4$*"#$0-8-*53$)+/?&*#17
!"#$'5%-)$'&-30-28$'3+).%$+,$0-8-*53$%>%*#/%$51#$3+8-)$)-1)&-*%$520$/#/+1>$)-1)&-*%7$F#
%"533$%*&0>$'+*"$-2$*"-%$'++.4$'#8-22-28$-2$<"5?*#1$@U7
C2#$,-253$1#/51.H$L3*"+&8"$*"#$0-8-*53$?1+)#%%-28$+,$%-8253%$-%$5*$?1#%#2*$5339?#1E5%-E#4
*"#1#$1#/5-2$/52>$%-82539?1+)#%%-28$,&2)*-+2%$ *"5*$51#$'#%*$?#1,+1/#0$'>$5253+8$)-1)&-*%7
;20##04$/52>$#3#)*1+2-)$%>%*#/%$-2)3&0#$'+*"$5253+8$520$0-8-*53$?51*%7$;*$,+33+6%$*"5*$5$8++0
#3#)*1+2-)%$#28-2##1$/&%*$'#$?1+,-)-#2*$-2$*"#$0#%-82$+,$'+*"$5253+8$520$0-8-*53$)-1)&-*%4$+1
!"F'1&+"2*3(,+1$!"F'1&!%1'$0#%-82$5%$-*$-%$)&11#2*3>$.2+627$I&)"$-%$*"#$5-/$+,$*"-%$'++.7
EXERCISE
1.9$ <+2%-0#1$5$^9'-*$0-8-*53$6+10$1$S$0U0B0@0A$:%##$JG7$@7U=$&%#0$*+$1#?1#%#2*$52$5253+8$%-8253$v8$*"5*$E51-#%
'#*6##2$A$Y$520$+@]$Y7
:5= j-E#$1$)+11#%?+20-28$*+$v8$S$A$Y4$@$Y4$B$Y4$520$@]$Y7
:'= F"5*$)"528#$-2$v8$)5&%#%$5$)"528#$,1+/$A$*+$@$-2$:-=$0A4$:--=$0@4$:---=$0B4$520$:-E=$0UX
:)= ;,$v8$S$]7B$Y4$6"5*$0+$>+&$#D?#)*$1$*+$'#X$F"5*$-%$*"#$1#%&3*-28$#11+1$-2$1#?1#%#2*5*-+2X
Ans. :5= AAAA4$AAA@4$AA@A4$@@@@M :'= +@$Y4$+B$Y4$+^$Y4$+Z$YM :)= A@A@4$h^[
1.4 Amplifiers
;2$*"-%$%#)*-+24$6#$%"533$-2*1+0&)#$*"#$/+%*$,&205/#2*53$%-82539?1+)#%%-28$,&2)*-+24$+2#$*"5*
-%$#/?3+>#0$-2$%+/#$,+1/$-2$53/+%*$#E#1>$#3#)*1+2-)$%>%*#/4$25/#3>4$%-8253$5/?3-,-)5*-+27
F#$%"533$%*&0>$*"#$5/?3-,-#1$5%$5$)-1)&-*$'&-30-289'3+).M$*"5*$-%4$6#$%"533$)+2%-0#1$-*%$#D*#1253
)"515)*#1-%*-)%$520$3#5E#$*"#$0#%-82$+,$-*%$-2*#1253$)-1)&-*$*+$35*#1$)"5?*#1%7
1.4.1 Signal Amplification
K1+/$5$)+2)#?*&53$?+-2*$+,$E-#6$*"#$%-/?3#%*$%-82539?1+)#%%-28$*5%.$-%$*"5*$+,$+"2*3(,3!/("9"#3&
)"%*7$!"#$2##0$,+1$5/?3-,-)5*-+2$51-%#%$'#)5&%#$*152%0&)#1%$?1+E-0#$%-8253%$*"5*$51#$%5-0$*+$'#
V6#5.4W$*"5*$-%4$-2$*"#$/-)1+E+3*$:µY=$+1$/-33-E+3*$:/Y=$1528#$520$?+%%#%%-28$3-**3#$#2#18>7$I&)"
1.4 Amplifiers
%-8253%$51#$*++$%/533$,+1$1#3-5'3#$?1+)#%%-284$520$?1+)#%%-28$-%$/&)"$#5%-#1$-,$*"#$%-8253$/582-9
*&0#$-%$/50#$3518#17$!"#$,&2)*-+253$'3+).$*"5*$5))+/?3-%"#%$*"-%$*5%.$-%$*"#$+"2*3(,3!/("9"'$7
;*$-%$5??1+?1-5*#$5*$*"-%$?+-2*$*+$0-%)&%%$*"#$2##0$,+1$("*'3$");$-2$5/?3-,-#1%7$<51#$/&%*$'#
#D#1)-%#0$-2$*"#$5/?3-,-)5*-+2$+,$5$%-82534$%+$*"5*$*"#$-2,+1/5*-+2$)+2*5-2#0$-2$*"#$%-8253$-%
2+*$)"528#0$520$2+$2#6$-2,+1/5*-+2$-%$-2*1+0&)#07$!"&%$6"#2$6#$,##0$*"#$%-8253$%"+62$-2$K-87
@7U$*+$52$5/?3-,-#14$6#$652*$*"#$+&*?&*$%-8253$+,$*"#$5/?3-,-#1$*+$'#$52$#D5)*$1#?3-)5$+,$*"5*$5*
*"#$-2?&*4$#D)#?*$+,$)+&1%#$,+1$"5E-28$3518#1$/582-*&0#7$;2$+*"#1$6+10%4$*"#$V6-883#%W$-2$*"#
+&*?&*$65E#,+1/$/&%*$'#$-0#2*-)53$*+$*"+%#$-2$*"#$-2?&*$65E#,+1/7$L2>$)"528#$-2$65E#,+1/
-%$)+2%-0#1#0$*+$'#$1"+)%$)"%*$520$-%$+'E-+&%3>$&20#%-15'3#7$
L2$5/?3-,-#1$*"5*$?1#%#1E#%$*"#$0#*5-3%$+,$*"#$%-8253$65E#,+1/$-%$)"515)*#1-T#0$'>$*"#$1#359
*-+2%"-?
v& ( " ) = 8 v$ ( " )
-($0.
6"#1#$v$$520$v&$51#$*"#$-2?&*$520$+&*?&*$%-8253%4$1#%?#)*-E#3>4$520$8$-%$5$)+2%*52*$1#?1#%#2*-28
*"#$/582-*&0#$+,$5/?3-,-)5*-+24$.2+62$5%$3!/("9"'$,23"*7$JG&5*-+2$:@7^=$-%$5$3-2#51$1#35*-+29
%"-?M$"#2)#$*"#$5/?3-,-#1$-*$0#%)1-'#%$-%$5$("*'3$,3!/("9"'$7$;*$%"+&30$'#$#5%>$*+$%##$*"5*$-,$*"#
1#35*-+2%"-?$'#*6##2$v&$520$v$$)+2*5-2%$"-8"#1$?+6#1%$+,$v$4$*"#2$*"#$65E#,+1/$+,$v&$6-33$2+
3+28#1$'#$-0#2*-)53$*+$*"5*$+,$v$7$!"#$5/?3-,-#1$-%$*"#2$%5-0$*+$#D"-'-*$*%*("*'3$,1"+)%$)"%*7
!"#$5/?3-,-#1%$0-%)&%%#0$%+$,51$51#$?1-/51-3>$-2*#20#0$*+$+?#15*#$+2$E#1>$%/533$-2?&*$%-8253%7
!"#-1$?&1?+%#$-%$*+$/5.#$*"#$%-8253$/582-*&0#$3518#1$520$*"#1#,+1#$51#$*"+&8"*$+,$5%$B%()32'
3!/("9"'$+7$!"#$/$'3!/("9"'$$-2$*"#$"+/#$%*#1#+$%>%*#/$-%$52$#D5/?3#$+,$5$E+3*58#$5/?3-,-#17
L*$*"-%$*-/#$6#$6-%"$*+$/#2*-+2$52+*"#1$*>?#$+,$5/?3-,-#14$25/#3>4$*"#$/%G'$,3!/("9"'$7
I&)"$52$5/?3-,-#1$/5>$?1+E-0#$+23>$5$/+0#%*$5/+&2*$+,$E+3*58#$85-2$'&*$%&'%*52*-53$)&11#2*
85-27$!"&%$6"-3#$5'%+1'-28$3-**3#$?+6#1$,1+/$*"#$-2?&*$%-8253$%+&1)#$*+$6"-)"$-*$-%$)+22#)*#04
+,*#2$5$?1#5/?3-,-#14$-*$0#3-E#1%$3518#$5/+&2*%$+,$?+6#1$*+$-*%$3+507$L2$#D5/?3#$-%$,+&20$-2$*"#
?+6#1$5/?3-,-#1$+,$*"#$"+/#$%*#1#+$%>%*#/4$6"+%#$?&1?+%#$-%$*+$?1+E-0#$%&,,-)-#2*$?+6#1$*+
01-E#$*"#$3+&0%?#5.#14$6"-)"$-%$*"#$5/?3-,-#1$3+507$a#1#$6#$%"+&30$2+*#$*"5*$*"#$3+&0%?#5.#1$-%
*"#$+&*?&*$*152%0&)#1$+,$*"#$%*#1#+$%>%*#/M$-*$)+2E#1*%$*"#$#3#)*1-)$+&*?&*$%-8253$+,$*"#$%>%*#/
-2*+$ 52$ 5)+&%*-)$ %-82537$ L$ ,&1*"#1$ 5??1#)-5*-+2$ +,$ *"#$ 2##0$ ,+1$ 3-2#51-*>$ )52$ '#$ 5)G&-1#0$ '>
1#,3#)*-28$+2$*"#$?+6#1$5/?3-,-#17$L$3-2#51$?+6#1$5/?3-,-#1$)5&%#%$'+*"$%+,*$520$3+&0$/&%-)
?5%%58#%$*+$'#$1#?1+0&)#0$6-*"+&*$0-%*+1*-+27
1.4.2 Amplifier Circuit Symbol
!"#$%-8253$5/?3-,-#1$-%$+'E-+&%3>$5$*6+9?+1*$2#*6+1.7$;*%$,&2)*-+2$-%$)+2E#2-#2*3>$1#?1#%#2*#0$'>
*"#$)-1)&-*$%>/'+3$+,$K-87$@7@@:5=7$!"-%$%>/'+3$)3#513>$0-%*-28&-%"#%$*"#$-2?&*$520$+&*?&*$?+1*%
520$-20-)5*#%$*"#$0-1#)*-+2$+,$%-8253$,3+67$!"&%4$-2$%&'%#G&#2*$0-5815/%$-*$6-33$2+*$'#$2#)#%%51>
*+$35'#3$*"#$*6+$?+1*%$V-2?&*W$520$V+&*?&*7W$K+1$8#2#153-*>$6#$"5E#$%"+62$*"#$5/?3-,-#1$*+$"5E#
*6+$-2?&*$*#1/-253%$*"5*$51#$0-%*-2)*$,1+/$*"#$*6+$+&*?&*$*#1/-253%7$L$/+1#$)+//+2$%-*&5*-+2$-%
-33&%*15*#0$-2$K-87$@7@@:'=4$6"#1#$5$)+//+2$*#1/-253$#D-%*%$'#*6##2$*"#$-2?&*$520$+&*?&*$?+1*%$+,
*"#$ 5/?3-,-#17$ !"-%$ )+//+2$ *#1/-253$ -%$ &%#0$ 5%$ 5$ 1#,#1#2)#$ ?+-2*$ 520$ -%$ )533#0$ *"#$ #"$#0")
2$%0*17
1.4.3 Voltage Gain
L$3-2#51$5/?3-,-#1$5))#?*%$52$-2?&*$%-8253$v9 :"=$520$?1+E-0#%$5*$*"#$+&*?&*4$5)1+%%$5$3+50$1#%-%9
*52)#$ #%$ :%##$ K-87$ @7@B:5==4$ 52$ +&*?&*$ %-8253$ v::"=$ *"5*$ -%$ 5$ /582-,-#0$ 1#?3-)5$ +,$ v9 :"=7$ !"#
B%()32',23"*$+,$*"#$5/?3-,-#1$-%$0#,-2#0$'>
v
Y+3*58#$85-2$ ( 8 v )$≡$ 9999:9
v9
-($).
15
16 Chapter 1 Signals and Amplifiers
(a)
Figure 1.11 437,<-1)&-*$%>/'+3$,+1$5/?3-,-#17$487$L2$5/?3-,-#1$6-*"$5$)+//+2$*#1/-253$:81+&20=$'#*6##2
*"#$-2?&*$520$+&*?&*$?+1*%7
K-87$@7@B:'=$%"+6%$*"#$)$3*+9'$,#.3$3#)'$"+)"#$+,$5$3-2#51$5/?3-,-#17$;,$6#$5??3>$*+$*"#$-2?&*
+,$*"-%$5/?3-,-#1$5$%-2&%+-053$E+3*58#$+,$5/?3-*&0#$ )k 4 $6#$+'*5-2$5*$*"#$+&*?&*$5$%-2&%+-0$+,
5/?3-*&0#$ 8 v)k 7
1.4.4 Power Gain and Current Gain
L2$5/?3-,-#1$-2)1#5%#%$*"#$%-8253$?+6#14$52$-/?+1*52*$,#5*&1#$*"5*$0-%*-28&-%"#%$52$5/?3-,-#1
,1+/$5$*152%,+1/#17$;2$*"#$)5%#$+,$5$*152%,+1/#14$53*"+&8"$*"#$E+3*58#$0#3-E#1#0$*+$*"#$3+50
)+&30$'#$81#5*#1$*"52$*"#$E+3*58#$,##0-28$*"#$-2?&*$%-0#$:*"#$?1-/51>=4$*"#$?+6#1$0#3-E#1#0$*+
*"#$3+50$:,1+/$*"#$%#)+2051>$%-0#$+,$*"#$*152%,+1/#1=$-%$3#%%$*"52$+1$5*$/+%*$#G&53$*+$*"#$?+6#1
%&??3-#0$'>$*"#$%-8253$%+&1)#7$C2$*"#$+*"#1$"5204$52$5/?3-,-#1$?1+E-0#%$*"#$3+50$6-*"$?+6#1
81#5*#1$*"52$*"5*$+'*5-2#0$,1+/$*"#$%-8253$%+&1)#7$!"5*$-%4$5/?3-,-#1%$"5E#$?+6#1$85-27$!"#
/%G'$,23"*$+,$*"#$5/?3-,-#1$-2$K-87$@7@B:5=$-%$0#,-2#0$5%
3+50$?+6#1$ ( - % )
9
l+6#1$85-2$ ( 8; )$≡$ 9999999999999999999999999999999999999999
-2?&*$?+6#1$ ( - 9 )
v: $:
9
=$ 999999999
v9 $9
(a)
Figure 1.12 437,L$E+3*58#$5/?3-,-#1$,#0$6-*"$5$%-8253$v9 :"=$520$)+22#)*#0$*+$5$3+50$1#%-%*52)#$#%7$
487,!152%,#1$)"515)*#1-%*-)$+,$5$3-2#51$E+3*58#$5/?3-,-#1$6-*"$E+3*58#$85-2$8v 7
-($1.
-($2.
1.4 Amplifiers
6"#1#$$:$-%$*"#$)&11#2*$*"5*$*"#$5/?3-,-#1$0#3-E#1%$*+$*"#$3+50$:#%=4$$:$=$v: /#%4$520$$9$-%$*"#$)&19
1#2*$*"#$5/?3-,-#1$0156%$,1+/$*"#$%-8253$%+&1)#7$!"#$#0$$'*),23"*,+,$*"#$5/?3-,-#1$-%$0#,-2#0$5%
$
<&11#2*$85-2$ ( 8 $ )$≡$ 999:9
$9
-($3.
K1+/$JG%7$:@7]=$*+$:@7Z=$6#$2+*#$*"5*
8 ; = 8v 8 $
-($#.
1.4.5 Expressing Gain in Decibels
!"#$5/?3-,-#1$85-2%$0#,-2#0$5'+E#$51#$15*-+%$+,$%-/-3513>$0-/#2%-+2#0$G&52*-*-#%7$!"&%$*"#>
6-33$'#$#D?1#%%#0$#-*"#1$5%$0-/#2%-+23#%%$2&/'#1%$+14$,+1$#/?"5%-%4$5%$Y`Y$,+1$*"#$E+3*58#
85-24$L`L$,+1$*"#$)&11#2*$85-24$520$F`F$,+1$*"#$?+6#1$85-27$L3*#125*-E#3>4$,+1$5$2&/'#1$+,
1#5%+2%4$%+/#$+,$*"#/$"-%*+1-)4$#3#)*1+2-)%$#28-2##1%$#D?1#%%$5/?3-,-#1$85-2$6-*"$5$3+851-*"9
/-)$/#5%&1#7$I?#)-,-)533>$*"#$E+3*58#$85-2$8v$)52$'#$#D?1#%%#0$5%
Y+3*58#$85-2$-2$0#)-'#3% " BA$3+8 8v
0i
520$*"#$)&11#2*$85-2$8$$)52$'#$#D?1#%%#0$5%
<&11#2*$85-2$-2$0#)-'#3% = BA$3+8 8 $
0i
I-2)#$?+6#1$-%$1#35*#0$*+$E+3*58#$:+1$)&11#2*=$%G&51#04$*"#$?+6#1$85-2$8;$)52$'#$#D?1#%%#0$-2
0#)-'#3%$5%
l+6#1$85-2$-2$0#)-'#3% = @A$3+8 8 ;
0i
!"#$5'%+3&*#$E53&#%$+,$*"#$E+3*58#$520$)&11#2*$85-2%$51#$&%#0$'#)5&%#$-2$%+/#$)5%#%$8v$+1
8$$6-33$'#$5$2#85*-E#$2&/'#17$L$2#85*-E#$85-2$8v$%-/?3>$/#52%$*"5*$*"#1#$-%$5$@ZA°$?"5%#$0-,9
,#1#2)#$'#*6##2$-2?&*$520$+&*?&*$%-8253%M$-*$0+#%$2+*$-/?3>$*"5*$*"#$5/?3-,-#1$-%$3))'*03)"*2
*"#$%-82537$C2$*"#$+*"#1$"5204$52$5/?3-,-#1$6"+%#$E+3*58#$85-2$-%4$%5>4$hBA$0i$-%$-2$,5)*$5**#29
&5*-28$*"#$-2?&*$%-8253$'>$5$,5)*+1$+,$@A$:-7#74$8v$=$A7@$Y`Y=7
1.4.6 The Amplifier Power Supplies
I-2)#$*"#$?+6#1$0#3-E#1#0$*+$*"#$3+50$-%$81#5*#1$*"52$*"#$?+6#1$01562$,1+/$*"#$%-8253$%+&1)#4
*"#$G&#%*-+2$51-%#%$5%$*+$*"#$%+&1)#$+,$*"-%$500-*-+253$?+6#17$!"#$52%6#1$-%$,+&20$'>$+'%#1E9
-28$*"5*$5/?3-,-#1%$2##0$0)$?+6#1$%&??3-#%$,+1$*"#-1$+?#15*-+27$!"#%#$0)$%+&1)#%$%&??3>$*"#
#D*15$?+6#1$0#3-E#1#0$*+$*"#$3+50$5%$6#33$5%$52>$?+6#1$*"5*$/-8"*$'#$0-%%-?5*#0$-2$*"#$-2*#19
253$)-1)&-*$+,$*"#$5/?3-,-#1$:%&)"$?+6#1$-%$)+2E#1*#0$*+$"#5*=7$;2$K-87$@7@B:5=$6#$"5E#$2+*
#D?3-)-*3>$%"+62$*"#%#$0)$%+&1)#%7
K-8&1#$@7@U:5=$%"+6%$52$5/?3-,-#1$*"5*$1#G&-1#%$*6+$0)$%+&1)#%H$+2#$?+%-*-E#$+,$E53&#$)<<
520$+2#$2#85*-E#$+,$E53&#$)==7$!"#$5/?3-,-#1$"5%$*6+$*#1/-253%4$35'#3#0$) f$520$) >4$,+1$)+22#)9
*-+2$*+$*"#$0)$%&??3-#%7$K+1$*"#$5/?3-,-#1$*+$+?#15*#4$*"#$*#1/-253$35'#3#0$) f$"5%$*+$'#$)+29
2#)*#0$ *+$ *"#$ ?+%-*-E#$ %-0#$ +,$ 5$ 0)$ %+&1)#$ 6"+%#$ E+3*58#$ -%$ )<<$ 520$ 6"+%#$ 2#85*-E#$ %-0#$ -%
)+22#)*#0$*+$*"#$)-1)&-*$81+&207$L3%+4$*"#$*#1/-253$35'#3#0$) >$"5%$*+$'#$)+22#)*#0$*+$*"#$2#859
*-E#$%-0#$+,$5$0)$%+&1)#$6"+%#$E+3*58#$-%$)==$520$6"+%#$?+%-*-E#$%-0#$-%$)+22#)*#0$*+$*"#$)-1)&-*
81+&207$O+64$-,$*"#$)&11#2*$01562$,1+/$*"#$?+%-*-E#$%&??3>$-%$0#2+*#0$9<<$520$*"5*$,1+/$*"#
2#85*-E#$%&??3>$-%$9==$:%##$K-87$@7@U5=4$*"#2$*"#$0)$?+6#1$0#3-E#1#0$*+$*"#$5/?3-,-#1$-%
17
18 Chapter 1 Signals and Amplifiers
- .' " ) << 9 << ! ) == 9 ==
;,$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#1$)-1)&-*$-%$0#2+*#0 -0-%%-?5*#04 *"#$?+6#19'5352)#$#G&59
*-+2$,+1$*"#$5/?3-,-#1$)52$'#$61-**#2$5%
- 0) + - 9 = - % + - 0-%%-?5*#0
6"#1#$-9$-%$*"#$?+6#1$01562$,1+/$*"#$%-8253$%+&1)#$520$-%$-%$*"#$?+6#1$0#3-E#1#0$*+$*"#$3+507
I-2)#$ *"#$ ?+6#1$ 01562$ ,1+/$ *"#$ %-8253$ %+&1)#$ -%$ &%&533>$ %/5334$ *"#$ 5/?3-,-#1$ ?+6#1$ '99"&
#"'*#;,-%$0#,-2#0$5%
η $≡$ 999999%9 × @AA
- 0)
-($(*.
!"#$?+6#1$#,,-)-#2)>$-%$52$-/?+1*52*$?#1,+1/52)#$?515/#*#1$,+1$5/?3-,-#1%$*"5*$"5203#$3518#
5/+&2*%$+,$?+6#17$I&)"$5/?3-,-#1%4$)533#0$?+6#1$5/?3-,-#1%4$51#$&%#04$,+1$#D5/?3#4$5%$+&*9
?&*$5/?3-,-#1%$+,$%*#1#+$%>%*#/%7
;2$+10#1$*+$%-/?3-,>$)-1)&-*$0-5815/%4$6#$%"533$50+?*$*"#$)+2E#2*-+2$-33&%*15*#0$-2$K-87 @7@U:'=7
a#1#$*"#$) ?$*#1/-253$-%$%"+62$)+22#)*#0$*+$52$511+6"#50$?+-2*-28$&?6510$520$*"#$) >$*#1/-253
*+$52$511+6"#50$?+-2*-28$0+6265107$!"#$)+11#%?+20-28$E+3*58#$-%$-20-)5*#0$2#D*$*+$#5)"$511+69
"#507$O+*#$*"5*$-2$/52>$)5%#%$6#$6-33$2+*$#D?3-)-*3>$%"+6$*"#$)+22#)*-+2%$+,$*"#$5/?3-,-#1$*+$*"#
0)$?+6#1$%+&1)#%7$K-2533>4$6#$2+*#$*"5*$%+/#$5/?3-,-#1%$1#G&-1#$+23>$+2#$?+6#1$%&??3>7
ICC
VCC
ICC
VCC
IEE
IEE
(a)
VEE
VEE
(b)
Figure 1.13 L2$5/?3-,-#1$*"5*$1#G&-1#%$*6+$0)$%&??3-#%$:%"+62$5%$'5**#1-#%=$,+1$+?#15*-+27
Example 1.2
<+2%-0#1$52$5/?3-,-#1$+?#15*-28$,1+/$±@A9Y$?+6#1$%&??3-#%7$;*$-%$,#0$6-*"$5$%-2&%+-053$E+3*58#$"5E-28$@$Y
?#5.$520$0#3-E#1%$5$%-2&%+-053$E+3*58#$+&*?&*$+,$\$Y$?#5.$*+$5$@9.Ω$3+507$!"#$5/?3-,-#1$0156%$5$)&11#2*$+,
\7]$/L$,1+/$#5)"$+,$-*%$*6+$?+6#1$%&??3-#%7$!"#$-2?&*$)&11#2*$+,$*"#$5/?3-,-#1$-%$,+&20$*+$'#$%-2&%+-053
6-*"$A7@$/L$?#5.7$K-20$*"#$E+3*58#$85-24$*"#$)&11#2*$85-24$*"#$?+6#1$85-24$*"#$?+6#1$01562$,1+/$*"#$0)
%&??3-#%4$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#14$520$*"# 5/?3-,-#1$#,,-)-#2)>7
Solution
\
8v = 999 = \$Y`Y
@
1.4 Amplifiers 19
+1
8 v = BA$3+8$\ = @\7@$0i
+1
\$Y
9k& = 999999999999 = \$/L
@$.Ω
9k
\
8 $ = 999&9 = 9999999 = \A$L`L
A7@
9k$
8 $ = BA$3+8$\A = U\7@$0i
\ \
- % = ) &1/% 9 & 1/% = 9999999 9999999 = ^A7]$/F
B B
@ A7@
- 9 = ) $1/% 9 $1/% = 9999999 9999999 = A7A]$/F
B B
-%
^A7]
8 ; = 999999 = 9999999999 = Z@A$F`F
-9
A7A]
+1
8 ; = @A$3+8$Z@A = B\7@$0i
- 0) = @A × \7] + @A × \7] = @\A$/F
- 0-%%-?5*#0 = - 0) + - 9 4 - %
= @\A + A7A] 4 ^A7] = @^\7b$/F
η = 999999%9 × @AA = B@7U[
- 0)
K1+/$ *"#$ 5'+E#$ #D5/?3#$ 6#$ +'%#1E#$ *"5*$ *"#$ 5/?3-,-#1$ )+2E#1*%$ %+/#$ +,$ *"#$ 0)$ ?+6#1$ -*
0156%$,1+/$*"#$?+6#1$%&??3-#%$*+$%-8253$?+6#1$*"5*$-*$0#3-E#1%$*+$*"#$3+507
1.4.7 Amplifier Saturation
l15)*-)533>$ %?#5.-284$ *"#$ 5/?3-,-#1$ *152%,#1$ )"515)*#1-%*-)$ 1#/5-2%$ 3-2#51$ +E#1$ +23>$ 5$ 3-/-*#0
1528#$+,$-2?&*$520$+&*?&*$E+3*58#%7$K+1$52$5/?3-,-#1$+?#15*#0$,1+/$*6+$?+6#1$%&??3-#%$*"#$+&*9
?&*$E+3*58#$)522+*$#D)##0$5$%?#)-,-#0$?+%-*-E#$3-/-*$520$)522+*$0#)1#5%#$'#3+6$5$%?#)-,-#0$2#89
5*-E#$ 3-/-*7$ !"#$ 1#%&3*-28$ *152%,#1$ )"515)*#1-%*-)$ -%$ %"+62$ -2$ K-87$ @7@^4$ 6-*"$ *"#$ ?+%-*-E#$ 520
2#85*-E#$%5*&15*-+2$3#E#3%$0#2+*#0$%f$520$%h 4$1#%?#)*-E#3>7$J5)"$+,$*"#$*6+$%5*&15*-+2$3#E#3%$-%
&%&533>$6-*"-2$5$,15)*-+2$+,$5$E+3*$+,$*"#$E+3*58#$+,$*"#$)+11#%?+20-28$?+6#1$%&??3>7
C'E-+&%3>4$-2$+10#1$*+$5E+-0$0-%*+1*-28$*"#$+&*?&*$%-8253$65E#,+1/4$*"#$-2?&*$%-8253$%6-28
/&%*$'#$.#?*$6-*"-2$*"#$3-2#51$1528#$+,$+?#15*-+24
%
%
9999−9 $ ≤ $v 9$ ≤ $ 9999+9
8v
8v
;2$K-87$@7@^4$6"-)"$%"+6%$*6+$-2?&*$65E#,+1/%$520$*"#$)+11#%?+20-28$+&*?&*$65E#,+1/%4
*"#$?#5.%$+,$*"#$3518#1$65E#,+1/$"5E#$'##2$)3-??#0$+,,$'#)5&%#$+,$5/?3-,-#1$%5*&15*-+27
20 Chapter 1 Signals and Amplifiers
Figure 1.14 L2$5/?3-,-#1$*152%,#1$)"515)*#1-%*-)$*"5*$-%$3-2#51$#D)#?*$,+1$+&*?&*$%5*&15*-+27
1.4.8 Symbol Convention
L*$*"-%$?+-2*4$6#$0156$*"#$1#50#1P%$5**#2*-+2$*+$*"#$*#1/-2+3+8>$6#$%"533$#/?3+>$*"1+&8"+&*
*"#$'++.7$!+$-33&%*15*#$*"#$*#1/-2+3+8>4$K-87$@7@]$%"+6%$*"#$65E#,+1/$+,$5$)&11#2*$$< :"=$*"5*
-%$,3+6-28$*"1+&8"$5$'152)"$-2$5$?51*-)&351$)-1)&-*7$!"#$)&11#2*$$< :"=$)+2%-%*%$+,$5$0)$)+/?+9
2#2*$9<$+2$6"-)"$-%$%&?#1-/?+%#0$5$%-2&%+-053$)+/?+2#2*$$':"=$6"+%#$?#5.$5/?3-*&0#$-%$9'7
C'%#1E#$*"5*$5*$5$*-/#$"4$*"#$)%)3(,"*+)3*)3*'%0+$)&11#2*$$< :"=$-%$*"#$%&/$+,$*"#$0)$)&11#2*$9<
520$*"#$%-8253$)&11#2*$ $ ' ( " ) 4
$< ( " ) " 9< ! $' ( " )
-($((.
6"#1#$*"#$%-8253$)&11#2*$-%$8-E#2$'>
$ ' ( " ) " 9 ' %-2 ω"
!"&%4$6#$%*5*#$%+/#$)+2E#2*-+2%H$!+*53$-2%*52*52#+&%$G&52*-*-#%$51#$0#2+*#0$'>$5$3+6#1)5%#
%>/'+3$6-*"$&??#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#4$$< :"=4$v1@ :"=7$Q-1#)*9)&11#2*$:0)=$G&52*-*-#%$51#
0#2+*#0$'>$52$&??#1)5%#$%>/'+3$6-*"$&??#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#$9< 4$V1@ 7$;2)1#/#2*53
1.5 Circuit Models for Amplifiers 21
iC
ic
Ic
iC
IC
0
t
Figure 1.15 I>/'+3$)+2E#2*-+2$#/?3+>#0$*"1+&8"+&*$*"#$'++.7
%-8253$G&52*-*-#%$51#$0#2+*#0$'>$5$3+6#1)5%#$%>/'+3$6-*"$3+6#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#4
$':"=4$vA!:"=7$;,$*"#$%-8253$-%$5$%-2#$65E#4$*"#2$-*%$5/?3-*&0#$-%$0#2+*#0$'>$52$&??#1)5%#$%>/'+3
6-*"$3+6#1)5%#$%&'%)1-?*:%=4$,+1$#D5/?3#$9' 4$)A!7$K-2533>4$53*"+&8"$2+*$%"+62$-2$K-87$@7@]4$0)
?+6#1$%&??3-#%$51#$0#2+*#0$'>$52$&??#1)5%#$3#**#1$6-*"$5$0+&'3#93#**#1$&??#1)5%#$%&'%)1-?*4$,+1
#D5/?3#4$)<< 4$)117$L$%-/-351$2+*5*-+2$-%$&%#0$,+1$*"#$0)$)&11#2*$01562$,1+/$*"#$?+6#1$%&??3>4
,+1$#D5/?3#4$9<< 4$9117$
EXERCISES
1.10 L2$5/?3-,-#1$"5%$5$E+3*58#$85-2$+,$@AA$Y`Y$520$5$)&11#2*$85-2$+,$@AAA$L`L7$JD?1#%%$*"#$E+3*58#$520
)&11#2*$85-2%$-2$0#)-'#3%$520$,-20$*"#$?+6#1$85-27
Ans. ^A$0iM$bA$0iM$]A$0i
1.11 L2$5/?3-,-#1$+?#15*-28$,1+/$5$%-283#$@]9Y$%&??3>$?1+E-0#%$5$@B9Y$?#5.9*+9?#5.$%-2#965E#$%-8253
*+$5$@9.Ω$3+50$520$0156%$2#83-8-'3#$-2?&*$)&11#2*$,1+/$*"#$%-8253$%+&1)#7$!"#$0)$)&11#2*$01562$,1+/$*"#
@]9Y$%&??3>$-%$Z$/L7$F"5*$-%$*"#$?+6#1$0-%%-?5*#0$-2$*"#$5/?3-,-#14$520$6"5*$-%$*"#$5/?3-,-#1$#,,-)-#2)>X
Ans. @AB$/FM$@][
1.5 Circuit Models for Amplifiers
L$%&'%*52*-53$?51*$+,$*"-%$'++.$-%$)+2)#12#0$6-*"$*"#$0#%-82$+,$5/?3-,-#1$)-1)&-*%$*"5*$&%#$*152%-%9
*+1%$+,$E51-+&%$*>?#%7$I&)"$)-1)&-*%$6-33$E51>$-2$)+/?3#D-*>$,1+/$*"+%#$&%-28$5$%-283#$*152%-%*+1$*+
*"+%#$6-*"$BA$+1$/+1#$0#E-)#%7$;2$+10#1$*+$'#$5'3#$*+$5??3>$*"#$1#%&3*-28$5/?3-,-#1$)-1)&-*$5%$5
'&-30-28$'3+).$-2$5$%>%*#/4$+2#$/&%*$'#$5'3#$*+$)"515)*#1-T#4$+1$!%1'(5$-*%$*#1/-253$'#"5E-+17$;2
*"-%$%#)*-+24$6#$%*&0>$%-/?3#$'&*$#,,#)*-E#$5/?3-,-#1$/+0#3%7$!"#%#$/+0#3%$5??3>$-11#%?#)*-E#$+,
*"#$)+/?3#D-*>$+,$*"#$-2*#1253$)-1)&-*$+,$*"#$5/?3-,-#17$!"#$E53&#%$+,$*"#$/+0#3$?515/#*#1%$)52$'#
,+&20$#-*"#1$'>$5253>T-28$*"#$5/?3-,-#1$)-1)&-*$+1$'>$?#1,+1/-28$/#5%&1#/#2*%$5*$*"#$5/?3-,-#1
*#1/-253%7
22 Chapter 1 Signals and Amplifiers
1.5.1 Voltage Amplifiers
K-8&1#$@7@b:5=$%"+6%$5$)-1)&-*$/+0#3$,+1$*"#$E+3*58#$5/?3-,-#17$!"#$/+0#3$)+2%-%*%$+,$5$E+3*9
58#9)+2*1+33#0$E+3*58#$%+&1)#$"5E-28$5$85-2$,5)*+1$ 8 v&4$52$-2?&*$1#%-%*52)#$#$$*"5*$5))+&2*%
,+1$*"#$,5)*$*"5*$*"#$5/?3-,-#1$0156%$52$-2?&*$)&11#2*$,1+/$*"#$%-8253$%+&1)#4$520$52$+&*?&*
1#%-%*52)#$#&$*"5*$5))+&2*%$,+1$*"#$)"528#$-2$+&*?&*$E+3*58#$5%$*"#$5/?3-,-#1$-%$)533#0$&?+2$*+
%&??3>$+&*?&*$)&11#2*$*+$5$3+507$!+$'#$%?#)-,-)4$6#$%"+6$-2$K-87$@7@b:'=$*"#$5/?3-,-#1$/+0#3
,#0$6-*"$5$%-8253$E+3*58#$%+&1)#$v!$"5E-28$5$1#%-%*52)#$#!$520$)+22#)*#0$5*$*"#$+&*?&*$*+$5
3+50$ 1#%-%*52)#$ #%7$ !"#$ 2+2T#1+$ +&*?&*$ 1#%-%*52)#$ #&$ )5&%#%$ +23>$ 5$ ,15)*-+2$ +,$ 8 v& v $ $ *+
5??#51$5)1+%%$*"#$+&*?&*7$d%-28$*"#$E+3*58#90-E-0#1$1&3#$6#$+'*5-2
#%
#% + #&
v & = 8 v& v $ 999999999999999999
!"&%$*"#$E+3*58#$85-2$-%$8-E#2$'>
v
#%
9
8 v ≡ 9999& = 8 v& 99999999999999999
v$
#% + #&
-($(+.
;*$,+33+6%$*"5*$-2$+10#1$2+*$*+$3+%#$85-2$-2$)+&?3-28$*"#$5/?3-,-#1$+&*?&*$*+$5$3+504$*"#$+&*9
?&*$1#%-%*52)#$#&$%"+&30$'#$/&)"$%/533#1$*"52$*"#$3+50$1#%-%*52)#$#%7$;2$+*"#1$6+10%4$,+1
5$8-E#2$#%$+2#$/&%*$0#%-82$*"#$5/?3-,-#1$%+$*"5*$-*%$#&$-%$/&)"$%/533#1$*"52$#%7$K&1*"#19
/+1#4$*"#1#$51#$5??3-)5*-+2%$-2$6"-)"$#%$-%$.2+62$*+$E51>$+E#1$5$)#1*5-2$1528#7$;2$+10#1$*+
.##?$*"#$+&*?&*$E+3*58#$v&$5%$)+2%*52*$5%$?+%%-'3#4$*"#$5/?3-,-#1$-%$0#%-82#0$6-*"$#&$/&)"
%/533#1$*"52$*"#$3+6#%*$E53&#$+,$#%7$L2$-0#53$E+3*58#$5/?3-,-#1$-%$+2#$6-*"$#&$=$A7$JG&59
*-+2$:@7@B=$-20-)5*#%$53%+$*"5*$,+1$#%$=$∞4$ 8 v = 8 v&7$!"&%$ 8 v& $-%$*"#$E+3*58#$85-2$+,$*"#
&23+50#0$5/?3-,-#14$+1$*"#$%/'*&#"$#0"),B%()32',23"*7$;*$%"+&30$53%+$'#$)3#51$*"5*$-2$%?#)9
-,>-28$*"#$E+3*58#$85-2$+,$52$5/?3-,-#14$+2#$/&%*$53%+$%?#)-,>$*"#$E53&#$+,$3+50$1#%-%*52)#
1
vo
2
(a)
ii
io
"
vo
vs
!
(b)
Figure 1.16 437$<-1)&-*$/+0#3$,+1$*"#$E+3*58#$5/?3-,-#17$487$!"#$E+3*58#$5/?3-,-#1$6-*"$-2?&*$%-8253$%+&1)#
520$3+507
1.5 Circuit Models for Amplifiers 23
5*$6"-)"$*"-%$85-2$-%$/#5%&1#0$+1$)53)&35*#07$;,$5$3+50$1#%-%*52)#$-%$2+*$%?#)-,-#04$-*$-%$2+19
/533>$5%%&/#0$*"5*$*"#$8-E#2$E+3*58#$85-2$-%$*"#$+?#29)-1)&-*$85-2$ 8 v& 7
!"#$,-2-*#$-2?&*$1#%-%*52)#$#$$-2*1+0&)#%$52+*"#1$E+3*58#90-E-0#1$5)*-+2$5*$*"#$-2?&*4$6-*"
*"#$1#%&3*$*"5*$+23>$5$,15)*-+2$+,$*"#$%+&1)#$%-8253$v!$5)*&533>$1#5)"#%$*"#$-2?&*$*#1/-253%$+,$*"#
5/?3-,-#1M$*"5*$-%4
#$
#$ + #!
v $ = v ! 9999999999999999
-($(/.
;*$,+33+6%$*"5*$-2$+10#1$2+*$*+$3+%#$5$%-82-,-)52*$?+1*-+2$+,$*"#$-2?&*$%-8253$-2$)+&?3-28$*"#
%-8253$%+&1)#$*+$*"#$5/?3-,-#1$-2?&*4$*"#$5/?3-,-#1$/&%*$'#$0#%-82#0$*+$"5E#$52$-2?&*$1#%-%9
m
*52)#$#$$/&)"$81#5*#1$*"52$*"#$1#%-%*52)#$+,$*"#$%-8253$%+&1)#4$ # $ $ # !7$K&1*"#1/+1#4$*"#1#
51#$ 5??3-)5*-+2%$ -2$ 6"-)"$*"#$%+&1)#$1#%-%*52)#$-%$.2+62$ *+$ E51>$+E#1$5$ )#1*5-2$1528#7$!+
/-2-/-T#$*"#$#,,#)*$+,$*"-%$E51-5*-+2$+2$*"#$E53&#$+,$*"#$%-8253$*"5*$5??#51%$5*$*"#$-2?&*$+,$*"#
5/?3-,-#14$*"#$0#%-82$#2%&1#%$*"5*$#$$-%$/&)"$81#5*#1$*"52$*"#$3518#%*$E53&#$+,$#!7$L2$-0#53
E+3*58#$5/?3-,-#1$-%$+2#$6-*"$#$$=$∞7$;2$*"-%$-0#53$)5%#$'+*"$*"#$)&11#2*$85-2$520$?+6#1$85-2
'#)+/#$-2,-2-*#7
!"#$+E#1533$E+3*58#$85-2$:v& /v!=$)52$'#$,+&20$'>$)+/'-2-28$JG%7$:@7@B=$520$:@7@U=4
#$
#%
v&
9 99999999999999999
9
9999 " 8 v& 999999999999999
#
+
#
#
v!
$
! % + #&
!"#1#$51#$%-*&5*-+2%$-2$6"-)"$+2#$-%$-2*#1#%*#0$2+*$-2$E+3*58#$85-2$'&*$+23>$-2$5$%-82-,-)52*
?+6#1$85-27$K+1$-2%*52)#4$*"#$%+&1)#$%-8253$)52$"5E#$5$1#%?#)*5'3#$E+3*58#$'&*$5$%+&1)#$1#%-%9
*52)#$*"5*$-%$/&)"$81#5*#1$*"52$*"#$3+50$1#%-%*52)#7$<+22#)*-28$*"#$%+&1)#$0-1#)*3>$*+$*"#$3+50
6+&30$1#%&3*$-2$%-82-,-)52*$%-8253$5**#2&5*-+27$;2$%&)"$5$)5%#4$+2#$1#G&-1#%$52$5/?3-,-#1$6-*"$5
"-8"$-2?&*$1#%-%*52)#$:/&)"$81#5*#1$*"52$*"#$%+&1)#$1#%-%*52)#=$520$5$3+6$+&*?&*$1#%-%*52)#
:/&)"$%/533#1$*"52$*"#$3+50$1#%-%*52)#=$'&*$6-*"$5$/+0#%*$E+3*58#$85-2$:+1$#E#2$&2-*>$85-2=7
I&)"$52$5/?3-,-#1$-%$1#,#11#0$*+$5%$5$8099'$,3!/("9"'$7$F#$%"533$#2)+&2*#1$'&,,#1$5/?3-,-#1%
+,*#2$*"1+&8"+&*$*"-%$'++.7
EXERCISES
1.12 L$*152%0&)#1$)"515)*#1-T#0$'>$5$E+3*58#$+,$@$Y$1/%$520$5$1#%-%*52)#$+,$@$_Ω$-%$5E5-35'3#$*+$01-E#
5$@A9Ω$3+507$;,$)+22#)*#0$0-1#)*3>4$6"5*$E+3*58#$520$?+6#1$3#E#3%$1#%&3*$5*$*"#$3+50X$;,$5$&2-*>985-2$:-7#74
8 v& " @=$'&,,#1$5/?3-,-#1$6-*"$@9_Ω$-2?&*$1#%-%*52)#$520$@A9Ω$+&*?&*$1#%-%*52)#$-%$-2*#1?+%#0$'#*6##2
%+&1)#$520$3+504$6"5*$0+$*"#$+&*?&*$E+3*58#$520$?+6#1$3#E#3%$'#)+/#X$K+1$*"#$2#6 511528#/#2*4$,-20
*"#$E+3*58#$85-2$,1+/$%+&1)#$*+$3+504$520$*"#$?+6#1$85-2$:'+*"$#D?1#%%#0$-2$0#)-'#3%=7
Ans. @A$µY$1/%M$@A−@@$FM$A7B]$YM$b7B]$/FM$−@B$0iM$^^$0i
1.13 !"#$+&*?&*$E+3*58#$+,$5$E+3*58#$5/?3-,-#1$"5%$'##2$,+&20$*+$0#)1#5%#$'>$BA[$6"#2$5$3+50$1#%-%*52)#
+,$@$.Ω$-%$)+22#)*#07$F"5*$-%$*"#$E53&#$+,$*"#$5/?3-,-#1$+&*?&*$1#%-%*52)#X
Ans. B]A$Ω
1.14 L2$5/?3-,-#1$6-*"$5$E+3*58#$85-2$+,$+^A$0i4$52$-2?&*$1#%-%*52)#$+,$@A$.Ω4$520$52$+&*?&*$1#%-%*52)#
+, @ .Ω$-%$&%#0$*+$01-E#$5$@9.Ω$3+507$F"5*$-%$*"#$E53&#$+,$ 8 v& X$K-20$*"#$E53&#$+,$*"#$?+6#1$85-2$-2
0#)-'#3%7
Ans. @AA$Y`YM$^^$0i$
24 Chapter 1 Signals and Amplifiers
1.5.2 Cascaded Amplifiers
!+$/##*$8-E#2$5/?3-,-#1$%?#)-,-)5*-+2%4$6#$+,*#2$2##0$*+$0#%-82$*"#$5/?3-,-#1$5%$5$)5%)50#$+,
*6+$+1$/+1#$%*58#%7$!"#$%*58#%$51#$&%&533>$2+*$-0#2*-)53M$15*"#14$#5)"$-%$0#%-82#0$*+$%#1E#$5
%?#)-,-)$?&1?+%#7$K+1$-2%*52)#4$-2$+10#1$*+$?1+E-0#$*"#$+E#1533$5/?3-,-#1$6-*"$5$3518#$-2?&*
1#%-%*52)#4$*"#$,-1%*$%*58#$-%$&%&533>$1#G&-1#0$*+$"5E#$5$3518#$-2?&*$1#%-%*52)#7$L3%+4$-2$+10#1$*+
#G&-?$*"#$+E#1533$5/?3-,-#1$6-*"$5$3+6$+&*?&*$1#%-%*52)#4$*"#$,-253$%*58#$-2$*"#$)5%)50#$-%$&%&9
533>$0#%-82#0$*+$"5E#$5$3+6$+&*?&*$1#%-%*52)#7$!+$-33&%*15*#$*"#$5253>%-%$520$0#%-82$+,$)5%9
)50#0$5/?3-,-#1%4$6#$)+2%-0#1$5$?15)*-)53$#D5/?3#7
Example 1.3
K-8&1#$@7@c$0#?-)*%$52$5/?3-,-#1$)+/?+%#0$+,$5$)5%)50#$+,$*"1##$%*58#%7$!"#$5/?3-,-#1$-%$,#0$'>$5$%-8253
%+&1)#$6-*"$5$%+&1)#$1#%-%*52)#$+,$@AA$.Ω$520$0#3-E#1%$-*%$+&*?&*$-2*+$5$3+50$1#%-%*52)#$+,$@AA$Ω7$!"#$,-1%*
%*58#$"5%$5$1#35*-E#3>$"-8"$-2?&*$1#%-%*52)#$520$5$/+0#%*$85-2$,5)*+1$+,$@A7$!"#$%#)+20$%*58#$"5%$5$"-8"#1$85-2
,5)*+1$'&*$3+6#1$-2?&*$1#%-%*52)#7$K-2533>4$*"#$35%*4$+1$+&*?&*4$%*58#$"5%$&2-*>$85-2$'&*$5$3+6$+&*?&*$1#%-%*52)#7
F#$6-%"$*+$#E53&5*#$*"#$+E#1533$E+3*58#$85-24$*"5*$-%4$v%/v!4$*"#$)&11#2*$85-24$520$*"#$?+6#1$85-27
Figure 1.17 !"1##9%*58#$5/?3-,-#1$,+1$JD5/?3#$@7U7
Solution
!"#$,15)*-+2$+,$%+&1)#$%-8253$5??#51-28$5*$*"#$-2?&*$*#1/-253%$+,$*"#$5/?3-,-#1$-%$+'*5-2#0$&%-28$*"#$E+3*9
58#90-E-0#1$1&3#$5*$*"#$-2?&*4$5%$,+33+6%H
v $@
@$_Ω
999999 = 999999999999999999999999999999999999999
9 = A7\A\$Y`Y
@$_Ω + @AA$.Ω
v!
!"#$E+3*58#$85-2$+,$*"#$,-1%*$%*58#$-%$+'*5-2#0$'>$)+2%-0#1-28$*"#$-2?&*$1#%-%*52)#$+,$*"#$%#)+20$%*58#$*+$'#
*"#$3+50$+,$*"#$,-1%*$%*58#M$*"5*$-%4
v
@AA$.Ω
8 v@ ≡ 99999$B9 = @A 9999999999999999999999999999999999999 = \7\$Y`Y
@AA$.Ω + @$.Ω
v $@
I-/-3513>4$*"#$E+3*58#$85-2$+,$*"#$%#)+20$%*58#$-%$+'*5-2#0$'>$)+2%-0#1-28$*"#$-2?&*$1#%-%*52)#$+,$*"#$*"-10
%*58#$*+$'#$*"#$3+50$+,$*"#$%#)+20$%*58#4
v
@A$.Ω
8 vB ≡ 99999$U9 = @AA 9999999999999999999999999999999999 = \A7\$Y`Y
@A$.Ω + @$.Ω
v $B
1.5 Circuit Models for Amplifiers
K-2533>4$*"#$E+3*58#$85-2$+,$*"#$+&*?&*$%*58#$-%$5%$,+33+6%H
v
@AA$Ω
8 vU ≡ 99999%9 = @ 9999999999999999999999999999999999 = A7\A\$Y`Y
@AA$Ω + @A$Ω
v $U
!"#$*+*53$85-2$+,$*"#$*"1##$%*58#%$-2$)5%)50#$)52$'#$2+6$,+&20$,1+/
v
v $@
8 v ≡ 99999%9 = 8 v@ 8 vB 8 vU = Z@Z$Y`Y
+1$]Z7U$0i7
!+$,-20$*"#$E+3*58#$85-2$,1+/$%+&1)#$*+$3+504$6#$/&3*-?3>$8v$'>$*"#$,5)*+1$1#?1#%#2*-28$*"#$3+%%$+,$85-2$5*
*"#$-2?&*M$*"5*$-%4
v%
v v
v
99999 = 99999%9 99999$@9 = 8 v 99999$@9
v!
v $@ v !
v!
= Z@Z × A7\A\ = c^U7b$Y`Y
+1$]c7^$0i7
!"#$)&11#2*$85-2$-%$,+&20$5%$,+33+6%H
$
v % / @AA$Ω
9
8 $ ≡ 999& = 9999999999999999999999999
v $@ ⁄ @$_Ω
$$
^
b
= @A × 8 v = Z7@Z × @A $L`L
+1$@UZ7U$0i7
!"#$?+6#1$85-2$-%$,+&20$,1+/
v% $
8 ; ≡ 99999%9 = 999999999&9
-9
v $@ $ $
b
Z
= 8 v 8 $ = Z@Z × Z7@Z × @A = bb7\ × @A $F`F
+1$\Z7U$0i7$O+*#$*"5*
8 ; ( 0i ) = @99B9 [ 8 v ( 0i ) + 8 $ ( 0i ) ]
L$,#6$)+//#2*%$+2$*"#$)5%)50#$5/?3-,-#1$-2$*"#$5'+E#$#D5/?3#$51#$-2$+10#17$!+$5E+-0$3+%-28
%-8253$ %*1#28*"$ 5*$ *"#$ 5/?3-,-#1$ -2?&*$ 6"#1#$ *"#$ %-8253$ -%$ &%&533>$ E#1>$ %/5334$ *"#$ ,-1%*$ %*58#$ -%
0#%-82#0$*+$"5E#$5$1#35*-E#3>$3518#$-2?&*$1#%-%*52)#$:@$_Ω=4$6"-)"$-%$/&)"$3518#1$*"52$*"#$%+&1)#
1#%-%*52)#7$!"#$*150#9+,,$5??#51%$*+$'#$5$/+0#15*#$E+3*58#$85-2$:@A$Y`Y=7$!"#$%#)+20$%*58#$0+#%
2+*$ 2##0$ *+$ "5E#$ %&)"$ 5$ "-8"$ -2?&*$ 1#%-%*52)#M$ 15*"#14$ "#1#$ 6#$ 2##0$ *+$ 1#53-T#$ *"#$ '&3.$ +,$ *"#
1#G&-1#0$E+3*58#$85-27$!"#$*"-10$520$,-2534$+1$+&*?&*4$%*58#$-%$2+*$5%.#0$*+$?1+E-0#$52>$E+3*58#$85-2M
15*"#14$-*$,&2)*-+2%$5%$5$'&,,#1$5/?3-,-#14$?1+E-0-28$5$1#35*-E#3>$3518#$-2?&*$1#%-%*52)#$520$5$3+6$+&*9
?&*$1#%-%*52)#4$/&)"$3+6#1$*"52$#%7$;*$-%$*"-%$%*58#$*"5*$#25'3#%$)+22#)*-28$*"#$5/?3-,-#1$*+$*"#$@A9
Ω$3+507$!"#%#$?+-2*%$)52$'#$/50#$/+1#$)+2)1#*#$'>$%+3E-28$*"#$,+33+6-28$#D#1)-%#%7$;2$%+$0+-284
+'%#1E#$*"5*$-2$,-20-28$*"#$85-2$+,$52$5/?3-,-#1$%*58#$-2$5$)5%)50#$5/?3-,-#14$*"#$3+50-28$#,,#)*$+,
*"#$%&))##0-28$5/?3-,-#1$%*58#$/&%*$'#$*5.#2$-2*+$5))+&2*$5%$6#$"5E#$0+2#$-2$*"#$5'+E#$#D5/?3#7
25
26 Chapter 1 Signals and Amplifiers
EXERCISES
1.15 F"5*$6+&30$*"#$+E#1533$E+3*58#$85-2$+,$*"#$)5%)50#$5/?3-,-#1$-2$JD5/?3#$@7U$'#$6-*"+&*$%*58#$UX
Ans. Z@7Z$Y`Y
1.16 K+1$*"#$)5%)50#$5/?3-,-#1$+,$JD5/?3#$@7U4$3#*$v!$'#$@$/Y7$K-20$v$@4$v$B4$v$U4$520$v%7
Ans. A7\@$/YM$\$/YM$Z@Z$/YM$c^^$/Y
1.17 :5=$_+0#3$*"#$*"1##9%*58#$5/?3-,-#1$+,$JD5/?3#$@7U$:6-*"+&*$*"#$%+&1)#$520$3+50=4$&%-28$*"#$E+3*58#
5/?3-,-#1$/+0#37$F"5*$51#$*"#$E53&#%$+,$#$4$8v &4$520$#&X
:'=$;,$#%$E51-#%$-2$*"#$1528#$@A$Ω$*+$@AAA$Ω4$,-20$*"#$)+11#%?+20-28$1528#$+,$*"#$+E#1533$E+3*58#$85-24$
v& `v!7
Ans. @$_Ω4$\AA$Y`Y4$@A$ΩM$^A\$Y`Y$*+$Z@A$Y`Y
1.5.3 Other Amplifier Types
;2$*"#$0#%-82$+,$52$#3#)*1+2-)$%>%*#/4$*"#$%-8253$+,$-2*#1#%*e6"#*"#1$5*$*"#$%>%*#/$-2?&*4$5*$52
-2*#1/#0-5*#$%*58#4$+1$5*$*"#$+&*?&*e)52$'#$#-*"#1$5$E+3*58#$+1$5$)&11#2*7$K+1$-2%*52)#4$%+/#$*152%9
0&)#1%$ "5E#$ E#1>$ "-8"$ +&*?&*$ 1#%-%*52)#%$ 520$ )52$ '#$ /+1#$ 5??1+?1-5*#3>$ /+0#3#0$ 5%$ )&11#2*
%+&1)#%7$I-/-3513>4$*"#1#$51#$5??3-)5*-+2%$-2$6"-)"$*"#$+&*?&*$)&11#2*$15*"#1$*"52$*"#$E+3*58#$-%$+,
Table 1.1 The Four Amplifier Types
$$$$$$$$$$$$$!>?#
$$$$$$$$$$$$$$$$$$$$<-1)&-*$_+0#3
$$Y+3*58#$L/?3-,-#1
Ri
"
!
"
vo
!
Avovi
ii
Aisi i
"
vo
!
Ro
$$!152%)+20&)*52)#$
$$L/?3-,-#1
Gmvi
Ri
ii
Ro
Ri
"
!
Rm i i
"
vo
!
Ro
$
8 $! ≡ 999&
$$
( L`L )
v & =A
$
B C ≡ 999&9
v $ v =A
( L`Y )
v
"
vo
!
#$$=$∞$
#& =$A
#$$=$A$
#& =$∞
#$ =$∞
#& =$∞
&
C?#29<-1)&-*$!152%1#%-%*52)#
io
;0#53$$<"515)*#1-%*-)%
&
I"+1*9<-1)&-*
!152%)+20&)*52)#
io
"
vi
!
v&
( Y`Y )
v $ $ =A
$$$ 8 v& ≡ 99999
I"+1*9<-1)&-*$<&11#2*$j5-2
io
Ri
$$!152%1#%-%*52)#
$$L/?3-,-#1
C?#29<-1)&-*$Y+3*58#$j5-2
io
Ro
"
vi
!
$$<&11#2*$L/?3-,-#1
$$$$$$$$j5-2$l515/#*#1
# C ≡ 9999&9
$$
( Y`L )
$ & =A
#$$=$A
#& =$A
1.5 Circuit Models for Amplifiers
-2*#1#%*7$!"&%4$53*"+&8"$-*$-%$*"#$/+%*$?+?&3514$*"#$E+3*58#$5/?3-,-#1$)+2%-0#1#0$5'+E#$-%$(&%*$+2#$+,
,+&1$?+%%-'3#$5/?3-,-#1$*>?#%7$!"#$+*"#1$*"1##$51#$*"#$)&11#2*$5/?3-,-#14$*"#$*152%)+20&)*52)#$5/?3-9
,-#14$520$*"#$*152%1#%-%*52)#$5/?3-,-#17$!5'3#$@7@$%"+6%$*"#$,+&1$5/?3-,-#1$*>?#%4$*"#-1$)-1)&-*$/+09
#3%4$*"#$0#,-2-*-+2$+,$*"#-1$85-2$?515/#*#1%4$520$*"#$-0#53$E53&#%$+,$*"#-1$-2?&*$520$+&*?&*$1#%-%*52)#%7
1.5.4 Relationships between the Four Amplifier Models
L3*"+&8"$,+1$5$8-E#2$5/?3-,-#1$5$?51*-)&351$+2#$+,$*"#$,+&1$/+0#3%$-2$!5'3#$@7@$-%$/+%*$?1#,9
#15'3#4$(4D+&*+"E6+*&37+'(4+06+3!6.+"&+C&.6F+(4D+(C;F$*$67G$;2$,5)*4$%-/?3#$1#35*-+2%"-?%$)52
'#$0#1-E#0$*+$1#35*#$*"#$?515/#*#1%$+,$*"#$E51-+&%$/+0#3%7$K+1$-2%*52)#4$*"#$+?#29)-1)&-*$E+3*9
58#$85-2$8v &$)52$'#$1#35*#0$*+$*"#$%"+1*9)-1)&-*$)&11#2*$85-2$8$!$5%$,+33+6%H$!"#$+?#29)-1)&-*
+&*?&*$E+3*58#$8-E#2$'>$*"#$E+3*58#$5/?3-,-#1$/+0#3$+,$!5'3#$@7@$-%$8v &v$7$!"#$)&11#2*$5/?3-9
,-#1$/+0#3$-2$*"#$%5/#$*5'3#$8-E#%$52$+?#29)-1)&-*$+&*?&*$E+3*58#$+,$8$!$$ #&7$JG&5*-28$*"#%#
*6+$E53&#%$520$2+*-28$*"5*$$$$=$v$ /#$$8-E#%
#
8 v& = 8 $! 99999& #$
I-/-3513>4$6#$)52$%"+6$*"5*
%%%%%
-($(0.
8 v& = B C # &
-($().
#
8 v& = 99999C9
#$
-($(1.
520
!"#$#D?1#%%-+2%$-2$JG%7$:@7@^=$*+$:@7@b=$)52$'#$&%#0$*+$1#35*#$52>$*6+$+,$*"#$85-2$?515/#*#1%
8v&4$8$!4$BC4$520$#C7
1.5.5 Determining Ri and Ro
K1+/$*"#$5/?3-,-#1$)-1)&-*$/+0#3%$8-E#2$-2$!5'3#$@7@4$6#$+'%#1E#$*"5*$*"#$-2?&*$1#%-%*52)#$#$$+,
*"#$5/?3-,-#1$)52$'#$0#*#1/-2#0$'>$5??3>-28$52$-2?&*$E+3*58#$v$$520$/#5%&1-28$:+1$)53)&35*-28=
*"#$-2?&*$)&11#2*$$$M$*"5*$-%4$#$+=+v$ /$$7$!"#$+&*?&*$1#%-%*52)#$-%$,+&20$5%$*"#$15*-+$+,$*"#$+?#29
)-1)&-*$+&*?&*$ E+3*58#$ *+$*"#$%"+1*9)-1)&-*$+&*?&*$)&11#2*7$ L3*#125*-E#3>4$*"#$+&*?&*$1#%-%*52)#
)52$'#$,+&20$'>$#3-/-25*-28$*"#$-2?&*$%-8253$%+&1)#$:*"#2$$$$520$v$$6-33$'+*"$'#$T#1+=$520$5??3>9
-28$5$E+3*58#$%-8253$vH$*+$*"#$+&*?&*$+,$*"#$5/?3-,-#14$5%$%"+62$-2$K-87$@7@Z7$;,$6#$0#2+*#$*"#
)&11#2*$01562$,1+/$vH$$4"&$*"#$+&*?&*$*#1/-253%$5%$$H$:2+*#$*"5*$$H$-%$+??+%-*#$-2$0-1#)*-+2$*+$$&=4
*"#2$ #&+ =+ vH /$H7$ L3*"+&8"$ *"#%#$ *#)"2-G&#%$ 51#$ )+2)#?*&533>$ )+11#)*4$ -2$ 5)*&53$ ?15)*-)#$ /+1#
1#,-2#0$/#*"+0%$51#$#/?3+>#0$-2$/#5%&1-28$#$$520$#&7
ix
"
!
Ro "
vx
ix
vx
Figure 1.18 Q#*#1/-2-28$*"#$+&*?&*$1#%-%*52)#7
27
28 Chapter 1 Signals and Amplifiers
1.5.6 Unilateral Models
!"#$5/?3-,-#1$/+0#3%$)+2%-0#1#0$5'+E#$51#$0*"(3)'$3(M,*"5*$-%4$%-8253$,3+6$-%$&2-0-1#)*-+2534
,1+/$-2?&*$*+$+&*?&*7$_+%*$1#53$5/?3-,-#1%$%"+6$%+/#$1#E#1%#$*152%/-%%-+24$6"-)"$-%$&%&533>
&20#%-15'3#$'&*$/&%*$2+2#*"#3#%%$'#$/+0#3#07$F#$%"533$2+*$?&1%&#$*"-%$?+-2*$,&1*"#1$5*$*"-%
*-/#$#D)#?*$*+$/#2*-+2$*"5*$/+1#$)+/?3#*#$/+0#3%$,+1$3-2#51$*6+9?+1*$2#*6+1.%$51#$8-E#2$-2
L??#20-D$<7$L3%+4$-2$35*#1$)"5?*#1%4$6#$6-33$,-20$-*$2#)#%%51>$-2$)#1*5-2$)5%#%$*+$5&8/#2*$*"#
/+0#3%$+,$!5'3#$@7@$*+$*5.#$-2*+$5))+&2*$*"#$2+2&2-35*#153$25*&1#$+,$%+/#$*152%-%*+1$5/?3-,-#1%7
Example 1.4
!"#$8"/%(3$,H0*#)"%*,)$3*+"+)%$,4AIJ74$6"-)"$6-33$'#$%*&0-#0$-2$<"5?*#1$b4$-%$5$*"1##9*#1/-253$0#E-)#
*"5*$6"#2$?+6#1#09&?$'>$5$0)$%+&1)#$:'5**#1>=$520$+?#15*#0$6-*"$%/533$%-8253%$)52$'#$/+0#3#0$'>$*"#$3-29
#51$)-1)&-*$%"+62$-2$K-87$@7@\:5=7$!"#$*"1##$*#1/-253%$51#$*"#$83+',4A74$*"#$'!"))'$,4K74$520$*"#$#%(('#)%$
4677$!"#$"#51*$+,$*"#$/+0#3$-%$5$*152%)+20&)*52)#$5/?3-,-#1$1#?1#%#2*#0$'>$52$-2?&*$1#%-%*52)#$'#*6##2$i
520$J$:0#2+*#0$7π =4$5$%"+1*9)-1)&-*$*152%)+20&)*52)#$AC4$520$52$+&*?&*$1#%-%*52)#$7&7
B
Rs
C
"
vbe
rp
ro
gmvbe
!
B
C
1
vbe
vs 1
2
rp
gmvbe
2
E
ro
RL
E
(a)
(b)
B ib
1
vbe
C
rp
ro
bib
2
E
(c)
Figure 1.19 437$ I/5339%-8253$ )-1)&-*$ /+0#3$ ,+1$ 5$'-?+351$ (&2)*-+2$ *152%-%*+1$ :in!=7$ 487, !"#$ in!$ )+22#)*#0$5%$52
5/?3-,-#1$6-*"$*"#$#/-**#1$5%$5$)+//+2$*#1/-253$'#*6##2$-2?&*$520$+&*?&*$:)533#0$5$)+//+29#/-**#1$5/?3-,-#1=7$
4#7$L2$53*#125*-E#$%/5339%-8253$)-1)&-*$/+0#3$,+1$*"#$in!7
:5= F-*"$*"#$#/-**#1$&%#0$5%$5$)+//+2$*#1/-253$'#*6##2$-2?&*$520$+&*?&*4$K-87$@7@\:'=$%"+6%$5$*1529
%-%*+1$5/?3-,-#1$.2+62$5%$5$#%!!%*&'!"))'$$+1$2$%0*1'1&'!"))'$$)-1)&-*7$Q#1-E#$52$#D?1#%%-+2$,+1$*"#
E+3*58#$85-2$ v& /v!4$520$#E53&5*#$-*%$/582-*&0#$,+1$*"#$)5%#$#!$=$]$.Ω4$7π$=$B7]$.Ω4$AC$= ^A$/L`Y4
7& = @AA$.Ω,$520$#%$= ]$.Ω7$F"5*$6+&30$*"#$85-2$E53&#$'#$-,$*"#$#,,#)*$+,$7&$6#1#$2#83#)*#0X
:'= L2$53*#125*-E#$/+0#3$,+1$*"#$*152%-%*+1$-2$6"-)"$5$)&11#2*$5/?3-,-#1$15*"#1$*"52$5$*152%)+20&)*52)#$5/9
?3-,-#1$-%$&*-3-T#0$-%$%"+62$-2$K-87$@7@\:)=7$F"5*$/&%*$*"#$%"+1*9)-1)&-*$)&11#2*$85-2$β$'#X$j-E#$'+*"$52
#D?1#%%-+2$520$5$E53&#7
1
vo
2
1.5 Circuit Models for Amplifiers 29
Solution
:5=$R#,#1$*+$K-87$@7@\:'=7$F#$&%#$*"#$E+3*58#90-E-0#1$1&3#$*+$0#*#1/-2#$*"#$,15)*-+2$+,$-2?&*$%-8253$*"5*
5??#51%$5*$*"#$5/?3-,-#1$-2?&*$5%
7π
9
v 06 = v ! 999999999999999
7π + #!
-($(2.
O#D*$6#$0#*#1/-2#$*"#$+&*?&*$E+3*58#$v&$'>$/&3*-?3>-28$*"#$)&11#2*$:ACv06=$'>$*"#$1#%-%*52)#$:#%$oo$7&=4
v & = 4 A C v 06 ( # % || 7 & )
-($(3.
I&'%*-*&*-28$,+1$v06$,1+/$JG7$:@7@c=$>-#30%$*"#$E+3*58#985-2$#D?1#%%-+2
7π
v&
99999 = 4 999999999999999
9 A ( # || 7 )
7π + #! C % &
v!
-($(#.
C'%#1E#$*"5*$*"#$85-2$-%$2#85*-E#4$-20-)5*-28$*"5*$*"-%$5/?3-,-#1$-%$-2E#1*-287$K+1$*"#$8-E#2$)+/?+2#2*$E53&#%4
v&
B7]
99999 = 4 9999999999999999 × ^A × ( ] || @AA )
B7] + ]
v!
= 4 bU7]$Y`Y
O#83#)*-28$*"#$#,,#)*$+,$7&4$6#$+'*5-2
v&
B7]
99999 ! 4 9999999999999999
× ^A × ]
B7] + ]
v!
= 4 bb7c$Y`Y
6"-)"$-%$G&-*#$)3+%#$*+$*"#$E53&#$+'*5-2#0$-2)3&0-28$7&7$!"-%$-%$2+*$%&1?1-%-284$%-2)#$ 7 & $ # %7
-6.%789%:;<%=8><?%@A%7@B$%($(#-C.%:8%6<%<DE@FG?<A:%:8%:;G:%@A%7@B$%($(#-G.5
β $0+ =+AC v06
i&*$ $ 0 = v 06 ⁄ 7 π M$*"&%4
K+1$*"#$E53&#%$8-E#24
β$ =$AC7π
β$ =$^A$/L`Y$×$B7]$.Ω
S$@AA$L`L
EXERCISES
1.18 <+2%-0#1$5$)&11#2*$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$*"#$%#)+20$1+6$+,$!5'3#$@7@7$p#*$*"#$5/?3-9
,-#1$'#$,#0$6-*"$5$%-8253$)&11#2*9%+&1)#$$!$"5E-28$5$1#%-%*52)#$#!4$520$3#*$*"#$+&*?&*$'#$)+22#)*#0$*+$5
3+50$1#%-%*52)#$#%7$I"+6$*"5*$*"#$+E#1533$)&11#2*$85-2$-%$8-E#2$'>
$&
#!
#&
999 = 8 $! 9999999999999999
99999999999999999
9
$!
#! + #$ #& + #%
1.19 <+2%-0#1$*"#$*152%)+20&)*52)#$5/?3-,-#1$6"+%#$/+0#3$-%$%"+62$-2$*"#$*"-10$1+6$+,$!5'3#$@7@7$p#*$5
E+3*58#$%-8253$%+&1)#$v!$6-*"$5$%+&1)#$1#%-%*52)#$#!$'#$)+22#)*#0$*+$*"#$-2?&*$520$5$3+50$1#%-%*52)#$#%
'#$)+22#)*#0$*+$*"#$+&*?&*7$I"+6$*"5*$*"#$+E#1533$E+3*58#985-2$-%$8-E#2$'>
#$
v&
99999 = B C 9999999999999999
( # & || # % )
#
v!
$ + #!
30 Chapter 1 Signals and Amplifiers
1.20 <+2%-0#1$5$*152%1#%-%*52)#$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$*"#$,+&1*"$1+6$+,$!5'3#$@7@7$p#*$*"#
5/?3-,-#1$'#$,#0$6-*"$5$%-8253$)&11#2*9%+&1)#$$!$"5E-28$5$1#%-%*52)#$#!4$520$3#*$*"#$+&*?&*$'#$)+22#)*#0
*+$5$3+50$1#%-%*52)#$#%7$I"+6$*"5*$*"#$+E#1533$85-2$-%$8-E#2$'>
#!
#%
v&
99999 = # C 9999999999999999
9
$ 99999999999999999
$!
#! + #$ #% + #&
1.21$ K-20$*"#$-2?&*$1#%-%*52)#$'#*6##2$*#1/-253%$i$520$j$-2$*"#$)-1)&-*$%"+62$-2$K-87$J@7B@7$!"#$E+3*58#
vH$-%$5$*#%*$E+3*58#$6-*"$*"#$-2?&*$1#%-%*52)#$#-2$0#,-2#0$5%$#-2 ≡+ vH / $HG
ix
Rin
Figure E1.21
Ans. #-2+=+7π+++:β+++@=#6
1.6 Frequency Response of Amplifiers2
K1+/$I#)*-+2$@7B$6#$.2+6$*"5*$*"#$-2?&*$%-8253$*+$52$5/?3-,-#1$)52$5365>%$'#$#D?1#%%#0$5%
*"#$%&/$+,$%-2&%+-053$%-8253%7$;*$,+33+6%$*"5*$52$-/?+1*52*$)"515)*#1-T5*-+2$+,$52$5/?3-,-#1$-%
-2$*#1/%$+,$-*%$1#%?+2%#$*+$-2?&*$%-2&%+-0%$+,$0-,,#1#2*$,1#G&#2)-#%7$I&)"$5$)"515)*#1-T5*-+2$+,
5/?3-,-#1$?#1,+1/52)#$-%$.2+62$5%$*"#$5/?3-,-#1$,1#G&#2)>$1#%?+2%#7
1.6.1 Measuring the Amplifier Frequency Response
F#$%"533$-2*1+0&)#$*"#$%&'(#)*$+,$5/?3-,-#1$,1#G&#2)>$1#%?+2%#$'>$%"+6-28$"+6$-*$)52$'#
/#5%&1#07$K-8&1#$@7BA$0#?-)*%$5$3-2#51$E+3*58#$5/?3-,-#1$,#0$5*$-*%$-2?&*$6-*"$5$%-2#965E#
%-8253$+,$5/?3-*&0#$)$$520$,1#G&#2)>$ ω7$L%$*"#$,-8&1#$-20-)5*#%4$*"#$%-8253$/#5%&1#0$5*$*"#
5/?3-,-#1$+&*?&*$53%+$-%$%-2&%+-053$6-*"$#D5)*3>$*"#$%5/#$,1#G&#2)>$ ω7$!"-%$-%$52$-/?+1*52*
?+-2*$*+$2+*#H$IE646J67+(+!$46KL(J6+!$A4(F+$!+(;;F$6.+"&+(+F$46(7+'$7'3$"M+"E6+76!3F"$4A+&3";3"
$!+!$43!&$.(F+L$"E+"E6+!(C6+*762364'D+(!+"E6+$4;3"7$;2$,5)*4$*"#$%-2#$65E#$-%$*"#$+23>$%-8253
*"5*$0+#%$2+*$)"528#$%"5?#$5%$-*$?5%%#%$*"1+&8"$5$3-2#51$)-1)&-*7$C'%#1E#4$"+6#E#14$*"5*$*"#
+&*?&*$%-2&%+-0$6-33$-2$8#2#153$"5E#$5$0-,,#1#2*$5/?3-*&0#$520$6-33$'#$%"-,*#0$-2$?"5%#$1#35*-E#
*+$*"#$-2?&*7$!"#$15*-+$+,$*"#$5/?3-*&0#$+,$*"#$+&*?&*$%-2&%+-0$:)&=$*+$*"#$5/?3-*&0#$+,$*"#
-2?&*$%-2&%+-0$:)$=$-%$*"#$/582-*&0#$+,$*"#$5/?3-,-#1$85-2$:+1$*152%/-%%-+2=$5*$*"#$*#%*$,1#9
G&#2)>$ ω7$L3%+4$*"#$5283#$ φ$-%$*"#$?"5%#$+,$*"#$5/?3-,-#1$*152%/-%%-+2$5*$*"#$*#%*$,1#G&#2)>
ω7$;,$6#$0#2+*#$*"#$3!/("9"'$,)$3*+!"++"%*4$+1$)$3*+9'$,90*#)"%*$5%$-*$-%$/+1#$)+//+23>
B
JD)#?*$,+1$-*%$&%#$-2$*"#$%*&0>$+,$*"#$,1#G&#2)>$1#%?+2%#$+,$+?95/?$)-1)&-*%$-2$I#)*-+2%$B7]$520$B7c4$*"#$
/5*#1-53$-2$*"-%$%#)*-+2$6-33$2+*$'#$2##0#0$-2$5$%&'%*52*-53$/522#1$&2*-3$<"5?*#1$\7$
1.6 Frequency Response of Amplifiers 31
Linear amplifier
"
vi % Vi sin & t
"
!
vo % Vo sin (& t " ' )
!
Figure 1.20 _#5%&1-28$*"#$,1#G&#2)>$1#%?+2%#$+,$5$3-2#51$5/?3-,-#1H$L*$*"#$*#%*$,1#G&#2)>$ ω4$*"#$5/?3-,-#1
85-2$-%$)"515)*#1-T#0$'>$-*%$/582-*&0#$:)& /)$=$520$?"5%#$φ7
.2+624$'>$,:ω=4$*"#2
)
, ( ω ) = 99999&
)$
∠, ( ω ) = φ
!"#$1#%?+2%#$+,$*"#$5/?3-,-#1$*+$5$%-2&%+-0$+,$,1#G&#2)>$ω$-%$)+/?3#*#3>$0#%)1-'#0$'>$o,:ω=o
520$ ∠,:ω=7$ O+64$ *+$ +'*5-2$ *"#$ )+/?3#*#$ ,1#G&#2)>$ 1#%?+2%#$ +,$ *"#$ 5/?3-,-#1$ 6#$ %-/?3>
)"528#$*"#$,1#G&#2)>$+,$*"#$-2?&*$%-2&%+-0$520$/#5%&1#$*"#$2#6$E53&#$,+1$o, o$520$∠,7$!"#
#20$ 1#%&3*$6-33$'#$5$*5'3#$520`+1$815?"$+,$85-2$/582-*&0#$qo,:ω=or$ E#1%&%$,1#G&#2)>$ 520$5
*5'3#$ 520`+1$ 815?"$ +,$ ?"5%#$ 5283#$ q∠,:ω=r$ E#1%&%$ ,1#G&#2)>7$ !"#%#$ *6+$ ?3+*%$ *+8#*"#1
)+2%*-*&*#$*"#$,1#G&#2)>$1#%?+2%#$+,$*"#$5/?3-,-#1M$*"#$,-1%*$-%$.2+62$5%$*"#$!32*")01'$+1
3!/(")01',$'+/%*+'4$520$*"#$%#)+20$-%$*"#$/.3+',$'+/%*+'7$K-2533>4$6#$%"+&30$/#2*-+2$*"5*
-*$-%$5$)+//+2$?15)*-)#$*+$#D?1#%%$*"#$/582-*&0#$+,$*152%/-%%-+2$-2$0#)-'#3%$520$*"&%$?3+*
BA$3+8$o,:ω=o$E#1%&%$,1#G&#2)>7
1.6.2 Amplifier Bandwidth
K-8&1#$@7B@$%"+6%$*"#$/582-*&0#$1#%?+2%#$+,$52$5/?3-,-#17$;*$-20-)5*#%$*"5*$*"#$85-2$-%$53/+%*
)+2%*52*$+E#1$5$6-0#$,1#G&#2)>$1528#4$1+&8"3>$'#*6##2$ω@$520$ωB7$I-8253%$6"+%#$,1#G&#2)-#%
51#$'#3+6$ ω@$+1$5'+E#$ ωB$6-33$#D?#1-#2)#$3+6#1$85-24$6-*"$*"#$85-2$0#)1#5%-28$5%$6#$/+E#
,51*"#1$565>$,1+/$ω@$520$ωB7$!"#$'520$+,$,1#G&#2)-#%$+E#1$6"-)"$*"#$85-2$+,$*"#$5/?3-,-#1$-%
53/+%*$)+2%*52*4$*+$6-*"-2$5$)#1*5-2$2&/'#1$+,$0#)-'#3%$:&%&533>$U$0i=4$-%$)533#0$*"#$3!/("9"'$
83*1G"1).7$ O+1/533>$ *"#$ 5/?3-,-#1$ -%$ 0#%-82#0$ %+$ *"5*$ -*%$ '5206-0*"$ )+-2)-0#%$ 6-*"$ *"#
%?#)*1&/$ +,$ *"#$ %-8253%$ -*$ -%$ 1#G&-1#0$ *+$ 5/?3-,>7$ ;,$ *"-%$ 6#1#$ 2+*$ *"#$ )5%#4$ *"#$ 5/?3-,-#1
6+&30$.$!"&7"$*"#$,1#G&#2)>$%?#)*1&/$+,$*"#$-2?&*$%-82534$6-*"$0-,,#1#2*$)+/?+2#2*%$+,$*"#
-2?&*$%-8253$'#-28$5/?3-,-#0$'>$0-,,#1#2*$5/+&2*%7
1.6.3 Evaluating the Frequency Response of Amplifiers
L'+E#4$6#$0#%)1-'#0$*"#$/#*"+0$&%#0$*+$/#5%&1#$*"#$,1#G&#2)>$1#%?+2%#$+,$52$5/?3-,-#17
F#$ 2+6$ '1-#,3>$ 0-%)&%%$ *"#$ /#*"+0$ ,+1$ 5253>*-)533>$ +'*5-2-28$ 52$ #D?1#%%-+2$ ,+1$ *"#$ ,1#9
G&#2)>$1#%?+2%#7$F"5*$6#$51#$5'+&*$*+$%5>$-%$(&%*$5$?1#E-#6$+,$*"-%$-/?+1*52*$%&'(#)*4$6"+%#
0#*5-3#0$%*&0>$-%$-2$<"5?*#1$\7
32 Chapter 1 Signals and Amplifiers
Figure 1.21 !>?-)53$/582-*&0#$1#%?+2%#$+,$52$5/?3-,-#1H$o,:ω=o$-%$*"#$/582-*&0#$+,$*"#$5/?3-,-#1$*152%,#1
,&2)*-+2e*"5*$-%4$*"#$15*-+$+,$*"#$+&*?&*$)&:ω=$*+$*"#$-2?&*$)$ :ω=7
!+$ #E53&5*#$ *"#$ ,1#G&#2)>$ 1#%?+2%#$ +,$ 52$ 5/?3-,-#14$ +2#$ "5%$ *+$ 5253>T#$ *"#$ 5/?3-,-#1
#G&-E53#2*$ )-1)&-*$ /+0#34$ *5.-28$ -2*+$ 5))+&2*$ 533$ 1#5)*-E#$ )+/?+2#2*%7U$ <-1)&-*$ 5253>%-%
?1+)##0%$ -2$ *"#$ &%&53$ ,5%"-+2$ '&*$ 6-*"$ -20&)*52)#%$ 520$ )5?5)-*52)#%$ 1#?1#%#2*#0$ '>$ *"#-1
1#5)*52)#%7$L2$-20&)*52)#$%$"5%$5$1#5)*52)#$+1$-/?#052)#$Nω%4$520$5$)5?5)-*52)#$<$"5%$5
1#5)*52)#$+1$-/?#052)#$@ ⁄ N ω < $+14$#G&-E53#2*3>4$5$%&%)#?*52)#$+1$50/-**52)#$Nω<7$!"&%$-2$5
*762364'DK.&C($4$5253>%-%$6#$0#53$6-*"$-/?#052)#%$520/+1$50/-**52)#%7$!"#$1#%&3*$+,$*"#
5253>%-%$-%$*"#$5/?3-,-#1$*152%,#1$,&2)*-+2$,:ω=
)& ( ω )
9
, ( ω ) = 99999999999999
)$ ( ω )
6"#1#$)$:ω=$520$)&:ω=$0#2+*#$*"#$-2?&*$520$+&*?&*$%-8253%4$1#%?#)*-E#3>7$,:ω=$-%$8#2#1533>$5
)+/?3#D$,&2)*-+2$6"+%#$/582-*&0#$o,:ω=o$8-E#%$*"#$/582-*&0#$+,$*152%/-%%-+2$+1$*"#$/589
2-*&0#$1#%?+2%#$+,$*"#$5/?3-,-#17$!"#$?"5%#$+,$,:ω=$8-E#%$*"#$?"5%#$1#%?+2%#$+,$*"#$5/?3-9
,-#17
;2$*"#$5253>%-%$+,$5$)-1)&-*$*+$0#*#1/-2#$-*%$,1#G&#2)>$1#%?+2%#4$*"#$538#'15-)$/52-?&35*-+2%
)52$'#$)+2%-0#15'3>$%-/?3-,-#0$'>$&%-28$*"#$#%!/('F,9$':0'*#;,B3$"38('$!7$;2$*#1/%$+,$!4$*"#
-/?#052)#$+,$52$-20&)*52)#$%$-%$!%$520$*"5*$+,$5$)5?5)-*52)#$<$-%$@ ⁄ !<7$R#?35)-28$*"#$1#5)*-E#
#3#/#2*%$6-*"$*"#-1$-/?#052)#%$520$?#1,+1/-28$%*520510$)-1)&-*$5253>%-%4$6#$+'*5-2$*"#$*152%,#1
,&2)*-+2+,:!=$5%
)& ( ! )
9
, ( ! ) ≡ 999999999999
)$ ( ! )
I&'%#G&#2*3>4$6#$1#?35)#$!$'>$Nω$*+$0#*#1/-2#$*"#$*152%,#1$,&2)*-+2$,+1$/.;+"#3(,9$':0'*&
#"'+4$,: Nω=7$O+*#$*"5*$,: Nω=$-%$*"#$%5/#$,&2)*-+2$6#$)533#0$,:ω=$5'+E#^M$*"#$500-*-+253$N$-%
-2)3&0#0$-2$+10#1$*+$#/?"5%-T#$*"5*$,: Nω=$-%$+'*5-2#0$,1+/$,:!=$'>$1#?35)-28$!$6-*"$Nω7
U
O+*#$*"5*$-2$*"#$/+0#3%$)+2%-0#1#0$-2$?1#E-+&%$%#)*-+2%$2+$1#5)*-E#$)+/?+2#2*%$6#1#$-2)3&0#07$!"#%#$
6#1#$%-/?3-,-#0$/+0#3%$520$)522+*$'#$&%#0$53+2#$*+$?1#0-)*$*"#$5/?3-,-#1$,1#G&#2)>$1#%?+2%#7
^
L*$*"-%$%*58#4$6#$51#$&%-28$!$%-/?3>$5%$5$%"+1*"520$,+1$Nω7$F#$%"533$2+*$1#G&-1#$0#*5-3#0$.2+63#08#$+,$
!9?352#$)+2)#?*%$&2*-3$<"5?*#1$\7$L$'1-#,$1#E-#6$+,$!9?352#$5253>%-%$-%$?1#%#2*#0$-2$L??#20-D$K7
1.6 Frequency Response of Amplifiers 33
1.6.4 Single-Time-Constant Networks
;2$5253>T-28$5/?3-,-#1$)-1)&-*%$*+$0#*#1/-2#$*"#-1$,1#G&#2)>$1#%?+2%#4$+2#$-%$81#5*3>$5-0#0$'>
.2+63#08#$+,$*"#$,1#G&#2)>91#%?+2%#$)"515)*#1-%*-)%$+,$%-283#9*-/#9)+2%*52*$:I!<=$2#*6+1.%7
L2$I!<$2#*6+1.$-%$+2#$*"5*$-%$)+/?+%#0$+,4$+1$)52$'#$1#0&)#0$*+4$+2#$1#5)*-E#$)+/?+2#2*
:-20&)*52)#$+1$)5?5)-*52)#=$520$+2#$1#%-%*52)#7$JD5/?3#%$51#$%"+62$-2$K-87$@7BB7$L2$I!<
2#*6+1.$,+1/#0$+,$52$-20&)*52)#$%$520$5$1#%-%*52)#$#$"5%$5$*-/#$)+2%*52*$τ " % ⁄ # 7$!"#
*-/#$)+2%*52*$τ$+,$52$I!<$2#*6+1.$)+/?+%#0$+,$5$)5?5)-*52)#$<$520$5$1#%-%*52)#$#$-%$8-E#2
'>$τ =$<#7
L??#20-D$J$?1#%#2*%$5$%*&0>$+,$I!<$2#*6+1.%$520$*"#-1$1#%?+2%#%$*+$%-2&%+-0534$%*#?4$520
?&3%#$-2?&*%7$s2+63#08#$+,$*"-%$/5*#1-53$6-33$'#$2##0#0$5*$E51-+&%$?+-2*%$*"1+&8"+&*$*"-%$'++.4
520$*"#$1#50#1$6-33$'#$#2)+&158#0$*+$1#,#1$*+$*"#$5??#20-D7$L*$*"-%$?+-2*$6#$2##0$-2$?51*-)&351
*"#$,1#G&#2)>$1#%?+2%#$1#%&3*%M$6#$6-334$-2$,5)*4$'1-#,3>$0-%)&%%$*"-%$-/?+1*52*$*+?-)4$2+67
_+%*$I!<$2#*6+1.%$)52$'#$)35%%-,-#0$-2*+$*6+$)5*#8+1-#%4]$(%G,/3++,4?L7$520$."2.,/3++
4ML74$6-*"$#5)"$+,$*"#$*6+$)5*#8+1-#%$0-%?35>-28$0-%*-2)*3>$0-,,#1#2*$%-8253$1#%?+2%#%7$L%$52
#D5/?3#4$ *"#$ I!<$ 2#*6+1.$ %"+62$ -2$ K-87$ @7BB:5=$ -%$ +,$ *"#$ F&LK;(!!$ *>?#$ 520$ *"5*$ -2$ K-87
@7BB:'=$-%$+,$*"#$E$AEK;(!!$*>?#7$!+$%##$*"#$1#5%+2-28$'#"-20$*"-%$)35%%-,-)5*-+24$+'%#1E#$*"5*
*"#$*152%,#1$,&2)*-+2$+,$#5)"$+,$*"#%#$*6+$)-1)&-*%$)52$'#$#D?1#%%#0$5%$5$E+3*58#90-E-0#1$15*-+4
6-*"$*"#$0-E-0#1$)+/?+%#0$+,$5$1#%-%*+1$520$5$)5?5)-*+17$O+64$1#)533-28$"+6$*"#$-/?#052)#$+,
5$)5?5)-*+1$E51-#%$6-*"$,1#G&#2)>$ :P = @ ⁄ N ω < =4$-*$-%$#5%>$*+$%##$*"5*$*"#$*152%/-%%-+2$+,$*"#
)-1)&-*$-2$K-87$@7BB:5=$6-33$0#)1#5%#$6-*"$,1#G&#2)>$520$5??1+5)"$T#1+$5%$ω$5??1+5)"#%$∞7$!"&%
*"#$)-1)&-*$+,$K-87$@7BB:5=$5)*%,5%,5,(%G&/3++,9"()'$bM$-*$?5%%#%$3+69,1#G&#2)>4$%-2#965E#$-2?&*%
6-*"$3-**3#$+1$2+$5**#2&5*-+2$:5*$ω$=$A4$*"#$*152%/-%%-+2$-%$&2-*>=$520$5**#2&5*#%$"-8"9,1#G&#2)>
-2?&*$%-2&%+-0%7$!"#$)-1)&-*$+,$K-87$@7BB:'=$0+#%$*"#$+??+%-*#M$-*%$*152%/-%%-+2$-%$&2-*>$5*$ω$=$∞
520$0#)1#5%#%$5%$ω$-%$1#0&)#04$1#5)"-28$A$,+1$ω$=$A7$!"#$35**#1$)-1)&-*4$*"#1#,+1#4$?#1,+1/%$5%$5
."2.&/3++,9"()'$7
!5'3#$ @7B$ ?1+E-0#%$ 5$ %&//51>$ +,$ *"#$ ,1#G&#2)>91#%?+2%#$ 1#%&3*%$ ,+1$ I!<$ 2#*6+1.%$ +,
'+*"$*>?#%7c$L3%+4$%.#*)"#%$+,$*"#$/582-*&0#$520$?"5%#$1#%?+2%#%$51#$8-E#2$-2$K-8%7$@7BU$520
@7B^7$!"#%#$,1#G&#2)>91#%?+2%#$0-5815/%$51#$.2+62$5%$A%1',/(%)+$520$*"#$N&1A,9$':0'*#;
C
R
Vi
"
!
C
(a)
]
"
Vo
!
Vi
"
!
R
(b)
"
Vo
!
Figure 1.22 !6+$#D5/?3#%$+,$I!<
2#*6+1.%H$437$5$3+69?5%%$2#*6+1.$520
487$5$"-8"9?5%%$2#*6+1.7
L2$-/?+1*52*$#D)#?*-+2$-%$*"#$3((&/3++$I!<$2#*6+1.$%*&0-#0$-2$<"5?*#1$@b7
L$,-3*#1$-%$5$)-1)&-*$*"5*$?5%%#%$%-8253%$-2$5$%?#)-,-#0$,1#G&#2)>$'520$:*"#$,-3*#1$?5%%'520=$520$%*+?%$+1$
%#E#1#3>$5**#2&5*#%$:,-3*#1%$+&*=$%-8253%$-2$52+*"#1$,1#G&#2)>$'520$:*"#$,-3*#1$%*+?'520=7$K-3*#1%$6-33$'#$
%*&0-#0$-2$<"5?*#1$@b7
c
!"#$*152%,#1$,&2)*-+2%$-2$!5'3#$@7B$51#$8-E#2$-2$8#2#153$,+1/7$K+1$*"#$)-1)&-*%$+,$K-87$@7BB4$O$=$@$520$
ω A$= @/<#7
b
34 Chapter 1 Signals and Amplifiers
Table 1.2 Frequency Response of STC Networks
p+69l5%%$:pl=
a-8"9l5%%$:al=
!152%,#1$K&2)*-+2$,:!=
O
99999999999999999999999999
@ + ( ! ⁄ ωA )
O!
99999999999999
! + ωA
!152%,#1$K&2)*-+2$:,+1$?">%-)53
,1#G&#2)-#%=$,: Nω=
O
999999999999999999999999999999
@ + N ( ω ⁄ ωA )
O
99999999999999999999999999999
9
@ 4 N ( ωA ⁄ ω )
_582-*&0#$R#%?+2%#$|,: Nω=|
O
99999999999999999999999999999999999
B
@ + ( ω ⁄ ωA )
O
99999999999999999999999999999999999
B
@ + ( ωA ⁄ ω )
l"5%#$R#%?+2%#$∠,: Nω=
4 *52 ( ω ⁄ ω A )
*52 ( ω A ⁄ ω )
O
A
A
O
!152%/-%%-+2$5*$ω$=$A
!152%/-%%-+2$5*$ω$=$∞
4@
:0)=
ω A+=+@/τ M+τ++≡+*-/#$)+2%*52*
τ++=+<#++1+%/#
U90i$K1#G&#2)>
i+0#$l3+*%
4@
-2$K-87$@7BU
-2$K-87$@7B^
(a)
(b)
Figure 1.23 437$_582-*&0#$520$487$?"5%#$1#%?+2%#$+,$I!<$2#*6+1.%$+,$*"#$3+69?5%%$*>?#7
1.6 Frequency Response of Amplifiers 35
(a)
(b)
Figure 1.24 437$_582-*&0#$520$487$?"5%#$1#%?+2%#$+,$I!<$2#*6+1.%$+,$$*"#$"-8"9?5%%$*>?#7
:ω A=$ -%$ 53%+$ .2+62$ 5%$ *"#$ #%$*'$, 9$':0'*#;4$ 8$'3O, 9$':0'*#;4, +1, /%(', 9$':0'*#;7$ !"#
1#50#1$-%$&18#0$*+$'#)+/#$,5/-3-51$6-*"$*"-%$-2,+1/5*-+2$520$*+$)+2%&3*$L??#20-D$J$-,$,&1*"#1
)351-,-)5*-+2%$ 51#$ 2##0#07$ ;2$ ?51*-)&3514$ -*$ -%$ -/?+1*52*$ *+$ 0#E#3+?$ 5$ ,5)-3-*>$ ,+1$ *"#$ 15?-0
0#*#1/-25*-+2$+,$*"#$*-/#$)+2%*52*$ τ$+,$52$I!<$)-1)&-*7$!"#$?1+)#%%$-%$E#1>$%-/?3#H$I#*$*"#
-20#?#20#2*$E+3*8#$+1$)&11#2*$%+&1)#$*+$T#1+M$V815'$"+30W$+,$*"#$*6+$*#1/-253%$+,$*"#$1#5)*-E#
#3#/#2*$:)5?5)-*+1$<$+1$-20&)*+1$%=M$520$0#*#1/-2#$*"#$#G&-E53#2*$1#%-%*52)#$#$*"5*$5??#51%
'#*6##2$*"#%#$*6+$*#1/-253%7$!"#$*-/#9)+2%*52*$-%$*"#2$<#$+1$%`#7
36 Chapter 1 Signals and Amplifiers
Example 1.5
K-8&1#$@7B]$%"+6%$5$E+3*58#$5/?3-,-#1$"5E-28$52$-2?&*$1#%-%*52)#$#$ 4$52$-2?&*$)5?5)-*52)#$<$ 4$5$85-2$,5)*+1
µ4$520$52$+&*?&*$1#%-%*52)#$#&7$!"#$5/?3-,-#1$-%$,#0$6-*"$5$E+3*58#$%+&1)#$)!$"5E-28$5 %+&1)#$1#%-%*52)#$#!4
520$5$3+50$+,$1#%-%*52)#$#%$-%$)+22#)*#0$*+$*"#$+&*?&*7
Rs
Ro
"
Vs
"
!
Vi
"
Ri
"
!
Ci
( Vi
!
RL
Vo
!
Figure 1.25 <-1)&-*$,+1$JD5/?3#$@7]7
:5= Q#1-E#$52$#D?1#%%-+2$,+1$*"#$5/?3-,-#1$E+3*58#$85-2$ )& ⁄ )!$5%$5$,&2)*-+2$+,$,1#G&#2)>7$K1+/$*"-%$,-20
#D?1#%%-+2%$,+1$*"#$0)$85-2$520$*"#$U90i$,1#G&#2)>7
:'= <53)&35*#$*"#$E53&#%$+,$*"#$0)$85-24$*"#$U90i$,1#G&#2)>4$520$*"#$,1#G&#2)>$5*$6"-)"$*"#$85-2$'#)+/#%
A$0i$:-7#74$&2-*>=$,+1$*"#$)5%#$#!$=$BA$.Ω4$#$$=$@AA$.Ω4$<$$=$bA$?K4$ µ " @^^$Y`Y4 +#&$=$BAA$Ω4$520$#%
=$@$.Ω7
:)= K-20$v&:"=$,+1$#5)"$+,$*"#$,+33+6-28$-2?&*%H
:-= v$$=$A7@$%-2$@AB$"4$Y
:--= v$$=$A7@$%-2$@A]$"4$Y
:---= v$$=$A7@$%-2$@Ab$"4$Y
:-E= v$$=$A7@$%-2$@AZ$"4$Y
Solution
-G.%H:@?@I@AB%:;<%F8?:GB<J>@F@><9%9E?<5%K<%CGA%<LM9<NN%)$%@A%:<9=N%8O%)!%GN%O8??8KN
P$
9
) $ = ) ! 999999999999999
P$ ! #!
6"#1#$P $$-%$*"#$5/?3-,-#1$-2?&*$-/?#052)#7$I-2)#$P $$-%$)+/?+%#0$+,$*6+$?51533#3$#3#/#2*%4$-*$-%$+'E-+&%3>
#5%-#1$*+$6+1.$-2$*#1/%$+,$ Q $ = @ ⁄ P $ 7$!+6510$*"5*$#20$6#$0-E-0#$*"#$2&/#15*+1$520$0#2+/-25*+1$'>$P$ 4
*"&%$+'*5-2-28
@
) $ = ) ! 9999999999999999999
@ + #! Q$
@
= ) ! 999999999999999999999999999999999999999999999999999
@ + # ! [ ( @ ⁄ # $ ) ! !< $ ]
!"&%4
)
@
99999$ = 999999999999999999999999999999999999999999999999
@ + ( # ! ⁄ # $ ) + !< $ # !
)!
1.6 Frequency Response of Amplifiers
!"-%$#D?1#%%-+2$)52$'#$?&*$-2$*"#$%*520510$,+1/$,+1$5$3+69?5%%$I!<$2#*6+1.$:%##$*"#$*+?$3-2#$+,$!5'3#$@7B=
'>$#D*15)*-28$[ @ ! ( # ! ⁄ # $ ) ]$,1+/$*"#$0#2+/-25*+1M$*"&%$6#$"5E#
)
@
@
99999$ = 999999999999999999999999999
9 999999999999999999999999999999999999999999999999999999999999999
9
)!
@ + ( # ! ⁄ # $ ) @ + !< $ [ ( # ! # $ ) ⁄ ( # ! + # $ ) ]
-($+*.
&:%:;<%8E:ME:%N@><%8O%:;<%G=M?@O@<9%K<%CGA%EN<%:;<%F8?:GB<J>@F@><9%9E?<%:8%K9@:<
#%
9
) & = µ ) $ 99999999999999999
#% + #&
P;@N%<DEG:@8A%CGA%6<%C8=6@A<>%K@:;%QD$%-($+*.%:8%86:G@A%:;<%G=M?@O@<9%:9GANO<9%OEAC:@8A%GN
)
@
@
@
99999& = µ 9999999999999999999999999999 99999999999999999999999999999
9 9999999999999999999999999999999999999999999999999999999999999999
@ + ( # ! ⁄ # $ ) @ + ( # & ⁄ # % ) @ + !< $ [ ( # ! # $ ) ⁄ ( # ! + # $ ) ]
)!
-($+(.
F#$2+*#$*"5*$+23>$*"#$35%*$,5)*+1$-2$*"-%$#D?1#%%-+2$-%$2#6$:)+/?51#0$6-*"$*"#$#D?1#%%-+2$0#1-E#0$-2$*"#
35%*$%#)*-+2=7$!"-%$,5)*+1$-%$5$1#%&3*$+,$*"#$-2?&*$)5?5)-*52)#$<$4$6-*"$*"#$*-/#$)+2%*52*$'#-28
##
#! + #$
! $
τ = < $ 9999999999999999
-($++.
$ = < $ ( # ! oo # $ )
F#$)+&30$"5E#$+'*5-2#0$*"-%$1#%&3*$'>$-2%?#)*-+2H$K1+/$K-87$@7B]$6#$%##$*"5*$*"#$-2?&*$)-1)&-*$-%$52$I!<
2#*6+1.$520$*"5*$-*%$*-/#$)+2%*52*$)52$'#$,+&20$'>$1#0&)-28$)!$*+$T#1+4$6-*"$*"#$1#%&3*$*"5*$*"#$1#%-%*52)#
%##2$'>$<$$-%$#$$-2$?51533#3$6-*"$#!7$!"#$*152%,#1$,&2)*-+2$-2$JG7$:@7B@=$-%$+,$*"#$,+1/$ O ⁄ ( @ + ( ! ⁄ ω A ) ) 4
6"-)"$)+11#%?+20%$*+$5$3+69?5%%$I!<$2#*6+1.7$!"#$0)$85-2$-%$,+&20$5%
)
@
@
O ≡ 99999& ( ! = A ) = µ 9999999999999999999999999999 999999999999999999999999999999
@ + ( #! ⁄ #$ ) @ + ( #& ⁄ #% )
)!
-($+/.
!"#$U90i$,1#G&#2)>$ωA$)52$'#$,+&20$,1+/
@
@
ω A = 999 = 999999999999999999999999999
< $ ( # ! $oo$# $ )
τ
-($+0.
I-2)#$*"#$,1#G&#2)>$1#%?+2%#$+,$*"-%$5/?3-,-#1$-%$+,$*"#$3+69?5%%$I!<$*>?#4$*"#$i+0#$?3+*%$,+1$*"#$85-2
/582-*&0#$520$?"5%#$6-33$*5.#$*"#$,+1/$%"+62$-2$K-87$@7BU4$6"#1#$O$-%$8-E#2$'>$JG7$:@7BU=$520$ωA$-%$8-E#2
'>$JG7$:@7B^=7
:'=$I&'%*-*&*-28$*"#$2&/#1-)53$E53&#%$8-E#2$-2*+$JG7$:@7BU=$1#%&3*%$-2
@
@
O = @^^ 999999999999999999999999999999999 999999999999999999999999999999999999999 = @AA$Y`Y
@ + ( BA ⁄ @AA ) @ + ( BAA ⁄ @AAA )
!"&%$*"#$5/?3-,-#1$"5%$5$0)$85-2$+,$^A$0i7$I&'%*-*&*-28$*"#$2&/#1-)53$E53&#%$-2*+$JG7$:@7B^=$8-E#%$*"#$U90i
,1#G&#2)>
@
bA$?K × ( BA$.Ω``@AA$.Ω )
@
9 = @A b $150`%
= 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
4 @B
U
bA × @A × ( BA × @AA ⁄ ( BA ! @AA ) ) × @A
ω A $= 999999999999999999999999999999999999999999999999999999999999999
37
38 Chapter 1 Signals and Amplifiers
Example 1.5 continued
!"&%4
b
@A
* A = 99999999 = @]\7B$.aT
Bπ
I-2)#$*"#$85-2$,533%$+,,$5*$*"#$15*#$+,$hBA$0i/0#)50#4$%*51*-28$5*$ω A$:%##$K-87$@7BU5=$*"#$85-2$6-33$1#5)"$A$0i
-2$*6+$0#)50#%$:5$,5)*+1$+,$@AA=M$*"&%$6#$"5E#
Z
d2-*>985-2$,1#G&#2)> " @AA × ω A " @A $150`% +1 @]7\B$_aT
:)=$!+$,-20$v&:"=$6#$2##0$*+$0#*#1/-2#$*"#$85-2$/582-*&0#$520$?"5%#$5*$@AB4$@A]4$@Ab4$520$@AZ$150/%7$!"-%$)52
'#$0+2#$#-*"#1$5??1+D-/5*#3>$&*-3-T-28$*"#$i+0#$?3+*%$+,$K-87$@7BU$+1$#D5)*3>$&*-3-T-28$*"#$#D?1#%%-+2$,+1
*"#$5/?3-,-#1$*152%,#1$,&2)*-+24
)
@AA
, ( N ω ) ≡ 99999& ( N ω ) " 9999999999999999999999999999999
9
b
)!
@ ! N ( ω ⁄ @A )
F#$%"533$0+$'+*"H
^
:-=$K+1$ ω$ =$@AB$150/%4$6"-)"$-%$ ( ω A ⁄ @A )4$*"#$i+0#$?3+*%$+,$K-87$@7BU$%&88#%*$*"5*$o, o$=$O$=$@AA$520
φ$=$A°7$!"#$*152%,#1$,&2)*-+2$#D?1#%%-+2$8-E#%$o, o$!$@AA$520$φ$=$h*52h@$@Ah^$!$A°7$!"&%4
v&:"=$=$@A$%-2$@AB"4$Y
:--=$K+1$ω$ =$@A]$150/%4$6"-)"$-%$ ( ω A ⁄ @A )4$*"#$i+0#$?3+*%$+,$K-87$@7BU$%&88#%*$*"5*$o, o$!$O$=$@AA$520
φ$=$−]7c°7$!"#$*152%,#1$,&2)*-+2$#D?1#%%-+2$8-E#%$o, o$=$\\7]$520$φ$=$−*52−@$A7@$=$−]7c°7$!"&%4
v&:"=$=$\7\]$%-2:@A]"$h$]7c°=4$Y
-@@@.%789%ω%=%(*1%9G>/N%=%ω *5% , = @AA ⁄ B = cA7c$Y`Y 89%/2%>R%GA>%φ%=%−0)°$%P;EN5
v&:"=$=$c7Ac$%-2:@Ab"$−$^]°=4$Y
:-E=$K+1$ ω$=$@AZ$150/%4$6"-)"$-%$:@AAω A=4$*"#$i+0#$?3+*%$%&88#%*$*"5*$o,o$=$@$520$ φ =$h\A°7$!"#$*152%,#1
,&2)*-+2$#D?1#%%-+2$8-E#%
o, o$!$@
520 φ = −*52h@$@AA = −Z\7^°
!"&%4
v&:"=$=$A7@$%-2:@AZ"$−$Z\7^°=4$Y
1.6.5 Classification of Amplifiers Based on
Frequency Response
L/?3-,-#1%$)52$'#$)35%%-,-#0$'5%#0$+2$*"#$%"5?#$+,$*"#-1$/582-*&0#91#%?+2%#$)&1E#7$K-8&1#$@7Bb
%"+6%$*>?-)53$,1#G&#2)>91#%?+2%#$)&1E#%$,+1$E51-+&%$5/?3-,-#1$*>?#%7$;2$K-87$@7Bb:5=$*"#$85-2
1#/5-2%$)+2%*52*$+E#1$5$6-0#$,1#G&#2)>$1528#4$'&*$,533%$+,,$5*$3+6$520$"-8"$,1#G&#2)-#%7$!"-%
*>?#$+,$,1#G&#2)>$1#%?+2%#$-%$)+//+2$-2$5&0-+$5/?3-,-#1%7
L%$ 6-33$ '#$ %"+62$ -2$ 35*#1$ )"5?*#1%4$ "*)'$*3(, #3/3#")3*#'+$ -2$ *"#$ 0#E-)#$ :5$ *152%-%*+1=
)5&%#$*"#$,533+,,$+,$85-2$5*$"-8"$,1#G&#2)-#%4$(&%*$5%$<$$0-0$-2$*"#$)-1)&-*$+,$JD5/?3#$@7]7$C2
*"#$+*"#1$"5204$*"#$,533+,,$+,$85-2$5*$3+6$,1#G&#2)-#%$-%$&%&533>$)5&%#0$'>$#%0/("*2,#3/3#")%$+
&%#0$*+$)+22#)*$+2#$5/?3-,-#1$%*58#$*+$52+*"#14$5%$-20-)5*#0$-2$K-87$@7Bc7$!"-%$?15)*-)#$-%$&%&9
533>$50+?*#0$*+$%-/?3-,>$*"#$0#%-82$?1+)#%%$+,$*"#$0-,,#1#2*$%*58#%7$!"#$)+&?3-28$)5?5)-*+1%
1.6 Frequency Response of Amplifiers 39
(a)
(b)
(c)
Figure 1.26 K1#G&#2)>$1#%?+2%#$,+1$437$5$)5?5)-*-E#3>$)+&?3#0$5/?3-,-#14$487$5$0-1#)*9)+&?3#0$5/?3-,-#14
520$4#7$5$*&2#0$+1$'520?5%%$5/?3-,-#17
s
Figure 1.27 d%#$ +,$ 5$ )5?5)-*+1
*+$)+&?3#$5/?3-,-#1$%*58#%7
51#$&%&533>$)"+%#2$G&-*#$3518#$:5$,15)*-+2$+,$5$/-)1+,5150$*+$5$,#6$*#2%$+,$/-)1+,5150%=$%+
*"5*$*"#-1$1#5)*52)#$:-/?#052)#=$-%$%/533$5*$*"#$,1#G&#2)-#%$+,$-2*#1#%*7$O#E#1*"#3#%%4$5*$%&,,-9
)-#2*3>$3+6$,1#G&#2)-#%$*"#$1#5)*52)#$+,$5$)+&?3-28$)5?5)-*+1$6-33$'#)+/#$3518#$#2+&8"$*+
)5&%#$?51*$+,$*"#$%-8253$'#-28$)+&?3#0$*+$5??#51$5%$5$E+3*58#$01+?$5)1+%%$*"#$)+&?3-28$)5?5)9
-*+14$*"&%$2+*$1#5)"-28$*"#$%&'%#G&#2*$%*58#7$<+&?3-28$)5?5)-*+1%$6-33$*"&%$)5&%#$3+%%$+,$85-2
5*$3+6$,1#G&#2)-#%$520$)5&%#$*"#$85-2$*+$'#$T#1+$5*$0)7$!"-%$-%$2+*$5*$533$%&1?1-%-284$%-2)#$,1+/
40 Chapter 1 Signals and Amplifiers
K-87$@7Bc$6#$+'%#1E#$*"5*$*"#$)+&?3-28$)5?5)-*+14$5)*-28$*+8#*"#1$6-*"$*"#$-2?&*$1#%-%*52)#$+,
*"#$ %&'%#G&#2*$ %*58#4$ ,+1/%$ 5$ "-8"9?5%%$ I!<$ )-1)&-*7$ ;*$ -%$ *"#$ ,1#G&#2)>$ 1#%?+2%#$ +,$ *"-%
"-8"9?5%%$ )-1)&-*$ *"5*$ 5))+&2*%$ ,+1$ *"#$ %"5?#$ +,$ *"#$ 5/?3-,-#1$ ,1#G&#2)>$ 1#%?+2%#$ -2$ K-87
@7Bb:5=$5*$*"#$3+69,1#G&#2)>$#207
!"#1#$51#$/52>$5??3-)5*-+2%$-2$6"-)"$-*$-%$-/?+1*52*$*"5*$*"#$5/?3-,-#1$/5-2*5-2$-*%$85-2$5*
3+6$ ,1#G&#2)-#%$ 0+62$ *+$ 0)7$ K&1*"#1/+1#4$ /+2+3-*"-)$ -2*#815*#09)-1)&-*$ :;<=$ *#)"2+3+8>
0+#%$2+*$533+6$*"#$,5'1-)5*-+2$+,$3518#$)+&?3-28$)5?5)-*+1%7$!"&%$;<$5/?3-,-#1%$51#$&%&533>
0#%-82#0$ 5%$ 1"$'#)(;, #%0/('1$ +1$ 1#, 3!/("9"'$+$ :5%$ +??+%#0$ *+$ #3/3#")"B'(;, #%0/('14$ +1
3# 3!/("9"'$+=7$K-8&1#$@7Bb:'=$%"+6%$*"#$,1#G&#2)>$1#%?+2%#$+,$5$0)$5/?3-,-#17$I&)"$5$,1#G&#2)>
1#%?+2%#$)"515)*#1-T#%$6"5*$-%$1#,#11#0$*+$5%$5$(%G&/3++,3!/("9"'$7
;2$5$2&/'#1$+,$5??3-)5*-+2%4$%&)"$5%$-2$*"#$0#%-82$+,$150-+$520$!Y$1#)#-E#1%4$*"#$2##0$51-%#%
,+1$52$5/?3-,-#1$6"+%#$,1#G&#2)>$1#%?+2%#$?#5.%$51+&20$5$)#1*5-2$,1#G&#2)>$:)533#0$*"#$#'*)'$
9$':0'*#;=$520$,533%$+,,$+2$'+*"$%-0#%$+,$*"-%$,1#G&#2)>4$5%$%"+62$-2$K-87$@7Bb:)=7$L/?3-,-#1%
6-*"$%&)"$5$1#%?+2%#$51#$)533#0$)0*'1,3!/("9"'$+4,83*1/3++,3!/("9"'$+4$+1$83*1/3++,9"()'$+7
L$*&2#0$5/?3-,-#1$,+1/%$*"#$"#51*$+,$*"#$,1+2*9#20$+1$*&2#1$+,$5$)+//&2-)5*-+2$1#)#-E#1M$'>
50(&%*-28$ -*%$ )#2*#1$ ,1#G&#2)>$ *+$ )+-2)-0#$ 6-*"$ *"#$ ,1#G&#2)>$ +,$ 5$ 0#%-1#0$ )+//&2-)5*-+2%
)"522#3$:#7874$5$150-+$%*5*-+2=4$*"#$%-8253$+,$*"-%$?51*-)&351$)"522#3$)52$'#$1#)#-E#0$6"-3#$*"+%#
+,$+*"#1$)"522#3%$51#$5**#2&5*#0$+1$,-3*#1#0$+&*7
EXERCISES
1.22 <+2%-0#1$5$E+3*58#$5/?3-,-#1$"5E-28$5$,1#G&#2)>$1#%?+2%#$+,$*"#$3+69?5%%$I!<$*>?#$6-*"$5$0)
85-2$+,$bA$0i$520$5$U90i$,1#G&#2)>$+,$@AAA$aT7$K-20$*"#$85-2$-2$0i$5*$*$=$@A$aT4$@A$.aT4$@AA
.aT4$520$@$_aT7
Ans. bA$0iM$^A$0iM$BA$0iM$A$0i
D1.23 <+2%-0#1$5$*152%)+20&)*52)#$5/?3-,-#1$"5E-28$*"#$/+0#3$%"+62$-2$!5'3#$@7@$6-*"$#$$=$]$.Ω4$#&$=$]A
.Ω4$520$BC$=$@A$/L/Y7$;,$*"#$5/?3-,-#1$3+50$)+2%-%*%$+,$5$1#%-%*52)#$#%$-2$?51533#3$6-*"$5$)5?5)-9
*52)#$<%4$)+2E-2)#$>+&1%#3,$*"5*$*"#$E+3*58#$*152%,#1$,&2)*-+2$1#53-T#04$)&/)$4$-%$+,$*"#$3+69?5%%
I!<$*>?#7$F"5*$-%$*"#$3+6#%*$E53&#$*"5*$#%$)52$"5E#$6"-3#$5$0)$85-2$+,$5*$3#5%*$^A$0i$-%$+'*5-2#0X
F-*"$*"-%$E53&#$+,$#%$)+22#)*#04$,-20$*"#$"-8"#%*$E53&#$*"5*$<%$)52$"5E#$6"-3#$5$U90i$'5206-0*"
+,$5*$3#5%*$@AA$.aT$-%$+'*5-2#07
Ans. @B7]$.ΩM$@]\7B$?K
D1.24 <+2%-0#1$*"#$%-*&5*-+2$-33&%*15*#0$-2$K-87$@7Bc7$p#*$*"#$+&*?&*$1#%-%*52)#$+,$*"#$,-1%*$E+3*58#$5/?3-9
,-#1$'#$@$.Ω$520$*"#$-2?&*$1#%-%*52)#$+,$*"#$%#)+20$E+3*58#$5/?3-,-#1$:-2)3&0-28$*"#$1#%-%*+1$%"+62=
'#$\$.Ω7$!"#$1#%&3*-28$#G&-E53#2*$)-1)&-*$-%$%"+62$-2$K-87$J@7B^$6"#1#$)!$520$#!$51#$*"#$+&*?&*
E+3*58#$520$+&*?&*$1#%-%*52)#$+,$*"#$,-1%*$5/?3-,-#14$<$-%$5$)+&?3-28$)5?5)-*+14$520$#$$-%$*"#$-2?&*
1#%-%*52)#$+,$*"#$%#)+20$5/?3-,-#17$<+2E-2)#$>+&1%#3,$*"5*$)B/)!$-%$5$"-8"9?5%%$I!<$,&2)*-+27$F"5*
-%$*"#$%/533#%*$E53&#$,+1$<$*"5*$6-33$#2%&1#$*"5*$*"#$U90i$,1#G&#2)>$-%$2+*$"-8"#1$*"52$@AA$aTX
Ans. A7@b$µK
Rs % 1 k)
C
"
Vs
"
!
Ri % 9 k)
V2
!
Figure E1.24
1.6 Frequency Response of Amplifiers 41
Summary
L2$#3#)*1-)53$%-8253$%+&1)#$)52$'#$1#?1#%#2*#0$-2$#-*"#1$*"#
!"NE#2-2$,+1/$:5$E+3*58#$%+&1)#$v!$-2$%#1-#%$6-*"$5$%+&1)#
1#%-%*52)#$#!=$+1$*"#$O+1*+2$,+1/$:5$)&11#2*$%+&1)#$$!$-2
?51533#3$6-*"$5$%+&1)#$1#%-%*52)#$#!=7$!"#$!"NE#2-2$E+3*9
58#$v!$-%$*"#$+?#29)-1)&-*$E+3*58#$'#*6##2$*"#$%+&1)#$*#19
/-253%M$*"#$O+1*+2$)&11#2*$$!$-%$#G&53$*+$*"#$%"+1*9)-1)&-*
)&11#2*$'#*6##2$*"#$%+&1)#$*#1/-253%7$K+1$*"#$*6+$1#?1#9
%#2*5*-+2%$*+$'#$#G&-E53#2*4$v!$520$ #!$!$/&%*$'#$#G&537
L$%-8253$)52$'#$1#?1#%#2*#0$#-*"#1$'>$-*%$65E#,+1/$E#1%&%
*-/#$+1$5%$*"#$%&/$+,$%-2&%+-0%7$!"#$35**#1$1#?1#%#2*5*-+2
-%$.2+62$5%$*"#$,1#G&#2)>$%?#)*1&/$+,$*"#$%-82537
!"#$%-2#965E#$%-8253$-%$)+/?3#*#3>$)"515)*#1-T#0$'>$-*%
?#5.$E53&#$:+1$1/%$E53&#$6"-)"$-%$*"#$?#5.$` B =4$-*%$,1#9
G&#2)>$:ω$-2$150`%$+1$*$-2$aTM$ω$= Bπ *$520$*$=$@`,4$6"#1#
, -%$*"#$?#1-+0$-2$%#)+20%=4$520$-*%$?"5%#$6-*"$1#%?#)*$*+
52$51'-*151>$1#,#1#2)#$*-/#7
L253+8$ %-8253%$ "5E#$ /582-*&0#%$ *"5*$ )52$ 5%%&/#$ 52>
E53&#7$J3#)*1+2-)$)-1)&-*%$*"5*$?1+)#%%$5253+8$%-8253%$51#
)533#0$5253+8$)-1)&-*%7$I5/?3-28$*"#$/582-*&0#$+,$52$529
53+8$%-8253$5*$0-%)1#*#$-2%*52*%$+,$*-/#$520$1#?1#%#2*-28
#5)"$%-8253$%5/?3#$'>$5$2&/'#1$1#%&3*%$-2$5$0-8-*53$%-82537
Q-8-*53$%-8253%$51#$?1+)#%%#0$'>$0-8-*53$)-1)&-*%7
!"#$%-/?3#%*$0-8-*53$%-8253%$51#$+'*5-2#0$6"#2$*"#$'-251>
%>%*#/$-%$&%#07$L2$-20-E-0&53$0-8-*53$%-8253$*"#2$5%%&/#%
+2#$+,$+23>$*6+$?+%%-'3#$E53&#%H$3+6$520$"-8"$:%5>4$A$Y
520$+]$Y=4$)+11#%?+20-28$*+$3+8-)$A$520$3+8-)$@4$1#%?#)9
*-E#3>7
L2$ 5253+89*+90-8-*53$ )+2E#1*#1$ :LQ<=$ ?1+E-0#%$ 5*$ -*%
+&*?&*$*"#$0-8-*%$+,$*"#$'-251>$2&/'#1$1#?1#%#2*-28$*"#
5253+8$%-8253$%5/?3#$5??3-#0$*+$-*%$-2?&*7$!"#$+&*?&*$0-89
-*53$ %-8253$ )52$ *"#2$ '#$ ?1+)#%%#0$ &%-28$ 0-8-*53$ )-1)&-*%7
R#,#1$*+$K-87$@7@A$520$JG7$:@7U=7
!"#$*152%,#1$)"515)*#1-%*-)4$v:$E#1%&%$v94$+,$5$3-2#51$5/?3-9
,-#1$ -%$ 5$ %*15-8"*$ 3-2#$ 6-*"$ 5$ %3+?#$ #G&53$ *+$ *"#$ E+3*58#
85-27$R#,#1$*+$K-87$@7@B7
L/?3-,-#1%$-2)1#5%#$*"#$%-8253$?+6#1$520$*"&%$1#G&-1#$0)
?+6#1$%&??3-#%$,+1$*"#-1$+?#15*-+27
!"#$5/?3-,-#1$E+3*58#$85-2$)52$'#$#D?1#%%#0$5%$5$15*-+
8v$ -2$ Y`Y$+1$-2$ 0#)-'#3%4$BA$ 3+8o8v o4$ 0i7$ I-/-3513>4$ ,+1
)&11#2*$85-2H$8$$L`L$+1$BA$3+8 o8$o4$0i7$K+1$?+6#1$85-2H
8;$F`F$+1$@A$3+8$8;4$0i7
Q#?#20-28$+2$*"#$%-8253$*+$'#$5/?3-,-#0$:E+3*58#$+1$)&19
1#2*=$520$+2$*"#$0#%-1#0$,+1/$+,$+&*?&*$%-8253$:E+3*58#$+1
)&11#2*=4$ *"#1#$ 51#$ ,+&1$ '5%-)$ 5/?3-,-#1$ *>?#%H$ E+3*58#4
)&11#2*4$ *152%)+20&)*52)#4$ 520$ *152%1#%-%*52)#$ 5/?3-,-9
#1%7$ K+1$ *"#$ )-1)&-*$ /+0#3%$ 520$ -0#53$ )"515)*#1-%*-)%$ +,
*"#%#$,+&1$5/?3-,-#1$*>?#%4$1#,#1$*+$!5'3#$@7@7$L$8-E#2$5/9
?3-,-#1$)52$'#$/+0#3#0$'>$52>$+2#$+,$*"#$,+&1$/+0#3%4$-2
6"-)"$)5%#$*"#-1$?515/#*#1%$51#$1#35*#0$'>$*"#$,+1/&35%$-2
JG%7 :@7@^=$*+$:@7@b=7
L$ %-2&%+-0$ -%$ *"#$ +23>$ %-8253$ 6"+%#$ 65E#,+1/$ -%$ &29
)"528#0$ *"1+&8"$ 5$ 3-2#51$)-1)&-*7$ I-2&%+-053$%-8253%$ 51#
&%#0$*+$/#5%&1#$*"#$,1#G&#2)>$1#%?+2%#$+,$5/?3-,-#1%7
!"#$*152%,#1$,&2)*-+2$ , ( ! ) ≡ ) & ( ! ) ⁄ ) $ ( ! ) $+,$5$E+3*58#
5/?3-,-#1$)52$'#$0#*#1/-2#0$,1+/$)-1)&-*$5253>%-%7$I&'9
%*-*&*-28$! =+Nω$8-E#%$,: N ω =4$6"+%#$/582-*&0#$o,: Nω=o$$-%
*"#$ /582-*&0#$ 1#%?+2%#4$ 520$ 6"+%#$ ?"5%#$ φ :ω=$ -%$ *"#
?"5%#$1#%?+2%#4$+,$*"#$5/?3-,-#17
L/?3-,-#1%$51#$)35%%-,-#0$5))+10-28$*+$*"#$%"5?#$+,$*"#-1
,1#G&#2)>$1#%?+2%#4$o,: Nω=o7$R#,#1$*+$K-87$@7Bb7
I-283#9*-/#9)+2%*52*$:I!<=$2#*6+1.%$51#$*"+%#$2#*6+1.%
*"5*$51#$)+/?+%#0$+,4$+1$)52$'#$1#0&)#0$*+4$+2#$1#5)*-E#
)+/?+2#2*$:%$+1$<=$520$+2#$1#%-%*52)#$:#=7$!"#$*-/#$)+29
%*52*$τ$-%$#-*"#1$%R#$+1$<#7
I!<$2#*6+1.%$)52$'#$)35%%-,-#0$-2*+$*6+$)5*#8+1-#%H$3+69
?5%%$:pl=$520$"-8"9?5%%$:al=7$pl$2#*6+1.%$?5%%$0)$520
3+6$,1#G&#2)-#%$520$5**#2&5*#$"-8"$,1#G&#2)-#%7$!"#$+?9
?+%-*#$-%$*1&#$,+1$al$2#*6+1.%7
!"#$85-2$+,$52$pl$:al=$I!<$)-1)&-*$01+?%$'>$U$0i$'#3+6
*"#$ T#1+9,1#G&#2)>$ :-2,-2-*#9,1#G&#2)>=$ E53&#$ 5*$ 5$ ,1#9
G&#2)>$ ωA$=$@`τ7$L*$"-8"$,1#G&#2)-#%$:3+6$,1#G&#2)-#%=
*"#$85-2$,533%$+,,$5*$*"#$15*#$+,$b$0i`+)*5E#$+1$BA$0i`0#9
)50#7$R#,#1$*+$!5'3#$@7B$+2$?58#$U^$520$K-8%7$@7BU$520
@7B^7$K&1*"#1$0#*5-3%$51#$8-E#2$-2$L??#20-D$J7
PROBLEMS
Computer Simulation Problems
l1+'3#/%$ -2E+3E-28$ 0#%-82$ 51#$ /51.#0$ 6-*"$ Q$ *"1+&8"+&*
*"#$ *#D*7$ L%$ 6#334$ ?1+'3#/%$ 51#$ /51.#0$ 6-*"$ 5%*#1-%.%$ *+
0#%)1-'#$ *"#-1$ 0#81##$ +,$ 0-,,-)&3*>7$ Q-,,-)&3*$ ?1+'3#/%$ 51#
/51.#0$ 6-*"$ 52$ 5%*#1-%.$ :t=M$ /+1#$ 0-,,-)&3*$ ?1+'3#/%$ 6-*"
*6+$ 5%*#1-%.%$ :tt=M$ 520$ E#1>$ )"533#28-28$ 520`+1$ *-/#9
)+2%&/-28$?1+'3#/%$6-*"$*"1##$5%*#1-%.%$:ttt=7
Circuit Basics
L%$5$1#E-#6$+,$*"#$'5%-)%$+,$)-1)&-*$5253>%-%$520$-2$+10#1$,+1
*"#$1#50#1%$*+$85&8#$*"#-1$?1#?51#02#%%$,+1$*"#$%*&0>$+,$#3#)9
*1+2-)$)-1)&-*%4$*"-%$%#)*-+2$?1#%#2*%$5$2&/'#1$+,$1#3#E52*$)-19
)&-*$ 5253>%-%$ ?1+'3#/%7$ K+1$ 5$ %&//51>$ +,$ !"NE#2-2P%$ 520
O+1*+2P%$*"#+1#/%4$1#,#1$*+$L??#20-D$Q7$!"#$?1+'3#/%$51#
81+&?#0$-2$5??1+?1-5*#$)5*#8+1-#%7
Resistors and Ohm’s Law
1.1 C"/P%$356$1#35*#%$)4+94$520$#$,+1$5$1#%-%*+17$K+1$#5)"$+,
*"#$%-*&5*-+2%$,+33+6-284$,-20$*"#$/-%%-28$-*#/H
-G. #+=%(%,Ω5%)+= (*%S
-6. )+=%(*%S5%9++=+(%=&
-C. #+=%(*%,Ω5%9+=%(*%=&
->. #%=%(**%Ω5%)%=%(*%S
1.2 _#5%&1#/#2*%$ *5.#2$ +2$ E51-+&%$ 1#%-%*+1%$ 51#$ %"+62
'#3+67$K+1$#5)"4$)53)&35*#$*"#$?+6#1$0-%%-?5*#0$-2$*"#$1#%-%*+1
520$*"#$?+6#1$15*-28$2#)#%%51>$,+1$%5,#$+?#15*-+2$&%-28$%*529
0510$)+/?+2#2*%$6-*"$?+6#1$15*-28%$+,$@`Z$F4$@`^$F4$@`B$F4
@ F4$+1$B$FH
-G. (%,Ω%C8A>EC:@AB%/*%=&
-6. (%,Ω%C8A>EC:@AB%0*%=&
-C. (*%,Ω%C8A>EC:@AB%/%=&
->. (*%,Ω%C8A>EC:@AB%0%=&
-<. (%,Ω%>98MM@AB%+*%S
-O. (%,Ω%>98MM@AB%((%S
)1#5*#$ &%-28$ %#1-#%$ 520$ ?51533#3$ )+/'-25*-+2%$ +,$ *"#%#$ *"1##X
p-%*$ *"#/$ -2$ E53&#$ +10#14$ 3+6#%*$ ,-1%*7$ i#$ *"+1+&8"$ 520
+1852-T#07$:S$4"T$;2$>+&1$%#51)"4$,-1%*$)+2%-0#1$533$?51533#3$)+/9
'-25*-+2%4$*"#2$)+2%-0#1$%#1-#%$)+/'-25*-+2%4$520$*"#2$)+2%-0#1
%#1-#%9?51533#3$)+/'-25*-+2%4$+,$6"-)"$*"#1#$51#$*6+$.-20%=7
1.5 ;2$*"#$5253>%-%$520$*#%*$+,$#3#)*1+2-)$)-1)&-*%4$-*$-%$+,9
*#2$&%#,&3$*+$)+22#)*$+2#$1#%-%*+1$-2$?51533#3$6-*"$52+*"#1
*+$+'*5-2$5$2+2%*520510$E53&#4$+2#$6"-)"$-%$%/533#1$*"52
*"#$%/533#1$+,$*"#$*6+$1#%-%*+1%7$C,*#24$?51*-)&3513>$0&1-28
)-1)&-*$*#%*-284$+2#$1#%-%*+1$-%$531#50>$-2%*533#04$-2$6"-)"
)5%#$ *"#$ %#)+204$ 6"#2$ )+22#)*#0$ -2$ ?51533#34$ -%$ %5-0$ *+
V%"&2*W$*"#$,-1%*7$;,$*"#$+1-8-253$1#%-%*+1$-%$@A$.Ω 4$6"5*$-%
*"#$ E53&#$ +,$ *"#$ %"&2*-28$ 1#%-%*+1$ 2##0#0$ *+$ 1#0&)#$ *"#
)+/'-2#0$E53&#$'>$@[4$][4$@A[4$520$]A[X$F"5*$-%$*"#$1#9
%&3*$+,$%"&2*-28$5$@A9.Ω$1#%-%*+1$'>$@$_ΩX$i>$@AA$.ΩX$i>
@A$.ΩX
Voltage Dividers
1.6 K-8&1#$ l@7b:5=$%"+6%$ 5$*6+91#%-%*+1$E+3*58#$ 0-E-0#17
;*%$,&2)*-+2$-%$*+$8#2#15*#$5$E+3*58#$):$:%/533#1$*"52$*"#
?+6#19%&??3>$E+3*58#$)11=$5*$-*%$+&*?&*$2+0#$v7$!"#$)-19
)&-*$3++.-28$'5).$5*$2+0#$v$-%$#G&-E53#2*$*+$*"5*$%"+62$-2
K-87$l@7b:'=7$C'%#1E#$*"5*$*"-%$-%$*"#$!"NE#2-2$#G&-E53#2*
+,$ *"#$ E+3*58#$ 0-E-0#1$ )-1)&-*7$ K-20$ #D?1#%%-+2%$ ,+1$ ):
520 #:7
VDD
R1
X
R2
-G. #%=%(%,Ω5%9+=%(*%=&
-6. )%=%(*%S5%9+=%(%=&
-C. )%=%(*%S5%-+=%(%T
->. 9%=%(*%=&5%-%=%*$(%T
-<. #%=%(%,Ω5%-%=%(%T
Combining Resistors
1.4 u+&$ 51#$ 8-E#2$ *"1##$ 1#%-%*+1%$ 6"+%#$ E53&#%$ 51#$ @A$ .Ω4
BA .Ω4$ 520$ ^A$ .Ω7$ a+6$ /52>$ 0-,,#1#2*$ 1#%-%*52)#%$ )52$ >+&
X
VO
1.3 C"/P%$356$520$*"#$?+6#1$356$,+1$5$1#%-%*+1$1#35*#$)4+94
#4$520$-4$/5.-28$+23>$*6+$E51-5'3#%$-20#?#20#2*7$K+1$#5)"
?5-1$-0#2*-,-#0$'#3+64$,-20$*"#$+*"#1$*6+H
RO
VO
RO
(a)
(b)
Figure P1.6
1.7 L$ *6+91#%-%*+1$ E+3*58#$ 0-E-0#1$ #/?3+>-28$ 5$ U7U9.Ω
520$5$b7Z9.Ω$1#%-%*+1$-%$)+22#)*#0$*+$5$\9Y$81+&2091#,#19
#2)#0$ ?+6#1$ %&??3>$ *+$ ?1+E-0#$ 5$ 1#35*-E#3>$ 3+6$ E+3*58#
:)3+%#$ *+$ UY=7$ I.#*)"$ *"#$ )-1)&-*7$ L%%&/-28$ #D5)*9E53&#0
1#%-%*+1%4$ 6"5*$ +&*?&*$ E+3*58#$ :/#5%&1#0$ *+$ 81+&20=$ 520
#G&-E53#2*$+&*?&*$1#%-%*52)#$1#%&3*X$;,$*"#$1#%-%*+1%$&%#0$51#
2+*$ -0#53$ '&*$ "5E#$ 5$ ±][$ /52&,5)*&1-28$ *+3#152)#4$ 6"5*
51#$ *"#$ #D*1#/#$ +&*?&*$ E+3*58#%$ 520$ 1#%-%*52)#%$ *"5*$ )52
1#%&3*X
Problems 43
D *1.9 !6+$1#%-%*+1%4$6-*"$2+/-253$E53&#%$+,$^7c$.Ω$520
@A$.Ω4$51#$&%#0$-2$5$E+3*58#$0-E-0#1$6-*"$5$+@]9Y$%&??3>
*+$)1#5*#$5$2+/-253$+@A9Y$+&*?&*7$L%%&/-28$*"#$1#%-%*+1$E53&#%
*+$'#$#D5)*4$6"5*$-%$*"#$5)*&53$+&*?&*$E+3*58#$?1+0&)#0X$F"-)"
1#%-%*+1$/&%*$'#$%"&2*#0$:?51533#3#0=$'>$6"5*$*"-10$1#%-%*+1$*+
)1#5*#$ 5$ E+3*58#90-E-0#1$ +&*?&*$ +,$ @A7AA$ YX$ ;,$ 52$ +&*?&*
1#%-%*52)#$ +,$ #D5)*3>$ U7UU$ .Ω$ -%$ 53%+$ 1#G&-1#04$ 6"5*$ 0+$ >+&
%&88#%*X$F"5*$%"+&30$'#$0+2#$-,$*"#$+1-8-253$^7c9.Ω$520$@A9.Ω
1#%-%*+1%$51#$&%#0$'&*$*"#$1#G&-1#/#2*$-%$@A7AA$Y$520$U7AA .Ω?
Current Dividers
1.10 <&11#2*$0-E-0#1%$?35>$52$-/?+1*52*$1+3#$-2$)-1)&-*$0#%-827
!"#1#,+1#$-*$-%$-/?+1*52*$*+$0#E#3+?$5$,5)-3-*>$,+1$0#53-28$6-*"
)&11#2*$0-E-0#1%$-2$)-1)&-*$5253>%-%7$K-8&1#$l@7@A$%"+6%$5$*6+9
1#%-%*+1$ )&11#2*$ 0-E-0#1$ ,#0$ 6-*"$ 52$ -0#53$ )&11#2*$ %+&1)#$ 97
I"+6$*"5*
#B
99
9 @ = 99999999999999999
#@ + #B
*"#$ 1#%-%*+1$ 1#G&-1#0X$ F"5*$ -%$ *"#$ -2?&*$ 1#%-%*52)#$ +,$ *"#
)&11#2*$0-E-0#1$-2$#5)"$)5%#X
D 1.13 L$ ?51*-)&351$ #3#)*1+2-)$ %-8253$ %+&1)#$ 8#2#15*#%$ )&19
1#2*%$-2$*"#$1528#$A$/L$*+$@$/L$&20#1$*"#$)+20-*-+2$*"5*$-*%
3+50$E+3*58#$2+*$#D)##0$@$Y7$K+1$3+50%$)5&%-28$/+1#$*"52$@$Y
*+$5??#51$5)1+%%$*"#$8#2#15*+14$*"#$+&*?&*$)&11#2*$-%$2+$3+28#1
5%%&1#0$'&*$6-33$'#$1#0&)#0$'>$%+/#$&2.2+62$5/+&2*7$!"-%
)-1)&-*$3-/-*5*-+24$+))&11-284$,+1$#D5/?3#4$5*$*"#$?#5.$+,$5$%-2#9
65E#$%-82534$6-33$3#50$*+$&20#%-15'3#$%-8253$0-%*+1*-+2$*"5*$/&%*
'#$5E+-0#07$;,$5$@A9.Ω$3+50$-%$*+$'#$)+22#)*#04$6"5*$/&%*$'#
0+2#X$ F"5*$ -%$ *"#$ 25/#$ +,$ *"#$ )-1)&-*$ >+&$ /&%*$ &%#X$ a+6
/52>$1#%-%*+1%$51#$2##0#0X$F"5*$-%$:51#=$*"#:-1=$E53&#:%=X
Thévenin Equivalent Circuits
1.14 K+1$*"#$)-1)&-*$-2$K-87$l@7@^4$,-20$*"#$!"NE#2-2$#G&-E59
3#2*$)-1)&-*$'#*6##2$*#1/-253%$:5=$@$520$B4$:'=$B$520$U4$520
:)=$@$520$U7
1
1k
3V
2
1k
#@
99
9 B = 99999999999999999
#@ + #B
3
520$,-20$*"#$E+3*58#$)$*"5*$0#E#3+?%$5)1+%%$*"#$)&11#2*$0-E-0#17
I
I1
I2
1
R1
R2
V
2
Figure P1.14
1.15 !"1+&8"$ 1#?#5*#0$ 5??3-)5*-+2$ +,$ !"NE#2-2P%$ *"#+1#/4
,-20$ *"#$ !"NE#2-2$ #G&-E53#2*$ +,$ *"#$ )-1)&-*$ -2$ K-87$ l@7@]
'#*6##2$2+0#$^$520$81+&204$520$"#2)#$,-20$*"#$)&11#2*$*"5*
,3+6%$*"1+&8"$5$3+50$1#%-%*52)#$+,$@7]$.Ω$)+22#)*#0$'#*6##2
2+0#$^$520$81+&207
1
Figure P1.10
D 1.11 Q#%-82$5$%-/?3#$)&11#2*$0-E-0#1$*"5*$6-33$1#0&)#$ *"#
)&11#2*$?1+E-0#0$*+$5$@9.Ω$3+50$*+$BA[$+,$*"5*$5E5-35'3#$,1+/
*"#$%+&1)#7
D 1.12 L$0#%-82#1$%#51)"#%$,+1$5$%-/?3#$)-1)&-*$*+$?1+E-0#
+2#9*"-10$+,$5$%-8253$)&11#2*$9$*+$5$3+50$1#%-%*52)#$#7$I&89
8#%*$5$%+3&*-+2$&%-28$+2#$1#%-%*+17$F"5*$/&%*$-*%$E53&#$'#X
F"5*$ -%$ *"#$ -2?&*$ 1#%-%*52)#$ +,$ *"#$ 1#%&3*-28$ )&11#2*
0-E-0#1X$ K+1$ 5$ ?51*-)&351$ E53&#$ #4$ *"#$ 0#%-82#1$ 0-%)+E#1%
*"5*$*"#$+*"#16-%#9'#%*95E5-35'3#$1#%-%*+1$-%$@A[$*++$"-8"7
I&88#%*$ *6+$ )-1)&-*$ *+?+3+8-#%$ &%-28$ +2#$ 500-*-+253
1#%-%*+1$*"5*$6-33$%+3E#$*"-%$?1+'3#/7$F"5*$-%$*"#$E53&#$+,
10 V
10 k
10 k
2
10 k
10 k
3
10 k
4
10 k
Figure P1.15
Circuit Analysis
1.16 K+1$*"#$)-1)&-*$%"+62$-2$K-87$l@7@b4$,-20$*"#$)&11#2*$-2
533$1#%-%*+1%$520$*"#$E+3*58#$:6-*"$1#%?#)*$*+$81+&20=$5*$*"#-1
)+//+2$2+0#$&%-28$*6+$/#*"+0%H
CHAPTER 1 P R O B L E M S
1.8 u+&$51#$8-E#2$*"1##$1#%-%*+1%4$#5)"$+,$@A$.Ω4$520$5$\9Y
'5**#1>$6"+%#$2#85*-E#$*#1/-253$-%$)+22#)*#0$*+$81+&207$F-*"
5$ E+3*58#$ 0-E-0#1$ &%-28$ %+/#$ +1$ 533$ +,$ >+&1$ 1#%-%*+1%4$ "+6
/52>$?+%-*-E#9E+3*58#$%+&1)#%$+,$/582-*&0#$3#%%$*"52$\$Y$)52
>+&$0#%-82X$p-%*$*"#/$-2$+10#14$%/533#%*$,-1%*7$F"5*$-%$*"#$+&*9
?&*$1#%-%*52)#$:-7#74$*"#$!"NE#2-2$1#%-%*52)#=$+,$#5)"X
CHAPTER 1 P R O B L E M S
44 Chapter 1 Signals and Amplifiers
-G. UE99<A:V% W<O@A<% 69GAC;% CE99<A:N% 9(% GA>% 9+% @A% #(% GA>% #+5
9<NM<C:@F<?X'%@><A:@OX%:K8%<DEG:@8AN'%GA>%N8?F<%:;<=$
-6. S8?:GB<V%W<O@A<%:;<%A8><%F8?:GB<%)%G:%:;<%C8==8A%A8><'
@><A:@OX%G%N@AB?<%<DEG:@8A'%GA>%N8?F<%@:$
F"-)"$/#*"+0$0+$>+&$?1#,#1X$F">X
X
Req
R1
1 kV
R5
"15 V
"10 V
R1
10 k!
R2
5 k!
R3
2 k!
R2
1 kV
1 kV
R3
1 kV
R4
1 kV
Figure P1.18
AC Circuits
Figure P1.16
1.17 !"#$)-1)&-*$%"+62$-2$K-87$l@7@c$1#?1#%#2*%$*"#$#G&-E59
3#2*$)-1)&-*$+,$52$&2'5352)#0$'1-08#7$;*$-%$1#G&-1#0$*+$)53)&35*#
*"#$)&11#2*$-2$*"#$0#*#)*+1$'152)"$:#]=$520$*"#$E+3*58#$5)1+%%
-*7$L3*"+&8"$*"-%$)52$'#$0+2#$'>$&%-28$3++?$520$2+0#$#G&59
*-+2%4$5$/&)"$#5%-#1$5??1+5)"$-%$?+%%-'3#H$K-20$*"#$!"NE#2-2
#G&-E53#2*$+,$*"#$)-1)&-*$*+$*"#$3#,*$+,$2+0#$@$520$*"#$!"NE#2-2
#G&-E53#2*$+,$*"#$)-1)&-*$*+$*"#$1-8"*$+,$2+0#$B7$!"#2$%+3E#$*"#
1#%&3*-28$%-/?3-,-#0$)-1)&-*7
19 V
1 kV
R1
1
R3
R5
9.1 kV
2
3 kV
R2
1.2 kV
R4
11 kV
Figure P1.17
1.18 K+1$*"#$)-1)&-*$ -2$ K-87$l@7@Z4$,-20$*"#$#G&-E53#2*$ 1#%-%9
*52)#$*+$81+&204$##G7$!+$0+$*"-%4$5??3>$5$E+3*58#$)H$'#*6##2
*#1/-253$ v$520$ 81+&20$ 520$,-20$*"#$)&11#2*$ 01562$,1+/$)H 7
O+*#$ *"5*$ >+&$ )52$ &%#$ ?51*-)&351$ %?#)-53$ ?1+?#1*-#%$ +,$ *"#
)-1)&-*$*+$8#*$*"#$1#%&3*$0-1#)*3>w$O+64$-,$#^$-%$15-%#0$*+$@7B$.Ω4
6"5*$0+#%$##G$'#)+/#X
1.19 !"#$ ?#1-+0-)-*>$ +,$ 1#)&11#2*$ 65E#,+1/%4$ %&)"$ 5%$ %-2#
65E#%$ +1$ %G&51#$ 65E#%4$ )52$ '#$ )+/?3#*#3>$ %?#)-,-#0$ &%-28
+23>$+2#$+,$*"1##$?+%%-'3#$?515/#*#1%H$150-52$,1#G&#2)>4$ω 4$-2
150-52%$ ?#1$ %#)+20$ :150`%=M$ :)+2E#2*-+253=$ ,1#G&#2)>4$ *4$ -2
"#1*T$:aT=M$+1$?#1-+0$,4$-2$%#)+20%$:%=7$L%$6#334$#5)"$+,$*"#
?515/#*#1%$ )52$ '#$ %?#)-,-#0$ 2&/#1-)533>$ -2$ +2#$ +,$ %#E#153
65>%H$ &%-28$ 3#**#1$ ?1#,-D#%$ 5%%+)-5*#0$ 6-*"$ *"#$ '5%-)$ &2-*%4
&%-28$%)-#2*-,-)$2+*5*-+24$+1$&%-28$%+/#$)+/'-25*-+2$+,$'+*"7
!"&%4$,+1$#D5/?3#4$5$?51*-)&351$?#1-+0$/5>$'#$%?#)-,-#0$5%
@AA$2%4$A7@$µ%4$@Ah@$µ%4$@A]$?%4$+1$@ ×$@A hc$%7$$:K+1$*"#$0#,-2-9
*-+2$+,$*"#$E51-+&%$?1#,-D#%$&%#0$-2$#3#)*1+2-)%4$%##$L??#20-D
a=$$K+1$#5)"$+,$*"#$/#5%&1#%$3-%*#0$'#3+64$#D?1#%%$*"#$*1-+$+,
*#1/%$ -2$ %)-#2*-,-)$ 2+*5*-+2$ 5%%+)-5*#0$ 6-*"$ *"#$ '5%-)$ &2-*
:#7874$@A hc$%$15*"#1$*"52$@A h@$µ%=7
-G. ,%=%(*40%=N
-6. *%=%(%YZI
-C. ω = 1$+3%×%(*+%9G>[N
->. , =%(*%N
-<. * =%1*%ZI
-O. ω %=%(%,9G>[N
-B. *% =%(#**%\ZI
1.20 K-20$*"#$)+/?3#D$-/?#052)#4$P4$+,$#5)"$+,$*"#$,+33+69
-28$'5%-)$)-1)&-*$#3#/#2*%$5*$bA$aT4$@AA$.aT4$520$@$jaTH
-G. #%=%(%,Ω
-6. <%=%(*%A7
-C. <%=%+%M7
->. %%=%(*%=Z
-<. %%=%(%AZ
1.21 K-20$*"#$)+/?3#D$-/?#052)#$5*$@A$.aT$+,$*"#$,+33+6-28
2#*6+1.%H
-G. (%,Ω%@A%N<9@<N%K@:;%(*%A7
-6. (%,Ω%@A%MG9G??<?%K@:;%*$*(%µ7
Problems 45
Section 1.1: Signals
1.22 L2>$8-E#2$%-8253$%+&1)#$?1+E-0#%$52$+?#29)-1)&-*$E+3*9
58#4$ v&'4$ 520$ 5$ %"+1*9)-1)&-*$ )&11#2*$ $!'7$ K+1$ *"#$ ,+33+6-28
%+&1)#%4$)53)&35*#$*"#$-2*#1253$1#%-%*52)#4$#!M$*"#$O+1*+2$)&19
1#2*4$$!M$520$*"#$!"NE#2-2$E+3*58#4$v%H
-G. v&'%=%(*%S5%$!'%=%(**%µ&
-6. v&'%=%*$(%S5%$!'%=%(*%µ&
1.23 L$?51*-)&351$%-8253$%+&1)#$?1+0&)#%$52$+&*?&*$+,$UA /Y
6"#2$3+50#0$'>$5$@AA9.Ω$1#%-%*+1$520$@A$/Y$6"#2$3+50#0$'>
5$@A9.Ω$1#%-%*+17$<53)&35*#$*"#$!"NE#2-2$E+3*58#4$O+1*+2$)&19
1#2*4$520$%+&1)#$1#%-%*52)#7
1.24 L$ *#/?#15*&1#$ %#2%+1$ -%$ %?#)-,-#0$ *+$ ?1+E-0#$ B$ /Y`°<7
F"#2$)+22#)*#0$*+$5$3+50$1#%-%*52)#$+,$@A$.Ω4$*"#$+&*?&*$E+3*58#
65%$/#5%&1#0$*+$)"528#$'>$@A$/Y4$)+11#%?+20-28$*+$5$)"528#$-2
*#/?#15*&1#$+,$@A°<7$F"5*$-%$*"#$%+&1)#$1#%-%*52)#$+,$*"#$%#2%+1X
1.25 R#,#1$*+$*"#$!"NE#2-2$520$O+1*+2$1#?1#%#2*5*-+2%$+,$*"#
%-8253$%+&1)#$:K-87$@7@=7$;,$*"#$)&11#2*$%&??3-#0$'>$*"#$%+&1)#
-%$ 0#2+*#0$ $&$ 520$ *"#$ E+3*58#$ 5??#51-28$ '#*6##2$ *"#$ %+&1)#
+&*?&*$*#1/-253%$-%$0#2+*#0$v& 4$%.#*)"$520$)3#513>$35'#3$v&$E#19
%&%$$&$,+1$A$≤$$&$≤$$!7
1.26 !"#$)+22#)*-+2$+,$5$%-8253$%+&1)#$*+$52$5%%+)-5*#0$%-8253
?1+)#%%+1$+1$5/?3-,-#1$8#2#1533>$-2E+3E#%$%+/#$0#81##$+,$%-8253
3+%%$5%$/#5%&1#0$5*$*"#$?1+)#%%+1$+1$5/?3-,-#1$-2?&*7$<+2%-0#1-28
*"#$*6+$%-82539%+&1)#$1#?1#%#2*5*-+2%$%"+62$-2$K-87$@7@4$?1+E-0#
*6+$ %.#*)"#%$ %"+6-28$ #5)"$ %-82539%+&1)#$ 1#?1#%#2*5*-+2$ )+29
2#)*#0$ *+$ *"#$ -2?&*$ *#1/-253%$ :520$ )+11#%?+20-28$ -2?&*$ 1#%-%9
*52)#=$ +,$ 5$ %-8253$ ?1+)#%%+17$ F"5*$ %-82539?1+)#%%+1$ -2?&*
1#%-%*52)#$6-33$1#%&3*$-2$\A[$+,$*"#$+?#29)-1)&-*$E+3*58#$'#-28
0#3-E#1#0$*+$*"#$?1+)#%%+1X$F"5*$-2?&*$1#%-%*52)#$6-33$1#%&3*$-2
\A[$+,$*"#$%"+1*9)-1)&-*$%-8253$)&11#2*$#2*#1-28$*"#$?1+)#%%+1X
Section 1.2: Frequency Spectrum of Signals
1.27 !+$ ,5/-3-51-T#$ >+&1%#3,$ 6-*"$ *>?-)53$ E53&#%$ +,$ 528&351
,1#G&#2)>$ ω 4$ )+2E#2*-+253$ ,1#G&#2)>$ *4$ 520$ ?#1-+0$ ,4$ )+/9
?3#*#$*"#$#2*1-#%$-2$*"#$,+33+6-28$*5'3#H
Case
G
6
C
>
<
O
v (rad/s)
f (Hz)
T (s)
#
(%× (*
( × (*#
(%×%(*4(*
1*
1$+3%×%(*/
(%×%(*41
1.28 K+1$*"#$,+33+6-28$?#5.$+1$1/%$E53&#%$+,$%+/#$-/?+1*52*
%-2#$65E#%4$)53)&35*#$*"#$)+11#%?+20-28$+*"#1$E53&#H
-G. ((2%S%1/%5%G%;8EN<;8?>JM8K<9%F8?:GB<%@A%]89:;%&=<9@CG
-6. //$#%S%?#5.5%G%N8=<K;G:%C8==8A%M<G,%F8?:GB<%@A%9<C:@J
O@<9%C@9CE@:N
-C. ++*% S$ 1/%5% G% ;8EN<;8?>JM8K<9% F8?:GB<% @A% MG9:N% 8O
QE98M<
->. ++*%,S%1/%5%G%;@B;JF8?:GB<%:9GAN=@NN@8AJ?@A<%F8?:GB<%@A
]89:;%&=<9@CG
1.29 j-E#$ #D?1#%%-+2%$ ,+1$ *"#$ %-2#965E#$ E+3*58#$ %-8253%
"5E-28H
-G. (*JS%M<G,%G=M?@:E><%GA>%(*J,ZI%O9<DE<ACX
-6. (+*JS%9=N%GA>%1*JZI%O9<DE<ACX
-C. *$+JS%M<G,J:8JM<G,%GA>%(***J9G>[N%O9<DE<ACX
->. (**J=S%M<G,%GA>%(J=N%M<9@8>
1.30 d%-28$*"#$-2,+1/5*-+2$?1+E-0#0$'>$JG7$:@7B=$-2$5%%+)-9
5*-+2$6-*"$K-87$@7]4$)"515)*#1-T#$*"#$%-8253$1#?1#%#2*#0$'>$v:*=$=
@`B$+$B`π$:%-2$BAAAπ "$+$ 99@U9 %-2$bAAAπ "$+ @99]9 %-2 @A4AAAπ " + 777=7
I.#*)"$*"#$65E#,+1/7$F"5*$-%$-*%$5E#158#$E53&#X$;*%$?#5.9*+9
?#5.$E53&#X$;*%$3+6#%*$E53&#X$;*%$"-8"#%*$E53&#X$;*%$,1#G&#2)>X
;*%$?#1-+0X
1.31 _#5%&1#/#2*%$ *5.#2$ +,$ 5$ %G&51#965E#$ %-8253$ &%-28$ 5
,1#G&#2)>9%#3#)*-E#$ E+3*/#*#1$ :)533#0$ 5$ %?#)*1&/$ 5253>T#1=
%"+6$ -*%$ %?#)*1&/$ *+$ )+2*5-2$ 50(5)#2*$ )+/?+2#2*%$ :%?#)*153
3-2#%=$5*$\Z$.aT$520$@Bb$.aT$+,$5/?3-*&0#%$bU$/Y$520$^\
/Y4$1#%?#)*-E#3>7$K+1$*"-%$%-82534$6"5*$6+&30$0-1#)*$/#5%&1#9
/#2*$+,$*"#$,&205/#2*53$%"+6$-*%$,1#G&#2)>$520$5/?3-*&0#$*+
'#X$F"5*$-%$*"#$1/%$E53&#$+,$*"#$,&205/#2*53X$F"5*$51#$*"#
?#5.9*+9?#5.$5/?3-*&0#$520$?#1-+0$+,$*"#$+1-8-25*-28$%G&51#
65E#X
1.32 F"5*$ -%$ *"#$ ,&205/#2*53$ ,1#G&#2)>$ +,$ *"#$ "-8"#%*9
,1#G&#2)>$%G&51#$65E#$,+1$6"-)"$*"#$,-,*"$"51/+2-)$-%$'51#3>
5&0-'3#$'>$5$1#35*-E#3>$>+&28$3-%*#2#1X$F"5*$-%$*"#$,&205/#29
*53$,1#G&#2)>$+,$*"#$3+6#%*9,1#G&#2)>$%G&51#$65E#$,+1$6"-)"
*"#$,-,*"$520$%+/#$+,$*"#$"-8"#1$"51/+2-)%$51#$0-1#)*3>$"#510X
:O+*#$ *"5*$ *"#$ ?%>)"+5)+&%*-)$ ?1+?#1*-#%$ +,$ "&/52$ "#51-28
533+6$5$3-%*#2#1$*+$%#2%#$*"#$3+6#1$"51/+2-)%$5%$6#337=
1.33 K-20$ *"#$ 5/?3-*&0#$ +,$ 5$ %>//#*1-)53$ %G&51#$ 65E#$ +,
?#1-+0$,$*"5*$?1+E-0#%$*"#$%5/#$?+6#1$5%$5$%-2#$65E#$+,$?#5.
5/?3-*&0#$ )k 520$*"#$%5/#$,1#G&#2)>7$Q+#%$*"-%$1#%&3*$0#?#20
+2$#G&53-*>$+,$*"#$,1#G&#2)-#%$+,$*"#$*6+$65E#,+1/%X
Section 1.3: Analog and Digital Signals
1.34 j-E#$*"#$'-251>$1#?1#%#2*5*-+2$+,$*"#$,+33+6-28$0#)-/53
2&/'#1%H$A4$]4$Z4$B]4$520$]c7
1.35 <+2%-0#1$5$^9'-*$0-8-*53$6+10$0U0B0@0A$-2$5$,+1/5*$)533#0
%-82#09/582-*&0#4$ -2$ 6"-)"$ *"#$ /+%*$ %-82-,-)52*$ '-*4$ 0U4$ -%
-2*#1?1#*#0$5%$5$%-82$'-*eA$,+1$?+%-*-E#$520$@$,+1$2#85*-E#$E539
&#%7$ p-%*$ *"#$ E53&#%$ *"5*$ )52$ '#$ 1#?1#%#2*#0$ '>$ *"-%$ %)"#/#7
F"5*$-%$?#)&3-51$5'+&*$*"#$1#?1#%#2*5*-+2$+,$T#1+X$K+1$5$?519
*-)&351$5253+89*+90-8-*53$)+2E#1*#1$:LQ<=4$#5)"$)"528#$-2$0A
)+11#%?+20%$*+$5$A7]9Y$)"528#$-2$*"#$5253+8$-2?&*7$F"5*$-%$*"#
,&33$1528#$+,$*"#$5253+8$%-8253$*"5*$)52$'#$1#?1#%#2*#0X$F"5*
%-82#09/582-*&0#$0-8-*53$)+0#$1#%&3*%$,+1$52$-2?&*$+,$+B7]$YX
K+1$−U7A$YX$K+1$+B7c$YX$K+1$−B7Z$YX
CHAPTER 1 P R O B L E M S
-C. (**%,Ω%@A%MG9G??<?%K@:;%(**%M7
->. (**%Ω%@A%N<9@<N%K@:;%(*%=Z
CHAPTER 1 P R O B L E M S
46 Chapter 1 Signals and Amplifiers
Vref
2R
0
b1
1
4R
0
b2
1
2NR
8R
0
b3
1
0
bN
1
iO
Figure P1.37
1.36 <+2%-0#1$ 52$ /9'-*$ LQ<$ 6"+%#$ 5253+8$ -2?&*$ E51-#%
'#*6##2$ A$ 520$ )U@$ :6"#1#$ *"#$ %&'%)1-?*$ U@$ 0#2+*#%$ V,&33
%)53#W=7
-G. ^;8K%:;G:%:;<%?<GN:%N@BA@O@CGA:%6@:%-_^R.%C899<NM8A>N%:8
/
G% C;GAB<% @A% :;<% GAG?8B% N@BAG?% 8O% ) U@ ⁄ ( B 4 @ ) 7% P;@N% @N% :;<
9<N8?E:@8A%8O%:;<%C8AF<9:<9$
-6. U8AF@AC<% X8E9N<?O% :;G:% :;<% =GL@=E=% <9989% @A% :;<% C8AJ
F<9N@8A%-CG??<>%:;<%DEGA:@IG:@8A%<9989.%@N%;G?O%:;<%9<N8?E:@8A'
/
:;G:%@N5%:;<%DEGA:@IG:@8A%<9989%= ) U@ ⁄ B ( B 4 @ )7
-C. 789%)U@%=%(*%S5%;8K%=GAX%6@:N%G9<%9<DE@9<>%:8%86:G@A%G
9<N8?E:@8A%8O%)%=S%89%6<::<9`%T;G:%@N%:;<%GC:EG?%9<N8?E:@8A
86:G@A<>`%T;G:%@N%:;<%9<NE?:@AB%DEGA:@IG:@8A%<9989`
1.37 K-8&1#$ l@7Uc$ %"+6%$ *"#$ )-1)&-*$ +,$ 52$ /9'-*$ 0-8-*539*+9
5253+8$ )+2E#1*#1$ :QL<=7$ J5)"$ +,$ *"#$ /$ '-*%$ +,$ *"#$ 0-8-*53
6+10$*+$'#$)+2E#1*#0$)+2*1+3%$+2#$+,$*"#$%6-*)"#%7$F"#2$*"#
'-*$-%$A4$*"#$%6-*)"$-%$-2$*"#$?+%-*-+2$35'#3#0$AM$6"#2$*"#$'-*$-%
@4$*"#$%6-*)"$-%$-2$*"#$?+%-*-+2$35'#3#0$@7$!"#$5253+8$+&*?&*$-%
*"#$)&11#2*$$:7$)1#,$-%$5$)+2%*52*$1#,#1#2)#$E+3*58#7
:5= I"+6$*"5*$
) 1#, 0 @ 0 B 7$7$7$ 0 /
$ : = 9999999
9 99999 + 99999 +
+ 99999/
# B@ BB
B
-6. T;@C;%6@:%@N%:;<%_^R`%T;@C;%@N%:;<%\^R`
-C. 789%)9<O%=%(*%S5%#%=%)%,Ω5%GA>%/%=%15%O@A>%:;<%=GL@=E=
FG?E<%8O%$:%86:G@A<>$%T;G:%@N%:;<%C;GAB<%@A%$:%9<NE?:@AB%O98=
:;<%_^R%C;GAB@AB%O98=%*%:8%(`
1.38 ;2$)+/?5)*90-%)$:<Q=$5&0-+$*#)"2+3+8>4$*"#$5&0-+$%-89
253$-%$%5/?3#0$5*$^^7@$.aT7$J5)"$%5/?3#$-%$1#?1#%#2*#0$'>$@b
'-*%7$F"5*$-%$*"#$%?##0$+,$*"-%$%>%*#/$-2$'-*%$?#1$%#)+20X
Section 1.4: Amplifiers
1.39 Y51-+&%$5/?3-,-#1$520$3+50$)+/'-25*-+2%$51#$/#5%&1#0
5%$3-%*#0$'#3+6$&%-28$1/%$E53&#%7$K+1$#5)"4$,-20$*"#$E+3*58#4
)&11#2*4$520$?+6#1$85-2%$:8v4$8$4$520$8;4$1#%?#)*-E#3>=$'+*"
5%$15*-+%$520$-2$0iH
-G. v9%=%(**%=S5%$9%=%(**%µ&5%v:%=%(*%S5%#%%=%(**%Ω
-6. v%=%(*%µS5%$9%=%(**%A&5%v:%=%+%S5%#%%=%(*%,Ω
-C. v9%=%(%S5%$9%=%(%=&5%v:%=%(*%S5+#%%=%(*%Ω
1.40 L2$5/?3-,-#1$+?#15*-28$,1+/$±U9Y$%&??3-#%$?1+E-0#%
5$ B7B9Y$ ?#5.$ %-2#$ 65E#$ 5)1+%%$ 5$ @AA9Ω$ 3+50$ 6"#2$ ?1+9
E-0#0$ 6-*"$ 5$ A7B9Y$ ?#5.$ -2?&*$ ,1+/$ 6"-)"$ @7A$ /L$ ?#5.$ -%
015627$!"#$5E#158#$)&11#2*$-2$#5)"$%&??3>$-%$/#5%&1#0$*+$'#
BA$/L7$K-20$*"#$E+3*58#$85-24$)&11#2*$85-24$520$?+6#1$85-2
#D?1#%%#0$ 5%$ 15*-+%$ 520$ -2$ 0#)-'#3%$ 5%$ 6#33$ 5%$ *"#$ %&??3>
?+6#14$5/?3-,-#1$0-%%-?5*-+24$520$5/?3-,-#1$#,,-)-#2)>7
1.41 L2$5/?3-,-#1$&%-28$'5352)#0$?+6#1$%&??3-#%$-%$.2+62$*+
%5*&15*#$ ,+1$%-8253%$#D*#20-28$6-*"-2$ @7B$Y$+,$ #-*"#1$%&??3>7
K+1$ 3-2#51$ +?#15*-+24$ -*%$ 85-2$ -%$ ]AA$ Y`Y7$ F"5*$ -%$ *"#$ 1/%
E53&#$ +,$ *"#$ 3518#%*$ &20-%*+1*#0$ %-2#965E#$ +&*?&*$ 5E5-35'3#4
520$-2?&*$2##0#04$6-*"$±]9Y$%&??3-#%X$F-*"$±@A9Y$%&??3-#%X
F-*"$±@]9Y$%&??3-#%X
1.42 I>//#*1-)533>$ %5*&15*-28$ 5/?3-,-#1%4$ +?#15*-28$ -2$ *"#
%+9)533#0$)3-??-28$/+0#4$)52$'#$&%#0$*+$)+2E#1*$%-2#$65E#%$*+
?%#&0+9%G&51#$ 65E#%7$ K+1$ 52$ 5/?3-,-#1$ 6-*"$ 5$ %/5339%-8253
85-2$+,$@AAA$520$)3-??-28$3#E#3%$+,$±\$Y4$6"5*$?#5.$E53&#$+,
-2?&*$%-2&%+-0$-%$2##0#0$*+$?1+0&)#$52$+&*?&*$6"+%#$#D*1#/#%
51#$ (&%*$ 5*$ *"#$ #08#$ +,$ )3-??-28X$ <3-??#0$ \A[$ +,$ *"#$ *-/#X
<3-??#0$\\[$+,$*"#$*-/#X
Section 1.5: Circuit Models for Amplifiers
1.43 U8AN@><9% :;<% F8?:GB<JG=M?@O@<9% C@9CE@:% =8><?% N;8KA
@A%7@B$%($(1-6.5%@A%K;@C;%8v &%"%(*%S[S%EA><9%:;<%O8??8K@AB
C8A>@:@8ANV
-G. #$%=%(*#!5%#%%=%(*#&
-6. #$+=+#!5+#% =+#&
-C. #$+=+#! R(*5+#% =+#& R(*
<53)&35*#$ *"#$ +E#1533$ E+3*58#$ 85-2$ v& `v!$ -2$ #5)"$ )5%#4
#D?1#%%#0$'+*"$0-1#)*3>$520$-2$0#)-'#3%7
1.44 L2$5/?3-,-#1$6-*"$^A$0i$+,$%/5339%-82534$+?#29)-1)&-*
E+3*58#$ 85-24$ 52$ -2?&*$ 1#%-%*52)#$ +,$ @$ _Ω4$ 520$ 52$ +&*?&*
1#%-%*52)#$+,$@A$Ω4$01-E#%$5$3+50$+,$@AA$Ω7$F"5*$E+3*58#$520
?+6#1$ 85-2%$ :#D?1#%%#0$ -2$ 0i=$ 6+&30$ >+&$ #D?#)*$ 6-*"$ *"#
3+50$ )+22#)*#0X$ ;,$ *"#$ 5/?3-,-#1$ "5%$ 5$ ?#5.$ +&*?&*9)&11#2*
3-/-*5*-+2$ +,$ @AA$ /L4$ 6"5*$ -%$ *"#$ 1/%$ E53&#$ +,$ *"#$ 3518#%*
%-2#965E#$-2?&*$,+1$6"-)"$52$&20-%*+1*#0$+&*?&*$-%$?+%%-'3#X
F"5*$-%$*"#$)+11#%?+20-28$+&*?&*$?+6#1$5E5-35'3#X
1.45 L$@A9/Y$%-8253$%+&1)#$"5E-28$52$-2*#1253$1#%-%*52)#$+,
@AA$.Ω$-%$)+22#)*#0$*+$52$5/?3-,-#1$,+1$6"-)"$*"#$-2?&*$1#%-%9
*52)#$-%$@A$.Ω4$*"#$+?#29)-1)&-*$E+3*58#$85-2$-%$@AAA$Y`Y4$520
*"#$+&*?&*$1#%-%*52)#$-%$@$.Ω7$!"#$5/?3-,-#1$-%$)+22#)*#0$-2
*&12$ *+$ 5$ @AA9Ω$ 3+507$ F"5*$ +E#1533$ E+3*58#$ 85-2$ 1#%&3*%$ 5%
Problems
1.46 L$'&,,#1$5/?3-,-#1$6-*"$ 5$85-2$+,$@$Y`Y$"5%$52$-2?&*
1#%-%*52)#$+,$@$_Ω$520$52$+&*?&*$1#%-%*52)#$+,$@A$Ω7$;*$-%
)+22#)*#0$'#*6##2$5$@9Y4$@AA9.Ω$%+&1)#$520$5$@AA9Ω$3+507
F"5*$3+50$E+3*58#$1#%&3*%X$F"5*$51#$*"#$)+11#%?+20-28$E+3*9
58#4$)&11#2*4$520$?+6#1$85-2%$:-2$0i=X
1.47 <+2%-0#1$ *"#$ )5%)50#$ 5/?3-,-#1$ +,$ JD5/?3#$ @7U7$ K-20
*"#$+E#1533$E+3*58#$85-2$v& `v!$+'*5-2#0$6"#2$*"#$,-1%*$520$%#)9
+20$ %*58#%$ 51#$ -2*#1)"528#07$ <+/?51#$ *"-%$ E53&#$ 6-*"$ *"#
1#%&3*$-2$JD5/?3#$@7U4$520$)+//#2*7
1.48 u+&$51#$8-E#2$*6+$5/?3-,-#1%4$L$520$i4$*+$)+22#)*$-2
)5%)50#$'#*6##2$5$@A9/Y4$@AA9.Ω$%+&1)#$520$5$@AA9Ω$3+507
!"#$5/?3-,-#1%$"5E#$E+3*58#$85-24$-2?&*$1#%-%*52)#4$520$+&*?&*
1#%-%*52)#$5%$,+33+6%H$,+1$L4$@AA$Y`Y4$@A$.Ω4$@A$.Ω4$1#%?#)9
*-E#3>M$,+1$i4$@$Y`Y4$@AA$.Ω4$@AA$Ω4$1#%?#)*-E#3>7$u+&1$?1+'9
3#/$-%$*+$0#)-0#$"+6$*"#$5/?3-,-#1%$%"+&30$'#$)+22#)*#07$!+
?1+)##04$ #E53&5*#$ *"#$ *6+$ ?+%%-'3#$ )+22#)*-+2%$ '#*6##2
%+&1)#$I$520$3+50$p4$25/#3>4$ILip$520$IiLp7$K-20$*"#$E+3*9
58#$85-2$,+1$#5)"$'+*"$5%$5$15*-+$520$-2$0#)-'#3%7$F"-)"$5/?3-9
,-#1$511528#/#2*$-%$'#%*X
D *1.49 L$0#%-82#1$"5%$5E5-35'3#$E+3*58#$5/?3-,-#1%$6-*"$52
-2?&*$1#%-%*52)#$+,$@A$.Ω4$52$+&*?&*$1#%-%*52)#$+,$@$.Ω4$520
52$+?#29)-1)&-*$E+3*58#$85-2$+,$@A7$!"#$%-8253$%+&1)#$"5%$5$@A9
.Ω$ 1#%-%*52)#$ 520$ ?1+E-0#%$ 5$ @A9/Y$ 1/%$ %-82534$ 520$ -*$ -%
1#G&-1#0$*+$?1+E-0#$5$%-8253$+,$5*$3#5%*$B$Y$1/%$*+$5$@9.Ω$3+507
a+6$/52>$5/?3-,-#1$%*58#%$51#$1#G&-1#0X$F"5*$-%$*"#$+&*?&*
E+3*58#$5)*&533>$+'*5-2#07
D *1.50 Q#%-82$52$5/?3-,-#1$*"5*$?1+E-0#%$A7]$F$+,$%-8253
?+6#1$*+$5$@AA9Ω$3+50$1#%-%*52)#7$!"#$%-8253$%+&1)#$?1+E-0#%
5$ UA9/Y$ 1/%$ %-8253$ 520$ "5%$ 5$ 1#%-%*52)#$ +,$ A7]$ _Ω7$ !"1##
*>?#%$+,$E+3*58#95/?3-,-#1$%*58#%$51#$5E5-35'3#H
-G. &%;@B;J@AME:J9<N@N:GAC<%:XM<%K@:;%#$%=%(%\Ω5%8v& %=%(*5
GA>%#&%=%(*%,Ω
-6. &%;@B;JBG@A%:XM<%K@:;%#$%=%(*%,Ω5%8v &%=%(**5%GA>+#&%=
(%,Ω
:)= L$ 3+69+&*?&*91#%-%*52)#$ *>?#$ 6-*"$ #$$ =$ @A$ .Ω4$ 8v & =$ @4
520$#&$=$BA$Ω
Q#%-82$ 5$ %&-*5'3#$ 5/?3-,-#1$ &%-28$ 5$ )+/'-25*-+2$ +,$ *"#%#
%*58#%7$ u+&1$ 0#%-82$ %"+&30$ &*-3-T#$ *"#$ /-2-/&/$ 2&/'#1$ +,
%*58#%$520$%"+&30$#2%&1#$*"5*$*"#$%-8253$3#E#3$-%$2+*$1#0&)#0
'#3+6$@A$/Y$5*$52>$?+-2*$-2$*"#$5/?3-,-#1$)"5-27$K-20$*"#$3+50
E+3*58#$520$?+6#1$+&*?&*$1#53-T#07
D *1.51 ;*$ -%$ 1#G&-1#0$ *+$ 0#%-82$ 5$ E+3*58#$ 5/?3-,-#1$ *+$ '#
01-E#2$,1+/$5$%-8253$%+&1)#$"5E-28$5$@A9/Y$?#5.$5/?3-*&0#
520$5$%+&1)#$1#%-%*52)#$+,$@A$.Ω$*+$%&??3>$5$?#5.$+&*?&*$+,
U Y$5)1+%%$5$@9.Ω$3+507
-G. T;G:%@N%:;<%9<DE@9<>%F8?:GB<%BG@A%O98=%:;<%N8E9C<%:8%:;<
?8G>`
-6. aO%:;<%M<G,%CE99<A:%GFG@?G6?<%O98=%:;<%N8E9C<%@N%*$(%µ&5
K;G:%@N%:;<%N=G??<N:%@AME:%9<N@N:GAC<%G??8K<>`%789%:;<%><N@BA
K@:;%:;@N%FG?E<%8O%#$5%O@A>%:;<%8F<9G??%CE99<A:%BG@A%GA>%M8K<9
BG@A$
-C. aO% :;<% G=M?@O@<9% M8K<9% NEMM?X% ?@=@:N% :;<% M<G,% FG?E<% 8O
:;<% 8E:ME:% 8M<AJC@9CE@:% F8?:GB<% :8% )% S5% K;G:% @N% :;<% ?G9B<N:
8E:ME:%9<N@N:GAC<%G??8K<>`
->. 789%:;<%><N@BA%K@:;%#$%GN%@A%-6.%GA>%#&%GN%@A%-C.5%K;G:%@N%:;<
v
9<DE@9<>%FG?E<%8O%8M<AJC@9CE@:%F8?:GB<%BG@A% -7#74$ 9999&9
%8O
v
$ # =∞
%
:;<%G=M?@O@<9`
:#= ;,4$5%$5$?+%%-'3#$0#%-82$+?*-+24$>+&$51#$5'3#$*+$-2)1#5%#
#$$*+$*"#$2#51#%*$E53&#$+,$*"#$,+1/$@$×$@A 4$Ω$520$*+$0#)1#5%#
#&$ *+$ *"#$ 2#51#%*$ E53&#$ +,$ *"#$ ,+1/$ @$ ×$ @A C$ Ω4$ ,-20$ :-=$ *"#
-2?&*$1#%-%*52)#$5)"-#E5'3#M$:--=$*"#$+&*?&*$1#%-%*52)#$5)"-#E9
5'3#M$ 520$ :---=$ *"#$ +?#29)-1)&-*$ E+3*58#$ 85-2$ 2+6$ 1#G&-1#0$ *+
/##*$*"#$%?#)-,-)5*-+2%7
D 1.52 L$ E+3*58#$ 5/?3-,-#1$ 6-*"$ 52$ -2?&*$ 1#%-%*52)#$ +,
@A .Ω4$52$+&*?&*$1#%-%*52)#$+,$BAA$Ω4$520$5$85-2$+,$@AAA$Y`Y
-%$ )+22#)*#0$ '#*6##2$ 5$ @AA9.Ω$ %+&1)#$ 6-*"$ 52$ +?#29)-1)&-*
E+3*58#$+,$@A$/Y$520$5$@AA9Ω$3+507$K+1$*"-%$%-*&5*-+2H
-G. T;G:%8E:ME:%F8?:GB<%9<NE?:N`
-6. T;G:%@N%:;<%F8?:GB<%BG@A%O98=%N8E9C<%:8%?8G>`
-C. T;G:%@N%:;<%F8?:GB<%BG@A%O98=%:;<%G=M?@O@<9%@AME:%:8%:;<
?8G>`
->. aO%:;<%8E:ME:%F8?:GB<%GC98NN%:;<%?8G>%@N%:K@C<%:;G:%A<<><>
GA>%:;<9<%G9<%N@BAN%8O%@A:<9AG?%G=M?@O@<9%8F<9?8G>5%NEBB<N:%:;<
?8CG:@8A%GA>%FG?E<%8O%G%N@AB?<%9<N@N:89%:;G:%K8E?>%M98>EC<%:;<
><N@9<>% 8E:ME:$% U;88N<% GA% G99GAB<=<A:% :;G:% K8E?>% CGEN<
=@A@=E=%>@N9EM:@8A%:8%GA%8M<9G:@AB%C@9CE@:$%-S$4"T%HN<%MG9J
G??<?%9G:;<9%:;GA%N<9@<N%C8AA<C:@8AN$.
1.53 L$)&11#2*$5/?3-,-#1$,+1$6"-)"$#$$=$@$.Ω4$#&$=$@A$.Ω4
520$ 8$!$ =$ @AA$ L`L$ -%$ *+$ '#$ )+22#)*#0$ '#*6##2$ 5$ @AA9/Y
%+&1)#$6-*"$5$1#%-%*52)#$+,$@AA$.Ω$520$5$3+50$+,$@$.Ω7$F"5*
51#$*"#$E53&#%$+,$)&11#2*$85-2$$& `$$ 4$+,$E+3*58#$85-2$v+ `v%4$520
+,$?+6#1$85-2$#D?1#%%#0$0-1#)*3>$520$-2$0#)-'#3%X
1.54 L$*152%)+20&)*52)#$5/?3-,-#1$6-*"$#$$=$B$.Ω 4$BC =
^A$/L`Y4$520$#&$=$BA$.Ω$-%$,#0$6-*"$5$E+3*58#$%+&1)#$"5E-28
5$%+&1)#$1#%-%*52)#$+,$B$.Ω$520$-%$3+50#0$6-*"$5$@9.Ω$1#%-%9
*52)#7$K-20$*"#$E+3*58#$85-2$1#53-T#07
D **1.55 L$0#%-82#1$-%$1#G&-1#0$*+$?1+E-0#4$5)1+%%$5$@A9.Ω
3+504$*"#$6#-8"*#0$%&/4$v:$=$@Av@$+$BAvB4$+,$-2?&*$%-8253%$v@
520$vB4$#5)"$"5E-28$5$%+&1)#$1#%-%*52)#$+,$@A$.Ω7$I"#$"5%$5
2&/'#1$+,$*152%)+20&)*52)#$5/?3-,-#1%$,+1$6"-)"$*"#$-2?&*
520$+&*?&*$1#%-%*52)#%$51#$'+*"$@A$.Ω$520$BC$=$BA$/L`Y4
*+8#*"#1$ 6-*"$ 5$ %#3#)*-+2$ +,$ %&-*5'3#$ 1#%-%*+1%7$ I.#*)"$ 52
5??1+?1-5*#$ 5/?3-,-#1$ *+?+3+8>$ 6-*"$ 500-*-+253$ 1#%-%*+1%
%#3#)*#0$*+$?1+E-0#$*"#$0#%-1#0$1#%&3*7$:S$4"H$;2$>+&1$0#%-824
511528#$*+$500$)&11#2*%7=
1.56 K-8&1#$ l@7]b$ %"+6%$ 5$ *152%)+20&)*52)#$ 5/?3-,-#1
6"+%#$+&*?&*$-%$*6.+0('V$*+$-*%$-2?&*7$K-20$*"#$-2?&*$1#%-%*52)#
CHAPTER 1 P R O B L E M S
/#5%&1#0$,1+/$*"#$%+&1)#$-2*#1253$E+3*58#$*+$*"#$3+50X$F"#1#
0-0$533$*"#$85-2$8+X$F"5*$6+&30$*"#$85-2$'#$-,$*"#$%+&1)#$65%
)+22#)*#0$0-1#)*3>$*+$*"#$3+50X$F"5*$-%$*"#$15*-+$+,$*"#%#$*6+
85-2%X$!"-%$15*-+$-%$5$&%#,&3$/#5%&1#$+,$*"#$'#2#,-*$*"#$5/?3-9
,-#1$'1-28%7
47
CHAPTER 1 P R O B L E M S
48 Chapter 1 Signals and Amplifiers
/+%*7$L3%+4$,+1$5$2+/-253$*152%0&)#1$+?#29)-1)&-*$+&*?&*$E+3*9
58#$+,$@A$/Y4$*"#$5/?3-,-#1$-%$1#G&-1#0$*+$?1+E-0#$5$/-2-/&/
+,$@$/L$)&11#2*$*"1+&8"$*"#$3+507$F"5*$*>?#$+,$5/?3-,-#1$-%
1#G&-1#0X$I.#*)"$*"#$5/?3-,-#1$)-1)&-*$/+0#34$520$%?#)-,>$E539
&#%$ ,+1$ -*%$ ?515/#*#1%7$ K+1$ #$$ 520$ #&4$ %?#)-,>$ E53&#%$ -2$ *"#
,+1/$@$×$@AC$Ω7
Rin
Figure P1.56
#-2$+,$*"#$1#%&3*-28$+2#9?+1*$2#*6+1.7$:a-2*H$L??3>$5$*#%*$E+3*9
58#$vH$'#*6##2$*"#$*6+$-2?&*$*#1/-253%4$520$,-20$*"#$)&11#2*$$H
01562$,1+/$*"#$%+&1)#7$!"#24$ # -2 ≡ v H ⁄ $ H 7=
D 1.57 ;*$ -%$ 1#G&-1#0$ *+$ 0#%-82$ 52$ 5/?3-,-#1$ *+$ %#2%#$ *"#
+?#29)-1)&-*$+&*?&*$E+3*58#$+,$5$*152%0&)#1$ 520$ *+$ ?1+E-0#$5
?1+?+1*-+253$ E+3*58#$ 5)1+%%$ 5$ 3+50$ 1#%-%*+17$ !"#$ #G&-E53#2*
%+&1)#$1#%-%*52)#$+,$*"#$*152%0&)#1$-%$%?#)-,-#0$*+$E51>$-2$*"#
1528#$+,$@$.Ω$*+$@A$.Ω7$L3%+4$*"#$3+50$1#%-%*52)#$E51-#%$-2$*"#
1528#$+,$ @$.Ω$*+$@A$.Ω7$!"#$)"528#$ -2$3+50$ E+3*58#$)+11#9
%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2$#!$%"+&30$'#$@A[$5*$/+%*7
I-/-3513>4$ *"#$ )"528#$ -2$ 3+50$ E+3*58#$ )+11#%?+20-28$ *+$ *"#
%?#)-,-#0$)"528#$-2$#%$%"+&30$'#$3-/-*#0$*+$@A[7$L3%+4$)+11#9
%?+20-28$*+$5$@A9/Y$*152%0&)#1$+?#29)-1)&-*$+&*?&*$E+3*58#4
*"#$ 5/?3-,-#1$ %"+&30$ ?1+E-0#$ 5$ /-2-/&/$ +,$ @$ Y$ 5)1+%%$ *"#
3+507$ F"5*$ *>?#$ +,$ 5/?3-,-#1$ -%$ 1#G&-1#0X$ I.#*)"$ -*%$ )-1)&-*
/+0#34$ 520$ %?#)-,>$ *"#$ E53&#%$ +,$ -*%$ ?515/#*#1%7$ I?#)-,>
5??1+?1-5*#$E53&#%$,+1$#$$520$#&$+,$*"#$,+1/$@$×$@AC$Ω7
D 1.58 ;*$ -%$ 1#G&-1#0$ *+$ 0#%-82$ 52$ 5/?3-,-#1$ *+$ %#2%#$ *"#
%"+1*9)-1)&-*$ +&*?&*$ )&11#2*$ +,$ 5$ *152%0&)#1$ 520$ *+$ ?1+E-0#$ 5
?1+?+1*-+253$ )&11#2*$ *"1+&8"$ 5$ 3+50$ 1#%-%*+17$ !"#$ #G&-E53#2*
%+&1)#$1#%-%*52)#$+,$*"#$*152%0&)#1$-%$%?#)-,-#0$*+$E51>$-2$*"#
1528#$ +,$ @$ .Ω$ *+$ @A$ .Ω7$ I-/-3513>4$ *"#$ 3+50$ 1#%-%*52)#$ -%
.2+62$*+$E51>$+E#1$*"#$1528#$+,$$@$.Ω$*+$@A$.Ω7$!"#$)"528#
-2$3+50$)&11#2*$)+11#%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2$#!$-%
1#G&-1#0$*+$'#$3-/-*#0$*+$@A[7$I-/-3513>4$*"#$)"528#$-2$3+50
)&11#2*$)+11#%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2$#%$%"+&30$'#
@A[$5*$/+%*7$L3%+4$,+1$5$2+/-253$%"+1*9)-1)&-*$+&*?&*$)&11#2*
+,$*"#$*152%0&)#1$+,$@A$µL4$*"#$5/?3-,-#1$-%$1#G&-1#0$*+$?1+9
E-0#$ 5$ /-2-/&/$ +,$ @$ /L$ *"1+&8"$ *"#$ 3+507$ F"5*$ *>?#$ +,
5/?3-,-#1$-%$1#G&-1#0X$I.#*)"$*"#$)-1)&-*$/+0#3$+,$*"#$5/?3-9
,-#14$520$%?#)-,>$E53&#%$,+1$-*%$?515/#*#1%7$I#3#)*$5??1+?1-5*#
E53&#%$,+1$#$$520$#&$-2$*"#$,+1/$@$×$@AC$Ω7
D 1.59 ;*$ -%$ 1#G&-1#0$ *+$ 0#%-82$ 52$ 5/?3-,-#1$ *+$ %#2%#$ *"#
+?#29)-1)&-*$+&*?&*$E+3*58#$+,$5$*152%0&)#1$ 520$ *+$ ?1+E-0#$5
?1+?+1*-+253$ )&11#2*$ *"1+&8"$ 5$ 3+50$ 1#%-%*+17$ !"#$ #G&-E53#2*
%+&1)#$1#%-%*52)#$+,$*"#$*152%0&)#1$-%$%?#)-,-#0$*+$E51>$-2$*"#
1528#$+,$@$.Ω$*+$@A$.Ω7$L3%+4$*"#$3+50$1#%-%*52)#$-%$.2+62$*+
E51>$-2$*"#$1528#$+,$@$.Ω$*+$@A$.Ω7$!"#$)"528#$-2$*"#$)&11#2*
%&??3-#0$*+$*"#$3+50$)+11#%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2
#!$-%$*+$'#$@A[$5*$/+%*7$I-/-3513>4$*"#$)"528#$-2$3+50$)&11#2*
)+11#%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2$#%$-%$*+$'#$@A[$5*
D 1.60 ;*$ -%$ 1#G&-1#0$ *+$ 0#%-82$ 52$ 5/?3-,-#1$ *+$ %#2%#$ *"#
%"+1*9)-1)&-*$ +&*?&*$ )&11#2*$ +,$ 5$ *152%0&)#1$ 520$ *+$ ?1+E-0#$ 5
?1+?+1*-+253$ E+3*58#$ 5)1+%%$ 5$ 3+50$ 1#%-%*+17$ !"#$ #G&-E53#2*
%+&1)#$1#%-%*52)#$+,$*"#$*152%0&)#1$-%$%?#)-,-#0$*+$E51>$-2$*"#
1528#$ +,$ @$ .Ω$ *+$ @A$ .Ω7$ I-/-3513>4$ *"#$ 3+50$ 1#%-%*52)#$ -%
.2+62$*+$E51>$-2$*"#$1528#$+,$@$.Ω$*+$@A$.Ω7$!"#$)"528#$-2
3+50$ E+3*58#$ )+11#%?+20-28$ *+$ *"#$ %?#)-,-#0$ )"528#$ -2$ #!
%"+&30$'#$@A[$5*$/+%*7$I-/-3513>4$*"#$)"528#$-2$3+50$E+3*58#
)+11#%?+20-28$*+$*"#$%?#)-,-#0$)"528#$-2$#%$-%$*+$'#$3-/-*#0$*+
@A[7$L3%+4$,+1$5$2+/-253$*152%0&)#1$%"+1*9)-1)&-*$+&*?&*$)&19
1#2*$+,$@A$µL4$*"#$5/?3-,-#1$-%$1#G&-1#0$*+$?1+E-0#$5$/-2-/&/
E+3*58#$ 5)1+%%$ *"#$ 3+50$ +,$ @$ Y7$ F"5*$ *>?#$ +,$ 5/?3-,-#1$ -%
1#G&-1#0X$I.#*)"$-*%$)-1)&-*$/+0#34$520$%?#)-,>$*"#$E53&#%$+,
*"#$/+0#3$?515/#*#1%7$K+1$#$$520$#&4$%?#)-,>$5??1+?1-5*#$E539
&#%$-2$*"#$,+1/$@$×$@AC$Ω7
1.61 K+1$*"#$)-1)&-*$-2$K-87$l@7b@4$%"+6$*"5*
4β #%
v
9
99999' = 9999999999999999999999999999999999
7
+
(
β + @ )# =
v0
π
520
#=
v
9
999996 = 9999999999999999999999999999999999999999999
#
+
[
7
v0
=
π ⁄ (β + @)]
B
C
ib
vb
1
2
1
b ib
rp
RL
E
vc
1
RE
ve
2
2
Figure P1.61
1.62 L2$ 5/?3-,-#1$ 6-*"$ 52$ -2?&*$ 1#%-%*52)#$ +,$ @A$ .Ω 4
6"#2$ 01-E#2$ '>$ 5$ )&11#2*$ %+&1)#$ +,$ @$ µL$ 520$ 5$ %+&1)#
1#%-%*52)#$+,$@AA$.Ω 4$"5%$5$%"+1*9)-1)&-*$+&*?&*$)&11#2*$+,
@A$ /L$ 520$ 52$ +?#29)-1)&-*$ +&*?&*$ E+3*58#$ +,$ @A$ Y7$ !"#
0#E-)#$ -%$ 01-E-28$ 5$ ^9.Ω$ 3+507$ j-E#$ *"#$ E53&#%$ +,$ *"#
Problems
1.63 K-8&1#$l@7bU:5=$%"+6%$*6+$*152%)+20&)*52)#$5/?3-,-9
#1%$)+22#)*#0$-2$5$%?#)-53$)+2,-8&15*-+27$K-20$v&$-2$*#1/%$+,$v@
520$vB7$p#*$AC$=$@AA$/L`Y$520$#$=$]$.Ω7$;,$v@$=$vB$=$@$Y4$,-20
*"#$E53&#$+,$v&7$L3%+4$,-20$v&$,+1$*"#$)5%#$v@$=$@7A@$Y$520$vB$=
A7\\$Y7$:O+*#H$!"-%$)-1)&-*$-%$)533#0$5$1"99'$'*)"3(,3!/("9"'$
520$-%$8-E#2$*"#$%>/'+3$%"+62$-2$K-87$l@7bU:'=7$L$?51*-)&351
*>?#$+,$0-,,#1#2*-53$5/?3-,-#1$.2+62$5%$52$%/'$3)"%*3(,3!/("&
9"'$$6-33$'#$%*&0-#0$-2$<"5?*#1$B7=
K-8&1#$l@7b^$%"+6%$52$#G&-E53#2*$)-1)&-*$1#?1#%#2*5*-+2$+,
*"#%#$*6+$#G&5*-+2%7$i>$)+/?51-28$*"-%$#G&-E53#2*$)-1)&-*
*+$*"5*$+,$*"#$E+3*58#$5/?3-,-#1$-2$K-87$@7@b:5=4$-0#2*-,>$)+19
1#%?+20-28$)&11#2*%$520$E+3*58#%$5%$6#33$5%$*"#$)+11#%?+29
0#2)#$ '#*6##2$ *"#$ ?515/#*#1%$ +,$ *"#$ 5/?3-,-#1$ #G&-E53#2*
)-1)&-*$ 520$ *"#$ A$ ?515/#*#1%7$ a#2)#$ 8-E#$ *"#$ A$ ?515/#*#1
*"5*$)+11#%?+20%$*+$#5)"$+,$#$4$8v &$520$#&7$O+*-)#$*"5*$*"#1#
-%$52$500-*-+253$A$?515/#*#1$6-*"$2+$)+11#%?+20#2)#$-2$*"#
5/?3-,-#1$#G&-E53#2*$)-1)&-*7$F"-)"$+2#X$F"5*$0+#%$-*$%-89
2-,>X$ F"5*$ 5%%&/?*-+2$ 0-0$ 6#$ /5.#$ 5'+&*$ *"#$ 5/?3-,-#1
*"5*$ 1#%&3*#0$ -2$ *"#$ 5'%#2)#$ +,$ *"-%$ ?51*-)&351$ A$ ?515/#*#1
,1+/$*"#$#G&-E53#2*$)-1)&-*$-2$K-87$@7@b:5=X
I1
g22
1
I2
1
1
g11
V1
g12 I2
2
g21V1
1
2
V2
2
Figure P1.64
Section 1.6: Frequency Response of Amplifiers
(a)
1.65 d%#$*"#$E+3*58#90-E-0#1$1&3#$*+$0#1-E#$*"#$*152%,#1$,&2)9
*-+2%$ , ( ! ) ≡ ) & ( ! ) ⁄ ) $ ( ! )$+,$*"#$)-1)&-*%$%"+62$-2$K-87$@7BB4
520$%"+6$*"5*$*"#$*152%,#1$,&2)*-+2%$51#$+,$*"#$,+1/$8-E#2$5*
*"#$*+?$+,$!5'3#$@7B7
vo
(b)
Figure P1.63
1.64 L2>$3-2#51$*6+9?+1*$2#*6+1.$-2)3&0-28$3-2#51$5/?3-,-9
#1%$ )52$ '#$ 1#?1#%#2*#0$ '>$ +2#$ +,$ ,+&1$ ?+%%-'3#$ ?515/#*#1
%#*%4$ 8-E#2$ -2$ L??#20-D$ <7$ K+1$ *"#$ E+3*58#$ 5/?3-,-#14$ *"#
/+%*$)+2E#2-#2*$1#?1#%#2*5*-+2$-%$-2$*#1/%$+,$*"#$A$?515/#9
*#1%7$;,$*"#$5/?3-,-#1$-2?&*$?+1*$-%$35'#3#0$5%$?+1*$@$520$*"#
+&*?&*$ ?+1*$ 5%$ ?+1*$ B4$ -*%$ A9?515/#*#1$ 1#?1#%#2*5*-+2$ -%
0#%)1-'#0$'>$*"#$*6+$#G&5*-+2%H
1.66 K-8&1#$l@7bb$%"+6%$5$%-8253$%+&1)#$)+22#)*#0$*+$*"#
-2?&*$+,$52$5/?3-,-#17$a#1#$#!$-%$*"#$%+&1)#$1#%-%*52)#4$520
#$$ 520$ <$$ 51#$ *"#$ -2?&*$ 1#%-%*52)#$ 520$ -2?&*$ )5?5)-*52)#4
1#%?#)*-E#3>4$ +,$ *"#$ 5/?3-,-#17$ Q#1-E#$ 52$ #D?1#%%-+2$ ,+1
) $ ( ! ) ⁄ ) ! ( ! ) 4$ 520$ %"+6$ *"5*$ -*$ -%$ +,$ *"#$ 3+69?5%%$ I!<$ *>?#7
K-20$*"#$U90i$,1#G&#2)>$,+1$*"#$)5%#$#!$=$BA$.Ω4$#$$=$ZA$.Ω4
520$<$$=$]$?U7
Rs
Vs
1
2
9 @ " A @@ ) @ ! A @B 9 B
) B " A B@ ) @ ! A BB 9 B
Figure P1.66
Ri
Ci
1
Vi
2
CHAPTER 1 P R O B L E M S
E+3*58#$ 85-24$ )&11#2*$ 85-24$ 520$ ?+6#1$ 85-2$ #D?1#%%#0$ 5%
15*-+%$520$-2$0#)-'#3%X
49
CHAPTER 1 P R O B L E M S
50 Chapter 1 Signals and Amplifiers
1.67 K+1$ *"#$ )-1)&-*$ %"+62$ -2$ K-87$ l@7bc4$ ,-20$ *"#$ *152%,#1
,&2)*-+2$, ( ! ) = ) & ( ! ) ⁄ ) $ ( ! ) 4$520$511528#$-*$-2$*"#$5??1+?1-9
5*#$%*520510$,+1/$,1+/$!5'3#$@7B7$;%$*"-%$5$"-8"9?5%%$+1$5$3+69
?5%%$2#*6+1.X$F"5*$-%$-*%$*152%/-%%-+2$5*$E#1>$"-8"$,1#G&#29
)-#%X$ qJ%*-/5*#$ *"-%$ 0-1#)*3>4$ 5%$ 6#33$ 5%$ '>$ 3#**-28$ ! → ∞ $ -2
>+&1$#D?1#%%-+2$,+1$ ,:!=7r$F"5*$-%$*"#$)+12#1$,1#G&#2)>$ ωAX
K+1$#@ =$@A$.Ω4$#B$=$^A$.Ω4$520$<$=$A7@$µK4$,-20$*A7$F"5*$-%
*"#$E53&#$+,$ ,:N ω A = X
R1
C
"
!
R2
Vo
!
Figure P1.67
D 1.68 ;*$-%$1#G&-1#0$*+$)+&?3#$5$E+3*58#$%+&1)#$)!$6-*"$5
1#%-%*52)#$ #!$ *+$ 5$ 3+50$ #%$ E-5$ 5$ )5?5)-*+1$ <7$ Q#1-E#$ 52
#D?1#%%-+2$ ,+1$ *"#$ *152%,#1$ ,&2)*-+2$ ,1+/$ %+&1)#$ *+$ 3+50
:-7#74$) % ⁄ ) ! =4$520$%"+6$*"5*$-*$-%$+,$*"#$"-8"9?5%%$I!<$*>?#7
K+1$#!$=$]$.Ω$520$#%$=$BA$.Ω 4$,-20$*"#$%/533#%*$)+&?3-28
)5?5)-*+1$ *"5*$ 6-33$ 1#%&3*$ -2$ 5$ U90i$ ,1#G&#2)>$ 2+$ 81#5*#1
*"52$@A$aT7
1.69 _#5%&1#/#2*$+,$*"#$,1#G&#2)>$1#%?+2%#$+,$52$5/?3-,-#1
>-#30%$*"#$05*5$-2$*"#$,+33+6-28$*5'3#H
f (Hz)
| T | (dB)
∠,T,4°7
%%%%%%%%*
%%%%(**
%%(***
%%%%(*0
%%%%(*)
%%%%%%%%%0*
%%%%%%%%%0*
%%%%%%%%%%%%%%%%*
%%%%%%%%%%%%%%%%*
%%%%%%%%%%%%
/2
%+*
%%%%%%%%%*
%%%%%%%%
−0)
%%%%%%%%%%
l1+E-0#$?35&%-'3#$5??1+D-/5*#$E53&#%$,+1$*"#$/-%%-28$#2*1-#%7
L3%+4$ %.#*)"$ 520$ )3#513>$ 35'#3$ *"#$ /582-*&0#$ ,1#G&#2)>
1#%?+2%#$:-7#74$?1+E-0#$5$i+0#$?3+*=$,+1$*"-%$5/?3-,-#17
Vi
Figure P1.71
f (Hz)
| T | (dB)
*
(*
(*+
(*/
%%+*
%%/2
%%0*
(*0
(*)
(*1
(*2
%%/2
%%+*
*
l1+E-0#$ 5??1+D-/5*#$ ?35&%-'3#$ E53&#%$ ,+1$ *"#$ /-%%-28$ *5'3#
#2*1-#%7$ L3%+4$ %.#*)"$ 520$ )3#513>$ 35'#3$ *"#$ /582-*&0#$ ,1#9
G&#2)>$1#%?+2%#$:i+0#$?3+*=$+,$*"-%$5/?3-,-#17
1.71 !"#$ &2-*>985-2$ E+3*58#$ 5/?3-,-#1%$ -2$ *"#$ )-1)&-*$ +,$ K-87
l@7c@$ "5E#$ -2,-2-*#$ -2?&*$ 1#%-%*52)#%$ 520$ T#1+$ +&*?&*$ 1#%-%9
*52)#%$520$*"&%$,&2)*-+2$5%$?#1,#)*$'&,,#1%7$<+2E-2)#$>+&1%#3,
*"5*$*"#$+E#1533$85-2$) & ⁄ ) $ $6-33$01+?$'>$U$0i$'#3+6$*"#$E53&#
5*$0)$5*$*"#$,1#G&#2)>$,+1$6"-)"$*"#$85-2$+,$#5)"$#<$)-1)&-*$-%
@7A$0i$0+627$F"5*$-%$*"5*$,1#G&#2)>$-2$*#1/%$+,$<#X
"
Vi
1.70 _#5%&1#/#2*$+,$*"#$,1#G&#2)>$1#%?+2%#$+,$52$5/?3-,-#1
>-#30%$*"#$05*5$-2$*"#$,+33+6-28$*5'3#H$
1.72 L$ /52&,5)*&1-28$ #11+1$ )5&%#%$ 52$ -2*#1253$ 2+0#$ +,$ 5
"-8"9,1#G&#2)>$ 5/?3-,-#1$ 6"+%#$ !"NE#2-29#G&-E53#2*$ 2+0#
1#%-%*52)#$-%$@AA$.Ω$*+$'#$5))-0#2*533>$%"&2*#0$*+$81+&20$'>$5
)5?5)-*+1$ :-7#74$ *"#$ 2+0#$ -%$ )+22#)*#0$ *+$ 81+&20$ *"1+&8"$ 5
)5?5)-*+1=7$;,$*"#$/#5%&1#0$U90i$'5206-0*"$+,$*"#$5/?3-,-#1$-%
1#0&)#0$,1+/$*"#$#D?#)*#0$b$_aT$*+$@BA$.aT4$#%*-/5*#$*"#
E53&#$ +,$ *"#$ %"&2*-28$ )5?5)-*+17$ ;,$ *"#$ +1-8-253$ )&*+,,$ ,1#9
G&#2)>$)52$'#$5**1-'&*#0$*+$5$%/533$?515%-*-)$)5?5)-*+1$5*$*"#
%5/#$-2*#1253$2+0#$:-7#74$'#*6##2$*"#$2+0#$520$81+&20=4$6"5*
6+&30$>+&$#%*-/5*#$-*$*+$'#X
D *1.73 L$0#%-82#1$6-%"-28$*+$3+6#1$*"#$+E#1533$&??#1$U90i
,1#G&#2)>$ +,$ 5$ *"1##9%*58#$ 5/?3-,-#1$ *+$ @A$ .aT$ )+2%-0#1%
%"&2*-28$+2#$+,$*6+$2+0#%H$O+0#$L4$'#*6##2$*"#$+&*?&*$+,$*"#
,-1%*$ %*58#$ 520$ *"#$ -2?&*$ +,$ *"#$ %#)+20$ %*58#4$ 520$ O+0#$ i4
'#*6##2$*"#$ +&*?&*$+,$ *"#$%#)+20$ %*58#$520$*"#$-2?&*$ +,$ *"#
*"-10$%*58#4$*+$81+&20$6-*"$5$%/533$)5?5)-*+17$F"-3#$/#5%&19
-28$*"#$+E#1533$,1#G&#2)>$1#%?+2%#$+,$*"#$5/?3-,-#14$%"#$)+29
2#)*%$5$)5?5)-*+1$+,$@$2K4$,-1%*$*+$2+0#$L$520$*"#2$*+$2+0#$i4
3+6#1-28$*"#$U90i$,1#G&#2)>$,1+/$B$_aT$*+$@]A$.aT$520$@]
.aT4$1#%?#)*-E#3>7$;,$%"#$.2+6%$*"5*$#5)"$5/?3-,-#1$%*58#$"5%
52$-2?&*$1#%-%*52)#$+,$@AA$.Ω4$6"5*$+&*?&*$1#%-%*52)#$/&%*$*"#
01-E-28$ %*58#$ "5E#$ 5*$ 2+0#$ LX$ L*$ 2+0#$ iX$ F"5*$ )5?5)-*+1
E53&#$%"+&30$%"#$)+22#)*$*+$6"-)"$2+0#$*+$%+3E#$"#1$0#%-82
?1+'3#/$/+%*$#)+2+/-)533>X
D 1.74 L2$5/?3-,-#1$6-*"$52$-2?&*$1#%-%*52)#$+,$@AA$.Ω$520
52$+&*?&*$1#%-%*52)#$+,$@$.Ω$-%$*+$'#$)5?5)-*+19)+&?3#0$*+$5
@A9.Ω$%+&1)#$520$5$@9.Ω$3+507$LE5-35'3#$)5?5)-*+1%$"5E#$E539
&#%$+23>$+,$*"#$,+1/$@$×$@A>4$K7$F"5*$ 51#$*"#$E53&#%$ +,$ *"#
Vo
Problems 51
"
"
Vs
"
!
C1
10 pF
CHAPTER 1 P R O B L E M S
C2
100 nF
R1
1 M)
Vi
!
G m Vi
R2
10 k)
R3
20 k)
Vo
!
Gm % 100 mA*V
Figure P1.76
@AA
# $ ≥ 999999999 4 @ # !
H
%/533#%*$)5?5)-*+1%$2##0#0$*+$#2%&1#$*"5*$*"#$)+12#1$,1#G&#2)>
5%%+)-5*#0$6-*"$#5)"$-%$3#%%$*"52$@AA$aTX$F"5*$5)*&53$)+12#1
,1#G&#2)-#%$1#%&3*X$K+1$*"#$%-*&5*-+2$-2$6"-)"$*"#$'5%-)$5/?3-9
,-#1$"5%$52$+?#29)-1)&-*$E+3*58#$85-2$ ( 8 v& ) $+,$@AA$Y`Y4$,-20
52$#D?1#%%-+2$,+1$, ( ! ) = ) & ( ! ) ⁄ ) ! ( ! )7
@
# & ≤ 9999999999999999999999999999999999999999999999
B π * U0i < % 4 ( @ ⁄ # % )
8 A ⁄ [ @ 4 ( H ⁄ @AA ) ]
9
B C ≥ 9999999999999999999999999999999999999999999
( # % || # & )
*1.75 L$E+3*58#$5/?3-,-#1$"5%$*"#$*152%,#1$,&2)*-+2
@AA
8 v " 9999999999999999999999999999999999999999999999999999
9
B
*
@A @ ! N 99999999 @ ! 9999999
9
^
N*
@A d%-28$ *"#$ i+0#$ ?3+*%$ ,+1$ 3+69?5%%$ 520$ "-8"9?5%%$ I!<$ 2#*9
6+1.%$:K-8%7$@7BU$520$@7B^=4$%.#*)"$5$i+0#$?3+*$,+1$o8vo7$j-E#
5??1+D-/5*#$E53&#%$,+1$*"#$85-2$/582-*&0#$5*$*$=$@A$aT4$@AB
aT4$@AU$aT4$@A^$aT4$@A]$aT4$@Ab$aT4$520$@Ac$aT7$K-20$*"#$'5209
6-0*"$ +,$ *"#$ 5/?3-,-#1$ :0#,-2#0$ 5%$ *"#$ ,1#G&#2)>$ 1528#$ +E#1
6"-)"$*"#$85-2$1#/5-2%$6-*"-2$U$0i$+,$*"#$/5D-/&/$E53&#=7
*1.76 K+1$ *"#$ )-1)&-*$ %"+62$ -2$ K-87$ l@7cb$ ,-1%*4$ #E53&5*#
, $ ( ! ) = ) $ ( ! ) ⁄ ) ! ( ! )$520$*"#$)+11#%?+20-28$)&*+,,$:)+12#1=
,1#G&#2)>7$I#)+204$#E53&5*#$ , & ( ! ) = ) & ( ! ) ⁄ ) $ ( ! )$520$*"#
)+11#%?+20-28$ )&*+,,$ ,1#G&#2)>7$ l&*$ #5)"$ +,$ *"#$ *152%,#1
,&2)*-+2%$ -2$ *"#$ %*520510$ ,+1/$ :%##$ !5'3#$ @7B=4$ 520$ )+/9
'-2#$ *"#/$ *+$ ,+1/$ *"#$ +E#1533$ *152%,#1$ ,&2)*-+24
, ( ! ) = , $ ( ! ) × , & ( ! ) 7$ l1+E-0#$ 5$ i+0#$ /582-*&0#$ ?3+*$ ,+1
, :N ω = 7$ F"5*$ -%$ *"#$ '5206-0*"$ '#*6##2$ U90i$ )&*+,,
?+-2*%X
D **1.77 L$ *152%)+20&)*52)#$ 5/?3-,-#1$ "5E-28$ *"#$ #G&-E59
3#2*$)-1)&-*$%"+62$-2$!5'3#$@7@$-%$,#0$6-*"$5$E+3*58#$%+&1)#$)!
"5E-28$5$%+&1)#$1#%-%*52)#$#!4$520$-*%$+&*?&*$-%$)+22#)*#0$*+$5
3+50$ )+2%-%*-28$ +,$ 5$ 1#%-%*52)#$ #%$ -2$ ?51533#3$ 6-*"$ 5$ )5?5)-9
*52)#$<%7$K+1$8-E#2$E53&#%$+,$#!4$#%4$520$<%4$-*$-%$1#G&-1#0$*+
%?#)-,>$*"#$E53&#%$+,$*"#$5/?3-,-#1$?515/#*#1%$#$4$BC4$520$#&
*+$/##*$*"#$,+33+6-28$0#%-82$)+2%*15-2*%H
:5= L*$/+%*4$H[$+,$*"#$-2?&*$%-8253$-%$3+%*$-2$)+&?3-28$*"#$%-89
253$%+&1)#$*+$*"#$5/?3-,-#1$( -7#74$) $ ≥ [ @ 4 ( H ⁄ @AA ) ]) ! )7
:'= !"#$U90i$,1#G&#2)>$+,$*"#$5/?3-,-#1$-%$#G&53$*+$+1$81#5*#1
*"52$5$%?#)-,-#0$E53&#$*U 0i7
:)= !"#$0)$85-2$) & ⁄ ) !$-%$#G&53$*+$+1$81#5*#1$*"52$5$%?#)-,-#0
E53&#$8A7
I"+6$*"5*$*"#%#$)+2%*15-2*%$)52$'#$/#*$'>$%#3#)*-28
K-20$ #$ 4$ #&4$ 520$ BC$ ,+1$ #!$ =$ @A$ .Ω 4$ H$ =$ BA[4$ 8&$ =$ ZA4
#% = @A$.Ω 4$<%$=$@A$?K4$520$*U0i$=$U$_aT7
*1.78 d%#$*"#$E+3*58#90-E-0#1$1&3#$*+$,-20$*"#$*152%,#1$,&2)9
*-+2$ ) & ( ! ) ⁄ ) $ ( ! )$+,$*"#$)-1)&-*$-2$K-87$l@7cZ7$I"+6$*"5*$*"#
*152%,#1$ ,&2)*-+2$ )52$ '#$ /50#$ -20#?#20#2*$ +,$ ,1#G&#2)>$ -,
*"#$)+20-*-+2$<@#@$=$<B # B$5??3-#%7$d20#1$*"-%$)+20-*-+2$*"#
)-1)&-*$ -%$ )533#0$ 5$ #%!/'*+3)'1, 3))'*03)%$$ 520$ -%$ ,1#9
G&#2*3>$#/?3+>#0$-2$*"#$0#%-82$+,$+%)-33+%)+?#$?1+'#%7$K-20
*"#$*152%/-%%-+2$+,$*"#$)+/?#2%5*#0$5**#2&5*+1$-2$*#1/%$+,
#@$520$#B7
Vi
R1
C1
R2
"
C2 Vo
!
"
!
Figure P1.78
*1.79 L2$ 5/?3-,-#1$ 6-*"$ 5$ ,1#G&#2)>$ 1#%?+2%#$ +,$ *"#$ *>?#
%"+62$-2$K-87$@7B@$-%$%?#)-,-#0$*+$"5E#$5$?"5%#$%"-,*$+,$/582-9
*&0#$ 2+$ 81#5*#1$ *"52$ @@7^°$ +E#1$ *"#$ 5/?3-,-#1$ '5206-0*"4
6"-)"$#D*#20%$,1+/$@AA$aT$*+$@$.aT7$;*$"5%$'##2$,+&20$*"5*
*"#$85-2$,533+,,$5*$*"#$3+69,1#G&#2)>$#20$-%$0#*#1/-2#0$'>$*"#
1#%?+2%#$ +,$ 5$ "-8"9?5%%$ I!<$ )-1)&-*$ 520$ *"5*$ 5*$ *"#$ "-8"9
,1#G&#2)>$ #20$ -*$ -%$ 0#*#1/-2#0$ '>$ 5$ 3+69?5%%$ I!<$ )-1)&-*7
F"5*$0+$>+&$#D?#)*$*"#$)+12#1$,1#G&#2)-#%$+,$*"#%#$*6+$)-19
)&-*%$*+$'#X$F"5*$-%$*"#$01+?$-2$85-2$-2$0#)-'#3%$:1#35*-E#$*+$*"#
/5D-/&/$85-2=$5*$*"#$*6+$,1#G&#2)-#%$*"5*$0#,-2#$*"#$5/?3-9
,-#1$'5206-0*"X$F"5*$51#$*"#$,1#G&#2)-#%$5*$6"-)"$*"#$01+?$-2
85-2$-%$U$0iX
CHAPTER 2
Operational
Amplifiers
Introduction
2.1
2.6 DC Imperfections
53
2.7 Effect of Finite Open-Loop Gain and
Bandwidth on Circuit Performance 97
The Ideal Op Amp 54
2.2 The Inverting Configuration
58
2.3 The Noninverting Configuration
2.4 Difference Amplifiers
67
71
2.5 Integrators and Differentiators
88
80
2.8 Large-Signal Operation of
Op Amps 102
Summary
107
Problems
108
IN THIS CHAPTER YOU WILL LEARN
1. The terminal characteristics of the ideal op amp.
2. How to analyze circuits containing op amps, resistors, and capacitors.
3. How to use op amps to design amplifiers having precise characteristics.
4. How to design more sophisticated op-amp circuits, including summing
amplifiers, instrumentation amplifiers, integrators, and differentiators.
5. Important nonideal characteristics of op amps and how these limit the
performance of basic op-amp circuits.
Introduction
!"#$%&'()"*%)+',"-$.'"/0($1$)*'.2%.)03-'"%+'3)*/$%2(2&45'6)'"*)'%26'*)"+4'32'7%+)*3"8)'39)
-37+4'21'"'.$*.7$3',7$(+$%&',(2.8'21'7%$#)*-"('$/02*3"%.):';9)'20)*"3$2%"('"/0($1$)*'<20'"/0=>
?0'"/0-'9"#)',))%'$%'7-)'12*'"'(2%&'3$/)5'39)$*'$%$3$"('"00($."3$2%-',)$%&'0*$/"*$(4'$%'39)'"*)"21' "%"(2&' .2/073"3$2%' "%+' -209$-3$."3)+' $%-3*7/)%3"3$2%>' @"*(4' 20' "/0-' 6)*)' .2%-3*7.3)+
1*2/'+$-.*)3)'.2/02%)%3-'<#".77/'37,)-'"%+'39)%'3*"%-$-32*-5'"%+'*)-$-32*-=5'"%+'39)$*'.2-3'6"0*29$,$3$#)(4'9$&9'<3)%-'21'+2(("*-=>'A%'39)'/$+BCDEF-'39)'1$*-3'$%3)&*"3)+B.$*.7$3'<AG='20'"/0
6"-'0*2+7.)+>';9$-'7%$3'<39)'µH'IFD='6"-'/"+)'70'21'"'*)("3$#)(4'("*&)'%7/,)*'21'3*"%-$-32*"%+'*)-$-32*-'"(('2%'39)'-"/)'-$($.2%'.9$0>'H(3927&9'$3-'.9"*".3)*$-3$.-'6)*)'022*'<,4'32+"4J-3"%+"*+-='"%+'$3-'0*$.)'6"-'-3$(('K7$3)'9$&95'$3-'"00)"*"%.)'-$&%"()+'"'%)6')*"'$%')().3*2%$.'.$*B
.7$3'+)-$&%>'@().3*2%$.-')%&$%))*-'-3"*3)+'7-$%&'20'"/0-'$%'("*&)'K7"%3$3$)-5'69$.9'."7-)+'39)$*
0*$.)'32'+*20'+*"/"3$."((4>';9)4'"(-2'+)/"%+)+',)33)*BK7"($34'20'"/0->'L)/$.2%+7.32*'/"%7B
1".37*)*-'*)-02%+)+'K7$.8(45'"%+'6$39$%'39)'-0"%'21'"'1)6'4)"*-5'9$&9BK7"($34'20'"/0-',)."/)
"#"$(",()'"3')M3*)/)(4'(26'0*$.)-'<3)%-'21'.)%3-='1*2/'"'("*&)'%7/,)*'21'-700($)*->
?%)'21'39)'*)"-2%-'12*'39)'0207("*$34'21'39)'20'"/0'$-'$3-'#)*-"3$($34>'H-'6)'6$(('-92*3(4
-))5'2%)'."%'+2'"(/2-3'"%439$%&'6$39'20'"/0-N'@K7"((4'$/02*3"%3'$-'39)'1".3'39"3'39)'AG'20
"/0'9"-'.9"*".3)*$-3$.-'39"3'.(2-)(4'"00*2".9'39)'"--7/)+'$+)"(>';9$-'$/0($)-'39"3'$3'$-'K7$3)
)"-4'32'+)-$&%'.$*.7$3-'7-$%&'39)'AG'20'"/0>'H(-25'20B"/0'.$*.7$3-'62*8'"3'0)*12*/"%.)'()#)(39"3'"*)'K7$3)'.(2-)'32'392-)'0*)+$.3)+'39)2*)3$."((4>'A3'$-'12*'39$-'*)"-2%'39"3'6)'"*)'-37+4$%&'20
"/0-'"3'39$-')"*(4'-3"&)>'A3'$-')M0).3)+'39"3',4'39)')%+'21'39$-'.9"03)*'39)'*)"+)*'-927(+'',)'",()
32'+)-$&%'%2%3*$#$"('.$*.7$3-'-7..)--17((4'7-$%&'20'"/0->
H-'"(*)"+4'$/0($)+5'"%'AG'20'"/0'$-'/"+)'70'21'"'("*&)'%7/,)*'<3)%-'2*'/2*)='21'3*"%B
-$-32*-5'*)-$-32*-5'"%+'<7-7"((4='2%)'."0".$32*'.2%%).3)+'$%'"'*"39)*'.2/0()M'.$*.7$3>'L$%.)
53
54 Chapter 2 Operational Amplifiers
6)' 9"#)' %23' 4)3' -37+$)+' 3*"%-$-32*' .$*.7$3-5' 39)' .$*.7$3' $%-$+)' 39)' 20' "/0' 6$((' %23' ,)' +$-B
.7--)+'$%'39$-'.9"03)*>'O"39)*5'6)'6$(('3*)"3'39)'20'"/0'"-'"'.$*.7$3',7$(+$%&',(2.8'"%+'-37+4
$3-'3)*/$%"('.9"*".3)*$-3$.-'"%+'$3-'"00($."3$2%->';9$-'"00*2".9'$-'K7$3)'-"3$-1".32*4'$%'/"%4
20B"/0'"00($."3$2%->'P)#)*39)()--5'12*'39)'/2*)'+$11$.7(3'"%+'+)/"%+$%&'"00($."3$2%-'$3'$K7$3)'7-)17('32'8%26'69"3'$-'$%-$+)'39)'20B"/0'0".8"&)>';9$-'320$.'6$((',)'-37+$)+'$%'G9"0B
3)*'CQ>'R2*)'"+#"%.)+'"00($."3$2%-'21'20'"/0-'6$(('"00)"*'$%'("3)*'.9"03)*->
2.1 The Ideal Op Amp
2.1.1 The Op-Amp Terminals
S*2/'"'-$&%"('02$%3'21'#$)6'39)'20'"/0'9"-'39*))'3)*/$%"(-:'362'$%073'3)*/$%"(-'"%+'2%)'273073
3)*/$%"(>'S$&7*)'Q>C'-926-'39)'-4/,2('6)'-9"(('7-)'32'*)0*)-)%3'39)'20'"/0>';)*/$%"(-'C'"%+'Q
"*)'$%073'3)*/$%"(-5'"%+'3)*/$%"('T'$-'39)'273073'3)*/$%"(>'H-')M0("$%)+'$%'L).3$2%'C>U5'"/0($1$)**)K7$*)'+.'026)*'32'20)*"3)>'R2-3'AG'20'"/0-'*)K7$*)'362'+.'026)*'-700($)-5'"-'-926%'$%
S$&>'Q>Q>';62'3)*/$%"(-5'U'"%+'V5'"*)',*27&93'273'21'39)'20B"/0'0".8"&)'"%+'.2%%).3)+'32'"'02-B
$3$#)'#2(3"&)'!""'"%+'"'%)&"3$#)'#2(3"&)'−!##5'*)-0).3$#)(4>'A%'S$&>'Q>Q<,='6) )M0($.$3(4'-926'39)
362'+.'026)*'-700($)-'"-',"33)*$)-'6$39'"'.2//2%'&*27%+>'A3'$-'$%3)*)-3$%&'32'%23)'39"3'39)'*)1)*B
)%.)'&*27%+$%&'02$%3'$%'20B"/0'.$*.7$3-'$-'W7-3'39)'.2//2%'3)*/$%"('21'39)'362'026)*'-700($)-X
39"3'$-5'%2'3)*/$%"('21'39)'20B"/0'0".8"&)'$-'094-$."((4'.2%%).3)+'32'&*27%+>'A%'69"3'12((266)'6$(('%235'12*'-$/0($.$345')M0($.$3(4'-926'39)'20B"/0'026)*'-700($)->
Figure 2.1 G$*.7$3'-4/,2('12*'39)'20'"/0>
VCC
VCC
VEE
!VEE
Figure 2.2 ;9)'20'"/0'-926%'.2%%).3)+'32'+.'026)*'-700($)->
2.1 The Ideal Op Amp
A%'"++$3$2%'32'39)'39*))'-$&%"('3)*/$%"(-'"%+'39)'362'026)*B-700(4'3)*/$%"(-5'"%'20'"/0
/"4'9"#)'239)*'3)*/$%"(-'12*'-0).$1$.'07*02-)->';9)-)'239)*'3)*/$%"(-'."%'$%.(7+)'3)*/$%"(12*'1*)K7)%.4'.2/0)%-"3$2%'"%+'3)*/$%"(-'12*'211-)3'%7(($%&X',239'17%.3$2%-'6$((',)')M0("$%)+
$%'("3)*'-).3$2%->''''''''''''''
EXERCISE
2.1' Y9"3' $-' 39)' /$%$/7/' %7/,)*' 21' 3)*/$%"(-' *)K7$*)+' ,4' "' -$%&()' 20' "/0\' Y9"3' $-' 39)' /$%$/7/
%7/,)*'21'3)*/$%"(-'*)K7$*)+'2%'"%'$%3)&*"3)+B.$*.7$3'0".8"&)'.2%3"$%$%&'127*'20'"/0-'<."(()+'"
K7"+'20 "/0=\
Ans. VX'CU
2.1.2 Function and Characteristics of the Ideal Op Amp
Y)'%26'.2%-$+)*'39)'.$*.7$3'17%.3$2%'21'39)'20'"/0>';9)'20'"/0'$-'+)-$&%)+'32'-)%-)'39)'+$1B
1)*)%.)',)36))%'39)'#2(3"&)'-$&%"(-'"00($)+'"3'$3-'362'$%073'3)*/$%"(-'<$>)>5'39)'K7"%3$34'vQ'−
vC=5'/7(3$0(4'39$-',4'"'%7/,)*'$5'"%+'."7-)'39)'*)-7(3$%&'#2(3"&)'$<vQ'−'vC='32'"00)"*'"3'273B
073'3)*/$%"('T>';97-'vT%Z%$<vQ'−'vC=>'!)*)'$3'-927(+',)')/09"-$[)+'39"3'69)%'6)'3"(8'",273
39)' #2(3"&)' "3' "' 3)*/$%"(' 6)' /)"%' 39)' #2(3"&)' ,)36))%' 39"3' 3)*/$%"(' "%+' &*27%+X' 397-' vC
/)"%-'39)'#2(3"&)'"00($)+',)36))%'3)*/$%"('C'"%+'&*27%+>
;9)'$+)"('20'"/0'$-'%23'-7002-)+'32'+*"6'"%4'$%073'.7**)%3X'39"3'$-5'39)'-$&%"('.7**)%3
$%32'3)*/$%"('C'"%+'39)'-$&%"('.7**)%3'$%32'3)*/$%"('Q'"*)',239'[)*2>'A%'239)*'62*+-5'&'(%)*+,&
)-+(./*0(%12%/*%).(/3%1+%/-+%)4%4,++14(.%&1%5(%)*2)*)&(6
!26'",273'39)'273073'3)*/$%"('T\';9$-'3)*/$%"('$-'-7002-)+'32'".3'"-'39)'273073'3)*/$B
%"(' 21' "%' $+)"(' #2(3"&)' -27*.)>' ;9"3' $-5' 39)' #2(3"&)' ,)36))%' 3)*/$%"(' T' "%+' &*27%+' 6$((
"(6"4-',)')K7"('32'$<vQ'−'vC=5'$%+)0)%+)%3'21'39)'.7**)%3'39"3'/"4',)'+*"6%'1*2/'3)*/$%"('T
$%32'"'(2"+'$/0)+"%.)>'A%'239)*'62*+-5'&'(%1,&+,&%)-+(./*0(%12%/*%).(/3%1+%/-+%)4%4,++14(.
&1%5(%7(816%%
]733$%&'32&)39)*'"(('21'39)'",2#)5'6)'"**$#)'"3'39)')K7$#"()%3'.$*.7$3'/2+)('-926%'$%
S$&>'Q>T>'P23)'39"3'39)'273073'$-'$%'09"-)'6$39'<9"-'39)'-"/)'-$&%'"-='vQ'"%+'$-'273'21'09"-)
6$39'<9"-'39)'2002-$3)'-$&%'21='vC>'S2*'39$-'*)"-2%5'$%073'3)*/$%"('C'$-'."(()+'39)'!"#$%&!"'
!"()&*&$%+!",-'"%+'$-'+$-3$%&7$-9)+',4'"'^−_'-$&%5'69$()'$%073'3)*/$%"('Q'$-'."(()+'39)'"."!"/
#$%&!"'*!"()&*&$%+!",-'"%+'$-'+$-3$%&7$-9)+',4'"'^+_'-$&%>'''
H-'."%',)'-))%'1*2/'39)'",2#)'+)-.*$03$2%5'39)'20'"/0'*)-02%+-'2%(4'32'39)'.)22(8(*0(
-$&%"('vQ'−'vC'"%+'9)%.)'$&%2*)-'"%4'-$&%"('01--1*'32',239'$%073->';9"3'$-5'$1'vC'='vQ'='C'`5
39)%'39)'273073'6$(('<$+)"((4=',)'[)*2>'Y)'."(('39$-'0*20)*34'0.++."/+.1$*%$2$0&!."5'"%+'6)
.2%.(7+)'39"3'"%'$+)"('20'"/0'9"-'[)*2'.2//2%B/2+)'&"$%'2*5')K7$#"()%3(45'$%1$%$3)'.2/B
/2%B/2+)'*)W).3$2%>'Y)'6$(('9"#)'/2*)'32'-"4'",273'39$-'02$%3'("3)*>'S2*'39)'3$/)',)$%&
%23)'39"3'39)'20'"/0'$-'"'1!33$%$"&!,-/!"()&5*4!"'-$/$"1$1/.)&()&'"/0($1$)*5'6$39 39)'("3B
3)*' 3)*/' *)1)**$%&' 32' 39)' 1".3' 39"3' 39)' 273073' "00)"*-' ,)36))%' 3)*/$%"(' T' "%+' &*27%+>C
C
L2/)'20'"/0-'"*)'+)-$&%)+'32'9"#)'+$11)*)%3$"('273073->';9$-'320$.'6$(('%23',)'+$-.7--)+'$%'39$-',228>'
O"39)*5'6)'.2%1$%)'27*-)(#)-'9)*)'32'-$%&()B)%+)+B273073'20'"/0-5'69$.9'.2%-3$373)'39)'#"-3'/"W2*$34'
21'.2//)*.$"((4'"#"$(",()'20'"/0->
55
56 Chapter 2 Operational Amplifiers
Inverting input
Output
Noninverting input
Figure 2.3 @K7$#"()%3'.$*.7$3'21'39)'$+)"('20'"/0>
S7*39)*/2*)5'&"$%'$'$-'."(()+'39)'1!33$%$"&!,-*',!"5'12*'2,#$27-'*)"-2%->'])*9"0-'%23'-2'2,#$B
27-'$-'"%239)*'%"/)'39"3'6)'6$(('"33".9'32'$:'39)'.($"/-..(*',!">';9)'*)"-2%'12*'39$-'%"/)
6$((',).2/)'2,#$27-'("3)*'2%'69)%'6)'^.(2-)'39)'(220_'"*27%+'39)'20'"/0'"%+'+)1$%)'"%239)*
&"$%5'39)'.(2-)+B(220'&"$%>
H%'$/02*3"%3'.9"*".3)*$-3$.'21'20'"/0-'$-'39"3'39)4'"*)'1!%$0&/0.)(-$1*2*'10*,+(-!3!$%45
69)*)' +.' -3"%+-' 12*' +$*).3B.270()+' <$3' .27(+' )K7"((4' 6)((' -3"%+' 12*' +$*).3' .7**)%35' -$%.)' "
+$*).3B.270()+'"/0($1$)*'$-'2%)'39"3'"/0($1$)-'-$&%"(-'692-)'1*)K7)%.4'$-'"-'(26'"-'[)*2=>';9)
1".3' 39"3' 20' "/0-' "*)' +$*).3B.270()+' +)#$.)-' 6$((' "((26' 7-' 32' 7-)' 39)/' $%' /"%4' $/02*3"%3
"00($."3$2%->' a%12*37%"3)(45' 3927&95' 39)' +$*).3B.270($%&' 0*20)*34' ."%' ."7-)' -2/)' -)*$270*".3$."('0*2,()/-5'"-'6$((',)'+$-.7--)+'$%'"'("3)*'-).3$2%>
!26'",273',"%+6$+39\';9)'$+)"('20'"/0'9"-'"'&"$%'$'39"3'*)/"$%-'.2%-3"%3'+26%'32
[)*2'1*)K7)%.4'"%+'70'32'$%1$%$3)'1*)K7)%.4>';9"3'$-5'$+)"('20'"/0-'6$(('"/0($14'-$&%"(-'21'"%4
1*)K7)%.4'6$39')K7"('&"$%5'"%+'"*)'397-'-"$+'32'9"#)')*2)*)&(%5/*.9).&'6
Y)'9"#)'+$-.7--)+'"(('21'39)'0*20)*3$)-'21'39)'$+)"('20'"/0')M.)03'12*'2%)5'69$.9'$%
1".3'$-'39)'/2-3'$/02*3"%3>';9$-'9"-'32'+2'6$39'39)'#"(7)'21'$>':'(%).(/3%1+%/-+%4'1,3.%'/;(
/%</)*%H%9'14(%;/3,(%)4%;(8=%3/8<(%/*.%).(/33=%)*2)*)&(>'?%)'/"4'W7-3$1$",(4'"-8:'A1'39)'&"$%'$
$-'$%1$%$3)5'926'"*)'6)'&2$%&'32'7-)'39)'20'"/0\';9)'"%-6)*'$-'#)*4'-$/0():'A%'"(/2-3'"((
"00($."3$2%-' 39)' 20' "/0' 6$((' *1&' ,)' 7-)+' "(2%)' $%' "' -2B."(()+' 20)%B(220' .2%1$&7*"3$2%>
O"39)*5' 6) 6$((' 7-)' 239)*' .2/02%)%3-' 32' "00(4' 1))+,".8' 32' .(2-)' 39)' (220' "*27%+' 39)' 20
"/05'"-'6$((',)'$((7-3*"3)+'$%'+)3"$('$%'L).3$2%'Q>Q>
S2*'1737*)'*)1)*)%.)5';",()'Q>C'($-3-'39)'.9"*".3)*$-3$.-'21'39)'$+)"('20'"/0>
Table 2.1 Characteristics of the Ideal Op Amp
C> A%1$%$3)'$%073'$/0)+"%.)
Q> b)*2'273073'$/0)+"%.)
T> b)*2'.2//2%B/2+)'&"$%'2*5')K7$#"()%3(45'$%1$%$3)'.2//2%B/2+)'*)W).3$2%
U> A%1$%$3)'20)%B(220'&"$%'$
V> A%1$%$3)',"%+6$+39
2.1 The Ideal Op Amp
2.1.3 Differential and Common-Mode Signals
;9)'+$11)*)%3$"('$%073'-$&%"('v>.'$-'-$/0(4'39)'+$11)*)%.)',)36))%'39)'362'$%073'-$&%"(vC'"%+'vQX'39"3'$-5
v >. = v Q ! v C
<Q>C=
;9)' .2//2%B/2+)' $%073' -$&%"(' v>0-' $-' 39)' "#)*"&)' 21' 39)' 362' $%073' -$&%"(-' vC' "%+' vQX
%"/)(45
v >0- = CBBQB ( v C + v Q )
<Q>Q=
@K7"3$2%-'<Q>C='"%+'<Q>Q='."%',)'7-)+'32')M0*)--'39)'$%073'-$&%"(-'vC'"%+'vQ'$%'3)*/-'21'39)$*
+$11)*)%3$"('"%+'.2//2%B/2+)'.2/02%)%3-'"-'12((26-:
v C = v >0- ! v >. ⁄ Q
<Q>T=
v Q = v >0- + v >. ⁄ Q
'<Q>U=
"%+
;9)-)')K7"3$2%-'."%'$%'37*%'()"+'32'39)'0$.32*$"('*)0*)-)%3"3$2%'$%'S$&>'Q>U>''''''
1
1
v1 "
!
vIcm
2
"
!
!
"
vId #2
!
"
vId #2
2
v2 "
!
Figure 2.4 O)0*)-)%3"3$2%'21'39)'-$&%"('-27*.)-'vC'"%+'vQ'$%'3)*/-'21'39)$*'+$11)*)%3$"('"%+'.2//2%B/2+)'
.2/02%)%3->
EXERCISES
2.2' G2%-$+)*'"%'20'"/0'39"3'$-'$+)"(')M.)03'39"3'$3-'20)%B(220'&"$%'$'='CFT>';9)'20'"/0'$-'7-)+'$%'"'1))+B
,".8'.$*.7$35'"%+'39)'#2(3"&)-'"00)"*$%&'"3'362'21'$3-'39*))'-$&%"('3)*/$%"(-'"*)'/)"-7*)+>'A%')".9'21
39)'12((26$%&'."-)-5'7-)'39)'/)"-7*)+'#"(7)-'32'1$%+'39)')M0).3)+'#"(7)'21'39)'#2(3"&)'"3'39)'39$*+'3)*B
/$%"(>'H(-2'&$#)'39)'+$11)*)%3$"('"%+'.2//2%B/2+)'$%073'-$&%"(-'$%')".9'."-)>'<"='vQ'='F'`'"%+'vT'=
Q `X'<,='vQ'='+V'`'"%+'vT'='−CF'`X'<.='vC'='C>FFQ'`'"%+'vQ'='F>DDc'`X'<+='vC'='−T>E'`'"%+'vT'='−T>E'`>
Ans. <"='vC'='−F>FFQ'`5'v>.'='Q'/`5'v>0-'Z'−C'/`X'<,='vC'='+V>FC'`5'v>.'='−CF'/`5'v>0-'='V>FFV'!'V `X
<.= vT'='−U'`5%v>.'='−U'/`5'v>0-'= C'`X'<+='vQ'='−T>EFTE'`5'v>.'='−T>E'/`5'v>0-'!'−T>E'`
57
58 Chapter 2 Operational Amplifiers
2.3' ;9)'$%3)*%"('.$*.7$3'21'"'0"*3$.7("*'20'"/0'."%',)'/2+)()+',4'39)'.$*.7$3'-926%'$%'S$&>'@Q>T>'@M0*)-vT'"-'"'17%.3$2%'21'vC'"%+'vQ>'S2*'39)'."-)'A-'='CF'/Hd`5'?'='CF'8Ω5'"%+' µ'='CFF5'1$%+'39)'#"(7)'21
39)'20)%B(220'&"$%'$>
Ans. vT'= µA-?<vQ'−'vC=X'$'='CF5FFF'`d`'2*'cF'+e
Figure E2.3
2.2 The Inverting Configuration
H-'/)%3$2%)+'",2#)5'20'"/0-'"*)'%23'7-)+'"(2%)X'*"39)*5'39)'20'"/0'$-'.2%%).3)+'32'0"--$#)
.2/02%)%3-'$%'"'1))+,".8'.$*.7$3>';9)*)'"*)'362'-7.9',"-$.'.$*.7$3'.2%1$&7*"3$2%-')/0(24$%&
"%'20'"/0'"%+'362'*)-$-32*-:'39)'$%#)*3$%&'.2%1$&7*"3$2%5'69$.9'$-'-37+$)+'$%'39$-'-).3$2%5'"%+
39)'%2%$%#)*3$%&'.2%1$&7*"3$2%5'69$.9'6)'-9"(('-37+4'$%'39)'%)M3'-).3$2%>
S$&7*)'Q>V'-926-'39)'$%#)*3$%&'.2%1$&7*"3$2%>'A3'.2%-$-3-'21'2%)'20'"/0'"%+'362'*)-$-32*-'?C
"%+'?Q>'O)-$-32*'?Q'$-'.2%%).3)+'1*2/'39)'273073'3)*/$%"('21'39)'20'"/05'3)*/$%"('T5'5/0@'32'39)
)*;(8&)*<'2*'*(</&);('$%073'3)*/$%"(5'3)*/$%"('C>'Y)'-0)"8'21'?Q'"-'"00(4$%&'"$',&!#$*3$$15,06X
$1'?Q'6)*)'.2%%).3)+',)36))%'3)*/$%"(-'T'"%+'Q'6)'627(+'9"#)'."(()+'39$-'(.4!&!#$*3$$15,06>
P23)'"(-2'39"3'?Q'0314(4%&'(%311+'"*27%+'39)'20'"/0>'A%'"++$3$2%'32'"++$%&'?Q5'6)'9"#)'&*27%+)+
3)*/$%"('Q'"%+'.2%%).3)+'"'*)-$-32*'?C',)36))%'3)*/$%"('C'"%+'"%'$%073'-$&%"('-27*.)'6$39'"'#2(3B
"&)' v>>' ;9)' 273073' 21' 39)' 2#)*"((' .$*.7$3' $-' 3"8)%' "3' 3)*/$%"(' T' <$>)>5 ,)36))%' 3)*/$%"(' T' "%+
2.2 The Inverting Configuration
Figure 2.5 ;9)'$%#)*3$%&'.(2-)+B(220
.2%1$&7*"3$2%>
&*27%+=>';)*/$%"('T'$-5'21'.27*-)5'"'.2%#)%$)%3'02$%3'1*2/'69$.9'32'3"8)'39)'2730735'-$%.)'39)
$/0)+"%.)'()#)('39)*)'$-'$+)"((4'[)*2>';97-'39)'#2(3"&)'vB'6$(('%23'+)0)%+'2%'39)'#"(7)'21'39)'.7*B
*)%3'39"3'/$&93',)'-700($)+'32'"'(2"+'$/0)+"%.)'.2%%).3)+',)36))%'3)*/$%"('T'"%+'&*27%+>
2.2.1 The Closed-Loop Gain
Y)'%26'6$-9'32'"%"(4[)'39)'.$*.7$3'$%'S$&>'Q>V'32'+)3)*/$%)'39)'0-.4$1/-..(*',!"*A5'+)1$%)+'"-
v
A ≡ BBBBBB
v>
Y)'6$(('+2'-2'"--7/$%&'39)'20'"/0'32',)'$+)"(>'S$&7*)'Q>E<"='-926-'39)')K7$#"()%3'.$*.7$35
"%+'39)'"%"(4-$-'0*2.))+-'"-'12((26-:';9)'&"$%'$'$-'#)*4'("*&)'<$+)"((4'$%1$%$3)=>'A1'6)'"--7/)
39"3' 39)' .$*.7$3' $-' ^62*8$%&_' "%+' 0*2+7.$%&' "' 1$%$3)' 273073' #2(3"&)' "3' 3)*/$%"(' T5' 39)%' 39)
#2(3"&)' ,)36))%' 39)' 20B"/0' $%073' 3)*/$%"(-' -927(+' ,)' %)&($&$,(4' -/"((' "%+' $+)"((4' [)*2>
L0).$1$."((45'$1'6)'."(('39)'273073'#2(3"&)'vB5'39)%5',4'+)1$%$3$2%5
v
v Q ! v C = BBBBBB = F '
$
A3' 12((26-' 39"3' 39)' #2(3"&)' "3' 39)' $%#)*3$%&' $%073' 3)*/$%"(' <vC=' $-' &$#)%' ,4' vC' =' vQ>' ;9"3' $-5
,)."7-)'39)'&"$%'$'"00*2".9)-'$%1$%$345'39)'#2(3"&)'vC'"00*2".9)-'"%+'$+)"((4')K7"(-'vQ>'Y)
-0)"8'21'39$-'"-'39)'362'$%073'3)*/$%"(-'^3*".8$%&')".9'239)*'$%'023)%3$"(>_'Y)'"(-2'-0)"8'21'"
^#$*37"('-92*3'.$*.7$3_'39"3')M$-3-',)36))%'39)'362'$%073'3)*/$%"(->'!)*)'39)'62*+';)8&,/3'-927(+
,)')/09"-$[)+5'"%+'2%)'-927(+'*1&'/"8)'39)'/$-3"8)'21'094-$."((4'-92*3$%&'3)*/$%"(-'C'"%+'Q
32&)39)*'69$()'"%"(4[$%&'"'.$*.7$3>'H'#!%&),-*47.%&*0!%0)!&'/)"%-'39"3'69"3)#)*'#2(3"&)'$-'"3'Q
6$(('"732/"3$."((4'"00)"*'"3'C',)."7-)'21'39)'$%1$%$3)'&"$%'$>'e73'3)*/$%"('Q'9"00)%-'32',)'.2%B
%).3)+'32'&*27%+X'397-'vQ'='F'"%+'vC'='F>'Y)'-0)"8'21'3)*/$%"('C'"-',)$%&'"'#!%&),-*'%.)"1f
39"3'$-5'9"#$%&'[)*2'#2(3"&)',73'%23'094-$."((4'.2%%).3)+'32'&*27%+>'
P26'39"3'6)'9"#)'+)3)*/$%)+'vC'6)'"*)'$%'"'02-$3$2%'32'"00(4'?9/J-'("6'"%+'1$%+'39)
.7**)%3')C'39*27&9'?C'<-))'S$&>'Q>E='"-'12((26-:
v> ! vC
v> ! F
v
B = BBBBBBBBBBBB
B = BBBBB>
) C = BBBBBBBBBBBBBB
?C
?C
?C
Y9)*)'6$(('39$-'.7**)%3'&2\'A3'."%%23'&2'$%32'39)'20'"/05'-$%.)'39)'$+)"('20'"/0'9"-'"%'$%1$%$3)
$%073'$/0)+"%.)'"%+'9)%.)'+*"6-'[)*2'.7**)%3>'A3'12((26-'39"3')C'6$(('9"#)'32'1(26'39*27&9'?Q'32
39)'(26B$/0)+"%.)'3)*/$%"('T>'Y)'."%'39)%'"00(4'?9/J-'("6'32'?Q'"%+'+)3)*/$%)'vBX'39"3'$-5
;97-5
vB = vC ! )C ?Q
v
= F ! BBBBB> ? Q
?C
v
?
BBBBBB = ! BBBBBQ
v>
?C
59
60 Chapter 2 Operational Amplifiers
5
3
4
!
1
"
6
2
Figure 2.6 H%"(4-$-'21'39)'$%#)*3$%&'.2%1$&7*"3$2%>';9)'.$*.()+'%7/,)*-'$%+$."3)'39)'2*+)*'21'39)'"%"(4-$-'
-3)0->
69$.9'$-'39)'*)K7$*)+'.(2-)+B(220'&"$%>'S$&7*)'Q>E<,=%$((7-3*"3)-'39)-)'-3)0-'"%+'$%+$."3)-',4
39)'.$*.()+'%7/,)*-'39)'2*+)*'$%'69$.9'39)'"%"(4-$-'$-'0)*12*/)+>
Y)'397-'-))'39"3'39)'.(2-)+B(220'&"$%'$-'-$/0(4'39)'*"3$2'21'39)'362'*)-$-3"%.)-'?Q'"%+'?C>
;9)' /$%7-' -$&%' /)"%-' 39"3' 39)' .(2-)+B(220' "/0($1$)*' 0*2#$+)-' -$&%"(' $%#)*-$2%>' ;97-' $1
? Q ⁄ ? C = CF '"%+'6)'"00(4'"3'39)'$%073'<vI ='"'-$%)B6"#)'-$&%"('21'C'`'0)"8B32B0)"85'39)%'39)
273073'vB'6$((',)'"'-$%)'6"#)'21'CF'`'0)"8B32B0)"8'"%+'09"-)B-9$13)+'CcF°'6$39'*)-0).3'32'39)
$%073'-$%)'6"#)>'e)."7-)'21'39)'/$%7-'-$&%'"--2.$"3)+'6$39'39)'.(2-)+B(220'&"$%5'39$-'.2%1$&B
7*"3$2%'$-'."(()+'39)'!"#$%&!"'*0."3!')%,&!.">
2.2 The Inverting Configuration
;9)' 1".3' 39"3' 39)' .(2-)+B(220' &"$%' +)0)%+-' )%3$*)(4' 2%' )M3)*%"(' 0"--$#)' .2/02%)%3<*)-$-32*-'?C'"%+'?Q='$-'#)*4'-$&%$1$."%3>'A3'/)"%-'39"3'6)'."%'/"8)'39)'.(2-)+B(220'&"$%'""..7*"3)' "-' 6)' 6"%3' ,4' -)().3$%&' 0"--$#)' .2/02%)%3-' 21' "00*20*$"3)' "..7*".4>' A3' "(-2
/)"%-'39"3'39)'.(2-)+B(220'&"$%'$-'<$+)"((4='$%+)0)%+)%3'21'39)'20B"/0'&"$%>';9$-'$-'"'+*"B
/"3$.'$((7-3*"3$2%'21'%)&"3$#)'1))+,".8:'Y)'-3"*3)+'273'6$39'"%'"/0($1$)*'9"#$%&'#)*4'("*&)
&"$%' $5' "%+' 39*27&9' "00(4$%&' %)&"3$#)' 1))+,".8' 6)' 9"#)' 2,3"$%)+' "' .(2-)+B(220' &"$%
? Q ⁄ ? C'39"3'$-'/7.9'-/"(()*'39"%'$',73'$-'-3",()'"%+'0*)+$.3",()>';9"3'$-5'6)'"*)'3*"+$%&'&"$%
12*'"..7*".4>
2.2.2 Effect of Finite Open-Loop Gain
;9)'02$%3-'W7-3'/"+)'"*)'/2*)'.()"*(4'$((7-3*"3)+',4'+)*$#$%&'"%')M0*)--$2%'12*'39)'.(2-)+B
(220'&"$%'7%+)*'39)'"--7/03$2%'39"3'39)'20B"/0'20)%B(220'&"$%'$'$-'1$%$3)>'S$&7*)'Q>I'-92639)' "%"(4-$->' A1' 6)' +)%23)' 39)' 273073' #2(3"&)' vB5' 39)%' 39)' #2(3"&)' ,)36))%' 39)' 362' $%073
3)*/$%"(-'21'39)'20'"/0'6$((',)' v B ⁄ $>'L$%.)'39)'02-$3$#)'$%073'3)*/$%"('$-'&*27%+)+5'39)
#2(3"&)'"3'39)'%)&"3$#)'$%073'3)*/$%"('/7-3',)' ! v B ⁄ $> ';9)'.7**)%3')C'39*27&9'?C'."%'%26',)
127%+'1*2/
v> ! ( !vB ⁄ $ )
v> + vB ⁄ $
B
) C = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
= BBBBBBBBBBBBBBBBBBBBBBB
?C
?C
Figure 2.7 H%"(4-$-' 21' 39)' $%#)*3$%&
.2%1$&7*"3$2%'3"8$%&'$%32'"..27%3'39)'1$%$3)
20)%B(220'&"$%'21'39)'20'"/0>
;9)'$%1$%$3)'$%073'$/0)+"%.)'21'39)'20'"/0'12*.)-'39)'.7**)%3')C'32'1(26')%3$*)(4'39*27&9
?Q>';9)'273073'#2(3"&)'vB'."%'397-',)'+)3)*/$%)+'1*2/
v
v B = ! BBBBBB ! ) C ? Q
$
v B v > + v B ⁄ $
= ! BBBBB ' ! ' BBBBBBBBBBBBBBBBBBBBBBBB ? Q
?C
$ G2(().3$%&'3)*/-5'39)'.(2-)+B(220'&"$%'A'$-'127%+'"-
v
!?Q ⁄ ?C
B
A ≡ BBBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
C + ( C + ?Q ⁄ ?C ) ⁄ $
v>
<Q>V=
Y)'%23)'39"3'"-'$'"00*2".9)-'∞5'A'"00*2".9)-'39)'$+)"('#"(7)'21' ! ? Q ⁄ ? C > 'H(-25'1*2/'S$&>'Q>I
6)'-))'39"3'"-'$'"00*2".9)-'∞5'39)'#2(3"&)'"3'39)'$%#)*3$%&'$%073'3)*/$%"('"00*2".9)-'[)*2>
;9$-'$-'39)'#$*37"(B&*27%+'"--7/03$2%'6)'7-)+'$%'27*')"*($)*'"%"(4-$-'69)%'39)'20'"/0'6"-
61
62 Chapter 2 Operational Amplifiers
"--7/)+' 32' ,)' $+)"(>' S$%"((45' %23)' 39"3' @K>' <Q>V=' $%' 1".3' $%+$."3)-' 39"3' 32' /$%$/$[)
39) +)0)%+)%.)'21'39)' .(2-)+B(220' &"$%' A'2%' 39)'#"(7)'21'39)' 20)%B(220' &"$%'$5'6)' -927(+
/"8)
?
C + BBBBBQ '$'$
?C
Example 2.1
G2%-$+)*'39)'$%#)*3$%&'.2%1$&7*"3$2%'6$39'?C'='C'8Ω'"%+'?Q'='CFF'8Ω>
<"= S$%+'39)'.(2-)+B(220'&"$%'12*'39)'."-)-'$'='CFT5'CFU5'"%+'CFV>'A%')".9'."-)'+)3)*/$%)'39)'0)*.)%3"&)
)**2*'$%'39)'/"&%$37+)'21'A'*)("3$#)'32'39)'$+)"('#"(7)'21' ? Q ⁄ ? C '<2,3"$%)+'6$39'$'='∞=>'H(-2'+)3)*B
/$%)'39)'#2(3"&)'vC'39"3'"00)"*-'"3'39)'$%#)*3$%&'$%073'3)*/$%"('69)%'v>'='F>C'`>
<,= A1'39)'20)%B(220'&"$%'$'.9"%&)-'1*2/'CFF5FFF'32'VF5FFF'<$>)>5'+*20-',4'VFg=5'69"3'$-'39)'.2**)-02%+B
$%&'0)*.)%3"&)'.9"%&)'$%'39)'/"&%$37+)'21'39)'.(2-)+B(220'&"$%'A\
Solution
<"= L7,-3$373$%&'39)'&$#)%'#"(7)-'$%'@K>'<Q>V=5'6)'2,3"$%'39)'#"(7)-'&$#)%'$%'39)'12((26$%&'3",()5'69)*)'39)
0)*.)%3"&)')**2*'ε'$-'+)1$%)+'"A ! (? ⁄ ? )
( ?Q ⁄ ?C )
Q
C
B × CFF
ε ≡ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
;9)'#"(7)-'21'vC'"*)'2,3"$%)+'1*2/' v C = ! v B ⁄ $ = Av > ⁄ $ '6$39'v>'='F>C'`>
A
|G|
ε
v1
CFT
CFU
CFV
'DF>cT
DD>FF
DD>DF
−D>CIg
−C>FFg
−F>CFg
−D>Fc'/`
−F>DD'/`
−F>CF'/`
<,= a-$%&'@K>'<Q>V=5'6)'1$%+'39"3'12*'$'='VF5FFF5'|A|'='DD>cF>';97-'"'−VFg'.9"%&)'$%'39)'20)%B(220'&"$%
*)-7(3-'$%'"'.9"%&)'21'2%(4'−F>Cg'$%'39)'.(2-)+B(220'&"$%N
2.2.3 Input and Output Resistances
H--7/$%&'"%'$+)"('20'"/0'6$39'$%1$%$3)'20)%B(220'&"$%5'39)'$%073'*)-$-3"%.)'21'39)'.(2-)+B(220
$%#)*3$%&'"/0($1$)*'21'S$&>'Q>V'$-'-$/0(4')K7"('32'?C>';9$-'."%',)'-))%'1*2/'S$&>'Q>E<,=5'69)*)
v
v>
B = ?C
? ) ≡ BBBB> = BBBBBBBBBBBBB
)C
v> ⁄ ?C
P26'*)."(('39"3'$%'L).3$2%'C>V'6)'()"*%)+'39"3'39)'"/0($1$)*'$%073'*)-$-3"%.)'12*/-'"'#2(3"&)
+$#$+)*'6$39'39)'*)-$-3"%.)'21'39)'-27*.)'39"3'1))+-'39)'"/0($1$)*>';97-5'32'"#2$+'39)'(2--'21'-$&%"(
-3*)%&395'#2(3"&)'"/0($1$)*-'"*)'*)K7$*)+'32'9"#)'9$&9'$%073'*)-$-3"%.)>'A%'39)'."-)'21'39)'$%#)*3B
$%&'20B"/0'.2%1$&7*"3$2%'6)'"*)'-37+4$%&5'32'/"8)'?)'9$&9'6)'-927(+'-)().3'"'9$&9'#"(7)'12*'?C>
!26)#)*5'$1'39)'*)K7$*)+'&"$%' ? Q ⁄ ? C $-'"(-2'9$&95'39)%'?Q'.27(+',).2/)'$/0*".3$."((4'("*&)
<)>&>5'&*)"3)*'39"%'"'1)6'/)&29/-=>'Y)'/"4'.2%.(7+)'39"3'39)'$%#)*3$%&'.2%1$&7*"3$2%'-711)*1*2/'"'(26'$%073'*)-$-3"%.)>'H'-2(73$2%'32'39$-'0*2,()/'$-'+$-.7--)+'$%'@M"/0()'Q>Q',)(26>'
2.2 The Inverting Configuration
L$%.)'39)'273073'21'39)'$%#)*3$%&'.2%1$&7*"3$2%'$-'3"8)%'"3'39)'3)*/$%"(-'21'39)'$+)"('#2(3"&)
-27*.)'$<vQ'−'vC='<-))'S$&>'Q>E"=5'$3'12((26-'39"3'39)'273073'*)-$-3"%.)'21'39)'.(2-)+B(220'"/0($B
1$)*'$-'[)*2>
Example 2.2
H--7/$%&'39)'20'"/0'32',)'$+)"(5'+)*$#)'"%')M0*)--$2%'12*'39)'.(2-)+B(220'&"$%' v B ⁄ v > '21'39)'.$*.7$3
-926%'$%'S$&>'Q>c>'a-)'39$-'.$*.7$3'32'+)-$&%'"%'$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'CFF'"%+'"%'$%073
*)-$-3"%.)'21'C'RΩ>'H--7/)'39"3'12*'0*".3$."('*)"-2%-'$3'$-'*)K7$*)+'%23'32'7-)'*)-$-32*-'&*)"3)*'39"%
C'RΩ>'G2/0"*)'427*'+)-$&%'6$39'39"3',"-)+'2%'39)'$%#)*3$%&'.2%1$&7*"3$2%'21'S$&>'Q>V>
5
4
vx
7
x
6
3
2
!
1
"
8
Figure 2.8 G$*.7$3'12*'@M"/0()'Q>Q>';9)'.$*.()+'%7/,)*-'$%+$."3)'39)'-)K7)%.)'21'39)'-3)0-'$%'39)'"%"(4-$->
Solution
;9)'"%"(4-$-',)&$%-'"3'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/05'69)*)'39)'#2(3"&)'$!v
!v
v C = BBBBBBBBBB = BBBBBBBBBB = F
$
∞
!)*)'6)'9"#)'"--7/)+'39"3'39)'.$*.7$3'$-'^62*8$%&_'"%+'0*2+7.$%&'"'1$%$3)'273073'#2(3"&)'vB>'h%26B
$%&'vC5'6)'."%'+)3)*/$%)'39)'.7**)%3')C'"-'12((26-:
v> ! F
v
v> ! vC
B = BBBBBBBBBBBB
B = BBBBB>
) C = BBBBBBBBBBBBBB
?C
?C
?C
L$%.)'[)*2'.7**)%3'1(26-'$%32'39)'$%#)*3$%&'$%073'3)*/$%"(5'"(('21')C'6$(('1(26'39*27&9'?Q5'"%+'397v
) Q = ) C = BBBBB>
?C
P26'6)'."%'+)3)*/$%)'39)'#2(3"&)'"3'%2+)'C:
?
v
v C = v C ! ) Q ? Q = F' ! ' BBBBB> ? Q = ! BBBBBQ v >
?C
?C
63
64 Chapter 2 Operational Amplifiers
Example 2.2 continued
;9$-'$%'37*%')%",()-'7-'32'1$%+'39)'.7**)%3')T:
?Q
F!v
Bv
) T = BBBBBBBBBBBBBC = BBBBBBBBBBB
?T
?C ?T >
P)M35'"'%2+)')K7"3$2%'"3'C'4$)(+-')U:
?Q
v
Bv
) U = ) Q + ) T = BBBBB> + BBBBBBBBBBB
?C ?C ?T >
S$%"((45'6)'."%'+)3)*/$%)'vB'1*2/
vB = vC ! )U ?U
?Q ?
v
Bv ?
= ! BBBBBQ v > ! BBBBB> + BBBBBBBBBBB
?C ?C ?T > U
?C
;97-'39)'#2(3"&)'&"$%'$-'&$#)%',4
vB
?
? ?
BBBBBB = ! BBBBBQ + BBBBBU C + BBBBBQB
v>
?C ?C ?T
69$.9'."%',)'6*$33)%'$%'39)'12*/
?
? ?
vB
BBBBBB = ! BBBBBQ C + BBBBBU + BBBBBU v>
?C ?Q ?T
P265'-$%.)'"%'$%073'*)-$-3"%.)'21'C'RΩ'$-'*)K7$*)+5'6)'-)().3'?C'='C'RΩ>';9)%5'6$39'39)'($/$3"B
3$2%'21'7-$%&'*)-$-32*-'%2'&*)"3)*'39"%'C'RΩ5'39)'/"M$/7/'#"(7)'02--$,()'12*'39)'1$*-3'1".32*'$%'39)
&"$%')M0*)--$2%'$-'C'"%+'$-'2,3"$%)+',4'-)().3$%&'?Q'='C'RΩ>';2'2,3"$%'"'&"$%'21'−CFF5'?T'"%+'?U
/7-3',)'-)().3)+'-2'39"3'39)'-).2%+'1".32*'$%'39)'&"$%')M0*)--$2%'$-'CFF>'A1'6)'-)().3'39)'/"M$/7/
"((26)+'<$%'39$-')M"/0()='#"(7)'21'C'RΩ'12*'?U5'39)%'39)'*)K7$*)+'#"(7)'21'?T'."%',)'."(.7("3)+'32
,)'CF>Q'8Ω>';97-'39$-'.$*.7$3'73$($[)-'39*))'CBRΩ'*)-$-32*-'"%+'"'CF>QB8Ω'*)-$-32*>'A%'.2/0"*$-2%5
$1'39)'$%#)*3$%&'.2%1$&7*"3$2%'6)*)'7-)+'6$39'?C'='C'RΩ'6)'627(+'9"#)'*)K7$*)+'"'1))+,".8'*)-$-B
32*'21'CFF'RΩ5'"%'$/0*".3$."((4'("*&)'#"(7)N
e)12*)'()"#$%&'39$-')M"/0()'$3'$-'$%-$&9317('32'$%K7$*)'$%32'39)'/).9"%$-/',4'69$.9'39)'.$*.7$3'$",()'32'*)"($[)'"'("*&)'#2(3"&)'&"$%'6$39273'7-$%&'("*&)'*)-$-3"%.)-'$%'39)'1))+,".8'0"39>';26"*+'39"3
)%+5'2,-)*#)'39"3',)."7-)'21'39)'#$*37"('&*27%+'"3'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/05'?Q'"%+%?T
"*)'$%')11).3'$%'0"*"(()(>';97-5',4'/"8$%&'?T'(26)*'39"%'?Q',45'-"45'"'1".32*'@'<$>)>5''69)*)'@'>'C=5'?T'$12*.)+'32'."**4'"'.7**)%3'@B3$/)-'39"3'$%'?Q>';97-5'69$()')Q'=')C5')T ='@)C%"%+')U'='<@'+'C=)C>'A3'$-'39)'.7**)%3
/7(3$0($."3$2%',4'"'1".32*'21'<@'+'C='39"3')%",()-'"'("*&)'#2(3"&)'+*20'32'+)#)(20'".*2--'?U'"%+'9)%.)'"
("*&)'vB'6$39273'7-$%&'"'("*&)'#"(7)'12*'?U>'P23$.)'"(-2'39"3'39)'.7**)%3'39*27&9'?U'$-'$%+)0)%+)%3'21'39)
#"(7)'21'?U>'A3'12((26-'39"3'39)'.$*.7$3'."%',)'7-)+'"-'"'.7**)%3'"/0($1$)*'"-'-926%'$%'S$&>'Q>D>'
i2 % iI
i4
R2
R4
R3
v1 % 0
iI
R2
i3 %
i
R3 I
!
"
"
i4 % 1 "
#
R2
i
R3 I
Figure 2.9 H'.7**)%3'"/0($1$)*',"-)+'2%'39)
.$*.7$3' 21' S$&>' Q>c>' ;9)' "/0($1$)*' +)($#)*-' $3273073' .7**)%3' 32' ?U>' A3' 9"-' "' .7**)%3' &"$%' 21
<C +' ?Q /?T=5'"'[)*2'$%073'*)-$-3"%.)5'"%+'"%'$%1$B
%$3)'273073'*)-$-3"%.)>';9)'(2"+'<?U=5'926)#)*5
/7-3',)'1(2"3$%&'<$>)>5'%)$39)*'21'$3-'362'3)*/$B
%"(-'."%',)'.2%%).3)+'32'&*27%+=>
2.2 The Inverting Configuration
EXERCISES
D2.4' a-)'39)'.$*.7$3'21'S$&>'Q>V'32'+)-$&%'"%'$%#)*3$%&'"/0($1$)*'9"#$%&'"'&"$%'21'−CF'"%+'"%'$%073'*)-$-3B
"%.)'21'CFF'8Ω>'i$#)'39)'#"(7)-'21'?C%"%+'?Q>
Ans. ?C'='CFF'8ΩX'?Q'Z'C'RΩ
2.5' ;9)'.$*.7$3'-926%'$%'S$&>'@Q>V<"='."%',)'7-)+'32'$/0()/)%3'"'3*"%-*)-$-3"%.)'"/0($1$)*'<-))';",()
C>C'$%'L).3$2%'C>V=>'S$%+'39)'#"(7)'21'39)'$%073'*)-$-3"%.)'?)5'39)'3*"%-*)-$-3"%.)'?-5'"%+'39)'273073
*)-$-3"%.)'?1'21'39)'3*"%-*)-$-3"%.)'"/0($1$)*>'A1'39)'-$&%"('-27*.)'-926%'$%'S$&>'@Q>V<,='$-'.2%%).3)+
32'39)'$%073'21'39)'3*"%-*)-$-3"%.)'"/0($1$)*5'1$%+'$3-'273073'#2(3"&)>
Ans. ?)'='FX'?-'= −CF'8ΩX'?1'='FX'vB'Z'−V'`
Figure E2.5
2.6' S2*'39)'.$*.7$3'$%'S$&>'@Q>E'+)3)*/$%)'39)'#"(7)-'21'vC5')C5')Q5'vB5')D5'"%+')B>'H(-2'+)3)*/$%)'39)'#2(3"&)
&"$%' v B ⁄ v > 5 '.7**)%3'&"$%' ) D ⁄ ) > 5 '"%+'026)*'&"$%' E B ⁄ E > >
Ans. F'`X'C'/HX'C'/HX'−CF'`X'−CF'/HX'−CC'/HX'−CF'`d`'<QF'+e=5'−CF'HdH'<QF'+e=X'CFF'YdY'<QF'+e=
i2
i1
1 k&
v1
1V
"
!
10 k&
!
"
iO
iL
vO
1 k&
Figure E2.6
2.2.4 An Important Application—The Weighted Summer
H'#)*4'$/02*3"%3'"00($."3$2%'21'39)'$%#)*3$%&'.2%1$&7*"3$2%'$-'39)'6)$&93)+B-7//)*'.$*B
.7$3'-926%'$%'S$&>'Q>CF>'!)*)'6)'9"#)'"'*)-$-3"%.)'?2'$%'39)'%)&"3$#)B1))+,".8'0"39'<",)12*)=X',73'6)'9"#)'"'%7/,)*'21'$%073'-$&%"(-'vC5'vQ5'>'>'>'5' v*')".9'"00($)+'32'"'.2**)B
-02%+$%&'*)-$-32*'?C5'?Q5'>'>'>'5'?*5'69$.9'"*)'.2%%).3)+'32'39)'$%#)*3$%&'3)*/$%"('21'39)'20
"/0>'S*2/'27*'0*)#$27-'+$-.7--$2%5'39)'$+)"('20'"/0'6$(('9"#)'"'#$*37"('&*27%+'"00)"*$%&
65
66 Chapter 2 Operational Amplifiers
"3' $3-' %)&"3$#)' $%073' 3)*/$%"(>' ?9/J-' ("6' 39)%' 3)((-' 7-' 39"3' 39)' .7**)%3-' )C5' )Q5' >' >' >' 5' )*' "*)
&$#)% ,4
v
) C = BBBBCB,
?C
v
) Q = BBBBQB,
?Q
>'>'>',
v
) * = BBBB*B
?*
0
Figure 2.10 H'6)$&93)+'-7//)*>
H(('39)-)'.7**)%3-'-7/'32&)39)*'32'0*2+7.)'39)'.7**)%3')X'39"3'$-5
) = )C + )Q + … + )*
<Q>E=
6$((',)'12*.)+'32'1(26'39*27&9'?2'<-$%.)'%2'.7**)%3'1(26-'$%32'39)'$%073'3)*/$%"(-'21'"%'$+)"('20
"/0=>';9)'273073'#2(3"&)'vB'/"4'%26',)'+)3)*/$%)+',4'"%239)*'"00($."3$2%'21'?9/J-'("65
v B = F ! )? 2 = ! )? 2
;97-5
?2
?2
?2
v B = ! ' BBBBB v C + BBBBB v Q + … + BBBBB v * '
?C
?Q
?*
'<Q>I=
;9"3'$-5'39)'273073'#2(3"&)'$-'"'6)$&93)+'-7/'21'39)'$%073'-$&%"(-'vC5'vQ5'>'>'>'5'v*>';9$-'.$*.7$3
$-'39)*)12*)'."(()+'"'8$!'7&$1*4)++$%>'P23)'39"3')".9'-7//$%&'.2)11$.$)%3'/"4',)'$%+)B
0)%+)%3(4' "+W7-3)+' ,4' "+W7-3$%&' 39)' .2**)-02%+$%&' ^1))+B$%_' *)-$-32*' <?C' 32' ?*=>' ;9$-' %$.)
0*20)*345'69$.9'&*)"3(4'-$/0($1$)-'.$*.7$3'"+W7-3/)%35'$-'"'+$*).3'.2%-)K7)%.)'21'39)'#$*37"(
&*27%+'39"3')M$-3-'"3'39)'$%#)*3$%&'20B"/0'3)*/$%"(>'H-'39)'*)"+)*'6$(('-22%'.2/)'32'"00*).$B
"3)5'#$*37"('&*27%+-'"*)')M3*)/)(4'^9"%+4>_'A%'39)'6)$&93)+'-7//)*'21'S$&>'Q>CF'"(('39)'-7/B
/$%&' .2)11$.$)%3-' /7-3' ,)' 21' 39)' -"/)' -$&%>' ;9)' %))+' 2.."-$2%"((4' "*$-)-' 12*' -7//$%&
-$&%"(-' 6$39' 2002-$3)' -$&%->' L7.9' "' 17%.3$2%' ."%' ,)' $/0()/)%3)+5' 926)#)*5' 7-$%&' 362' 20
"/0-'"-'-926%'$%'S$&>'Q>CC>'H--7/$%&'$+)"('20'"/0-5'$3'."%',)')"-$(4'-926%'39"3'39)'273073
#2(3"&)'$-'&$#)%',4''''
?
?
?
?
?
?
''
v B = v C BBBBB/ BBBBB0 + v Q BBBBB/ BBBBB0 ! v T BBBBB0 ! v U BBBBB0 ''''
?C ?5
?Q ?5
?T
?U
<Q>c=
2.3 The Noninverting Configuration
Rc
Ra
v1
v2
R1
!
Rb
"
R3
!
R2
v3
vO
"
R4
v4
Figure 2.11 H'6)$&93)+'-7//)*'."0",()'21'$/0()/)%3$%&'-7//$%&'.2)11$.$)%3-'21',239'-$&%->
EXERCISES
D2.7' j)-$&%' "%' $%#)*3$%&' 20B"/0' .$*.7$3' 32' 12*/' 39)' 6)$&93)+' -7/' vB' 21' 362' $%073-' vC' "%+' vQ>' A3' $*)K7$*)+'39"3'vB'= − <vC'+'VvQ=>'G922-)'#"(7)-'12*'?C5'?Q5'"%+'?2''-2'39"3'12*'"'/"M$/7/'273073'#2(3B
"&)'21'CF'`'39)'.7**)%3'$%'39)'1))+,".8'*)-$-32*'6$(('%23')M.))+'C'/H>
Ans. H'02--$,()'.92$.):'?C'='CF'8Ω5'?Q'='Q'8Ω5'"%+'?2''='CF'8Ω
D2.8' a-)'39)'$+)"'0*)-)%3)+'$%'S$&>'Q>CC'32'+)-$&%'"'6)$&93)+'-7//)*'39"3'0*2#$+)v B = Qv C + v Q ! Uv T
Ans. H'02--$,()'.92$.):'?C'='V'8Ω5'?Q'='CF'8Ω5'?/%='CF'8Ω5'?5'='CF'8Ω5'?T'='Q>V'8Ω5
?0'='CF'8Ω>''
2.3 The Noninverting Configuration
;9)'-).2%+'.(2-)+B(220'.2%1$&7*"3$2%'6)'-9"(('-37+4'$-'-926%'$%'S$&>'Q>CQ>'!)*)'39)'$%073
-$&%"('v>'$-'"00($)+'+$*).3(4'32'39)'02-$3$#)'$%073'3)*/$%"('21'39)'20'"/0'69$()'2%)'3)*/$%"('21
?C'$-'.2%%).3)+'32'&*27%+>''
2.3.1 The Closed-Loop Gain
H%"(4-$-'21'39)'%2%$%#)*3$%&'.$*.7$3'32'+)3)*/$%)'$3-'.(2-)+B(220'&"$%' ( v B ⁄ v > ) '$-'$((7-3*"3)+
$%' S$&>' Q>CT>' H&"$%' 39)' 2*+)*' 21' 39)' -3)0-' $%' 39)' "%"(4-$-' $-' $%+$."3)+' ,4' .$*.()+' %7/,)*->
H--7/$%&'39"3'39)'20'"/0'$-'$+)"('6$39'$%1$%$3)'&"$%5'"'#$*37"('-92*3'.$*.7$3')M$-3-',)36))%'$3362'$%073'3)*/$%"(->'!)%.)'39)'+$11)*)%.)'$%073'-$&%"('$-
v
v >. = BBBBBB = F
$
12*'$ = ∞ '
;97-'39)'#2(3"&)'"3'39)'$%#)*3$%&'$%073'3)*/$%"('6$((',)')K7"('32'39"3'"3'39)'%2%$%#)*3$%&'$%073
3)*/$%"(5'69$.9'$-'39)'"00($)+'#2(3"&)'v>>';9)'.7**)%3'39*27&9'?C'."%'39)%',)'+)3)*/$%)+'"v > ⁄ ? C>'e)."7-)'21'39)'$%1$%$3)'$%073'$/0)+"%.)'21'39)'20'"/05'39$-'.7**)%3'6$(('1(26'39*27&9
?Q5'"-'-926%'$%'S$&>'Q>CT>'P26'39)'273073'#2(3"&)'."%',)'+)3)*/$%)+'1*2/
v
v B = v > + BBBBB> ? Q
?C
67
68 Chapter 2 Operational Amplifiers
Figure 2.12 ;9)'%2%$%#)*3$%&'.2%1$&7*"3$2%>
5
3
vI
R1
2v
R1
vI
R1
I
! 0
1 vId % 0 V 4
"
"
vI
!
R2
vO % vI "
!
"
R
vI
R % vI 1 " 2
R1 2
R1
6
"
vO
!
Figure 2.13 H%"(4-$-'21'39)'%2%$%#)*3$%&'.$*.7$3>';9)'-)K7)%.)'21'39)'-3)0-'$%'39)'"%"(4-$-'$-'$%+$."3)+',4'
39)'.$*.()+'%7/,)*->
69$.9'4$)(+-
vB
?
BBBBB = C + BBBBBQ '
v>
?C
<Q>D=
S7*39)*'$%-$&93'$%32'39)'20)*"3$2%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'."%',)'2,3"$%)+',4
.2%-$+)*$%&'39)'12((26$%&:'L$%.)'39)'.7**)%3'$%32'39)'20B"/0'$%#)*3$%&'$%073'$-'[)*25'39)'.$*B
.7$3'.2/02-)+'21'?C'"%+'?Q'".3-'$%')11).3'"-'"'#2(3"&)'+$#$+)*'1))+$%&'"'1*".3$2%'21'39)'273073
#2(3"&)',".8'32'39)'$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/0X'39"3'$-5
?C B
v C = v B BBBBBBBBBBBBBBBB
?C + ?Q
'<Q>CF=
;9)%'39)'$%1$%$3)'20B"/0'&"$%'"%+'39)'*)-7(3$%&'#$*37"('-92*3'.$*.7$3',)36))%'39)'362'$%073'3)*/$B
%"(-'21'39)'20'"/0'12*.)-'39$-'#2(3"&)'32',)')K7"('32'39"3'"00($)+'"3'39)'02-$3$#)'$%073'3)*/$%"(X'397-5
?C = v>
v B BBBBBBBBBBBBBBBBB
?C + ?Q
69$.9'4$)(+-'39)'&"$%')M0*)--$2%'&$#)%'$%'@K>'<Q>D=>
;9$-'$-'"%'"00*20*$"3)'02$%3'32'*)1().3'17*39)*'2%'39)'".3$2%'21'39)'%)&"3$#)'1))+,".8'0*)-)%3
$%' 39)' %2%$%#)*3$%&' .$*.7$3' 21' S$&>' Q>CQ>' k)3' v>' $%.*)"-)>' L7.9' "' .9"%&)' $%' v>' 6$((' ."7-)' v>.' 32
$%.*)"-)5'"%+'vB'6$(('.2**)-02%+$%&(4'$%.*)"-)'"-'"'*)-7(3'21'39)'9$&9'<$+)"((4'$%1$%$3)='&"$%'21'39)
20'"/0>'!26)#)*5'"'1*".3$2%'21'39)'$%.*)"-)'$%'vB%6$((',)'1)+',".8'32'39)'$%#)*3$%&'$%073'3)*/$%"(
21'39)'20'"/0'39*27&9'39)'<?C5'?Q='#2(3"&)'+$#$+)*>';9)'*)-7(3'21'39$-'1))+,".8'6$((',)'32'.27%3)*B
".3'39)'$%.*)"-)'$%'v>. 5'+*$#$%&'v>.',".8'32'[)*25'"(,)$3'"3'"'9$&9)*'#"(7)'21'vB'39"3'.2**)-02%+-'32
39)'$%.*)"-)+'#"(7)'21'v> >';9$-'.(<(*(8/&);('".3$2%'21'%)&"3$#)'1))+,".8'&$#)-'$3'39)'"(3)*%"3$#)
%"/)'1$'$"$%,&!#$*3$$15,06>'S$%"((45'%23)'39"3'39)'"*&7/)%3'",2#)'"00($)-')K7"((4'6)(('$1'v>
+).*)"-)->'H'12*/"('"%+'+)3"$()+'-37+4'21'1))+,".8'$-'0*)-)%3)+'$%'G9"03)*'CF>'
2.3 The Noninverting Configuration
2.3.2 Effect of Finite Open-Loop Gain
H-'6)'9"#)'+2%)'12*'39)'$%#)*3$%&'.2%1$&7*"3$2%5'6)'%26'.2%-$+)*'39)')11).3'21'39)'1$%$3)
20B"/0'20)%B(220'&"$%'$'2%'39)'&"$%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%>'H--7/$%&'39)'20'"/0
32',)'$+)"(')M.)03'12*'9"#$%&'"'1$%$3)'20)%B(220'&"$%'$5'$3'."%',)'-926%'39"3'39)'.(2-)+B(220
&"$%'21'39)'%2%$%#)*3$%&'"/0($1$)*'.$*.7$3'21'S$&>'Q>CQ'$-'&$#)%',4
v
C 2 ( ?Q ⁄ ?C )
A ≡ BBBBBB 3 BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
v>
C 2 ( ?Q ⁄ ?C )
C 2 BBBBBBBBBBBBBBBBBBBBBBBBBBBBB
$
"#$%%&
?,-)*#)'39"3'39)'+)%2/$%"32*'$-'$+)%3$."('32'39"3'12*'39)'."-)'21'39)'$%#)*3$%&'.2%1$&7*"3$2%
<@K>'Q>V=>';9$-'$-'%2'.2$%.$+)%.)X'$3'$-'"'*)-7(3'21'39)'1".3'39"3',239'39)'$%#)*3$%&'"%+'39)'%2%B
$%#)*3$%&'.2%1$&7*"3$2%-'9"#)'39)'-"/)'1))+,".8'(2205'69$.9'."%',)'*)"+$(4'-))%'$1'39)'$%073
-$&%"('-27*.)'$-')($/$%"3)+'<$>)>5'-92*3B.$*.7$3)+=>';9)'%7/)*"32*-5'926)#)*5'"*)'+$11)*)%35'12*
39)'%7/)*"32*'&$#)-'39)'$+)"('2*'%2/$%"('.(2-)+B(220'&"$%'< ! ? Q ⁄ ? C '12*'39)'$%#)*3$%&'.2%B
1$&7*"3$2%5'"%+' C 2 ? Q ⁄ ? C 12*'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%=>'S$%"((45'6)'%23)'<6$39'*)"-B
-7*"%.)='39"3'39)'&"$%')M0*)--$2%'$%'@K>'<Q>CC='*)+7.)-'32'39)'$+)"('#"(7)'12*'$'='∞>'A%'1".35'$3
"00*2M$/"3)-'39)'$+)"('#"(7)'12*
?Q
l C 2 BBBBB
$>
l
?C
;9$-'$-'39)'-"/)'.2%+$3$2%'"-'$%'39)'$%#)*3$%&'.2%1$&7*"3$2%5')M.)03'39"3'9)*)'39)'K7"%3$34'2%
39)'*$&93B9"%+'-$+)'$-'39)'%2/$%"('.(2-)+B(220'&"$%>;9)')M0*)--$2%-'12*'39)'".37"('"%+'$+)"(
#"(7)-'21'39)'.(2-)+B(220'&"$%'A'$%'@K->'<Q>CC='"%+'<Q>D=5'*)-0).3$#)(45'."%',)'7-)+'32'+)3)*B
/$%)'39)'0)*.)%3"&)')**2*'$%'A'*)-7(3$%&'1*2/'39)'1$%$3)'20B"/0'&"$%'$'"C 2 ( ?Q ⁄ ?C )
B × CFF
'()*(+,-./0+-())1)- 3 ! BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
$ 2 C 2 ( ?Q ⁄ ?C )
"#$%#&
;97-5'"-'"%')M"/0()5'$1'"%'20'"/0'6$39'"%'20)%B(220'&"$%'21'CFFF'$-'7-)+'32'+)-$&%'"'%2%$%B
#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('.(2-)+B(220'&"$%'21'CF5'6)'627(+')M0).3'39)'.(2-)+B(220
&"$%'32',)'",273'Cg',)(26'39)'%2/$%"('#"(7)>
2.3.3 Input and Output Resistance
;9)'&"$%'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'$-'02-$3$#)f9)%.)'39)'%"/)'*1*)*;(8&)*<>';9)
$%073'$/0)+"%.)'21'39$-'.(2-)+B(220'"/0($1$)*'$-'$+)"((4'$%1$%$3)5'-$%.)'%2'.7**)%3'1(26-'$%32
39)'02-$3$#)'$%073'3)*/$%"('21'39)'20'"/0>';9)'273073'21'39)'%2%$%#)*3$%&'"/0($1$)*'$-'3"8)%
"3'39)'3)*/$%"(-'21'39)'$+)"('#2(3"&)'-27*.)'$<vQ'−'vC='<-))'39)'20B"/0')K7$#"()%3'.$*.7$3'$%
S$&>'Q>T=5'397-'39)'273073'*)-$-3"%.)'21'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'$-'[)*2>
2.3.4 The Voltage Follower
;9)'0*20)*34'21'9$&9'$%073'$/0)+"%.)'$-'"'#)*4'+)-$*",()'1)"37*)'21'39)'%2%$%#)*3$%&'.2%1$&7*"B
3$2%>'A3')%",()-'7-$%&'39$-'.$*.7$3'"-'"',711)*'"/0($1$)*'32'.2%%).3'"'-27*.)'6$39'"'9$&9'$/0)+B
"%.)'32'"'(26B$/0)+"%.)'(2"+>'Y)'9"#)'+$-.7--)+'39)'%))+'12*',711)*'"/0($1$)*-'$%'L).3$2%'C>V>
A%'/"%4'"00($."3$2%-'39)',711)*'"/0($1$)*'$-'%23'*)K7$*)+'32'0*2#$+)'"%4'#2(3"&)'&"$%X'*"39)*5'$3
$-'7-)+'/"$%(4'"-'"%'$/0)+"%.)'3*"%-12*/)*'2*'"'026)*'"/0($1$)*>'A%'-7.9'."-)-'6)'/"4'/"8)
?Q'='F'"%+'?C'='∞'32'2,3"$%'39)')"!&9/',!"*,+(-!3!$%'-926%'$%'S$&> Q>CU<"=>';9$-'.$*.7$3'$.2//2%(4'*)1)**)+'32'"-'"'#.-&,'$*3.--.8$%5'-$%.)'39)'273073'^12((26-_'39)'$%073>'A%'39)'$+)"(
."-)5'vB'= v> 5'?$%'='∞5'?273'='F5'"%+'39)'12((26)*'9"-'39)')K7$#"()%3'.$*.7$3'-926%'$%'S$&>'Q>CU<,=>'
69
70 Chapter 2 Operational Amplifiers
!
"
vI
"
vO % vI
"
!
"
"
"
!
vI
1 ' vI
!
vO
!
!
(b )
(a)
Figure 2.14 :,;';9)'7%$34B&"$%',711)*'2*'12((26)*'"/0($1$)*>':5;'A3-')K7$#"()%3'.$*.7$3'/2+)(>
L$%.)'$%'39)'#2(3"&)B12((26)*'.$*.7$3'39)')%3$*)'273073'$-'1)+',".8'32'39)'$%#)*3$%&'$%0735
39)'.$*.7$3'$-'-"$+'32'9"#)'CFFg'%)&"3$#)'1))+,".8>';9)'$%1$%$3)'&"$%'21'39)'20'"/0'39)%'".332'/"8)'v>.'='F'"%+'9)%.)'vB'='v>>'?,-)*#)'39"3'39)'.$*.7$3'$-')()&"%3'$%'$3-'-$/0($.$34N'
L$%.)'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%'9"-'"'&"$%'&*)"3)*'39"%'2*')K7"('32'7%$345'+)0)%+$%&
2%'39)'.92$.)'21' ? Q ⁄ ? C5'-2/)'0*)1)*'32'."(('$3'^"'12((26)*'6$39'&"$%>_'''
EXERCISES
2.9' a-)'39)'-70)*02-$3$2%'0*$%.$0()'32'1$%+'39)'273073'#2(3"&)'21'39)'.$*.7$3'-926%'$%'S$&>'@Q>D>
Ans. vB'='EvC'+'UvQ
Figure E2.9
2.10' A1'$%'39)'.$*.7$3'21'S$&>'@Q>D'39)'CB8Ω'*)-$-32*'$-'+$-.2%%).3)+'1*2/'&*27%+'"%+'.2%%).3)+'32'"'39$*+
-$&%"('-27*.)'vT5'7-)'-70)*02-$3$2%'32'+)3)*/$%)'vB'$%'3)*/-'21'vC5'vQ5'"%+'vT>
Ans. vB'='EvC'+'UvQ'−'DvT'
D2.11 j)-$&%'"'%2%$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'Q>'H3'39)'/"M$/7/'273073'#2(3"&)'21'CF'`'39)'.7*B
*)%3'$%'39)'#2(3"&)'+$#$+)*'$-'32',)'CF'µH>
Ans. ?C'='?Q'='F>V'RΩ
2.12' <"='L926'39"3'$1'39)'20'"/0'$%'39)'.$*.7$3'21'S$&>'Q>CQ'9"-'"'1$%$3)'20)%B(220'&"$%'$5'39)%'39)'.(2-)+B
(220'&"$%'$-'&$#)%',4'@K>'<Q>CC=>'<,='S2*'?C'='C'8Ω'"%+'?Q'='D'8Ω'1$%+'39)'0)*.)%3"&)'+)#$"3$2%'ε
21'39)'.(2-)+B(220'&"$%'1*2/'39)'$+)"('#"(7)'21' ( C 2 ? Q ⁄ ? C ) '12*'39)'."-)-'$'='CFT5'CFU5'"%+'CFV>
S2*'v>'='C'`5'1$%+'$%')".9'."-)'39)'#2(3"&)',)36))%'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0>
Ans. ε'='−Cg5'− F>Cg5 − F>FCgX'vQ'−'vC'='D>D'/`5'C'/`5'F>C'/`
2.4 Difference Amplifiers
2.13' S2*'39)'.$*.7$3'$%'S$&>'@Q>CT'1$%+'39)'#"(7)-'21')>5'vC5')C5')Q5'vB5%)D5'"%+')B>'H(-2'1$%+'39)'#2(3"&)'&"$%
v B ⁄ v > 5 '39)'.7**)%3'&"$%' ) D ⁄ ) > 5 '"%+'39)'026)*'&"$%' E D ⁄ E > >
Ans. FX'C'`X'C'/HX'C'/HX'CF'`X'CF'/HX'CC'/HX'CF'`d`'<QF'+e=X'∞X'∞
i2 9 k&
i1 1 k&
v1
!
iO
"
iL
iI
vI % 1 V
vO
1 k&
"
!
Figure E2.13
2.14' A3'$-'*)K7$*)+'32'.2%%).3'"'3*"%-+7.)*'9"#$%&'"%'20)%B.$*.7$3'#2(3"&)'21'C'`'"%+'"'-27*.)'*)-$-3"%.)
21'C RΩ'32'"'(2"+'21'CB8Ω'*)-$-3"%.)>'S$%+'39)'(2"+'#2(3"&)'$1'39)'.2%%).3$2%'$-'+2%)'<"='+$*).3(4'"%+
<,= 39*27&9'"'7%$34B&"$%'#2(3"&)'12((26)*>
Ans. <"='C'/`X'<,='C'`
2.4 Difference Amplifiers
!"#$%&'-37+$)+'39)'362',"-$.'.2%1$&7*"3$2%-'21'20B"/0'.$*.7$3-'32&)39)*'6$39'-2/)'21'39)$*
+$*).3' "00($."3$2%-5' 6)' "*)' %26' *)"+4' 32' .2%-$+)*' "' -2/)69"3' /2*)' $%#2(#)+' ,73' #)*4
$/02*3"%3'"00($."3$2%>'L0).$1$."((45'6)'-9"(('-37+4'39)'7-)'21'20'"/0-'32'+)-$&%'+$11)*)%.)'2*
+$11)*)%3$"('"/0($1$)*->Q'H'+$11)*)%.)'"/0($1$)*'$-'2%)'39"3'*)-02%+-'32'39)'+$11)*)%.)',)36))%
39)'362'-$&%"(-'"00($)+'"3'$3-'$%073'"%+'$+)"((4'*)W).3-'-$&%"(-'39"3'"*)'.2//2%'32'39)'362
$%073->';9)'*)0*)-)%3"3$2%'21'-$&%"(-'$%'3)*/-'21'39)$*'+$11)*)%3$"('"%+'.2//2%B/2+)'.2/B
02%)%3-'6"-'&$#)%'$%'S$&>'Q>U>'A3'$-'*)0)"3)+'9)*)'$%'S$&>'Q>CV'6$39'-($&93(4'+$11)*)%3'-4/,2(32'-)*#)'"-'39)'$%073'-$&%"(-'12*'39)'+$11)*)%.)'"/0($1$)*-'6)'"*)'",273'32'+)-$&%>'H(3927&9
$+)"((4'39)'+$11)*)%.)'"/0($1$)*'6$(('"/0($14'2%(4'39)'+$11)*)%3$"('$%073'-$&%"('v>.'"%+'*)W).3
.2/0()3)(4'39)'.2//2%B/2+)'$%073'-$&%"('v>0-5'0*".3$."('.$*.7$3-'6$(('9"#)'"%'273073'#2(3"&)
vB'&$#)%',4
v B = $ . v >. + $ 0- v >0-
<Q>CT=
69)*)'$.'+)%23)-'39)'"/0($1$)*'+$11)*)%3$"('&"$%'"%+'$0-'+)%23)-'$3-'.2//2%B/2+)'&"$%'<$+)B
"((4'[)*2=>';9)')11$.".4'21'"'+$11)*)%3$"('"/0($1$)*'$-'/)"-7*)+',4'39)'+)&*))'21'$3-'*)W).3$2%
21'.2//2%B/2+)'-$&%"(-'$%'0*)1)*)%.)'32'+$11)*)%3$"('-$&%"(->';9$-'$-'7-7"((4'K7"%3$1$)+',4'"
/)"-7*)'8%26%'"-'39)'0.++."/+.1$*%$2$0&!."*%,&!.*:<=>>;5'+)1$%)+'"-
$.
B
GROO = QF'(2& BBBBBBBBBBB
$ 0Q
<Q>CU=
;9)'3)*/-'.)22(8(*0('"%+'.)22(8(*&)/3'"*)'7-7"((4'7-)+'32'+)-.*$,)'-2/)69"3'+$11)*)%3'"/0($1$)*'340)->'
S2*'27*'07*02-)-'"3'39$-'02$%35'39)'+$-3$%.3$2%'$-'%23'-711$.$)%3(4'-$&%$1$."%3>'Y)'6$((',)'/2*)'0*).$-)'%)"*'
39)')%+'21'39$-'-).3$2%>
71
72 Chapter 2 Operational Amplifiers
vI1 % vIcm ! vId #2
!
"
vId #2
vId % vI2 ! vI1
1
2
vIcm % (vI1 " vI2)
vIcm
"
!
!
"
vId #2
vI2 % vIcm " vId #2
Figure 2.15 O)0*)-)%3$%&'39)'$%073'-$&%"(-'32'"
+$11)*)%3$"('"/0($1$)*' $%'3)*/-'21' 39)$*' +$11)*)%3$"(
"%+'.2//2%B/2+)'.2/02%)%3->
;9)'%))+'12*'+$11)*)%.)'"/0($1$)*-'"*$-)-'1*)K7)%3(4'$%'39)'+)-$&%'21')().3*2%$.'-4-3)/-5')-0)B
.$"((4'392-)')/0(24)+'$%'$%-3*7/)%3"3$2%>'H-'"'.2//2%')M"/0()5'.2%-$+)*'"'3*"%-+7.)*'0*2B
#$+$%&' "'-/"(('<)>&>5'C'/`='-$&%"(' ,)36))%'$3-' 362'273073'3)*/$%"(-'69$()' )".9' 21'39)' 362
6$*)-'()"+$%&'1*2/' 39)'3*"%-+7.)*'3)*/$%"(-'32'39)'/)"-7*$%&'$%-3*7/)%3'/"4'9"#)'"'("*&)
$%3)*1)*)%.)'-$&%"('<)>&>5'C'`='*)("3$#)'32'39)'.$*.7$3'&*27%+>';9)'$%-3*7/)%3'1*2%3')%+'2,#$B
27-(4'%))+-'"'+$11)*)%.)'"/0($1$)*>
e)12*)'6)'0*2.))+'"%4'17*39)*'6)'-927(+'"++*)--'"'K7)-3$2%'39"3'39)'*)"+)*'/$&93'9"#):
;9)'20'"/0'$-'$3-)(1'"'+$11)*)%.)'"/0($1$)*X'694'%23'W7-3'7-)'"%'20'"/0\';9)'"%-6)*'$-'39"3
39)'#)*4'9$&9'<$+)"((4'$%1$%$3)='&"$%'21'39)'20'"/0'/"8)-'$3'$/02--$,()'32'7-)',4'$3-)(1>'O"39)*5
"-'6)'+$+',)12*)5'6)'9"#)'32'+)#$-)'"%'"00*20*$"3)'1))+,".8'%)362*8'32'.2%%).3'32'39)'20
"/0'32'.*)"3)'"'.$*.7$3'692-)'.(2-)+B(220'&"$%'$-'1$%$3)5'0*)+$.3",()5'"%+'-3",()>
2.4.1 A Single-Op-Amp Difference Amplifier
?7*'1$*-3'"33)/03'"3'+)-$&%$%&'"'+$11)*)%.)'"/0($1$)*'$-'/23$#"3)+',4'39)'2,-)*#"3$2%'39"3'39)
&"$%'21'39)'%2%$%#)*3$%&'"/0($1$)*'.2%1$&7*"3$2%'$-'02-$3$#)5' ( C 2 ? Q ⁄ ? C )5 '69$()'39"3'21'39)
$%#)*3$%&'.2%1$&7*"3$2%'$-'%)&"3$#)5'( ! ? Q ⁄ ? C )>'G2/,$%$%&'39)'362'.2%1$&7*"3$2%-'32&)39)*'$39)%'"'-3)0'$%'39)'*$&93'+$*).3$2%⎯%"/)(45'&)33$%&'39)'+$11)*)%.)',)36))%'362'$%073'-$&%"(->
?1'.27*-)5'6)'9"#)'32'/"8)'39)'362'&"$%'/"&%$37+)-')K7"('$%'2*+)*'32'*)W).3'.2//2%B/2+)
-$&%"(->' ;9$-5' 926)#)*5' ."%' ,)' )"-$(4' ".9$)#)+' ,4' "33)%7"3$%&' 39)' 02-$3$#)' $%073' -$&%"(' 32
*)+7.)'39)'&"$%'21'39)'02-$3$#)'0"39'1*2/' ( C 2 ? Q ⁄ ? C ) '32' ( ? Q ⁄ ? C ) >';9)'*)-7(3$%&'.$*.7$3
627(+'39)%'(228'($8)'39"3'-926%'$%'S$&>'Q>CE5'69)*)'39)'"33)%7"3$2%'$%'39)'02-$3$#)'$%073'0"39
$-'".9$)#)+',4'39)'#2(3"&)'+$#$+)*'<?T5'?U=>';9)'0*20)*'*"3$2'21'39$-'#2(3"&)'+$#$+)*'."%',)
+)3)*/$%)+'1*2/
?U ?
?
BBBBBBBBBBBBBBBBB
C + BBBBBQ = BBBBBQ
?U + ?T ?C
?C
69$.9'."%',)'073'$%'39)'12*/
?U
?Q
BBBBBBBBBBBBBBBBB
= BBBBBBBBBBBBBBBBB
?U + ?T
?Q + ?C
;9$-'.2%+$3$2%'$-'-"3$-1$)+',4'-)().3$%&
?
?
BBBBBU = BBBBBQ
?T
?C
<Q>CV=
2.4 Difference Amplifiers
vI 1
vI 2
Figure 2.16 H'+$11)*)%.)'"/0($1$)*>
;9$-'.2/0()3)-'27*'62*8>'!26)#)*5'6)'9"#)'0)*9"0-'0*2.))+)+'"'($33()'322'1"-3N'k)3J-'-3)0
,".8'"%+'#)*$14'39"3'39)'.$*.7$3'$%'S$&>'Q>CE'6$39'?T'"%+'?U'-)().3)+'"..2*+$%&'32'@K>'<Q>CV=
+2)-'$%'1".3'17%.3$2%'"-'"'+$11)*)%.)'"/0($1$)*>'L0).$1$."((45'6)'6$-9'32'+)3)*/$%)'39)'273073
#2(3"&)'vB'$%'3)*/-'21'v>C'"%+'v> Q>';26"*+'39"3')%+5'6)'2,-)*#)'39"3'39)'.$*.7$3'$-'($%)"*5'"%+
397-'6)'."%'7-)'-70)*02-$3$2%>
;2' "00(4' -70)*02-$3$2%5' 6)' 1$*-3' *)+7.)' v> Q' 32' [)*2⎯39"3' $-5' &*27%+' 39)' 3)*/$%"(' 32
69$.9' v>Q' $-' "00($)+⎯"%+' 39)%' 1$%+' 39)' .2**)-02%+$%&' 273073' #2(3"&)5' 69$.9' 6$((' ,)' +7)
)%3$*)(4'32'v>C>'Y)'+)%23)'39$-'273073'#2(3"&)'vBC>'A3-'#"(7)'/"4',)'127%+'1*2/'39)'.$*.7$3'$%
S$&>'Q>CI<"=5'69$.9'6)'*).2&%$[)'"-'39"3'21'39)'$%#)*3$%&'.2%1$&7*"3$2%>';9)')M$-3)%.)'21'?T
"%+'?U'+2)-'%23'"11).3'39)'&"$%')M0*)--$2%5'-$%.)'%2'.7**)%3'1(26-'39*27&9')$39)*'21'39)/>
;97-5
?
v BC 3 ! BBBBBQ v >C
?C
P)M35'6)'*)+7.)'v>C'32'[)*2'"%+')#"(7"3)'39)'.2**)-02%+$%&'273073'#2(3"&)'vBQ>';9)'.$*.7$3
6$(('%26'3"8)'39)'12*/'-926%'$%'S$&>'Q>CI<,=5'69$.9'6)'*).2&%$[)'"-'39)'%2%$%#)*3$%&'.2%B
1$&7*"3$2%'6$39'"%'"++$3$2%"('#2(3"&)'+$#$+)*5'/"+)'70'21'?T'"%+'?U5'.2%%).3)+'32'39)'$%073
v>Q>';9)'273073'#2(3"&)'vBQ'$-'39)*)12*)'&$#)%',4
?U ?
?
B C + BBBBBQ = BBBBBQ v >Q
v BQ = v >Q BBBBBBBBBBBBBBBB
?T + ?U
?C
?C
69)*)'6)'9"#)'73$($[)+'@K>'<Q>CV=>
;9)'-70)*02-$3$2%'0*$%.$0()'3)((-'7-'39"3'39)'273073'#2(3"&)'vB'$-')K7"('32'39)'-7/'21'vBC
"%+'vBQ>';97-'6)'9"#)
?
?C
?
?C
'v B = BBBBBQ ( v >Q ! v >C )' = BBBBBQ v >. ''''
<Q>CE=
;97-5'"-')M0).3)+5'39)'.$*.7$3'".3-'"-'"'+$11)*)%.)'"/0($1$)*'6$39'"'+$11)*)%3$"('&"$%'$.'21
?
$ . = BBBBBQ
?C
<Q>CI=
?1'.27*-)'39$-'$-'0*)+$."3)+'2%'39)'20'"/0',)$%&'$+)"('"%+'17*39)*/2*)'2%'39)'-)().3$2%'21'?T
"%+' ?U' -2' 39"3' 39)$*' *"3$2' /"3.9)-' 39"3' 21' ?C' "%+' ?Q' <@K>' Q>CV=>' ;2' /"8)' 39$-' /"3.9$%&
*)K7$*)/)%3'"'($33()')"-$)*'32'-"3$-145'6)'7-7"((4'-)().3
73
74 Chapter 2 Operational Amplifiers
vI1
vI 2
Figure 2.17 H00($."3$2%'21'-70)*02-$3$2%'32'39)'"%"(4-$-'21'39)'.$*.7$3'21'S$&>'Q>CE>
?T = ?C
"%+
?U = ?Q
k)3J-' %)M3' .2%-$+)*' 39)' .$*.7$3' 6$39' 2%(4' "' .2//2%B/2+)' -$&%"(' "00($)+' "3' 39)' $%0735' "-926%'$%'S$&>'Q>Cc>';9)'1$&7*)'"(-2'-926-'-2/)'21'39)'"%"(4-$-'-3)0->';97-5
?U
C
Bv
) C = BBBBB v >0- ! BBBBBBBBBBBBBBBB
? U + ? T >0?C
?T C
BBBBB
= v >0- BBBBBBBBBBBBBBBBB
?U + ?T ?C
<Q>Cc=
;9)'273073'#2(3"&)'."%'%26',)'127%+'1*2/'
?U
Bv ! ) ?
v B = BBBBBBBBBBBBBBBB
? U + ? T >0- Q Q
L7,-3$373$%&')Q'=')C'"%+'12*')C'1*2/'@K>'<Q>Cc=5
?
?
?
?U + ?T
?C ?U + ?T
?U ?Q ?T = BBBBBBBBBBBBBBBBB C ! BBBBB ' BBBBB v >0?U + ?T ?C ?U
U
T
B v >0- ! BBBBBQ BBBBBBBBBBBBBBBB
B v >0' v B = BBBBBBBBBBBBBBBB
;97-5
vB
?U ? ?
B C ! BBBBBQ ' BBBBBT $ 0- ≡ BBBBBBBB
= BBBBBBBBBBBBBBBB
?U + ?T v >0?C ?U
<Q>CD=
S2*'39)'+)-$&%'6$39'39)'*)-$-32*'*"3$2-'-)().3)+'"..2*+$%&'32'@K>'<Q>CV=5'6)'2,3"$%
$ 0- = F
"-')M0).3)+>'P23)5'926)#)*5'39"3'"%4'/$-/"3.9'$%'39)'*)-$-3"%.)'*"3$2-'."%'/"8)'$0-'%2%[)*25
"%+'9)%.)'GROO'1$%$3)>''
A%'"++$3$2%'32'*)W).3$%&'.2//2%B/2+)'-$&%"(-5'"'+$11)*)%.)'"/0($1$)*'$-'7-7"((4'*)K7$*)+
32'9"#)'"'9$&9'$%073'*)-$-3"%.)>';2'1$%+'39)'$%073'*)-$-3"%.)',)36))%'39)'362'$%073'3)*/$%"(-
2.4 Difference Amplifiers
i2
i1
R2
R1
!
vO
"
R3
vIcm
"
!
"
#
R4
R4
v
R4 " R3 Icm
Figure 2.18 H%"(4-$-'21'39)'+$11)*)%.)'"/0($1$)*'32'+)3)*/$%)'$3-'.2//2%B/2+)'&"$%' $ 0- ≡ v B ⁄ v >0- > '
<$>)>5'39)'*)-$-3"%.)'-))%',4'v>.=5'."(()+'39)'1!33$%$"&!,-*!"()&*%$4!4&,"0$'?). 5'.2%-$+)*'S$&>'Q>CD>
!)*)'6)'9"#)'"--7/)+'39"3'39)'*)-$-32*-'"*)'-)().3)+'-2'39"3
?T = ?C
"%+
?U = ?Q
P26
v
? ). ≡ BBBBB>.B
)>
L$%.)'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0'3*".8')".9'239)*'$%'023)%3$"(5'6)'/"4'6*$3)'"
(220')K7"3$2%'"%+'2,3"$%
v >. = ? C ) > + F + ? C ) >
;97-5
? ). = Q? C
<Q>QF=
P23)'39"3'$1'39)'"/0($1$)*'$-'*)K7$*)+'32'9"#)'"'("*&)'+$11)*)%3$"('&"$%' ( ? Q ⁄ ? C ) 5'39)%'?C'21
%).)--$34' 6$((' ,)' *)("3$#)(4' -/"((' "%+' 39)' $%073' *)-$-3"%.)' 6$((' ,)' .2**)-02%+$%&(4' (265' "
+*"6,".8'21'39$-'.$*.7$3>'H%239)*'+*"6,".8'21'39)'.$*.7$3'$-'39"3'$3'$-'%23')"-4'32'#"*4'39)'+$1B
1)*)%3$"('&"$%'21'39)'"/0($1$)*>'e239'21'39)-)'+*"6,".8-'"*)'2#)*.2/)'$%'39)'$%-3*7/)%3"3$2%
"/0($1$)*'+$-.7--)+'%)M3>''
I
vId
Rid
I
Figure 2.19 S$%+$%&'39)'$%073'*)-$-B
3"%.)' 21' 39)' +$11)*)%.)' "/0($1$)*' 12*
39)'."-)'?T'='?C'"%+'?U'='?Q>
75
76 Chapter 2 Operational Amplifiers
EXERCISES
2.15 G2%-$+)*'39)'+$11)*)%.)B"/0($1$)*'.$*.7$3'21'S$&>'Q>CE'12*'39)'."-)'?C'='?T'='Q'8Ω'"%+'?Q'='?U'=
QFF 8Ω>'<"='S$%+'39)'#"(7)'21'39)'+$11)*)%3$"('&"$%'$.>'<,='S$%+'39)'#"(7)'21'39)'+$11)*)%3$"('$%073
*)-$-3"%.)'?).'"%+'39)'273073'*)-$-3"%.)'?1>'<.='A1'39)'*)-$-32*-'9"#)'Cg'32()*"%.)'<$>)>5')".9'."%',)
6$39$%'±Cg'21'$3-'%2/$%"('#"(7)=5'7-)'@K>'<Q>CD='32'1$%+'39)'62*-3B."-)'.2//2%B/2+)'&"$%'$0"%+'9)%.)'39)'.2**)-02%+$%&'#"(7)'21'GROO>
Ans. <"='CFF'`d`'<UF'+e=X'<,='U'8Ω5'F'ΩX'<.='F>FU'`d`5'Ec'+e
D2.16 S$%+'#"(7)-'12*'39)'*)-$-3"%.)-'$%'39)'.$*.7$3'21'S$&>'Q>CE'-2'39"3'39)'.$*.7$3',)9"#)-'"-'"'+$11)*)%.)
"/0($1$)*'6$39'"%'$%073'*)-$-3"%.)'21'QF'8Ω'"%+'"'&"$%'21'CF>
Ans. ?C'='?T'='CF'8ΩX'?Q'='?U'='CFF'8Ω
2.4.2 A Superior Circuit—The Instrumentation Amplifier
;9)'(26B$%073B*)-$-3"%.)'0*2,()/'21'39)'+$11)*)%.)'"/0($1$)*'21'S$&>'Q>CE'."%',)'-2(#)+',4'7-$%&
#2(3"&)'12((26)*-'32',711)*'39)'362'$%073'3)*/$%"(-X'39"3'$-5'"'#2(3"&)'12((26)*'21'39)'340)'$%'S$&>'Q>CU
$-'.2%%).3)+',)36))%')".9'$%073'3)*/$%"('"%+'39)'.2**)-02%+$%&'$%073'3)*/$%"('21'39)'+$11)*)%.)
"/0($1$)*>'!26)#)*5'$1'6)'"*)'&2$%&'32'7-)'362'"++$3$2%"('20'"/0-5'6)'-927(+'"-8'39)'K7)-3$2%:'G"%
6)' &)3' /2*)' 1*2/' 39)/' 39"%' W7-3' $/0)+"%.)' ,711)*$%&\' H%' 2,#$27-' "%-6)*' 627(+' ,)' 39"3' 6)
-927(+'3*4'32'&)3'-2/)'#2(3"&)'&"$%>'A3'$-')-0).$"((4'$%3)*)-3$%&'39"3'6)'."%'".9$)#)'39$-'6$39273'.2/B
0*2/$-$%&'39)'9$&9'$%073'*)-$-3"%.)'-$/0(4',4'7-$%&'12((26)*-'6$39'&"$%'*"39)*'39"%'7%$34B&"$%'12(B
(26)*->' H.9$)#$%&' -2/)' 2*' $%+))+' 39)' ,7(8' 21' 39)' *)K7$*)+' &"$%' $%' 39$-' %)6' 1$*-3' -3"&)' 21' 39)
"1 " RR # v
2
vI1
"
A1
!
R2
1
I1
R4
R1
R3
!
A3
"
X
R1
R3
R2
R4
"
vO
!
vI2
!
A2
"
"1 " RR # v
2
1
I2
(a)
Figure 2.20 H'0207("*'.$*.7$3'12*'"%'$%-3*7/)%3"3$2%'"/0($1$)*>':,;'A%$3$"('"00*2".9'32'39)'.$*.7$3':5;';9)
.$*.7$3'$%':,;'6$39'39)'.2%%).3$2%',)36))%'%2+)'m'"%+'&*27%+'*)/2#)+'"%+'39)'362'*)-$-32*-'?C'"%+'?C'(7/0)+
32&)39)*>' ;9$-' -$/0()' 6$*$%&' .9"%&)' +*"/"3$."((4' $/0*2#)-' 0)*12*/"%.)>' :0;' H%"(4-$-' 21' 39)' .$*.7$3' $%
:5; "--7/$%&'$+)"('20'"/0->
2.4 Difference Amplifiers
vI1
"
A1
!
R4
R2
R3
!
2R1
!
A3
R3
"
R2
vO
R4
A2
vI2
"
!
"
(b)
vI1
"
"
0
vI1
! R
2
R4
R3
vId /2R1
!
(vI2 ! vI1)
% vId
"
vI2
vI2
vO1
A1
0V
!
2R1
!
0V
"
!
2R2
vId 1 "
2R1
"
vId
2R1
vId /2R1
0
!
A3
"
R3
R4
R2
A2
!
"
vO %
R4
R
1" 2
R3
R1
vId
!
vO2
"
(c )
Figure 2.20 <"1*&)*,(.=
+$11)*)%3$"('"/0($1$)*')"-)-'39)',7*+)%'2%'39)'+$11)*)%.)'"/0($1$)*'$%'39)'-).2%+'-3"&)5'()"#$%&'$3'32
$3-'/"$%'3"-8'21'$/0()/)%3$%&'39)'+$11)*)%.$%&'17%.3$2%'"%+'397-'*)W).3$%&'.2//2%B/2+)'-$&%"(->
;9)'*)-7(3$%&'.$*.7$3'$-'-926%'$%'S$&>'Q>QF<"=>'A3'.2%-$-3-'21'362'-3"&)-'$%'."-."+)>';9)'1$*-3
-3"&)'$-'12*/)+',4'20'"/0-'$C'"%+'$Q'"%+'39)$*'"--2.$"3)+'*)-$-32*-5'"%+'39)'-).2%+'-3"&)'$-'39)
,4B%26B1"/$($"*'+$11)*)%.)'"/0($1$)*'12*/)+',4'20'"/0'$T'"%+'$3-'127*'"--2.$"3)+'*)-$-32*->
?,-)*#)'39"3'"-'6)'-)3'273'32'+25')".9'21'$C'"%+'$Q'$-'.2%%).3)+'$%'39)'%2%$%#)*3$%&'.2%1$&7*"B
3$2%'"%+'397-'*)"($[)-'"'&"$%'21'( C + ? Q ⁄ ? C )>'A3'12((26-'39"3')".9'21'v>C'"%+'v>Q'$-'"/0($1$)+',4
39$-'1".32*5'"%+'39)'*)-7(3$%&'"/0($1$)+'-$&%"(-'"00)"*'"3'39)'273073-'21'$C'"%+'$Q5'*)-0).3$#)(4>
;9)' +$11)*)%.)' "/0($1$)*' $%' 39)' -).2%+' -3"&)' 20)*"3)-' 2%' 39)' +$11)*)%.)' -$&%"(
( C + ? Q ⁄ ? C ) ( v >Q ! v >C ) =' ( C + ? Q ⁄ ? C )v >. '"%+'0*2#$+)-'"3'$3-'273073
?
?
v B = BBBBBU C + BBBBBQ v >.
?T
?C
;97-'39)'+$11)*)%3$"('&"$%'*)"($[)+'$-
?
?
$ . = BBBBBU C + BBBBBQ
?T ?C
<Q>QC=
77
78 Chapter 2 Operational Amplifiers
;9)'.2//2%B/2+)'&"$%'6$((',)'[)*2',)."7-)'21'39)'+$11)*)%.$%&'".3$2%'21'39)'-).2%+B-3"&)
"/0($1$)*>
;9)'.$*.7$3'$%'S$&>'Q>QF<"='9"-'39)'"+#"%3"&)'21'#)*4'9$&9'<$+)"((4'$%1$%$3)='$%073'*)-$-B
3"%.)'"%+'9$&9'+$11)*)%3$"('&"$%>'H(-25'0*2#$+)+'$C'"%+'$Q'"%+'39)$*'.2**)-02%+$%&'*)-$-32*"*)'/"3.9)+5'39)'362'-$&%"('0"39-'"*)'-4//)3*$.⎯"'+)1$%$3)'"+#"%3"&)'$%'39)'+)-$&%'21'"'+$1B
1)*)%3$"('"/0($1$)*>';9)'.$*.7$35'926)#)*5'9"-'39*))'/"W2*'+$-"+#"%3"&)-:
1. ;9)'$%073'.2//2%B/2+)'-$&%"('v>0-'$-'"/0($1$)+'$%'39)'1$*-3'-3"&)',4'"'&"$%')K7"('32
39"3')M0)*$)%.)+',4'39)'+$11)*)%3$"('-$&%"('v>.>';9$-'$-'"'#)*4'-)*$27-'$--7)5'12*'$3'.27(+
*)-7(3'$%'39)'-$&%"(-'"3'39)'273073-'21'$C'"%+'$T',)$%&'21'-7.9'("*&)'/"&%$37+)-'39"3'39)
20'"/0-'-"37*"3)'</2*)'2%'20B"/0'-"37*"3$2%'$%'L).3$2%'Q>c=>'e73')#)%'$1'39)'20'"/0+2' %23' -"37*"3)5' 39)' +$11)*)%.)' "/0($1$)*' 21' 39)' -).2%+' -3"&)' 6$((' %26' 9"#)' 32' +)"(
6$39'/7.9'("*&)*'.2//2%B/2+)'-$&%"(-5'6$39'39)'*)-7(3'39"3'39)'GROO'21'39)'2#)*"((
"/0($1$)*'6$(('$%)#$3",(4',)'*)+7.)+>
2. ;9)'362'"/0($1$)*'.9"%%)(-'$%'39)'1$*-3'-3"&)'9"#)'32',)'0)*1).3(4'/"3.9)+5'239)*6$-)
"' -07*$27-' -$&%"(' /"4' "00)"*' ,)36))%' 39)$*' 362' 273073->' L7.9' "' -$&%"(' 627(+' &)3
"/0($1$)+',4'39)'+$11)*)%.)'"/0($1$)*'$%'39)'-).2%+'-3"&)>
3. ;2'#"*4'39)'+$11)*)%3$"('&"$%'$. 5'362'*)-$-32*-'9"#)'32',)'#"*$)+'-$/7(3"%)27-(45'-"4
39)'362'*)-$-32*-'(",)()+'?C>'H3')".9'&"$%'-)33$%&'39)'362'*)-$-32*-'9"#)'32',)'0)*1).3(4
/"3.9)+:'"'+$11$.7(3'3"-8>
H(('39*))'0*2,()/-'."%',)'-2(#)+'6$39'"'#)*4'-$/0()'6$*$%&'.9"%&):'L$/0(4'+$-.2%%).3'39)
%2+)',)36))%'39)'362'*)-$-32*-'(",)()+'?C5'%2+)'m5'1*2/'&*27%+>';9)'.$*.7$3'6$39'39$-'-/"((
,73'17%.3$2%"((4'0*2127%+'.9"%&)'$-'*)+*"6%'$%'S$&>'Q>QF<,=5'69)*)'6)'9"#)'(7/0)+'39)'362
*)-$-32*-'<?C'"%+'?C='32&)39)*'$%32'"'-$%&()'*)-$-32*'<Q?C=>
H%"(4-$-'21'39)'.$*.7$3'$%'S$&>'Q>QF<,=5'"--7/$%&'$+)"('20'"/0-5'$-'-3*"$&9312*6"*+5'"-'$$((7-3*"3)+'$%'S$&>'Q>QF<.=>';9)'8)4'02$%3'$-'39"3'39)'#$*37"('-92*3'.$*.7$3-'"3'39)'$%073-'21'20
"/0-'$C'"%+'$Q'."7-)'39)'$%073'#2(3"&)-'v>C'"%+'v>Q'32'"00)"*'"3'39)'362'3)*/$%"(-'21'*)-$-32*
<Q?C=>';97-'39)'+$11)*)%3$"('$%073'#2(3"&)'v>Q'−'v>C'≡'v>.'"00)"*-'".*2--'Q?C'"%+'."7-)-'"'.7**)%3
) = v >. ⁄ Q? C%32'1(26'39*27&9'Q?C'"%+'39)'362'*)-$-32*-'(",)()+'?Q>';9$-'.7**)%3'$%'37*%'0*2B
+7.)-'"'#2(3"&)'+$11)*)%.)',)36))%'39)'273073'3)*/$%"(-'21'$C'"%+'$Q'&$#)%',4
Q?
v BQ ! v BC = C + BBBBBBBBQB v >.
Q? C
;9)'+$11)*)%.)'"/0($1$)*'12*/)+',4'20'"/0'$T'"%+'$3-'"--2.$"3)+'*)-$-32*-'-)%-)-'39)'#2(3"&)
+$11)*)%.)'<vBQ'−'vBC='"%+'0*2#$+)-'"'0*202*3$2%"('273073'#2(3"&)'vB :
?
v B = BBBBBU ( v BQ ! v BC )
?T
?U ?
= BBBBB C + BBBBBQB v >.
?T ?C
;97-'39)'2#)*"(('+$11)*)%3$"('#2(3"&)B&"$%'$-'&$#)%',4
v
?
?
$ . ≡ BBBBBBB = BBBBBU C + BBBBBQB
v >.
?T ?C
<Q>QQ=
?,-)*#)'39"3'0*20)*'+$11)*)%3$"('20)*"3$2%'+2)-'*1&'+)0)%+'2%'39)'/"3.9$%&'21'39)'362'*)-$-32*(",)()+'?Q>'A%+))+5'$1'2%)'21'39)'362'$-'21'+$11)*)%3'#"(7)5'-"4'?Q′5 39)')M0*)--$2%'12*'$.',).2/)-
? Q + ?′Q ?
B
$ . = BBBBBU C + BBBBBBBBBBBBBBBBBB
Q? C
?T <Q>QT=
2.4 Difference Amplifiers
G2%-$+)*'%)M3'69"3'9"00)%-'69)%'39)'362'$%073'3)*/$%"(-'"*)'.2%%).3)+'32&)39)*'32'"'.2//2%B
/2+)'$%073'#2(3"&)'v>0->'A3'$-')"-4'32'-))'39"3'"%')K7"('#2(3"&)'"00)"*-'"3'39)'%)&"3$#)'$%073'3)*/$%"(21'$C'"%+'$Q5'."7-$%&'39)'.7**)%3'39*27&9'Q?C'32',)'[)*2>';97-'39)*)'6$((',)'%2'.7**)%3'1(26$%&'$%'39)
?Q'*)-$-32*-5'"%+'39)'#2(3"&)-'"3'39)'273073'3)*/$%"(-'21'$C'"%+'$Q'6$((',)')K7"('32'39)'$%073'<$>)>5'v>0-=>
;97-'39)'1$*-3'-3"&)'%2'(2%&)*'"/0($1$)-'v>0-X'$3'-$/0(4'0*20"&"3)-'v>0-'32'$3-'362'273073'3)*/$%"(-5
69)*)'39)4'"*)'-7,3*".3)+'32'0*2+7.)'"'[)*2'.2//2%B/2+)'273073',4'$T>';9)'+$11)*)%.)'"/0($1$)*
$%'39)'-).2%+'-3"&)5'926)#)*5'%26'9"-'"'/7.9'$/0*2#)+'-$37"3$2%'"3'$3-'$%073:';9)'+$11)*)%.)'-$&%"(
9"-',))%'"/0($1$)+',4'( C + ? Q ⁄ ? C )'69$()'39)'.2//2%B/2+)'#2(3"&)'*)/"$%)+'7%.9"%&)+>
S$%"((45' 6)' 2,-)*#)' 1*2/' 39)' )M0*)--$2%' $%' @K>' <Q>QQ=' 39"3' 39)' &"$%' ."%' ,)' #"*$)+' ,4
.9"%&$%&'2%(4'2%)'*)-$-32*5'Q?C>'Y)'.2%.(7+)'39"3'39$-'$-'"%')M.)(()%3'+$11)*)%3$"('"/0($1$)*
.$*.7$3'"%+'$-'6$+)(4')/0(24)+'"-'"%'$%-3*7/)%3"3$2%'"/0($1$)*X'39"3'$-5'"-'39)'$%073'"/0($1$)*
7-)+'$%'"'#"*$)34'21')().3*2%$.'$%-3*7/)%3->
Example 2.3
j)-$&%'39)'$%-3*7/)%3"3$2%'"/0($1$)*'.$*.7$3'$%'S$&>'Q>QF<,='32'0*2#$+)'"'&"$%'39"3'."%',)'#"*$)+'2#)*
39)'*"%&)'21'Q'32'CFFF'73$($[$%&'"'CFFB8Ω'#"*$",()'*)-$-3"%.)'<"'023)%3$2/)3)*5'2*'^023_'12*'-92*3=>
Solution
A3'$-'7-7"((4'0*)1)*",()'32'2,3"$%'"(('39)'*)K7$*)+'&"$%'$%'39)'1$*-3'-3"&)5'()"#$%&'39)'-).2%+'-3"&)'32
0)*12*/'39)'3"-8'21'3"8$%&'39)'+$11)*)%.)',)36))%'39)'273073-'21'39)'1$*-3'-3"&)'"%+'39)*),4'*)W).3$%&'39)
.2//2%B/2+)'-$&%"(>'A%'239)*'62*+-5'39)'-).2%+'-3"&)'$-'7-7"((4'+)-$&%)+'12*'"'&"$%'21'C>'H+203$%&
39$-'"00*2".95'6)'-)().3'"(('39)'-).2%+B-3"&)'*)-$-32*-'32',)')K7"('32'"'0*".3$."((4'.2%#)%$)%3'#"(7)5
-"4'CF'8Ω>';9)'0*2,()/'39)%'*)+7.)-'32'+)-$&%$%&'39)'1$*-3'-3"&)'32'*)"($[)'"'&"$%'"+W7-3",()'2#)*'39)
*"%&)'21'Q'32'CFFF>'A/0()/)%3$%&'Q?C'"-'39)'-)*$)-'.2/,$%"3$2%'21'"'1$M)+'*)-$-32*'?C2'"%+'39)'#"*$B
",()'*)-$-32*'?Cv'2,3"$%)+'7-$%&'39)'CFFB8Ω'023'<S$&>'Q>QC=5'6)'."%'6*$3)
Q? Q
C + BBBBBBBBBBBBBBBBBBBBB
= Q'32'CFFF
? C2 + ? Cv
;97-5
Q?
C + BBBBBBBBQB = CFFF
? C2
"%+
Q? Q
B = Q
C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
? C2 + CFF'8Ω
;9)-)' 362' )K7"3$2%-' 4$)(+' ?C2' =' CFF>Q' Ω' "%+' ?Q' =' VF>FVF' 8Ω>' ?39)*' 0*".3$."(' #"(7)-' /"4' ,)
-)().3)+X' 12*' $%-3"%.)5' ?C2' =' CFF' Ω' "%+' ?Q' =' UD>D' 8Ω' <,239' #"(7)-' "*)' "#"$(",()' "-' -3"%+"*+' CgB
32()*"%.)' /)3"(B1$(/' *)-$-32*-X' -))' H00)%+$M' !=' *)-7(3-' $%' "' &"$%' .2#)*$%&' "00*2M$/"3)(4' 39)
*)K7$*)+'*"%&)>
R1f
2R1
100 k&
pot
R1v
Figure 2.21 ;2'/"8)'39)'&"$%'21'39)'.$*.7$3'$%'S$&>'Q>QF<,='#"*$",()5'Q?C'$$/0()/)%3)+'"-'39)'-)*$)-'.2/,$%"3$2%'21'"'1$M)+'*)-$-32*'?C2 "%+'"'#"*$",()
*)-$-32*'?Cv>'O)-$-32*'?C2' )%-7*)-'39"3'39)'/"M$/7/'"#"$(",()'&"$%'$-'($/$3)+>
79
80 Chapter 2 Operational Amplifiers
EXERCISE
2.17' G2%-$+)*'39)'$%-3*7/)%3"3$2%'"/0($1$)*'21'S$&>'Q>QF<,='6$39'"'.2//2%B/2+)'$%073'#2(3"&)'21'+V'`
<+.='"%+'"'+$11)*)%3$"('$%073'-$&%"('21'CFB/`B0)"8'-$%)'6"#)>'k)3'<Q?C='='C'8Ω5'?Q'='F>V'RΩ5'"%+
?T'='?U'='CF'8Ω>'S$%+'39)'#2(3"&)'"3')#)*4'%2+)'$%'39)'.$*.7$3>
Ans. v>C'='V'−'F>FFV'-$%'ω &X v>Q'='V'+'F>FFV'-$%'ω &X vn'<20'"/0'$C='='V'−'F>FFV'-$%'ω &X'vn'<20'"/0
$Q='='V'+'F>FFV'-$%'ω &X vBC'='V'−'V>FFV'-$%'ω &X' vBQ'='V'+'V>FFV'-$%'ω &X vn'<$T='='v +'<$T='='Q>V'+'Q>VFQV
-$%'ω &X%vB'='CF>FC'-$%'ω &%<"(('$%'#2(3-=
2.5 Integrators and Differentiators
;9)' 20B"/0' .$*.7$3' "00($."3$2%-' 6)' 9"#)' -37+$)+' 397-' 1"*' 73$($[)+' *)-$-32*-' $%' 39)' 20B"/0
1))+,".8'0"39'"%+'$%'.2%%).3$%&'39)'-$&%"('-27*.)'32'39)'.$*.7$35'39"3'$-5'$%'39)'1))+B$%'0"39>
H-'"'*)-7(35'.$*.7$3'20)*"3$2%'9"-',))%'<$+)"((4='$%+)0)%+)%3'21'1*)K7)%.4>'e4'"((26$%&'39)
7-)'21' ."0".$32*-' 32&)39)*' 6$39' *)-$-32*-' $%' 39)'1))+,".8'"%+' 1))+B$%' 0"39-' 21' 20B"/0' .$*B
.7$3-5'6)'20)%'39)'+22*'32'"'#)*4'6$+)'*"%&)'21'7-)17('"%+')M.$3$%&'"00($."3$2%-'21'39)'20
"/0>' Y)' ,)&$%' 27*' -37+4' 21' 20B"/0n?"' .$*.7$3-' ,4' .2%-$+)*$%&' 362' ,"-$.' "00($."3$2%-5
%"/)(45'-$&%"('$%3)&*"32*-'"%+'+$11)*)%3$"32*->
2.5.1 The Inverting Configuration with General Impedances
;2',)&$%'6$395'.2%-$+)*'39)'$%#)*3$%&'.(2-)+B(220'.2%1$&7*"3$2%'6$39'$/0)+"%.)-'FC<4='"%+
FQ <4='*)0(".$%&'*)-$-32*-'?C'"%+'?Q5'*)-0).3$#)(4>';9)'*)-7(3$%&'.$*.7$3'$-'-926%'$%'S$&>'Q>QQ
"%+5'12*'"%'$+)"('20'"/05'9"-'39)'.(2-)+B(220'&"$%'2*5'/2*)'"00*20*$"3)(45'39)'.(2-)+B(220
3*"%-1)*'17%.3$2%
!1 ( 4 )
FQ ( 4 )
BBBBBBBBBBBB
B = − BBBBBBBBBBBB
!) ( 4 )
FC ( 4 )
<Q>QU=
H-')M0("$%)+'$%'L).3$2%'C>E5'*)0(".$%&'4',4'Gω'0*2#$+)-'39)'3*"%-1)*'17%.3$2%'12*'094-$."('1*)B
K7)%.$)-' ω5'39"3'$-5'39)'3*"%-/$--$2%'/"&%$37+)'"%+'09"-)'12*'"'-$%7-2$+"('$%073'-$&%"('21
1*)K7)%.4'ω>''
Figure 2.22 ;9)'$%#)*3$%&'.2%1$&7*"3$2%'6$39'&)%)*"('$/0)+"%.)-'$%'39)'1))+,".8'"%+'39)'1))+B$%'0"39->
2.5 Integrators and Differentiators
Example 2.4
S2*'39)'.$*.7$3'$%'S$&>'Q>QT5'+)*$#)'"%')M0*)--$2%'12*'39)'3*"%-1)*'17%.3$2%' !1 ( 4 ) ⁄ !) ( 4 )>'L926'39"3'39)
3*"%-1)*'17%.3$2%'$-'39"3'21'"'(26B0"--'L;G'.$*.7$3>'e4')M0*)--$%&'39)'3*"%-1)*'17%.3$2%'$%'39)'-3"%B
+"*+'12*/'-926%'$%';",()'C>Q'2%'0"&)'TU5'1$%+'39)'+.'&"$%'"%+'39)'TB+e'1*)K7)%.4>'j)-$&%'39)'.$*.7$3
32'2,3"$%'"'+.'&"$%'21'UF'+e5'"'TB+e'1*)K7)%.4'21'C'8![5'"%+'"%'$%073'*)-$-3"%.)'21'C'8Ω>'H3'69"3'1*)B
K7)%.4' +2)-' 39)' /"&%$37+)' 21' 3*"%-/$--$2%' ,).2/)' 7%$34\' Y9"3' $-' 39)' 09"-)' "%&()' "3' 39$1*)K7)%.4\
Figure 2.23 G$*.7$3'12*'@M"/0()'Q>U>
Solution
;2'2,3"$%'39)'3*"%-1)*'17%.3$2%'21'39)'.$*.7$3'$%'S$&>'Q>QT5'6)'-7,-3$373)'$%'@K>'<Q>QU=5'FC'='?C'"%+
F Q = ? Q || ( C ⁄ 4" Q )>'L$%.)'FQ'$-'39)'0"*"(()('.2%%).3$2%'21'362'.2/02%)%3-5'$3'$-'/2*)'.2%#)%$)%3'32
62*8'$%'3)*/-'21'HQX'39"3'$-5'6)'7-)'39)'12((26$%&'"(3)*%"3$#)'12*/'21'39)'3*"%-1)*'17%.3$2%:
!1 ( 4 )
C
BBBBBBBBBBBB
B = ! BBBBBBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
F C ( 4 )H Q ( 4 )
"%+'-7,-3$373)'FC'='?C'"%+' H Q ( 4 ) = ( C ⁄ ? Q ) + 4" Q '32'2,3"$%
!1 ( 4 )
C
B
BBBBBBBBBBBB
B = ! BBBBBBBBBBBBBBBBBBBBBBBBBB
!) ( 4 )
?C
BBBBB + 4" Q ? C
?Q
;9$-'3*"%-1)*'17%.3$2%'$-'21'1$*-3'2*+)*5'9"-'"'1$%$3)'+.'&"$%' ( "3'4 = F, !1 ⁄ !) = ! ? Q ⁄ ? C )5'"%+'9"-'[)*2
&"$%'"3'$%1$%$3)'1*)K7)%.4>';97-'$3'$-'39)'3*"%-1)*'17%.3$2%'21'"'(26B0"--'L;G'%)362*8'"%+'."%',)
)M0*)--)+'$%'39)'-3"%+"*+'12*/'21';",()'C>Q'"-'12((26-:
!1 ( 4 )
! ?Q ⁄ ?C
BBBBBBBBBBBB
B = BBBBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
C + 4" Q ? Q
1*2/'69$.9'6)'1$%+'39)'+.'&"$%'I'32',)
?
I = ! BBBBBQ
?C
81
82 Chapter 2 Operational Amplifiers
Example 2.4 continued
"%+'39)'TB+e'1*)K7)%.4'ω F'"C
"Q ?Q
ω F = BBBBBBBBBBBB
Y)'.27(+'9"#)'127%+'"(('39$-'1*2/'39)'.$*.7$3'$%'S$&>'Q>QT',4'$%-0).3$2%>'L0).$1$."((45'%23)'39"3'39)
."0".$32*' ,)9"#)-' "-' "%' 20)%' .$*.7$3' "3' +.X' 397-' "3' +.' 39)' &"$%' $-' -$/0(4' ( ! ? Q ⁄ ? C )>' S7*39)*/2*)5
,)."7-)'39)*)'$-'"'#$*37"('&*27%+'"3'39)'$%#)*3$%&'$%073'3)*/$%"(5'39)'*)-$-3"%.)'-))%',4'39)'."0".$32*
$-'?Q5'"%+'397-'39)'3$/)'.2%-3"%3'21'39)'L;G'%)362*8'$-'"Q?Q>
P26'32'2,3"$%'"'+.'&"$%'21'UF'+e5'39"3'$-5'CFF'`d`5'6)'-)().3' ? Q ⁄ ? C = CFF> 'S2*'"%'$%073'*)-$-B
3"%.)'21'C'8Ω5'6)'-)().3'?C'='C'8Ω5'"%+'397-'?Q'='CFF'8Ω>'S$%"((45'12*'"'TB+e'1*)K7)%.4'2F'='C 8![5
6)'-)().3'"Q'1*2/
C
T
Q π × C × CF = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBTB
" Q × CFF × CF
69$.9'4$)(+-'"Q'='C>VD'%S>
;9)'.$*.7$3'9"-'&"$%'"%+'09"-)'e2+)'0(23-'21'39)'-3"%+"*+'12*/'$%'S$&>'C>QT>'H-'39)'&"$%'1"((-'211'"3'39)
*"3)' 21' nQF'+e/+)."+)5' $3' 6$(('*)".9' F' +e' $%'362' +)."+)-5' 39"3' $-5' "3'2' =' CFF2F' =' CFF' 8![>' H-' S$&>
C>QT<,='$%+$."3)-5'"3'-7.9'"'1*)K7)%.4'69$.9'$-'/7.9'&*)"3)*'39"%'2F5'39)'09"-)'$-'"00*2M$/"3)(4'−DF°>
;2'39$-5'926)#)*5'6)'/7-3'"++'39)'CcF°'"*$-$%&'1*2/'39)'$%#)*3$%&'%"37*)'21'39)'"/0($1$)*'<$>)>5'39)
%)&"3$#)'-$&%'$%'39)'3*"%-1)*'17%.3$2%')M0*)--$2%=>';97-'"3'CFF'8![5'39)'323"('09"-)'-9$13'6$((',)'−QIF°
2*5')K7$#"()%3(45'+DF°>
2.5.2 The Inverting Integrator
e4'0(".$%&'"'."0".$32*'$%'39)'1))+,".8'0"39'<$>)>5'$%'0(".)'21'FQ'$%'S$&>'Q>QQ='"%+'"'*)-$-32*'"3
39)'$%073'<$%'0(".)'21'FC=5'6)'2,3"$%'39)'.$*.7$3'21'S$&>'Q>QU<"=>'Y)'-9"(('%26'-926'39"3'39$.$*.7$3' *)"($[)-' 39)' /"39)/"3$."(' 20)*"3$2%' 21' $%3)&*"3$2%>' k)3' 39)' $%073',)' "' 3$/)B#"*4$%&
17%.3$2%' v> <&=>' ;9)' #$*37"(' &*27%+' "3' 39)' $%#)*3$%&' 20B"/0' $%073' ."7-)-' v> <&=' 32' "00)"*' $%
)11).3'".*2--'?5'"%+'397-'39)'.7**)%3')C<&='6$((',)' v > ( & ) ⁄ ?> ';9$-'.7**)%3'1(26-'39*27&9'39)
."0".$32*'"5'."7-$%&'.9"*&)'32'"..7/7("3)'2%'">'A1'6)'"--7/)'39"3'39)'.$*.7$3',)&$%-'20)*"B
3$2%' "3' 3$/)' &' =' F5' 39)%' "3' "%' "*,$3*"*4' 3$/)' &' 39)' .7**)%3' )C<&=' 6$((' 9"#)' +)02-$3)+' 2%' "' "
&
&
.9"*&)')K7"('32' F ) C ( & ) .&> ';97-'39)'."0".$32*'#2(3"&)'v"<&='6$(('.9"%&)',4' BBB"CB F ) C ( & ) .&> 'A1
39)'$%$3$"('#2(3"&)'2%'"'<"3'&'='F='$-'+)%23)+'!" 5'39)%
C &
v " ( & ) = !" + BBBB ) C ( & ) .&
" F
P26'39)'273073'#2(3"&)'vB<&='='−v"<&=X'397-5'
C &
v B ( & ) = ! BBBBBBBB v > ( & ) .& ! !"
"? F
<Q>QV=
;97-'39)'.$*.7$3'0*2#$+)-'"%'273073'#2(3"&)'39"3'$-'0*202*3$2%"('32'39)'3$/)'$%3)&*"('21'39)
$%0735'6$39'!"',)$%&'39)'$%$3$"('.2%+$3$2%'21'$%3)&*"3$2%'"%+'"?'39)'!"&$'%,&.%*&!+$*0."4&,"&>
P23)'39"35'"-')M0).3)+5'39)*)'$-'"'%)&"3$#)'-$&%'"33".9)+'32'39)'273073'#2(3"&)5'"%+'397-'39$-
2.5 Integrators and Differentiators
" vC !
i1
i1
"
vI (t)
R
0
0V
vO(t) % !
C
!
"
vO(t)
!
"
!
1 t
vI (t) dt!VC
CR 0
$
Vo
1
%!
Vi
sCR
(a)
(b)
Figure 2.24 :,;';9)'R$(()*'2*'$%#)*3$%&'$%3)&*"32*>':5;'S*)K7)%.4'*)-02%-)'21'39)'$%3)&*"32*>
$%3)&*"32*'.$*.7$3'$-'-"$+'32',)'"%'!"#$%&!"'*!"&$'%,&.%>'A3'$-'"(-2'8%26%'"-'"'=!--$%*!"&$'%,/
&.%'"13)*'"%')"*(4'62*8)*'$%'39$-'1$)(+>
;9)'20)*"3$2%'21'39)'$%3)&*"32*'.$*.7$3'."%',)'+)-.*$,)+'"(3)*%"3$#)(4'$%'39)'1*)K7)%.4
+2/"$%',4'-7,-3$373$%&'FC<4='='?'"%+' F Q ( 4 ) = C ⁄ 4" '$%'@K>'<Q>QU='32'2,3"$%'39)'3*"%-1)*
17%.3$2%
!1 ( 4 )
C
BBBBBBBBBBBB
B = ! BBBBBBBBBB
!) ( 4 )
4"?
<Q>QE=
!1 ( G ω )
C
BBBBBBBBBBBBBBBBB
B = ! BBBBBBBBBBBBBB
!) ( G ω )
G ω "?
<Q>QI=
S2*'094-$."('1*)K7)%.$)-5'4'='Gω'"%+
;97-'39)'$%3)&*"32*'3*"%-1)*'17%.3$2%'9"-'/"&%$37+)
C
!1 = BBBBBBBBBBB
B
BBBBB
ω
"?
!)
<Q>Qc=
83
84 Chapter 2 Operational Amplifiers
"%+'09"-)
φ = +DF°
<Q>QD=
;9)'e2+)'0(23'12*'39)'$%3)&*"32*'/"&%$37+)'*)-02%-)'."%',)'2,3"$%)+',4'%23$%&'1*2/'@K>'<Q>Qc=
39"3'"-' ω'+27,()-'<$%.*)"-)-',4'"%'2.3"#)='39)'/"&%$37+)'$-'9"(#)+'<+).*)"-)+',4'E'+e=>
;97-' 39)' e2+)' 0(23' $-' "' -3*"$&93' ($%)' 21' -(20)' nE' +e/2.3"#)' <2*5' )K7$#"()%3(45' nQF' +e/
+)."+)=>';9$-'($%)'<-926%'$%'S$&>'Q>QU,='$%3)*.)03-'39)'FB+e'($%)'"3'39)'1*)K7)%.4'39"3'/"8)!1 ⁄ !) = C5 '69$.9'1*2/'@K>'<Q>Qc='$-
C
"?
ω )*& = BBBBBBBB '
<Q>TF=
;9)'1*)K7)%.4' ω)*&'$-'8%26%'"-'39)'!"&$'%,&.%*3%$?)$"09'"%+'$-'-$/0(4'39)'$%#)*-)'21'39)
$%3)&*"32*'3$/)'.2%-3"%3>
G2/0"*$-2%'21'39)'1*)K7)%.4'*)-02%-)'21'39)'$%3)&*"32*'32'39"3'21'"%'L;G'(26B0"--'%)3B
62*8'$%+$."3)-'39"3'39)'$%3)&*"32*',)9"#)-'"-'"'(26B0"--'1$(3)*'6$39'"'.2*%)*'1*)K7)%.4'21'[)*2>
?,-)*#)'"(-2'39"3'"3' ω'='F5'39)'/"&%$37+)'21'39)'$%3)&*"32*'3*"%-1)*'17%.3$2%'$-'$%1$%$3)>';9$$%+$."3)-'39"3'"3'+.'39)'20'"/0'$-'20)*"3$%&'6$39'"%'20)%'(220>';9$-'-927(+'"(-2',)'2,#$271*2/'39)'$%3)&*"32*'.$*.7$3'$3-)(1>'O)1)*)%.)'32'S$&>'Q>QU<"='-926-'39"3'39)'1))+,".8')()/)%3'$"'."0".$32*5'"%+'397-'"3'+.5'69)*)'39)'."0".$32*',)9"#)-'"-'"%'20)%'.$*.7$35'39)*)'$-'%2'%)&"B
3$#)'1))+,".8N';9$-'$-'"'#)*4'-$&%$1$."%3'2,-)*#"3$2%'"%+'2%)'39"3'$%+$."3)-'"'-27*.)'21'0*2,B
()/-'6$39'39)'$%3)&*"32*'.$*.7$3:'H%4'3$%4'+.'.2/02%)%3'$%'39)'$%073'-$&%"('6$(('39)2*)3$."((4
0*2+7.)'"%'$%1$%$3)'273073>'?1'.27*-)5'%2'$%1$%$3)'273073'#2(3"&)'*)-7(3-'$%'0*".3$.)X'*"39)*5'39)
273073' 21' 39)' "/0($1$)*' -"37*"3)-' "3' "' #2(3"&)' .(2-)' 32' 39)' 20B"/0' 02-$3$#)' 2*' %)&"3$#)
026)*'-700(4'<D+'2*'D−=5'+)0)%+$%&'2%'39)'02("*$34'21'39)'$%073'+.'-$&%"(>
' ;9)' +.' 0*2,()/' 21' 39)' $%3)&*"32*' .$*.7$3' ."%' ,)' "(()#$"3)+' ,4' .2%%).3$%&' "' *)-$-32*' ?J
".*2--'39)'$%3)&*"32*'."0".$32*'"5'"-'-926%'$%'S$&>'Q>QV'"%+'397-'39)'&"$%'"3'+.'6$((',)'n?J d?
*"39)*'39"%'$%1$%$3)>'L7.9'"'*)-$-32*'0*2#$+)-'"'+.'1))+,".8'0"39>'a%12*37%"3)(45'926)#)*5'39)
$%3)&*"3$2%'$-'%2'(2%&)*'$+)"(5'"%+'39)'(26)*'39)'#"(7)'21'?J 5'39)'()--'$+)"('39)'$%3)&*"32*'.$*.7$3
,).2/)->';9$-'$-',)."7-)'?J'."7-)-'39)'1*)K7)%.4'21'39)'$%3)&*"32*'02()'32'/2#)'1*2/'$3-'$+)"(
(2."3$2%'"3'ω'='F'32'2%)'+)3)*/$%)+',4'39)'.2*%)*'1*)K7)%.4'21'39)'L;G'%)362*8'<?J 5'"=>'L0)B
.$1$."((45'39)'$%3)&*"32*'3*"%-1)*'17%.3$2%',).2/)-
!1 ( 4 )
?J ⁄ ?
BBBBBBBBBBBB
B = ! BBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
C + 4"? J
RF
C
R
!
"
v I (t)
!
"
"
vO (t)
!
Figure 2.25 ;9)'R$(()*'$%3)&*"32*'6$39'"'("*&)'*)-$-3"%.)'?J
.2%%).3)+'$%'0"*"(()('6$39'"'$%'2*+)*'32'0*2#$+)'%)&"3$#)'1))+B
,".8'"%+'9)%.)'1$%$3)'&"$%'"3'+.>
2.5 Integrators and Differentiators
"-' 2002-)+' 32' 39)' $+)"(' 17%.3$2%' 21' ! C ⁄ 4"? >' ;9)' (26)*' 39)' #"(7)' 6)' -)().3' 12*' ?J 5' 39)
9$&9)*' 39)' .2*%)*' 1*)K7)%.4' ( C ⁄ "? J ) ' 6$((' ,)' "%+' 39)' /2*)' %2%$+)"(' 39)' $%3)&*"32*
,).2/)->' ;97-'-)().3$%&'"'#"(7)'12*'?J'0*)-)%3-'39)'+)-$&%)*'6$39'"'3*"+)B211',)36))%'+.
0)*12*/"%.)'"%+'-$&%"('0)*12*/"%.)>';9)')11).3'21'?J'2%'$%3)&*"32*'0)*12*/"%.)'$-'$%#)-3$B
&"3)+'17*39)*'$%'39)'@M"/0()'Q>V>
Example 2.5
S$%+'39)'273073'0*2+7.)+',4'"'R$(()*'$%3)&*"32*'$%'*)-02%-)'32'"%'$%073'07(-)'21'CB`'9)$&93'"%+'CB/6$+39'oS$&>'Q>QE<"=p>'k)3'?'='CF'8Ω'"%+'"'='CF'%S>'A1'39)'$%3)&*"32*'."0".$32*'$-'-97%3)+',4'"'CBRΩ
*)-$-32*5'926'6$(('39)'*)-02%-)',)'/2+$1$)+\';9)'20'"/0'$-'-0).$1$)+'32'-"37*"3)'"3'±CT'`>
Solution
A%'*)-02%-)'32'"'CB`5'CB/-'$%073'07(-)5'39)'$%3)&*"32*'273073'6$((',)
&
C
v B ( & ) = ! BBBBBBBB C .&5
F ≤ & ≤ C'/- ''''
"? F
69)*)'6)'9"#)'"--7/)+'39"3'39)'$%$3$"('#2(3"&)'2%'39)'$%3)&*"32*'."0".$32*'$-'F>'S2*'"'='CF'%S'"%+
?'='CF'8Ω5'"?'='F>C'/-5'"%+
v B ( & ) = ! CF&5
F ≤ & ≤ C'/-
69$.9'$-'39)'($%)"*'*"/0'-926%'$%'S$&>'Q>QE<,=>'A3'*)".9)-'"'/"&%$37+)'21' −CF'`'"3'&'='C'/-'"%+
*)/"$%-'.2%-3"%3'39)*)"13)*>
;9"3'39)'273073'$-'"'($%)"*'*"/0'-927(+'"(-2',)'2,#$27-'1*2/'39)'1".3'39"3'39)'CB`'$%073'07(-)
0*2+7.)-'"'.2%-3"%3'.7**)%3'39*27&9'39)'."0".$32*'21' C'` ⁄ CF'8Ω = F>C'/H>';9$-'.2%-3"%3'.7**)%3
> ='F>C'/H'-700($)-'39)'."0".$32*'6$39'"'.9"*&)' >&5 "%+'397-'39)'."0".$32*'#2(3"&)'.9"%&)-'($%)"*(4
"-' ( >& ⁄ " )5 '*)-7(3$%&'$%' v B = ! ( > ⁄ " )& > 'A3'$-'62*39'*)/)/,)*$%&'39"3'.9"*&$%&'"'."0".$32*'6$39'"
.2%-3"%3'.7**)%3'0*2+7.)-'"'($%)"*'#2(3"&)'".*2--'$3>
P)M3'.2%-$+)*'39)'-$37"3$2%'6$39'*)-$-32*' ? J = C'RΩ '.2%%).3)+'".*2--'">'H-',)12*)5'39)'CB`
07(-)'6$(('0*2#$+)'"'.2%-3"%3'.7**)%3'>%='F>C'/H>'P265'926)#)*5'39$-'.7**)%3'$-'-700($)+'32'"%'L;G
%)362*8'.2/02-)+'21'?J'$%'0"*"(()('6$39'">';97-5'39)'273073'6$((',)'"%')M02%)%3$"('9)"+$%&'326"*+
−CFF'`'6$39'"'3$/)'.2%-3"%3'21'"?J'= CF ' CF−D'' C ''CFE = CF'/-5
v B ( & ) = ! CFF ( C ! (
! & ⁄ CF
)5
F ≤ & ≤ C'/-
?1'.27*-)5'39)')M02%)%3$"('6$((',)'$%3)**703)+'"3'39)')%+'21'39)'07(-)5'39"3'$-5'"3'&%='C'/-5'"%+'39)'273B
073'6$(('*)".9'39)'#"(7)
v B ( C'/- ) = ! CFF ( C ! (
! C ⁄ CF
) = ! D>V'`
;9)'273073'6"#)12*/'$-'-926%'$%'S$&>'Q>QE<.=5'1*2/'69$.9'6)'-))'39"3'$%.(7+$%&'?J'."7-)-'39)'*"/0'32
,)'-($&93(4'*27%+)+'-7.9'39"3'39)'273073'*)".9)-'2%(4'−D>V'`5'F>V'`'-92*3'21'39)'$+)"('#"(7)'21'−CF'`>
S7*39)*/2*)5'12*'&%>'C'/-5'39)'."0".$32*'+$-.9"*&)-'39*27&9'?J'6$39'39)'*)("3$#)(4'(2%&'3$/)B.2%-3"%3'21
CF'/->'S$%"((45'6)'%23)'39"3'20'"/0'-"37*"3$2%5'-0).$1$)+'32'2..7*'"3'±CT'`5'9"-'%2')11).3'2%'39)'20)*"B
3$2%'21'39$-'.$*.7$3>
85
86 Chapter 2 Operational Amplifiers
>
Example 2.5 continued
vI (t)
1V
0
0
t
1 ms
(a)
vO (t)
0
t
1 ms
!10 V
(b)
vO (t)
0
t
1 ms
to 0 V
!9.5 V
Exponentials with
time constant of 10 ms
to !100 V
(c)
Figure 2.26 Y"#)12*/-'12*'@M"/0()'Q>V:':,;'A%073'07(-)>':5;'?73073'($%)"*'*"/0'21'$+)"('$%3)&*"32*'6$39'3$/)'.2%B
-3"%3'21'F>C'/->':0;'?73073')M02%)%3$"('*"/0'6$39'*)-$-32*'?J'.2%%).3)+'".*2--'$%3)&*"32*'."0".$32*>
;9)'0*).)+$%&')M"/0()'9$%3-'"3'"%'$/02*3"%3'"00($."3$2%'21'$%3)&*"32*-5'%"/)(45'39)$*'7-)
$%' 0*2#$+$%&' 3*$"%&7("*' 6"#)12*/-' $%' *)-02%-)' 32' -K7"*)B6"#)' $%073->' ;9$-' "00($."3$2%' $)M0(2*)+'$%'@M)*.$-)'Q>Cc>'A%3)&*"32*-'9"#)'/"%4'239)*'"00($."3$2%-5'$%.(7+$%&'39)$*'7-)'$%'39)
+)-$&%'21'1$(3)*-'<G9"03)*'CE=>
2.5 Integrators and Differentiators
2.5.3 The Op-Amp Differentiator
A%3)*.9"%&$%&' 39)' (2."3$2%' 21' 39)' ."0".$32*' "%+' 39)' *)-$-32*' 21' 39)' $%3)&*"32*' .$*.7$3
*)-7(3-'$%'39)'.$*.7$3'$%'S$&>'Q>QI<"=5'69$.9'0)*12*/-'39)'/"39)/"3$."('17%.3$2%'21'+$11)*B
)%3$"3$2%>';2'-))'926'39$-'.2/)-'",2735'()3'39)'$%073',)'39)'3$/)B#"*4$%&'17%.3$2%' v > ( & )5
"%+' %23)' 39"3' 39)' #$*37"(' &*27%+' "3' 39)' $%#)*3$%&' $%073' 3)*/$%"(' 21' 39)' 20' "/0' ."7-)v > ( & ) ' 32' "00)"*' $%' )11).3' ".*2--' 39)' ."0".$32*' ">' ;97-' 39)' .7**)%3' 39*27&9' "' 6$((' ,)
" ( .v > ⁄ .& )5 ' "%+' 39$-' .7**)%3' 1(26-' 39*27&9' 39)' 1))+,".8' *)-$-32*' ?' 0*2#$+$%&' "3' 39)
20B"/0'273073'"'#2(3"&)' v B ( & )5
.v > ( & )
B
v B ( & ) = ! "? BBBBBBBBBBBBB
.&
<Q>TC=
;9)'1*)K7)%.4B+2/"$%'3*"%-1)*'17%.3$2%'21'39)'+$11)*)%3$"32*'.$*.7$3'."%',)'127%+',4'-7,-3$B
373$%&'$%'@K>'<Q>QU=5' F C ( 4 ) = C ⁄ 4" '"%+' F Q ( 4 ) = ? '32'2,3"$%
!1 ( 4 )
BBBBBBBBBBBB
B = ! 4"?
!) ( 4 )
<Q>TQ=
69$.9'12*'094-$."('1*)K7)%.$)-' 4 = G ω '4$)(+-
!1 ( G ω )
BBBBBBBBBBBBBBBBB
B = ! G ω "?
!) ( G ω )
i
i
C
R
0
dvI (t)
dt
dv (t)
vO (t) % !CR I
dt
Vo
% !sCR
Vi
i (t) % C
!
"
vI (t)
!
<Q>TT=
"
vO (t)
!
"
0V
(a)
Vo
(dB)
Vi
"6 dB/octave
0
( (log scale)
1
CR
(b)
Figure 2.27 :,;*H'+$11)*)%3$"32*>':5;'S*)K7)%.4'*)-02%-)'21'"'+$11)*)%3$"32*'6$39'"'3$/)B.2%-3"%3'"?>'
87
88 Chapter 2 Operational Amplifiers
;97-'39)'3*"%-1)*'17%.3$2%'9"-'/"&%$37+)
!1
BBBBB = ω "?
!)
<Q>TU=
φ = ! DF°
<Q>TV=
"%+'09"-)
;9)'e2+)'0(23'21'39)'/"&%$37+)'*)-02%-)'."%',)'127%+'1*2/'@K>'<Q>TU=',4'%23$%&'39"3'12*'"%
2.3"#)'$%.*)"-)'$%' ω5'39)'/"&%$37+)'+27,()-'<$%.*)"-)-',4'E'+e=>';97-'39)'0(23'$-'-$/0(4'"
-3*"$&93'($%)'21'-(20)'+E'+ed2.3"#)'<2*5')K7$#"()%3(45'+QF'+ed+)."+)='$%3)*-).3$%&'39)'FB+e
($%)'<69)*)' !1 ⁄ !) = C= '"3'ω = C ⁄ "?5 '69)*)'"?'$-'39)'1!33$%$"&!,&.%*&!+$/0."4&,"&'o-))
S$&>'Q>QI<,=p>'
;9)'1*)K7)%.4'*)-02%-)'21'39)'+$11)*)%3$"32*'."%',)'3927&93'21'"-'39"3'21'"%'L;G'9$&90"-1$(3)*'6$39'"'.2*%)*'1*)K7)%.4'"3'$%1$%$34'<*)1)*'32'S$&>'C>QU=>'S$%"((45'6)'-927(+'%23)'39"3'39)
#)*4'%"37*)'21'"'+$11)*)%3$"32*'.$*.7$3'."7-)-'$3'32',)'"'^%2$-)'/"&%$1$)*>_';9$-'$-'+7)'32'39)
-0$8)' $%3*2+7.)+' "3' 39)' 273073' )#)*4' 3$/)' 39)*)' $-' "' -9"*0' .9"%&)' $%' v > ( & )X' -7.9' "' .9"%&)
.27(+' ,)' $%3)*1)*)%.)' .270()+' )().3*2/"&%)3$."((4' <^0$.8)+' 70_=' 1*2/' "+W".)%3' -$&%"(
-27*.)->'S2*'39$-'*)"-2%'"%+',)."7-)'39)4'-711)*'1*2/'-3",$($34'0*2,()/-'<G9"03)*'CF=5'+$11)*B
)%3$"32*'.$*.7$3-'"*)'&)%)*"((4'"#2$+)+'$%'0*".3$.)>'Y9)%'39)'.$*.7$3'21'S$&>'Q>QI<"='$-'7-)+5'$3
$-' 7-7"((4' %).)--"*4' 32' .2%%).3' "' -/"((B#"(7)+' *)-$-32*' $%' -)*$)-' 6$39' 39)' ."0".$32*>' ;9$/2+$1$."3$2%5'7%12*37%"3)(45'37*%-'39)'.$*.7$3'$%32'"'%2%$+)"('+$11)*)%3$"32*>''''
EXERCISES
2.18 G2%-$+)*'"'-4//)3*$."('-K7"*)'6"#)'21'QFB`'0)"8B32B0)"85'F'"#)*"&)5'"%+'QB/-'0)*$2+'"00($)+
32'"'R$(()*'$%3)&*"32*>'S$%+'39)'#"(7)'21'39)'3$/)'.2%-3"%3'"?'-7.9'39"3'39)'3*$"%&7("*'6"#)12*/'"3
39)'273073'9"-'"'QFB`'0)"8B32B0)"8'"/0($37+)>
Ans. F>V'/D2.19 a-)'"%'$+)"('20'"/0'32'+)-$&%'"%'$%#)*3$%&'$%3)&*"32*'6$39'"%'$%073'*)-$-3"%.)'21'CF'8Ω'"%+'"%
$%3)&*"3$2%'3$/)'.2%-3"%3'21'CF−T'->'Y9"3'$-'39)'&"$%'/"&%$37+)'"%+'09"-)'"%&()'21'39$-'.$*.7$3'"3
CF'*"+d-'"%+'"3'C'*"+d-\'Y9"3'$-'39)'1*)K7)%.4'"3'69$.9'39)'&"$%'/"&%$37+)'$-'7%$34\
Ans. ?'='CF'8Ω, "'='F>C'µSX'"3'ω''='CF'*"+d-:' !1 ⁄ !) = CFF `d`'"%+'φ'='+DF°X'"3'ω ='C'*"+d-:
! 1 ⁄ ! ) = 'C5FFF'`d`'"%+'φ ='+DF°; 1000'*"+dD2.20 j)-$&%'"'+$11)*)%3$"32*'32'9"#)'"'3$/)'.2%-3"%3'21'CF−Q'-'"%+'"%'$%073'."0".$3"%.)'21'F>FC'µS>'Y9"3
$-'39)'&"$%'/"&%$37+)'"%+'09"-)'21'39$-'.$*.7$3'"3'CF'*"+d-5'"%+'"3'CFT'*"+d-\'A%'2*+)*'32'($/$3'39)
9$&9B1*)K7)%.4'&"$%'21'39)'+$11)*)%3$"32*'.$*.7$3'32'CFF5'"'*)-$-32*'$-'"++)+'$%'-)*$)-'6$39'39)'."B
0".$32*>'S$%+'39)'*)K7$*)+'*)-$-32*'#"(7)>
Ans. "'='F>FC'µSX ?'='C'RΩX'"3'ω''='CF'*"+d-:' !1 ⁄ !) = F>C `d`'"%+'φ'='−DF°X'"3'ω'='CFFF'*"+d-:
!1 ⁄ !) = CF `d`'"%+'φ ='−DF°; 10'8Ω
2.6 DC Imperfections
;97-'1"*'6)'9"#)'.2%-$+)*)+'39)'20'"/0'32',)'$+)"(>';9)'2%(4')M.)03$2%'9"-',))%'"',*$)1'+$-B
.7--$2%'21'39)')11).3'21'39)'20B"/0'1$%$3)'&"$%'$'2%'39)'.(2-)+B(220'&"$%'21'39)'$%#)*3$%&'"%+
%2%$%#)*3$%&' .2%1$&7*"3$2%->' H(3927&9' $%' /"%4' "00($."3$2%-' 39)' "--7/03$2%' 21' "%' $+)"(' 20
2.6 DC Imperfections
"/0'$-'%23'"',"+'2%)5'"'.$*.7$3'+)-$&%)*'9"-'32',)'392*27&9(4'1"/$($"*'6$39'39)'.9"*".3)*$-3$.21'0*".3$."('20'"/0-'"%+'39)')11).3-'21'-7.9'.9"*".3)*$-3$.-'2%'39)'0)*12*/"%.)'21'20B"/0'.$*B
.7$3->'?%(4' 39)%'6$(('39)'+)-$&%)*',)' ",()'32'7-)'39)'20' "/0'$%3)(($&)%3(45')-0).$"((4'$1'39)
"00($."3$2%'"3'9"%+'$-'%23'"'-3*"$&9312*6"*+'2%)>';9)'%2%$+)"('0*20)*3$)-'21'20'"/0-'6$((5'21
.27*-)5'($/$3'39)'*"%&)'21'20)*"3$2%'21'39)'.$*.7$3-'"%"(4[)+'$%'39)'0*)#$27-')M"/0()->
A%'39$-'"%+'39)'362'-).3$2%-'39"3'12((265'6)'.2%-$+)*'-2/)'21'39)'$/02*3"%3'%2%$+)"(
0*20)*3$)-'21'39)'20'"/0>T'Y)'+2'39$-',4'3*)"3$%&'2%)'%2%$+)"($34'"3'"'3$/)5',)&$%%$%&'$%'39$-).3$2%'6$39'39)'+.'0*2,()/-'32'69$.9'20'"/0-'"*)'-7-.)03$,()>
2.6.1 Offset Voltage
e)."7-)' 20' "/0-' "*)' +$*).3B.270()+' +)#$.)-' 6$39' ("*&)' &"$%-' "3' +.5' 39)4' "*)' 0*2%)' 32' +.
0*2,()/->';9)'1$*-3'-7.9'0*2,()/'$-'39)'+.'211-)3'#2(3"&)>';2'7%+)*-3"%+'39$-'0*2,()/'.2%B
-$+)*'39)'12((26$%&'01*0(+&,/3')M0)*$/)%3:'A1'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0'"*)'3$)+
32&)39)*'"%+'.2%%).3)+'32'&*27%+5'$3'6$((',)'127%+'39"3'+)-0$3)'39)'1".3'39"3'v>.'Z'F5'"'1$%$3)'+.
#2(3"&)')M$-3-'"3'39)'273073>'A%'1".35'$1'39)'20'"/0'9"-'"'9$&9'+.'&"$%5'39)'273073'6$((',)'"3
)$39)*'39)'02-$3$#)'2*'%)&"3$#)'-"37*"3$2%'()#)(>';9)'20B"/0'273073'."%',)',*27&93',".8'32'$3$+)"('#"(7)'21'F'`',4'.2%%).3$%&'"'+.'#2(3"&)'-27*.)'21'"00*20*$"3)'02("*$34'"%+'/"&%$37+)
,)36))%'39)'362'$%073'3)*/$%"(-'21'39)'20'"/0>';9$-')M3)*%"('-27*.)',"("%.)-'273'39)'$%073
211-)3'#2(3"&)'21'39)'20'"/0>'A3'12((26-'39"3'39)'!"()&*.334$&*#.-&,'$'<!BK='/7-3',)'21')K7"(
/"&%$37+)'"%+'21'2002-$3)'02("*$34'32'39)'#2(3"&)'6)'"00($)+')M3)*%"((4>'
;9)'$%073'211-)3'#2(3"&)'"*$-)-'"-'"'*)-7(3'21'39)'7%"#2$+",()'/$-/"3.9)-']*)-)%3'$%'39)'$%073
+$11)*)%3$"('-3"&)'$%-$+)'39)'20'"/0>'A%'("3)*'.9"03)*-'<$%'0"*3$.7("*'G9"03)*-'c'"%+'CQ='6)'-9"((
-37+4'39$-'320$.'$%'+)3"$(>'!)*)5'926)#)*5'27*'.2%.)*%'$-'32'$%#)-3$&"3)'39)')11).3'21'!BK'2%'39)'20)*B
"3$2%' 21' .(2-)+B(220' 20B"/0' .$*.7$3->' ;26"*+' 39"3' )%+5' 6)' %23)' 39"3' &)%)*"(B07*02-)' 20' "/0)M9$,$3'!BK'$%'39)'*"%&)'21'C'/`'32'V'/`>'H(-25'39)'#"(7)'21'!BK'+)0)%+-'2%'3)/0)*"37*)>';9)'20B
"/0'+"3"'-9))3-'7-7"((4'-0).$14'340$."('"%+'/"M$/7/'#"(7)-'12*'!BK'"3'*22/'3)/0)*"37*)'"-'6)((
"-'39)'3)/0)*"37*)' .2)11$.$)%3' 21' !BK' <7-7"((4' $%' µ`d°G=>' ;9)4' +2' %235' 926)#)*5' -0).$14' 39)
02("*$34'21'!BK',)."7-)'39)'.2/02%)%3'/$-/"3.9)-'39"3'&$#)'*$-)'32'!BK'"*)'2,#$27-(4'%23'8%26%'"
0*$2*$X'+$11)*)%3'7%$3-'21'39)'-"/)'20B"/0'340)'/"4')M9$,$3')$39)*'"'02-$3$#)'2*'"'%)&"3$#)'!BK >
;2'"%"(4[)'39)')11).3'21'!BK'2%'39)'20)*"3$2%'21'20B"/0'.$*.7$3-5'6)'%))+'"'.$*.7$3'/2+)(
12*'39)'20'"/0'6$39'$%073'211-)3'#2(3"&)>'L7.9'"'/2+)('$-'-926%'$%'S$&>'Q>Qc>'A3'.2%-$-3-'21'"
Figure 2.28 G$*.7$3'/2+)('12*'"%'20'"/0'6$39'
$%073'211-)3'#2(3"&)'!BK>
T
Y)'-927(+'%23)'39"3'*)"('20'"/0-'9"#)'%2%$+)"(')11).3-'"++$3$2%"('32'392-)'+$-.7--)+'$%'39$-'.9"03)*>
;9)-)' $%.(7+)' 1$%$3)' <%2%[)*2=' .2//2%B/2+)' &"$%' 2*5' )K7$#"()%3(45' %2%$%1$%$3)' GROO5' %2%$%1$%$3)
$%073'*)-$-3"%.)5'"%+'%2%[)*2'273073'*)-$-3"%.)>';9)')11).3'21'39)-)5'926)#)*5'2%'39)'0)*12*/"%.)'21
/2-3'21'39)'.(2-)+B(220'.$*.7$3-'-37+$)+'9)*)'$-'%23'#)*4'-$&%$1$."%35'"%+'39)$*'-37+4'6$((',)'02-302%)+
32'("3)*'.9"03)*-'<$%'0"*3$.7("*'G9"03)*-'c5'D5'"%+'CQ=>'
89
90 Chapter 2 Operational Amplifiers
+.'-27*.)'21'#"(7)'!BK'0(".)+'$%'-)*$)-'6$39'39)'02-$3$#)'$%073'()"+'21'"%'211-)3B1*))'20'"/0>
;9)'W7-3$1$."3$2%'12*'39$-'/2+)('12((26-'1*2/'39)'+)-.*$03$2%'",2#)>'
EXERCISE
2.21 a-)'39)'/2+)('21'S$&>'Q>Qc'32'-8)3.9'39)'3*"%-1)*'.9"*".3)*$-3$.'vB'#)*-7-'v>.'<vB'≡'vT'"%+'v>.' ≡'vQ'−
vC='21 "%'20'"/0'9"#$%&'"%'20)%B(220'+.'&"$%'$F'='CFU'`d`5'273073'-"37*"3$2%'()#)(-'21'±CF'`5'"%+
!BK'21'+V'/`>
Ans. L))'S$&>'@Q>QC>'?,-)*#)'39"3'3*7)'32'$3-'%"/)5'39)'$%073'211-)3'#2(3"&)'."7-)-'"%'211-)3'$%'39)
#2(3"&)B3*"%-1)*'.9"*".3)*$-3$.X'*"39)*'39"%'0"--$%&'39*27&9'39)'2*$&$%'$3'$-'%26'-9$13)+'32'39)'()13',4'!BK>
Figure E2.21 ;*"%-1)*'.9"*".3)*$-3$.'21'"%'20'"/0'6$39'!BK'='V'/`>
H%"(4-$-'21'20B"/0'.$*.7$3-'32'+)3)*/$%)'39)')11).3'21'39)'20B"/0'!BK'2%'39)$*'0)*12*B
/"%.)' $-' -3*"$&9312*6"*+:' ;9)' $%073' #2(3"&)' -$&%"(' -27*.)' $-' -92*3B.$*.7$3)+' "%+' 39)' 20
"/0'$-'*)0(".)+'6$39'39)'/2+)('21'S$&>'Q>Qc>'<@($/$%"3$%&'39)'$%073'-$&%"(5'+2%)'32'-$/B
0($14' /"33)*-5' $-' ,"-)+' 2%' 39)' 0*$%.$0()' 21' -70)*02-$3$2%>=' S2((26$%&' 39$-' 0*2.)+7*)5' 6)
1$%+' 39"3' ,239' 39)' $%#)*3$%&' "%+' 39)' %2%$%#)*3$%&' "/0($1$)*' .2%1$&7*"3$2%-' *)-7(3' $%' 39)
-"/)'.$*.7$35'39"3'-926%'$%'S$&>'Q>QD5'1*2/'69$.9'39)'273073'+.'#2(3"&)'+7)'32'!BK'$-'127%+
32',)'
?
!B = !BK C + BBBBBQ
?C
<Q>TE=
;9$-'273073'+.'#2(3"&)'."%'9"#)'"'("*&)'/"&%$37+)>'S2*'$%-3"%.)5'"'%2%$%#)*3$%&'"/0($1$)*
6$39'"'.(2-)+B(220'&"$%'21'CFFF5'69)%'.2%-3*7.3)+'1*2/'"%'20'"/0'6$39'"'VB/`'$%073
211-)3'#2(3"&)5'6$(('9"#)'"'+.'273073'#2(3"&)'21'+V'`'2*'−V'`'<+)0)%+$%&'2%'39)'02("*$34
21' !BK='*"39)*'39"%'39)'$+)"('#"(7)'21'F'`>'P265'69)%'"%'$%073'-$&%"('$-'"00($)+'32'39)
2.6 DC Imperfections
R2
R1
!"
!
R2
VO % VOS 1 " R
"
VO
1
VOS
Offset-free
op amp
Figure 2.29 @#"(7"3$%&'39)'273073'+.'211-)3'#2(3"&)'+7)'32'!BK'$%'"'.(2-)+B(220'"/0($1$)*>
V"
To rest
of circuit
!
"
Offset-nulling
terminals
V!
Figure 2.30 ;9)' 273073' +.' 211-)3' #2(3"&)' 21' "%' 20' "/0' ."%' ,)' 3*$//)+' 32' [)*2' ,4' .2%%).3$%&' "
023)%3$2/)3)*' 32' 39)' 362' 211-)3B%7(($%&' 3)*/$%"(->' ;9)' 6$0)*' 21' 39)' 023)%3$2/)3)*' $-' .2%%).3)+' 32' 39)
%)&"3$#)'-700(4'21'39)'20'"/0>
"/0($1$)*5' 39)' .2**)-02%+$%&' -$&%"(' 273073' 6$((' ,)' -70)*$/02-)+' 2%' 39)' VB`' +.>' ?,#$B
27-(4'39)%5'39)'"((26",()'-$&%"('-6$%&'"3'39)'273073'6$((',)'*)+7.)+>'@#)%'62*-)5'$1'39)
-$&%"('32',)'"/0($1$)+'$-'+.5'6)'627(+'%23'8%26'69)39)*'39)'273073'$-'+7)'32'!BK'2*'32'39)
-$&%"(N
L2/)'20'"/0-'"*)'0*2#$+)+'6$39'362'"++$3$2%"('3)*/$%"(-'32'69$.9'"'-0).$1$)+'.$*.7$3
."%',)'.2%%).3)+'32'3*$/'32'[)*2'39)'273073'+.'#2(3"&)'+7)'32'!BK >'S$&7*)'Q>TF'-926-'-7.9
"%'"**"%&)/)%3'39"3'$-'340$."((4'7-)+'6$39'&)%)*"(B07*02-)'20'"/0->'H'023)%3$2/)3)*'$.2%%).3)+',)36))%'39)'211-)3B%7(($%&'3)*/$%"(-'6$39'39)'6$0)*'21'39)'023)%3$2/)3)*'.2%B
%).3)+' 32' 39)' 20B"/0' %)&"3$#)' -700(4>' R2#$%&' 39)' 023)%3$2/)3)*' 6$0)*' $%3*2+7.)-' "%
$/,"("%.)'39"3'.27%3)*".3-'39)'"-4//)3*4'0*)-)%3'$%'39)'$%3)*%"('20B"/0'.$*.7$3*4'"%+'39"3
&$#)-'*$-)'32'!BK>'Y)'-9"(('*)37*%'32'39$-'02$%3'$%'39)'.2%3)M3'21'27*'-37+4'21'39)'$%3)*%"('.$*B
.7$3*4'21'20'"/0-'$%'G9"03)*'CQ>'A3'-927(+',)'%23)+5'926)#)*5'39"3')#)%'3927&9'39)'+.'273B
073'211-)3'."%',)'3*$//)+'32'[)*25'39)'0*2,()/'*)/"$%-'21'39)'#"*$"3$2%'<2*'+*$13='21'!BK
6$39'3)/0)*"37*)>
?%)'6"4'32'2#)*.2/)'39)'+.'211-)3'0*2,()/'$-',4'."0".$3$#)(4'.270($%&'39)'"/0($1$)*>
;9$-5'926)#)*5'6$((',)'02--$,()'2%(4'$%'"00($."3$2%-'69)*)'39)'.(2-)+B(220'"/0($1$)*'$-'%23
*)K7$*)+' 32' "/0($14' +.' 2*' #)*4B(26B1*)K7)%.4' -$&%"(->' S$&7*)' Q>TC<"=' -926-' "' ."0".$3$#)(4
.270()+'"/0($1$)*>'e)."7-)'21'$3-'$%1$%$3)'$/0)+"%.)'"3'+.5'39)'.270($%&'."0".$32*'6$(('."7-)
39)' &"$%' 32' ,)' [)*2' "3' +.>' H-' "' *)-7(3' 39)' )K7$#"()%3' .$*.7$3' 12*' +)3)*/$%$%&' 39)' +.' 273073
91
92 Chapter 2 Operational Amplifiers
R2
!
!"
VOS
(a)
VO % VOS
"
Offset free
(b)
Figure 2.31 :,;'H'."0".$3$#)(4'.270()+'$%#)*3$%&'"/0($1$)*>':5;';9)')K7$#"()%3'.$*.7$3'12*'+)3)*/$%$%&'$3-'
+.'273073'211-)3'#2(3"&)'!B>
#2(3"&)'*)-7(3$%&'1*2/'39)'20B"/0'$%073'211-)3'#2(3"&)%!BK'6$((',)'39"3'-926%'$%'S$&>'Q>TC<,=>
;97-'!BK'-))-'$%')11).3'"'7%$34B&"$%'#2(3"&)'12((26)*5'"%+'39)'+.'273073'#2(3"&)' !B'6$((',)
)K7"('32'!BK'*"39)*'39"%'!BK ( C + ? Q ⁄ ? C )5'69$.9'$-'39)'."-)'6$39273'39)'.270($%&'."0".$32*>
H-'1"*'"-'$%073'-$&%"(-'"*)'.2%.)*%)+5'39)'.270($%&'."0".$32*'"'12*/-'32&)39)*'6$39'?C'"%'L;G
9$&9B0"--'.$*.7$3'6$39'"'.2*%)*'1*)K7)%.4'21'ω F = C ⁄ "? C >';97-'39)'&"$%'21'39)'."0".$3$#)(4
.270()+'"/0($1$)*'6$(('1"(('211'"3'39)'(26B1*)K7)%.4')%+'o1*2/'"'/"&%$37+)'21'( C + ? Q ⁄ ? C )'"3
9$&9'1*)K7)%.$)-p'"%+'6$((',)'T'+e'+26%'"3'ω F>
EXERCISES
2.22 G2%-$+)*'"%'$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'CFFF'.2%-3*7.3)+'1*2/'"%'20'"/0'6$39'"%
$%073'211-)3'#2(3"&)'21'T'/`'"%+'6$39'273073'-"37*"3$2%'()#)(-'21'±CF'`>'<"='Y9"3'$-'<"00*2M$/"3)(4=
39)'0)"8'-$%)B6"#)'$%073'-$&%"('39"3'."%',)'"00($)+'6$39273'273073'.($00$%&\'<,='A1'39)')11).3'21'!BK
$-'%7(()+'"3'*22/'3)/0)*"37*)'<QV°G=5'926'("*&)'"%'$%073'."%'2%)'%26'"00(4'$1:'<$='39)'.$*.7$3'$-'32
20)*"3)'"3'"'.2%-3"%3'3)/0)*"37*)\'<$$='39)'.$*.7$3'$-'32'20)*"3)'"3'"'3)/0)*"37*)'$%'39)'*"%&)'F°G'32
IV°G'"%+'39)'3)/0)*"37*)'.2)11$.$)%3'21'!BK'$-'CF'µ`d°G\
Ans. <"='I'/`X'<,='CF'/`5'D>V'/`
2.23 G2%-$+)*'39)'-"/)'"/0($1$)*'"-'$%'@M)*.$-)'Q>QQf39"3'$-5'"%'$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%
21'CFFF'.2%-3*7.3)+'1*2/'"%'20'"/0'6$39'"%'$%073'211-)3'#2(3"&)'21'T'/`'"%+'6$39'273073'-"37*"3$2%
()#)(-'21'±CF'`f)M.)03'9)*)'()3'39)'"/0($1$)*',)'."0".$3$#)(4'.270()+'"-'$%'S$&>'Q>TC<"=>'<"='Y9"3
$-'39)'+.'211-)3'#2(3"&)'"3'39)'2730735'"%+'69"3'<"00*2M$/"3)(4='$-'39)'0)"8'-$%)B6"#)'-$&%"('39"3'."%
,)'"00($)+'"3'39)'$%073'6$39273'273073'.($00$%&\'A-'39)*)'"'%))+'12*'211-)3'3*$//$%&\'<,='A1'?C'='C'8Ω
"%+'?Q'='C RΩ5'1$%+'39)'#"(7)'21'39)'.270($%&'."0".$32*'"C'39"3'6$((')%-7*)'39"3'39)'&"$%'6$((',)'&*)"3)*
39"%'VI'+e'+26%'32'CFF'![>
Ans. <"='T'/`5'CF'/`5'%2'%))+'12*'211-)3'3*$//$%&X'<,='C>E'µS
2.6 DC Imperfections
2.6.2 Input Bias and Offset Currents
;9)'-).2%+'+.'0*2,()/')%.27%3)*)+'$%'20'"/0-'$-'$((7-3*"3)+'$%'S$&>'Q>TQ>'A%'2*+)*'12*'39)'20
"/0' 32' 20)*"3)5' $3-' 362' $%073' 3)*/$%"(-' 9"#)' 32' ,)' -700($)+' 6$39' +.' .7**)%3-5' 3)*/)+' 39)
!"()&*5!,4*0)%%$"&4>U'A%'S$&>'Q>TQ'39)-)'362'.7**)%3-'"*)'*)0*)-)%3)+',4'362'.7**)%3'-27*.)-5
>LC'"%+'>LQ5'.2%%).3)+'32'39)'362'$%073'3)*/$%"(->'A3'-927(+',)')/09"-$[)+'39"3'39)'$%073',$".7**)%3-'"*)'$%+)0)%+)%3'21'39)'1".3'39"3'"'*)"('20'"/0'9"-'1$%$3)'<3927&9'("*&)='$%073'*)-$-B
3"%.)'<%23'-926%'$%'S$&>'Q>TQ=>';9)'20B"/0'/"%71".37*)*'7-7"((4'-0).$1$)-'39)'"#)*"&)'#"(7)
21'>LC'"%+'>LQ'"-'6)(('"-'39)$*')M0).3)+'+$11)*)%.)>';9)'"#)*"&)'#"(7)'>L'$-'."(()+'39)'!"()&
5!,4*0)%%$"&5
>LC + >LQ
B
>L = BBBBBBBBBBBBBBBBBB
Q
"%+'39)'+$11)*)%.)'$-'."(()+'39)'!"()&*.334$&*0)%%$"&'"%+'$-'&$#)%',4
>BK = >LC − >LQ
;40$."('#"(7)-'12*'&)%)*"(B07*02-)'20'"/0-'39"3'7-)',$02("*'3*"%-$-32*-'"*)'>L'= CFF'%H'"%+
>BK'= CF'%H>
Y)' %26' 6$-9' 32' 1$%+' 39)' +.' 273073' #2(3"&)' 21' 39)' .(2-)+B(220' "/0($1$)*' +7)' 32' 39)
$%073',$"-'.7**)%3->';2'+2'39$-'6)'&*27%+'39)'-$&%"('-27*.)'"%+'2,3"$%'39)'.$*.7$3'-926%'$%
S$&> Q>TT'12*',239'39)'$%#)*3$%&'"%+'%2%$%#)*3$%&'.2%1$&7*"3$2%->'H-'-926%'$%'S$&>'Q>TT5'39)
273073'+.'#2(3"&)'$-'&$#)%',4
!B = >LC ? Q ! > L ? Q
<Q>TI=
;9$-'2,#$27-(4'0(".)-'"%'700)*'($/$3'2%'39)'#"(7)'21'?Q>'S2*37%"3)(45'926)#)*5'"'3).9%$K7)
)M$-3-' 12*' *)+7.$%&' 39)' #"(7)' 21' 39)' 273073' +.' #2(3"&)' +7)' 32' 39)' $%073' ,$"-' .7**)%3->' ;9)
/)392+'.2%-$-3-'21'$%3*2+7.$%&'"'*)-$-3"%.)'?T'$%'-)*$)-'6$39'39)'%2%$%#)*3$%&'$%073'()"+5'"-
Figure 2.32 ;9)'20B"/0'$%073',$"-'.7**)%3-'
*)0*)-)%3)+',4'362'.7**)%3'-27*.)-'>LC'"%+'>LQ>
U
;9$-' $-' 39)' ."-)' 12*' 20' "/0-' .2%-3*7.3)+' 7-$%&' ,$02("*' W7%.3$2%' 3*"%-$-32*-' <eq;-=>' ;92-)' 7-$%&
R?LS@;-'$%'39)'1$*-3'<$%073='-3"&)'+2'%23'+*"6'"%'"00*).$",()'$%073',$"-'.7**)%3X'%)#)*39)()--5'39)'$%073
3)*/$%"(-'-927(+'9"#)'.2%3$%727-'+.'0"39-'32'&*27%+>'R2*)'2%'39$-'$%'("3)*'.9"03)*->
93
94 Chapter 2 Operational Amplifiers
Figure 2.33 H%"(4-$-'21'39)'.(2-)+B(220'"/0($1$)*5'3"8$%&'$%32'"..27%3'39)'$%073',$"-'.7**)%3->
Figure 2.34 O)+7.$%&'39)')11).3'21'39)'$%073',$"-'.7**)%3-',4'$%3*2+7.$%&'"'*)-$-32*'?T>
-926%'$%'S$&>'Q>TU>'S*2/'"'-$&%"('02$%3'21'#$)65'?T'9"-'"'%)&($&$,()')11).3'<$+)"((4'%2')11).3=>
;9)'"00*20*$"3)'#"(7)'12*'?T'."%',)'+)3)*/$%)+',4'"%"(4[$%&'39)'.$*.7$3'$%'S$&>'Q>TU5'69)*)
"%"(4-$-'+)3"$(-'"*)'-926%5'"%+'39)'273073'#2(3"&)'$-'&$#)%',4
!B = − >LQ ? T + ? Q ( >LC ! >LQ ? T ⁄ ? C )
G2%-$+)*'1$*-3'39)'."-)'>LC'='>LQ'='>L5'69$.9'*)-7(3-'$%
!B = >L [ ? Q ! ? T ( C + ? Q ⁄ ? C ) ]
<Q>Tc=
2.6 DC Imperfections
;97-'6)'."%'*)+7.)'!B'32'[)*2',4'-)().3$%&'?T'-7.9'39"3
?Q
?C ?Q
B
? T = BBBBBBBBBBBBBBBBBBBBBBBB
= BBBBBBBBBBBBBBBB
C + ?Q ⁄ ?C
?C + ?Q
<Q>TD=
;9"3'$-5'?T'-927(+',)'/"+)')K7"('32'39)'0"*"(()(')K7$#"()%3'21'?C'"%+'?Q>''
!"#$%&'-)().3)+'?T'"-'",2#)5'()3'7-')#"(7"3)'39)')11).3'21'"'1$%$3)'211-)3'.7**)%3'>BK>'k)3
>LC = >L + >BK ⁄ Q '"%+' >LQ = >L ! >BK ⁄ Q 5 '"%+'-7,-3$373)'$%'@K>'<Q>Tc=>';9)'*)-7(3'$-
!B = >BK ? Q
<Q>UF=
69$.9'$-'7-7"((4'",273'"%'2*+)*'21'/"&%$37+)'-/"(()*'39"%'39)'#"(7)'2,3"$%)+'6$39273'?T
<@K>'Q>TI=>'Y)'.2%.(7+)'39"3'32'/$%$/$[)'39)')11).3'21'39)'$%073',$"-'.7**)%3-5'2%)'-927(+
+3/0(%)*%&'(%+14)&);(%3(/.%/%8(4)4&/*0(%(M,/3%&1%&'(%(M,);/3/*&%+.%8(4)4&/*0(%4((*%5=%&'(
)*;(8&)*<%&(8-)*/36'Y)')/09"-$[)'39)'62*+'.0'$%'39)'("-3'-3"3)/)%3X'%23)'39"3'$1'39)'"/0($B
1$)*'$-'".B.270()+5'6)'-927(+'-)().3'?T'='?Q5'"-'-926%'$%'S$&>'Q>TV>
Y9$()'6)'"*)'2%'39)'-7,W).3'21'".B.270()+'"/0($1$)*-5'6)'-927(+'%23)'39"3'2%)'/7-3
"(6"4-'0*2#$+)'"'.2%3$%727-'+.'0"39',)36))%')".9'21'39)'$%073'3)*/$%"(-'21'39)'20'"/0
"%+'&*27%+>';9$-'$-'39)'."-)'%2'/"33)*'926'-/"(('>L'$->'S2*'39$-'*)"-2%'39)'".B.270()+
%2%$%#)*3$%&' "/0($1$)*'21'S$&>' Q>TE'6$((' *1&'62*8'6$39273' 39)' *)-$-3"%.)' ?T'32'&*27%+>
a%12*37%"3)(45'$%.(7+$%&'?T'(26)*-'.2%-$+)*",(4'39)'$%073'*)-$-3"%.)'21'39)'.(2-)+B(220
"/0($1$)*>''
Figure 2.35 A%'"%'".B.270()+'"/0($1$)*'39)'+.'*)-$-3"%.)'-))%',4'39)'$%#)*3$%&'3)*/$%"('$-'?QX'9)%.)
?T'$-'.92-)%')K7"('32'?Q>
% R2
Figure 2.36 A((7-3*"3$%&'39)'%))+'12*'"'.2%3$%727-'+.'0"39'12*')".9'21'39)'20B"/0'$%073'3)*/$%"(->'L0).$1$B
."((45'%23)'39"3'39)'"/0($1$)*'6$(('*1&'62*8'6$39273'*)-$-32*'?T>
95
96 Chapter 2 Operational Amplifiers
EXERCISE
2.24 G2%-$+)*'"%'$%#)*3$%&'"/0($1$)*'.$*.7$3'+)-$&%)+'7-$%&'"%'20'"/0'"%+'362'*)-$-32*-5'?C'='CF'8Ω'"%+
?Q ='C'RΩ>'A1'39)'20'"/0'$-'-0).$1$)+'32'9"#)'"%'$%073',$"-'.7**)%3'21'CFF'%H'"%+'"%'$%073'211-)3
.7**)%3'21'CF'%H5'1$%+'39)'273073'+.'211-)3'#2(3"&)'*)-7(3$%&'"%+'39)'#"(7)'21'"'*)-$-32*'?T'32',)'0(".)+
$%'-)*$)-'6$39'39)'02-$3$#)'$%073'()"+'$%'2*+)*'32'/$%$/$[)'39)'273073'211-)3'#2(3"&)>'Y9"3'$-'39)'%)6
#"(7)'21%!B\
Ans. F>C'`X'D>D'8Ω'<!'CF'8Ω=X'F>FC'`
2.6.3 Effect of VOS and IOS on the Operation of the
Inverting Integrator
?7*'+$-.7--$2%'21'39)'$%#)*3$%&'$%3)&*"32*'.$*.7$3'$%'L).3$2%'Q>V>Q'/)%3$2%)+'39)'-7-.)03$,$($34
21' 39$-' .$*.7$3' 32' -"37*"3$2%' $%' 39)' 0*)-)%.)' 21' -/"((' +.' #2(3"&)-' 2*' .7**)%3->' A3' ,)922#)-' 739)*)12*)'32'.2%-$+)*'39)')11).3'21'39)'20B"/0'+.'211-)3-'2%'$3-'20)*"3$2%>'H-'6$((',)'-))%5'39)-)
)11).3-'."%',)'K7$3)'+*"/"3$.>
;2'-))'39)')11).3'21'39)'$%073'+.'211-)3'#2(3"&)'!BK 5'.2%-$+)*'39)'$%3)&*"32*'.$*.7$3'$%'S$&>
Q>Tc5'69)*)'12*'-$/0($.$34'6)'9"#)'-92*3B.$*.7$3)+'39)'$%073'-$&%"('-27*.)>'H%"(4-$-'21'39)
.$*.7$3'$-'-3*"$&9312*6"*+'"%+'$-'-926%'$%'S$&>'Q>TI>'H--7/$%&'12*'-$/0($.$34'39"3'"3'3$/)'&'='F
39)'#2(3"&)'".*2--'39)'."0".$32*'$-'[)*25'39)'273073'#2(3"&)'"-'"'17%.3$2%'21'3$/)'$-'&$#)%',4'''
!BK
B &'
v B = !BK + BBBBBBB
"?
<Q>UC=
;97-'vB'$%.*)"-)-'($%)"*(4'6$39'3$/)'7%3$('39)'20'"/0'-"37*"3)-f.()"*(4'"%'7%"..)03",()'-$3B
7"3$2%N'H-'-927(+',)')M0).3)+5'39)'+.'$%073'211-)3'.7**)%3'>BK'0*2+7.)-'"'-$/$("*'0*2,()/>
S$&7*)'Q>Tc'$((7-3*"3)-'39)'-$37"3$2%>'?,-)*#)'39"3'6)'9"#)'"++)+'"'*)-$-3"%.)'?'$%'39)'20B
"/0'02-$3$#)B$%073'()"+'$%'2*+)*'32'8))0'39)'$%073',$"-'.7**)%3'>L'1*2/'1(26$%&'39*27&9'">
P)#)*39)()--5'39)'211-)3'.7**)%3'>BK'6$(('1(26'39*27&9'"'"%+'."7-)'vB'32'*"/0'($%)"*(4'6$39
3$/)'7%3$('39)'20'"/0'-"37*"3)->
H-'/)%3$2%)+'$%'L).3$2%'Q>V>Q'39)'+.'0*2,()/'21'39)'$%3)&*"32*'.$*.7$3'."%',)'"(()#$B
"3)+',4'.2%%).3$%&'"'*)-$-32*'?J'".*2--'39)'$%3)&*"32*'."0".$32*'"5'"-'-926%'$%'S$&>'Q>QV>
!
"
t
Figure 2.37 j)3)*/$%$%&'39)')11).3'21'39)'20B"/0'$%073'211-)3'#2("&)'!BK'2%'39)'R$(()*'$%3)&*"B
32*'.$*.7$3>'P23)'39"3'-$%.)'39)'273073'*$-)-'6$39'3$/)5'39)'20'"/0')#)%37"((4'-"37*"3)->
2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance
L7.9' "' *)-$-32*' 0*2#$+)-' "' +.' 0"39' 39*27&9' 69$.9' 39)' +.' .7**)%3-' <!BK ⁄ ? =' "%+' >BK' ."%
1(265' 6$39' 39)' *)-7(3' 39"3' vB' 6$((' %26' 9"#)' "' +.' .2/02%)%3' o!BK ( C + ? J ⁄ ? ) + > BK ? J p
$%-3)"+'21'*$-$%&'($%)"*(4>';2'8))0'39)'+.'211-)3'"3'39)'273073'-/"((5'2%)'627(+'-)().3'"
(26'#"(7)'12*'?J>'a%12*37%"3)(45'926)#)*5'39)'(26)*'39)'#"(7)'21'?J5'39)'()--'$+)"('39)
$%3)&*"32*'.$*.7$3',).2/)->'''
C
(IB1 ! IB2) % IOS
IB2R#R % IB2
R
IB1
!
IB2
R
!IB2R
"
vO
vO % !IB2R "
Figure 2.38 @11).3'21'39)'20B"/0'
IOS $%073',$"-'"%+'211-)3'.7**)%3-'2%'39)'
t
C
0)*12*/"%.)'21'39)'R$(()*'$%3)&*"32*'
.$*.7$3>
EXERCISE
2.25'G2%-$+)*'"'R$(()*'$%3)&*"32*'6$39'"'3$/)'.2%-3"%3'21'C'/-'"%+'"%'$%073'*)-$-3"%.)'21'CF'8Ω>'k)3'39)
20'"/0'9"#)'!BK'='Q'/`'"%+'273073'-"37*"3$2%'#2(3"&)-'21''±CQ'`>'<"='H--7/$%&'39"3'69)%'39)
026)*'-700(4'$-'37*%)+'2%'39)'."0".$32*'#2(3"&)'$-'[)*25'926'(2%&'+2)-'$3'3"8)'12*'39)'"/0($1$)*'32
-"37*"3)\'<,='L)().3'39)'("*&)-3'02--$,()'#"(7)'12*'"'1))+,".8'*)-$-32*'?J'-2'39"3'"3'()"-3'±10'`'21
273073' -$&%"(' -6$%&'*)/"$%-' "#"$(",()>' Y9"3'$-' 39)' .2*%)*' 1*)K7)%.4' 21' 39)'*)-7(3$%&' L;G'%)3B
62*8\
Ans. <"='E'-X'<,='CF'RΩ5'F>CE'!['
2.7 Effect of Finite Open-Loop Gain and
Bandwidth on Circuit Performance
2.7.1 Frequency Dependence of the Open-Loop Gain
;9)'+$11)*)%3$"('20)%B(220'&"$%'$%21'"%'20'"/0'$-'%23'$%1$%$3)X'*"39)*5'$3'$-'1$%$3)'"%+'+).*)"-)6$39'1*)K7)%.4>'S$&7*)'Q>TD'-926-'"'0(23'12*' $ 5'6$39'39)'%7/,)*-'340$."('21'-2/)'.2//)*B
.$"((4'"#"$(",()'&)%)*"(B07*02-)'20'"/0-'<-7.9'"-'39)'0207("*'IUCB340)'20'"/05'"#"$(",()'1*2/
/"%4'-)/$.2%+7.32*'/"%71".37*)*-X'$3-'$%3)*%"('.$*.7$3'$-'-37+$)+'$%'G9"03)*'CQ=>
P23)'39"3'"(3927&9'39)'&"$%'$-'K7$3)'9$&9'"3'+.'"%+'(26'1*)K7)%.$)-5'$3'-3"*3-'32'1"(('211
"3'"'*"39)*'(26'1*)K7)%.4'<CF'!['$%'27*')M"/0()=>';9)'7%$12*/'nQFB+ed+)."+)'&"$%'*2((211
-926%'$-'340$."('21'!"&$%",--9*0.+($"4,&$1'20'"/0->';9)-)'"*)'7%$3-'39"3'9"#)'"'%)362*8
<7-7"((4'"'-$%&()'."0".$32*='$%.(7+)+'6$39$%'39)'-"/)'AG'.9$0'692-)'17%.3$2%'$-'32'."7-)
39)' 20B"/0' &"$%'32' 9"#)'39)'-$%&()B3$/)B.2%-3"%3' <L;G=' (26B0"--'*)-02%-)'-926%>' ;9$-
97
98 Chapter 2 Operational Amplifiers
Figure 2.39 ?0)%B(220'&"$%'21'"'340$."('&)%)*"(B07*02-)'$%3)*%"((4'.2/0)%-"3)+'20'"/0>
0*2.)--' 21' /2+$14$%&' 39)' 20)%B(220' &"$%' $-' 3)*/)+' 3%$?)$"09* 0.+($"4,&!."5' "%+' $307*02-)'$-'32')%-7*)'39"3'20B"/0'.$*.7$3-'6$((' ,)'-3",()'<"-'2002-)+'32'2-.$(("32*4=>';9)
-7,W).3'21'-3",$($34'21'20B"/0'.$*.7$3-f2*5'/2*)'&)%)*"((45'21'1))+,".8'"/0($1$)*-f6$((
,)'-37+$)+'$%'G9"03)*'CF>
e4' "%"(2&4' 32' 39)' *)-02%-)' 21' (26B0"--' L;G' .$*.7$3-' <-))' L).3$2%' C>E' "%+5' 12*' /2*)
+)3"$(5'H00)%+$M'@=5'39)'&"$%'$<4='21'"%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'/"4',)')M0*)--)+'"-
$F
$ ( 4 ) = BBBBBBBBBBBBBBBBBBBBB
C + 4 ⁄ ω5
<Q>UQ=
69$.9'12*'094-$."('1*)K7)%.$)-5'4'='Gω5',).2/)-
$F
B
$ ( G ω ) = BBBBBBBBBBBBBBBBBBBBBBBB
C + G ω ⁄ ω5
<Q>UT=
69)*)'$F'+)%23)-'39)'+.'&"$%'"%+'ω5'$-'39)'TB+e'1*)K7)%.4'<.2*%)*'1*)K7)%.4'2*'^,*)"8_'1*)B
K7)%.4=>'S2*'39)')M"/0()'-926%'$%'S$&>'Q>TD5'$F'='CFV'"%+'ω5'='Qπ '×'CF'*"+d->'S2*'1*)K7)%.$)-'
ω')'ω5'<",273'CF'3$/)-'"%+'9$&9)*='@K>'<Q>UT='/"4',)'"00*2M$/"3)+',4
$F ω5
B
$ ( G ω )'!' BBBBBBBBBBB
Gω
<Q>UU=
$F ω5
B
$ ( G ω ) ' = BBBBBBBBBBB
<Q>UV=
;97-5
ω
1*2/'69$.9'$3'."%',)'-))%'39"3'39)'&"$%'r$r'*)".9)-'7%$34'<F'+e='"3'"'1*)K7)%.4'+)%23)+',4'ω&'
"%+'&$#)%',4
ω& 3 $F ω5
<Q>UE=
2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance
L7,-3$373$%&'$%'@K>'<Q>UU='&$#)-
ω
$ ( G ω )'!' BBBBBB&
Gω
<Q>UI=
;9)'1*)K7)%.4' 2 & = ω & ⁄ Q π '$-'7-7"((4'-0).$1$)+'2%'39)'+"3"'-9))3-'21'.2//)*.$"((4'"#"$(",()
20'"/0-'"%+'$-'8%26%'"-'39)')"!&9/',!"*5,"18!1&7>V'H(-2'%23)'39"3'12*' ω')' ω5'39)'20)%B
(220'&"$%'$%'@K>'<Q>UQ=',).2/)-
ω
$ ( 4 )'!' BBBBB&
4
<Q>Uc=
;9)'&"$%'/"&%$37+)'."%',)'2,3"$%)+'1*2/'@K>'<Q>UI='"-
ω 2
$ ( G ω ) ! BBBBB& = BB&
ω 2
<Q>UD=
;97-'$1'2&'$-'8%26%'<CFE'!['$%'27*')M"/0()=5'2%)'."%')"-$(4'+)3)*/$%)'39)'/"&%$37+)'21'39)
20B"/0'&"$%' "3'"' &$#)%' 1*)K7)%.4' 2>' S7*39)*/2*)5' 2,-)*#)'39"3' 39$-' *)("3$2%-9$0' .2**)("3)6$39'39)'e2+)'0(23'$%'S$&>'Q>TD>'L0).$1$."((45'12*'2')'255%+27,($%&'2'<"%'2.3"#)'$%.*)"-)='*)-7(3$%' 9"(#$%&' 39)' &"$%' <"' EB+e' *)+7.3$2%=>' L$/$("*(45' $%.*)"-$%&% 2' ,4' "' 1".32*' 21' CF' <"' +)."+)
$%.*)"-)='*)-7(3-'$%'*)+7.$%&'r$r',4'"'1".32*'21'CF'<QF'+e=>
H-'"'/"33)*'21'0*".3$."('$/02*3"%.)5'6)'%23)'39"3'39)'0*2+7.3$2%'-0*)"+'$%'39)'#"(7)'21'2&
,)36))%'20B"/0'7%$3-'21'39)'-"/)'340)'$-'7-7"((4'/7.9'-/"(()*'39"%'39"3'2,-)*#)+'12*'$F'"%+
25>'S2*'39$-'*)"-2%'2&'$-'0*)1)**)+'"-'"'-0).$1$."3$2%'0"*"/)3)*>'S$%"((45'$3'-927(+',)'/)%3$2%)+
39"3' "%' 20' "/0' 9"#$%&' 39$-' 7%$12*/' nEB+ed2.3"#)' <2*' )K7$#"()%3(4' nQFB+ed+)."+)=' &"$%
*2((211'$-'-"$+'32'9"#)'"'4!"'-$/(.-$*+.1$->'H(-25'-$%.)'39$-'-$%&()'02()'.1-)*/&(4'39)'"/0($B
1$)*'1*)K7)%.4'*)-02%-)5'$3'$-'."(()+'"'.1-)*/*&%+13(>*S2*'/2*)'2%'02()-'<"%+'[)*2-=5'39)'*)"+)*
/"4'6$-9'32'.2%-7(3'H00)%+$M'S>
EXERCISE
2.26 H%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'$-'-0).$1$)+'32'9"#)'"%'20)%B(220'+.'&"$%'21'CFE'+e'"%+'"'7%$34B
&"$%',"%+6$+39'21'T'R![>'S$%+'25'"%+'39)'20)%B(220'&"$%'<$%'+e='"3'255'TFF'![5'T'8![5'CQ'8![5'"%+
EF'8![>
Ans. CV'![X'CFT'+eX'cF'+eX'EF'+eX'Uc'+eX'TU'+e
2.7.2 Frequency Response of Closed-Loop Amplifiers
Y)'%)M3'.2%-$+)*'39)')11).3'21'($/$3)+'20B"/0'&"$%'"%+',"%+6$+39'2%'39)'.(2-)+B(220'3*"%-1)*
17%.3$2%-'21'39)'362',"-$.'.2%1$&7*"3$2%-:'39)'$%#)*3$%&'.$*.7$3'21'S$&>'Q>V'"%+'39)'%2%$%#)*3$%&
.$*.7$3'21'S$&>'Q>CQ>';9)'.(2-)+B(220'&"$%'21'39)'$%#)*3$%&'"/0($1$)*5'"--7/$%&'"'1$%$3)'20B"/0
20)%B(220'&"$%'$5'6"-'+)*$#)+'$%'L).3$2%'Q>Q'"%+'&$#)%'$%'@K>'<Q>V=5'69$.9'6)'*)0)"3'9)*)'"-
!1
!?Q ⁄ ?C
BBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
C + ( C + ?Q ⁄ ?C ) ⁄ $
!)
<Q>VF=
L$%.)'2&'$-'39)'0*2+7.3'21'39)'+.'&"$%'$F'"%+'39)'TB+e',"%+6$+39'25'<69)*)'25 = ω5 /Qπ=5'$3'$-'"(-2'8%26%
"-'39)'',!"@5,"18!1&7*(%.1)0&'<ie=>';9)'*)"+)*'$-'."73$2%)+5'926)#)*5'39"3'$%'-2/)'"/0($1$)*-5'39)
7%$34B&"$%'1*)K7)%.4'"%+'39)'&"$%B,"%+6$+39'0*2+7.3'"*)'*1&')K7"(>
V
99
100 Chapter 2 Operational Amplifiers
L7,-3$373$%&'12*'$'1*2/'@K>'<Q>UQ='"%+'7-$%&'@K>'<Q>UE='&$#)-
!1 ( 4 )
!?Q ⁄ ?C
BBBBBBBBBBBB
B = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
?Q C
4
BBBB
B
BBBBB
B
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
C+
C+
+
?C
ω& ⁄ ( C + ?Q ⁄ ?C )
$F <Q>VC=
l C + ? Q ⁄ ? C 5 '69$.9'$-'7-7"((4'39)'."-)5
S2*' $ F s
l
!1 ( 4 )
!?Q ⁄ ?C
BBBBBBBBBBBB
B ≈ BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
4
C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
ω& ⁄ ( C + ?Q ⁄ ?C )
<Q>VQ=
69$.9'$-'21'39)'-"/)'12*/'"-'39"3'12*'"'(26B0"--'L;G'%)362*8'<-))';",()'C>Q5'0"&)'TU=>';9739)'$%#)*3$%&'"/0($1$)*'9"-'"%'L;G'(26B0"--'*)-02%-)'6$39'"'+.'&"$%'21'/"&%$37+)')K7"('32
?Q /?C>';9)'.(2-)+B(220'&"$%'*2((-'211'"3'"'7%$12*/'nQFB+ed+)."+)'-(20)'6$39'"'.2*%)*'1*)B
K7)%.4'<TB+e'1*)K7)%.4='&$#)%',4
ω&
ω T+e = BBBBBBBBBBBBBBBBBBBBBBBB
C + ?Q ⁄ ?C
<Q>VT=
L$/$("*(45'"%"(4-$-'21'39)'%2%$%#)*3$%&'"/0($1$)*'21'S$&>'Q>CQ5'"--7/$%&'"'1$%$3)'20)%B(220
&"$%'$5'4$)(+-'39)'.(2-)+B(220'3*"%-1)*'17%.3$2%
!1
C + ?Q ⁄ ?C
BBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
!)
C + ( C + ?Q ⁄ ?C ) ⁄ $
<Q>VU=
l C + ? Q ⁄ ? C'*)-7(3-'$%
L7,-3$373$%&'12*'$'1*2/'@K>'<Q>UQ='"%+'/"8$%&'39)'"00*2M$/"3$2%' $ F s
l
!1 ( 4 )
C + ?Q ⁄ ?C
BBBBBBBBBBBB
B ! BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
!) ( 4 )
4
C + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
ω& ⁄ ( C + ?Q ⁄ ?C )
<Q>VV=
;97-'39)'%2%$%#)*3$%&'"/0($1$)*'9"-'"%'L;G'(26B0"--'*)-02%-)'6$39'"'+.'&"$%'21'( C + ? Q ⁄ ? C )
"%+'"'TB+e'1*)K7)%.4'&$#)%'"(-2',4'@K>'<Q>VT=>
Example 2.6
G2%-$+)*'"%'20'"/0'6$39'2& = C'R![>'S$%+'39)'TB+e'1*)K7)%.4'21'.(2-)+B(220'"/0($1$)*-'6$39'%2/$B
%"(' &"$%-' 21' +CFFF5' +CFF5' +CF5' +C5' −C5' −CF5' −CFF5' "%+' −CFFF>' L8)3.9' 39)' /"&%$37+)' 1*)K7)%.4
*)-02%-)'12*'39)'"/0($1$)*-'6$39'.(2-)+B(220'&"$%-'21'+CF'"%+'nCF>
Solution
Y)'7-)'@K>'<Q>VT='32'2,3"$%'39)'*)-7(3-'&$#)%'$%'39)'12((26$%&'3",()>
Closed-Loop Gain
+CFFF
+CFF
+CF
+C
−C
−CF
−CFF
−CFFF
R2 ⁄ R1
'''''''''''''''''''DDD
'''''''''''''DD
D
F
C
CF
CFF
CFFF
f3 dB = ft / (1 + R2 ⁄R1)
C'8![
CF'8![
CFF'8![
''C'R![
F>V'R![
DF>D'8![
D>D'8![
!C'8![
2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance
S$&7*)'Q>UF'-926-'39)'1*)K7)%.4'*)-02%-)'12*'39)'"/0($1$)*'692-)'%2/$%"('+.'&"$%'$-'tCF
<QF +e=5'"%+'S$&>'Q>UC'-926-'39)'1*)K7)%.4'*)-02%-)'12*'39)'nCF'<"(-2'QF'+e='."-)>'H%'$%3)*)-3B
$%&'2,-)*#"3$2%'12((26-'1*2/'39)'3",()'",2#):';9)'7%$34B&"$%'$%#)*3$%&'"/0($1$)*'9"-'"'TB+e'1*)B
K7)%.4'21'2& dQ'"-'.2/0"*)+'32'2&'12*'39)'7%$34B&"$%'%2%$%#)*3$%&'"/0($1$)*'<39)'7%$34B&"$%'#2(3"&)
12((26)*=>''''
Figure 2.40 S*)K7)%.4'*)-02%-)'21'"%'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'+CF'`d`>
Figure 2.41 S*)K7)%.4'*)-02%-)'21'"%'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'−CF'`d`>
;9)'3",()'$%'@M"/0()'Q>E'",2#)'.()"*(4'$((7-3*"3)-'39)'3*"+)B211',)36))%'&"$%'"%+',"%+B
6$+39:'S2*'"'&$#)%'20'"/05'39)'(26)*'39)'.(2-)+B(220'&"$%'*)K7$*)+5'39)'6$+)*'39)',"%+6$+39
".9$)#)+>'A%+))+5'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%')M9$,$3-'"'.2%-3"%3'',!"@5,"18!1&7*(%.1)0&
)K7"('32'2&'21'39)'20'"/0>'H%'$%3)*0*)3"3$2%'21'39)-)'*)-7(3-'$%'3)*/-'21'1))+,".8'39)2*4'6$((',)
&$#)%'$%'G9"03)*'CF>
101
102 Chapter 2 Operational Amplifiers
EXERCISES
2.27 H%'$%3)*%"((4'.2/0)%-"3)+'20'"/0'9"-'"'+.'20)%B(220'&"$%'21'CFE'`d`'"%+'"%'".'20)%B(220'&"$%'21'UF
+e'"3'CF'8![>'@-3$/"3)'$3-'TB+e'1*)K7)%.45'$3-'7%$34B&"$%'1*)K7)%.45'$3-'&"$%n,"%+6$+39'0*2+7.35
"%+'$3-')M0).3)+'&"$%'"3'C'8![>
Ans. C'![X'C'R![X'C'R![X'EF'+e
2.28 H%'20'"/0'9"#$%&'"'CFEB+e'&"$%'"3'+.'"%+'"'-$%&()B02()'1*)K7)%.4'*)-02%-)'6$39'2&'Z'Q'R!['$7-)+'32'+)-$&%'"'%2%$%#)*3$%&'"/0($1$)*'6$39'%2/$%"('+.'&"$%'21'CFF>'S$%+'39)'TB+e'1*)K7)%.4'21
39)'.(2-)+B(220'&"$%>
Ans. QF'8![
2.8 Large-Signal Operation of Op Amps
A%'39$-'-).3$2%5'6)'-37+4'39)'($/$3"3$2%-'2%'39)'0)*12*/"%.)'21'20B"/0'.$*.7$3-'69)%'("*&)
273073'-$&%"(-'"*)'0*)-)%3>
2.8.1 Output Voltage Saturation
L$/$("*'32'"(('239)*'"/0($1$)*-5'20'"/0-'20)*"3)'($%)"*(4'2#)*'"'($/$3)+'*"%&)'21'273073'#2(3B
"&)->'L0).$1$."((45'39)'20B"/0'273073'-"37*"3)-'$%'39)'/"%%)*'-926%'$%'S$&>'C>CU'6$39'Dt'"%+
Dn'6$39$%'C'`'2*'-2'21'39)'02-$3$#)'"%+'%)&"3$#)'026)*'-700($)-5'*)-0).3$#)(4>';97-5'"%'20
"/0' 39"3' $-' 20)*"3$%&' 1*2/' ±CVB`' -700($)-' 6$((' -"37*"3)' 69)%' 39)' 273073' #2(3"&)' *)".9)",273'+CT'`'$%'39)'02-$3$#)'+$*).3$2%'"%+'nCT'`'$%'39)'%)&"3$#)'+$*).3$2%>'S2*'39$-'0"*3$.7("*
20'"/0'39)'%,&$1*.)&()&*#.-&,'$'$-'-"$+'32',)'±CT'`>';2'"#2$+'.($00$%&'211'39)'0)"8-'21'39)
273073'6"#)12*/5'"%+'39)'*)-7(3$%&'6"#)12*/'+$-32*3$2%5'39)'$%073'-$&%"('/7-3',)'8)03'.2**)B
-02%+$%&(4'-/"((>
2.8.2 Output Current Limits
H%239)*' ($/$3"3$2%'2%'39)' 20)*"3$2%'21'20'"/0-'$-'39"3' 39)$*'273073'.7**)%3'$-'($/$3)+'32'"
-0).$1$)+'/"M$/7/>'S2*'$%-3"%.)5'39)'0207("*'IUC'20'"/0'$-'-0).$1$)+'32'9"#)'"'/"M$/7/
273073' .7**)%3' 21' ±QF' /H>' ;97-5' $%' +)-$&%$%&' .(2-)+B(220' .$*.7$3-' 73$($[$%&' 39)' IUC5' 39)
+)-$&%)*'9"-'32')%-7*)'39"3'7%+)*'%2'.2%+$3$2%'6$(('39)'20'"/0',)'*)K7$*)+'32'-700(4'"%'273B
073'.7**)%35'$%')$39)*'+$*).3$2%5')M.))+$%&'QF'/H>';9$-5'21'.27*-)5'9"-'32'$%.(7+)',239'39)
.7**)%3'$%'39)'1))+,".8'.$*.7$3'"-'6)(('"-'39)'.7**)%3'-700($)+'32'"'(2"+'*)-$-32*>'A1'39)'.$*.7$3
*)K7$*)-'"'("*&)*'.7**)%35'39)'20B"/0'273073'#2(3"&)'6$(('-"37*"3)'"3'39)'()#)('.2**)-02%+$%&
32'39)'/"M$/7/'"((26)+'273073'.7**)%3>
103
2.8 Large-Signal Operation of Op Amps
Example 2.7
G2%-$+)*'39)'%2%$%#)*3$%&'"/0($1$)*'.$*.7$3'-926%'$%'S$&>'Q>UQ>'H-'-926%5'39)'.$*.7$3'$-'+)-$&%)+'12*
"'%2/$%"('&"$%' ( C + ? Q ⁄ ? C ) = CF'`d`>'A3'$-'1)+'6$39'"'(26B1*)K7)%.4'-$%)B6"#)'-$&%"('21'0)"8'#2(3"&)
!+'"%+'$-'.2%%).3)+'32'"'(2"+'*)-$-32*'?D>';9)'20'"/0'$-'-0).$1$)+'32'9"#)'273073'-"37*"3$2%'#2(3"&)21'±CT'`'"%+'273073'.7**)%3'($/$3-'21'±QF'/H>
<"= S2*'!+'='C'`'"%+'?D'='C'8Ω, -0).$14'39)'-$&%"('*)-7(3$%&'"3'39)'273073'21'39)'"/0($1$)*>
<,= S2*'!+'='C>V'`'"%+'?D'='C'8Ω5'-0).$14'39)'-$&%"('*)-7(3$%&'"3'39)'273073'21'39)'"/0($1$)*>
<.= S2*'?D' ='C'8Ω5'69"3'$-'39)'/"M$/7/'#"(7)'21'!+'12*'69$.9'"%'7%+$-32*3)+'-$%)B6"#)'273073'$2,3"$%)+\
<+= S2*' !+' =' C' `5' 69"3' $-' 39)' (26)-3' #"(7)' 21' ?D' 12*' 69$.9' "%' 7%+$-32*3)+' -$%)B6"#)' 273073' $2,3"$%)+\
vO
15 V
R2 % 9 k&
1 k&
!
R1
"
Vp
0
t
vI
iO
13 V
iF
vO
RL
"
!
0
t
iL
!13 V
!15 V
(a)
(b)
Figure 2.42 :,;'H'%2%$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%'21'CF `d`'+)-$&%)+'7-$%&'"%'20'"/0'39"3'-"37*"3)-'"3
±CTB`'273073'#2(3"&)'"%+'9"-'±QFB/H'273073'.7**)%3'($/$3->':5;*Y9)%'39)'$%073'-$%)'6"#)'9"-'"'0)"8'21'C>V `5'39)
273073'$-'.($00)+'211'"3'±CT'`>
Solution
<"= S2*'!+'='C'`'"%+'?D'='C'8Ω5'39)'273073'6$((',)'"'-$%)'6"#)'6$39'0)"8'#"(7)'21'CF'`>';9$-'$(26)*'39"%'273073'-"37*"3$2%'()#)(-'21'±CT'`5'"%+'397-'39)'"/0($1$)*'$-'%23'($/$3)+'39"3'6"4>'H(-25
69)%'39)'273073'$-'"3'$3-'0)"8'<CF'`=5'39)'.7**)%3'$%'39)'(2"+'6$((',)' CF'` ⁄ C '8Ω'='CF'/H5'"%+
39)'.7**)%3'$%'39)'1))+,".8'%)362*8'6$((',)'CF' ` ⁄ ( D + C )'8Ω'='C'/H5'12*'"'323"('20B"/0'273073
.7**)%3'21'CC'/H5'6)(('7%+)*'$3-'($/$3'21'QF'/H>
<,= P26'$1'!+'$-'$%.*)"-)+'32'C>V'`5'$+)"((4'39)'273073'627(+',)'"'-$%)'6"#)'21'CVB`'0)"8>';9)'20
"/05'926)#)*5'6$(('-"37*"3)'"3'±CT'`5'397-'.($00$%&'39)'-$%)B6"#)'273073'"3'39)-)'()#)(->'k)3J%)M3'.9).8'2%'39)'20B"/0'273073'.7**)%3:'H3'CTB`'273073'"%+'?D'='C'8Ω5')D'='CT'/H'"%+')J'=
C>T'/HX'397-')B'='CU>T'/H5'"&"$%'7%+)*'39)'QFB/H'($/$3>';97-'39)'273073'6$((',)'"'-$%)'6"#)
6$39'$3-'0)"8-'.($00)+'211'"3'±CT'`5'"-'-926%'$%'S$&>'Q>UQ<,=>
104 Chapter 2 Operational Amplifiers
Example 2.7 continued
<.= S2*'?D'='C'8Ω5'39)'/"M$/7/'#"(7)'21'!+'12*'7%+$-32*3)+'-$%)B6"#)'273073'$-'C>T'`>';9)'273073
6$((',)'"'CTB`'0)"8'-$%)'6"#)5'"%+'39)'20B"/0'273073'.7**)%3'"3'39)'0)"8-'6$((',)'CU>T'/H>
<+= S2*'!+'='C'`'"%+'?D'*)+7.)+5'39)'(26)-3'#"(7)'02--$,()'12*'?D'69$()'39)'273073'$-'*)/"$%$%&'"%
7%+$-32*3)+'-$%)'6"#)'21'CFB`'0)"8'."%',)'127%+'1*2/
CF'`
CF'`
) B/"M = QF'/H = BBBBBBBBBBBB + BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
? D/$% D'8Ω + C'8Ω
69$.9'*)-7(3-'$%
? D/$% = VQE'Ω
2.8.3 Slew Rate
H%239)*' 09)%2/)%2%' 39"3' ."%' ."7-)' %2%($%)"*' +$-32*3$2%' 69)%' ("*&)' 273073' -$&%"(-' "*)
0*)-)%3'$-'-()6B*"3)'($/$3$%&>';9)'%"/)'*)1)*-'32'39)'1".3'39"3'39)*)'$-'"'-0).$1$.'-/C)-,8/&(%12%0'/*<('02--$,()'"3'39)'273073'21'"'*)"('20'"/0>';9$-'/"M$/7/'$-'8%26%'"-'39)'4-$8
%,&$'<LO='21'39)'20'"/0'"%+'$-'+)1$%)+'"-
.v B
LO = BBBBBBBB
B
.& /"M
<Q>VE=
"%+'$-'7-7"((4'-0).$1$)+'2%'39)'20B"/0'+"3"'-9))3'$%'7%$3-'21'`dµ->' A3'12((26-'39"3'$1'39)'$%073
-$&%"('"00($)+'32'"%'20B"/0'.$*.7$3'$-'-7.9'39"3'$3'+)/"%+-'"%'273073'*)-02%-)'39"3'$-'1"-3)*
39"%'39)'-0).$1$)+'#"(7)'21'LO5'39)'20'"/0'6$(('%23'.2/0(4>'O"39)*5'$3-'273073'6$(('.9"%&)'"3
39)'/"M$/7/'02--$,()'*"3)5'69$.9'$-')K7"('32'$3-'LO>'H-'"%')M"/0()5'.2%-$+)*'"%'20'"/0
.2%%).3)+'$%'39)'7%$34B&"$%'#2(3"&)B12((26)*'.2%1$&7*"3$2%'-926%'$%'S$&>'Q>UT<"=5'"%+'()3'39)
$%073'-$&%"(',)'39)'-3)0'#2(3"&)'-926%'$%'S$&>'Q>UT<,=>';9)'273073'21'39)'20'"/0'6$(('%23',)
",()'32'*$-)'$%-3"%3"%)27-(4'32'39)'$+)"('#"(7)'!X'*"39)*5'39)'273073'6$((',)'39)'($%)"*'*"/0'21
-(20)')K7"('32'LO5'-926%'$%'S$&>'Q>UT<.=>';9)'"/0($1$)*'$-'39)%'-"$+'32',)'4-$8!"'5'"%+'$3273073'$-'4-$8/%,&$*-!+!&$1>
A%'2*+)*'32'7%+)*-3"%+'39)'2*$&$%'21'39)'-()6B*"3)'09)%2/)%2%5'6)'%))+'32'8%26'",273
39)'$%3)*%"('.$*.7$3'21'39)'20'"/05'"%+'6)'6$(('-37+4'$3'$%'G9"03)*'CQ>'S2*'39)'3$/)',)$%&5
926)#)*5'$3'$-'-711$.$)%3'32'8%26'",273'39)'09)%2/)%2%'"%+'32'%23)'39"3'$3'$-'+$-3$%.3'1*2/
39)'1$%$3)'20B"/0',"%+6$+39'39"3'($/$3-'39)'1*)K7)%.4'*)-02%-)'21'39)'.(2-)+B(220'"/0($1$B
)*-5' -37+$)+' $%' 39)' 0*)#$27-' -).3$2%>' ;9)' ($/$3)+' ,"%+6$+39' $-' "' ($%)"*' 09)%2/)%2%' "%+
+2)-'%23'*)-7(3'$%'"'.9"%&)'$%'39)'-9"0)'21'"%'$%073'-$%7-2$+X'39"3'$-5'$3'+2)-'%23'()"+'32'%2%B
($%)"*'+$-32*3$2%>';9)'-()6B*"3)'($/$3"3$2%5'2%'39)'239)*'9"%+5'."%'."7-)'%2%($%)"*'+$-32*3$2%
32' "%' $%073' -$%7-2$+"(' -$&%"(' 69)%' $3-' 1*)K7)%.4' "%+' "/0($37+)' "*)' -7.9' 39"3' 39)' .2**)B
-02%+$%&'$+)"('273073'627(+'*)K7$*)'vB'32'.9"%&)'"3'"'*"3)'&*)"3)*'39"%'LO>';9$-'$-'39)'2*$B
&$%'21'"%239)*'*)("3)+'20B"/0'-0).$1$."3$2%5'$3-'17((B026)*',"%+6$+395'32',)')M0("$%)+'("3)*>
e)12*)'()"#$%&'39)')M"/0()'$%'S$&>'Q>UT5'926)#)*5'6)'-927(+'02$%3'273'39"3'$1'39)'-3)0
$%073'#2(3"&)'!'$-'-711$.$)%3(4'-/"((5'39)'273073'."%',)'39)')M02%)%3$"((4'*$-$%&'*"/0'-926%'$%
S$&>'Q>UT<+=>'L7.9'"%'273073'627(+',)')M0).3)+'1*2/'39)'12((26)*'$1'39)'2%(4'($/$3"3$2%'2%'$3+4%"/$.'0)*12*/"%.)'6)*)'39)'1$%$3)'20B"/0',"%+6$+39>'L0).$1$."((45'39)'3*"%-1)*'17%.3$2%'21
39)'12((26)*'."%',)'127%+',4'-7,-3$373$%&'?C'='∞'"%+'?Q'='F'$%'@K>'<Q>VV='32'2,3"$%
!1
C
BBBBB = BBBBBBBBBBBBBBBBBBBBB
!)
C + 4 ⁄ ω&
<Q>VI=
2.8 Large-Signal Operation of Op Amps
v1
V
0
t
(b)
vO
Slope % SR
V
0
t
(c)
vO
Slope % ( tV * SR
V
0
t
(d)
Figure 2.43 :,;' a%$34B&"$%' 12((26)*>' :5;' A%073' -3)0' 6"#)12*/>' :0;' k$%)"*(4' *$-$%&' 273073' 6"#)12*/
2,3"$%)+'69)%'39)'"/0($1$)*'$-'-()6B*"3)'($/$3)+>':1;'@M02%)%3$"((4'*$-$%&'273073'6"#)12*/'2,3"$%)+'69)%
! $-'-711$.$)%3(4'-/"(('-2'39"3'39)'$%$3$"('-(20)'<ω&!='$-'-/"(()*'39"%'2*')K7"('32'LO>
69$.9'$-'"'(26B0"--'L;G'*)-02%-)'6$39'"'3$/)'.2%-3"%3'C ⁄ ω & >'A3-'-3)0'*)-02%-)'627(+'39)*)B
12*)',)'<-))'H00)%+$M'@=
v B ( & ) = ! ( C ! ( !ω& & )
<Q>Vc=
;9)'$%$3$"('-(20)'21'39$-')M02%)%3$"((4'*$-$%&'17%.3$2%'$-'<ω&!=>';97-5'"-'(2%&'"-'!'$-'-711$B
.$)%3(4'-/"(('-2'39"3'ω&!'≤'LO5'39)'273073'6$((',)'"-'$%'S$&>'Q>UT<+=>
EXERCISE
2.29 H%'20'"/0'39"3'9"-'"'-()6'*"3)'21'C'`dµ-'"%+'"'7%$34B&"$%',"%+6$+39'2&'21'C'R!['$-'.2%%).3)+'$%'39)
7%$34B&"$%'12((26)*'.2%1$&7*"3$2%>'S$%+'39)'("*&)-3'02--$,()'$%073'#2(3"&)'-3)0'12*'69$.9'39)'273073
6"#)12*/'6$(('-3$((',)'&$#)%',4'39)')M02%)%3$"('*"/0'21'@K>'<Q>Vc=>'S2*'39$-'$%073'#2(3"&)5'69"3'$39)'CFg'32'DFg'*$-)'3$/)'21'39)'273073'6"#)12*/\'A1'"%'$%073'-3)0'CF'3$/)-'"-'("*&)'$-'"00($)+5'1$%+
39)'CFg'32'DFg'*$-)'3$/)'21'39)'273073'6"#)12*/>
Ans. F>CE'`X'F>TV'µ-X'C>Qc'µ-
105
106 Chapter 2 Operational Amplifiers
2.8.4 Full-Power Bandwidth
?0B"/0'-()6B*"3)'($/$3$%&'."%'."7-)'%2%($%)"*'+$-32*3$2%'$%'-$%7-2$+"('6"#)12*/->'G2%-$+)*
2%.)'/2*)'39)'7%$34B&"$%'12((26)*'6$39'"'-$%)B6"#)'$%073'&$#)%',4
v > = !u) -$% ω &
;9)'*"3)'21'.9"%&)'21'39$-'6"#)12*/'$-'&$#)%',4
.v
BBBBBBB> = ω !u) .2- ω &
.&
6$39' "' /"M$/7/' #"(7)'21' ω!u) >';9$-'/"M$/7/'2..7*-'"3'39)'[)*2'.*2--$%&-' 21'39)'$%073
-$%7-2$+>' P26' $1' ω!u) ' )M.))+-' 39)' -()6' *"3)' 21' 39)' 20' "/05' 39)' 273073' 6"#)12*/' 6$((' ,)
+$-32*3)+'$%'39)'/"%%)*'-926%'$%'S$&>'Q>UU>'?,-)*#)'39"3'39)'273073'."%%23'8))0'70'6$39'39)
("*&)'*"3)'21'.9"%&)'21'39)'-$%7-2$+'"3'$3-'[)*2'.*2--$%&-5'"%+'39)'20'"/0'-()6->'
;9)'20B"/0'+"3"'-9))3-'7-7"((4'-0).$14'"'1*)K7)%.4'2N'."(()+'39)'3)--/(.8$%*5,"18!1&7>
A3'$-'39)'1*)K7)%.4'"3'69$.9'"%'273073'-$%7-2$+'6$39'"/0($37+)')K7"('32'39)'*"3)+'273073'#2(3B
"&)'21'39)'20'"/0',)&$%-'32'-926'+$-32*3$2%'+7)'32'-()6B*"3)'($/$3$%&>'A1'6)'+)%23)'39)'*"3)+
273073'#2(3"&)'!1/"M 5'39)%'2N'$-'*)("3)+'32'LO'"-'12((26-:
ω N !1/"M = LO
;97-5
LO
2N = BBBBBBBBBBBBBBBBBBB
Q π !1/"M
<Q>VD=
A3'-927(+',)'2,#$27-'39"3'273073'-$%7-2$+-'21'"/0($37+)-'-/"(()*'39"%'!1/"M '6$(('-926'-()6B
*"3)'+$-32*3$2%'"3'1*)K7)%.$)-'9$&9)*'39"%' ωN >'A%'1".35'"3'"'1*)K7)%.4' ω'9$&9)*'39"%' ωN 5'39)
/"M$/7/'"/0($37+)'21'39)'7%+$-32*3)+'273073'-$%7-2$+'$-'&$#)%',4
ω
!1 = !1/"M BBBBBBNB '
ω
Figure 2.44 @11).3'21'-()6B*"3)'($/$3$%&'2%'273073'-$%7-2$+"('6"#)12*/->
<Q>EF=
2.8 Large-Signal Operation of Op Amps
107
EXERCISE
2.30' H%'20'"/0'9"-'"'*"3)+'273073'#2(3"&)'21'±CF'`'"%+'"'-()6'*"3)'21'C'`dµ->'Y9"3'$-'$3-'17((B026)*
,"%+6$+39\'A1'"%'$%073'-$%7-2$+'6$39'1*)K7)%.4'2'='V2N'$-'"00($)+'32'"'7%$34B&"$%'12((26)*'.2%B
-3*7.3)+'7-$%&'39$-'20'"/05'69"3'$-'39)'/"M$/7/'02--$,()'"/0($37+)'39"3'."%',)'"..2//2+"3)+
"3'39)'273073'6$39273'$%.7**$%&'LO'+$-32*3$2%\
Ans. CV>D'8![X'Q'`'<0)"8=
Summary
;9)'AG'20'"/0'$-'"'#)*-"3$()'.$*.7$3',7$(+$%&',(2.8>'A3'$-
;9)'%2%$%#)*3$%&'.(2-)+B(220'.2%1$&7*"3$2%'1)"37*)-'"'#)*4
)"-4' 32' "00(45' "%+' 39)' 0)*12*/"%.)' 21' 20B"/0' .$*.7$3.(2-)(4'/"3.9)-'39)2*)3$."('0*)+$.3$2%->
9$&9'$%073'*)-$-3"%.)>'H'-0).$"('."-)'$-'39)'7%$34B&"$%'12(B
(26)*5'1*)K7)%3(4')/0(24)+'"-'"',711)*'"/0($1$)*'32'.2%B
%).3'"'9$&9B*)-$-3"%.)'-27*.)'32'"'(26B*)-$-3"%.)'(2"+>
;9)'20B"/0'3)*/$%"(-'"*)'39)'$%#)*3$%&'$%073'3)*/$%"(
<C=5'39)'%2%$%#)*3$%&'$%073'3)*/$%"('<Q=5'39)'273073'3)*B
/$%"('<T=5'39)'02-$3$#)B-700(4'3)*/$%"('<U='32',)'.2%B
%).3)+' 32' 39)' 02-$3$#)' 026)*' -700(4' <!""=5' "%+' 39)
%)&"3$#)B-700(4' 3)*/$%"(' <V=' 32' ,)' .2%%).3)+' 32' 39)
%)&"3$#)'-700(4'<−!##=>';9)'.2//2%'3)*/$%"('21'39)
362'-700($)-'$-'39)'.$*.7$3'&*27%+>
;9)'$+)"('20'"/0'*)-02%+-'2%(4'32'39)'+$11)*)%.)'$%073
-$&%"(5' 39"3' $-5 ( v Q ! v C )X ' 0*2#$+$%&' "3' 39)' 2730735' ,)B
36))%'3)*/$%"('T'"%+'&*27%+5'"'-$&%"(' $ ( v Q ! v C )5^'69)*)
$5'39)'20)%B(220'&"$%5'$-'#)*4'("*&)'<CFU'32'CFE='"%+'$+)B
"((4' $%1$%$3)X' "%+' 9"-' "%' $%1$%$3)' $%073' *)-$-3"%.)' "%+' "
[)*2'273073'*)-$-3"%.)>'<L))';",()'T>C>=
P)&"3$#)'1))+,".8'$-'"00($)+'32'"%'20'"/0',4'.2%%).3$%&
"'0"--$#)'.2/02%)%3',)36))%'$3-'273073'3)*/$%"('"%+'$3$%#)*3$%&' <%)&"3$#)=' $%073' 3)*/$%"(>' P)&"3$#)' 1))+,".8
."7-)-'39)'#2(3"&)',)36))%'39)'362'$%073'3)*/$%"(-'32
,).2/)'#)*4'-/"(('"%+'$+)"((4'[)*2>'G2**)-02%+$%&(45'"
#$*37"('-92*3'.$*.7$3'$-'-"$+'32')M$-3',)36))%'39)'362'$%073
3)*/$%"(->'A1'39)'02-$3$#)'$%073'3)*/$%"('$-'.2%%).3)+'32
&*27%+5'"'#$*37"('&*27%+'"00)"*-'2%'39)'%)&"3$#)'$%073
3)*/$%"(>
;9)' +$11)*)%.)' "/0($1$)*' 21' S$&>' Q>CE' $-' +)-$&%)+' 6$39
? U ⁄ ? T 3 ? Q ⁄ ? C5'
( v >Q ! v >C ) >
*)-7(3$%&'
$%'
vB 3 ( ?Q ⁄ ?C )
;9)' $%-3*7/)%3"3$2%' "/0($1$)*' 21' S$&>' Q>QF<,=' $-' "' #)*4
0207("*'.$*.7$3>'A3'0*2#$+)-' v B 3 ( C 2 ? Q ⁄ ? C ) ( ? U ⁄ ? T )
( v >Q ! v >C ) >'A3'$-'7-7"((4'+)-$&%)+'6$39' ? T 3 ? U 5'"%+' ? C
"%+' ? Q '-)().3)+'32'0*2#$+)'39)'*)K7$*)+'&"$%>'A1'"%'"+W7-3B
",()'&"$%'$-'%))+)+5'0"*3'21' ? C'."%',)'/"+)'#"*$",()>
;9)'$%#)*3$%&'R$(()*'$%3)&*"32*'21'S$&>'Q>QU'$-'"'0207("*'.$*B
.7$35'1*)K7)%3(4')/0(24)+'$%'"%"(2&'-$&%"(B0*2.)--$%&'17%.B
3$2%-'-7.9'"-'1$(3)*-'<G9"03)*'CE='"%+'2-.$(("32*-'<G9"03)*'CI=>
;9)'$%073'211-)3'#2(3"&)5'!BK 5''$-'39)'/"&%$37+)'21'+.'#2(3B
"&)'39"3'69)%'"00($)+',)36))%'39)'20'"/0'$%073'3)*/$B
%"(-5' 6$39' "00*20*$"3)' 02("*$345' *)+7.)-' 39)' +.' 211-)3
#2(3"&)'"3'39)'273073'32'[)*2>
;9)')11).3'21'!BK'2%'0)*12*/"%.)'."%',)')#"(7"3)+',4
$%.(7+$%&'$%'39)'"%"(4-$-'"'+.'-27*.)'!BK'$%'-)*$)-'6$39
39)'20B"/0'02-$3$#)'$%073'()"+>'S2*',239'39)'$%#)*3$%&
"%+'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%-5'!BK'*)-7(3-'$%'"'+.
211-)3'#2(3"&)'"3'39)'273073'21 !BK ( C + ? Q ⁄ ? C )>
;9)'362'/2-3'$/02*3"%3'"--7/03$2%-'$%'39)'"%"(4-$-'21
G"0".$3$#)(4'.270($%&'"%'20'"/0'*)+7.)-'39)'+.'211-)3
20B"/0' .$*.7$3-5' 0*)-7/$%&' %)&"3$#)' 1))+,".8' )M$-3"%+'39)'20 "/0-'"*)'$+)"(5'"*)'"-'12((26-:'39)'362'$%073
3)*/$%"(-' 21' 39)' 20' "/0' "*)' "3' 39)' -"/)' #2(3"&)5' "%+
[)*2'.7**)%3'1(26-'$%32'39)'20B"/0'$%073'3)*/$%"(->
;9)'"#)*"&)'21'39)'362'+.'.7**)%3-5'>LC'"%+'>LQ5'39"3'1(26'$%
Y$39' %)&"3$#)' 1))+,".8' "00($)+' "%+' 39)' (220' .(2-)+5
39)' .(2-)+B(220' &"$%' $-' "(/2-3' )%3$*)(4' +)3)*/$%)+' ,4
)M3)*%"(' .2/02%)%3-:' S2*' 39)' $%#)*3$%&' .2%1$&7*"3$2%5
!1 ⁄ !) = ! ? Q ⁄ ? C X '"%+'12*'39)'%2%$%#)*3$%&'.2%1$&7*"3$2%5
!1 ⁄ !) = C + ? Q ⁄ ? C >
#2(3"&)'"3'39)'273073'.2%-$+)*",(4>
39)'$%073'3)*/$%"(-'21'39)'20'"/05'$-'."(()+'39)'$%073',$".7**)%35'>L>'A%'"'.(2-)+B(220'"/0($1$)*5'>L'&$#)-'*$-)'32'"'+.
211-)3'#2(3"&)'"3'39)'273073'21'/"&%$37+)'>L?Q>';9$-'#2(3"&)
."%',)'*)+7.)+'32'>BK ?Q',4'.2%%).3$%&'"'*)-$-3"%.)'$%'-)B
*$)-'6$39'39)'02-$3$#)'$%073'3)*/$%"(')K7"('32'39)'323"('+.'*)B
-$-3"%.)'-))%',4'39)'%)&"3$#)'$%073'3)*/$%"(>'>BK'$-'39)'$%073
211-)3'.7**)%3X'39"3'$-5' > BK = > LC ! > LQ >
108 Chapter 2 Operational Amplifiers
G2%%).3$%&'"'("*&)'*)-$-3"%.)'$%'0"*"(()('6$39'39)'."0".$B
;9)'/"M$/7/'*"3)'"3'69$.9'39)'20B"/0'273073'#2(3"&)
32*' 21' /%' 20B"/0' $%#)*3$%&' $%3)&*"32*' 0*)#)%3-' 20B"/0
-"37*"3$2%'<+7)'32'39)')11).3''21'!BK'"%+'>L=>
."%'.9"%&)'$-'."(()+'39)'-()6'*"3)>';9)'-()6'*"3)5'LO5'$7-7"((4'-0).$1$)+'$%'`dµ4>'?0B"/0'-()6$%&'."%'*)-7(3'$%
%2%($%)"*'+$-32*3$2%'21'273073'-$&%"('6"#)12*/->
S2*'/2-3'$%3)*%"((4'.2/0)%-"3)+'20'"/0-5'39)'20)%B(220
&"$%'1"((-'211'6$39'1*)K7)%.4'"3'"'*"3)'21'−QF'+ed+)."+)5
*)".9$%&' 7%$34' "3' "' 1*)K7)%.4' 2&' <39)' 7%$34B&"$%' ,"%+B
6$+39=>'S*)K7)%.4'2&''$-'"(-2'8%26%'"-'39)'&"$%n,"%+6$+39
0*2+7.3'21'39)'20'"/0:'2&'='$F'255'69)*)'$F'$-'39)'+.'&"$%5
"%+'25'$-'39)'TB+e'1*)K7)%.4'21'39)'20)%B(220'&"$%>'H3'"%4
1*)K7)%.4'2 < 2 )'25=5'39)'20B"/0'&"$%' $ ! 2& ⁄ 2>
;9)'17((B026)*',"%+6$+395'2N5'$-'39)'/"M$/7/'1*)K7)%.4
"3'69$.9'"%'273073'-$%7-2$+'6$39'"%'"/0($37+)')K7"('32
39)'20B"/0'*"3)+'273073'#2(3"&)'<!1/"M='."%',)'0*2+7.)+
6$39273'+$-32*3$2%:' 2N = LO ⁄ Q π !1/"M>
S2*' ,239' 39)' $%#)*3$%&' "%+' 39)' %2%$%#)*3$%&' .(2-)+B(220
.2%1$&7*"3$2%-5' 39)' TB+e' 1*)K7)%.4' $-' )K7"(' 32
2& ⁄ ( C + ? Q ⁄ ? C )>
PROBLEMS
Computer Simulation Problems
]*2,()/-'$+)%3$1$)+',4'39$-'$.2%'"*)'$%3)%+)+'32'+)/B
2%-3*"3)'39)'#"(7)'21'7-$%&'L]AG@'-$/7("3$2%'32'#)*$14'9"%+
"%"(4-$-'"%+'+)-$&%5'"%+'32'$%#)-3$&"3)'$/02*3"%3'$--7)-'-7.9
"-'"((26",()'-$&%"('-6$%&'"%+'"/0($1$)*'%2%($%)"*'+$-32*3$2%>
A%-3*7.3$2%-'32'"--$-3'$%'-)33$%&'70']L0$.)'"%+'R7(3$-/'-$/7B
("3$2%-' 12*' "((' 39)' $%+$."3)+' 0*2,()/-' ."%' ,)' 127%+' $%' 39)
.2**)-02%+$%&' 1$()-' 2%' 39)' +$-.>' P23)' 39"3' $1' "' 0"*3$.7("*
0"*"/)3)*' #"(7)' $-' %23' -0).$1$)+' $%' 39)' 0*2,()/' -3"3)/)%35
427'"*)'32'/"8)'"'*)"-2%",()'"--7/03$2%>'v'+$11$.7(3'0*2,B
()/X' vv' /2*)' +$11$.7(3X' vvv' #)*4' .9"(()%&$%&' "%+d2*' 3$/)B
.2%-7/$%&X'j:'+)-$&%'0*2,()/>
Section 2.1: The Ideal Op Amp
2.1 Y9"3'$-'39)'/$%$/7/'%7/,)*'21'0$%-'*)K7$*)+'12*'"'-2B
."(()+' +7"(B20B"/0' AG' 0".8"&)5' 2%)' .2%3"$%$%&' 362' 20
"/0-\'Y9"3'$-'39)'%7/,)*'21'0$%-'*)K7$*)+'12*'"'-2B."(()+
K7"+B20B"/0'0".8"&)5'2%)'.2%3"$%$%&'127*'20B"/0-\
2.2 ;9)'.$*.7$3'21'S$&>']Q>Q'7-)-'"%'20'"/0'39"3'$-'$+)"(
)M.)03' 12*' 9"#$%&' "' 1$%$3)' &"$%' $>' R)"-7*)/)%3-' $%+$."3)
vB'='U>F'`'69)%'v>'='Q>F'`>'Y9"3'$-'39)'20B"/0'&"$%'$\
2.3 R)"-7*)/)%3'21'"'.$*.7$3'$%.2*02*"3$%&'69"3'$-'3927&93
32',)'"%'$+)"('20'"/0'-926-'39)'#2(3"&)'"3'39)'20B"/0'273073
32',)'−Q>FFF'`'"%+'39"3'"3'39)'%)&"3$#)'$%073*32',)'−C>FFF'`>
S2*'39)'"/0($1$)*'32',)'$+)"(5'69"3'627(+'427')M0).3'39)'#2(3B
"&)'"3'39)'02-$3$#)'$%073'32*,)\'A1'39)'/)"-7*)+'#2(3"&)'"3'39)
02-$3$#)'$%073'$-'−C>FCF'`5'69"3'$-'($8)(4'32',)'39)'".37"('&"$%
21'39)'"/0($1$)*\
Figure P2.2
2.4 H'-)3'21')M0)*$/)%3-'$-'*7%'2%'"%'20'"/0'39"3'$-'$+)"(
)M.)03'12*'9"#$%&'"'1$%$3)'&"$%'$>';9)'*)-7(3-'"*)'3",7("3)+
,)(26>' H*)' 39)' *)-7(3-' .2%-$-3)%3\' A1' %235' "*)' 39)4' *)"-2%B
",()5'$%'#$)6'21'39)'02--$,$($34'21')M0)*$/)%3"(')**2*\'Y9"3
+2'39)4'-926'39)'&"$%'32',)\'a-$%&'39$-'#"(7)5'0*)+$.3'#"(7)21'39)'/)"-7*)/)%3-'39"3'6)*)'"..$+)%3"((4'2/$33)+'<39)',("%8
)%3*$)-=>
Experiment #
v1
v2
%
#
5
6
7
9
:
4$44
%$44
4$44-- ------------4$44
%$44 ------------4$44
%$44 ------------%$44
%$%4-----------%4$%
#$44------- ---−4$88
#$44 ------------%$44
------------------−7$%4
%$44
#$4%
%$88
7$%4
vO
Problems 109
2.7 P2%$+)"(' <$>)>5' *)"(=' 20)*"3$2%"(' "/0($1$)*-' *)-02%+
32',239'39)'+$11)*)%3$"('"%+'.2//2%B/2+)'.2/02%)%3-'21
39)$*'$%073'-$&%"(-'<*)1)*'32'S$&>'Q>U'12*'-$&%"('*)0*)-)%3"B
3$2%=>' ;97-' 39)' 273073' #2(3"&)' 21' 39)' 20' "/0' ."%' ,)
)M0*)--)+'"v B = $ . v >. + $ 0- v >069)*)'$.%$-'39)'+$11)*)%3$"('&"$%'<*)1)**)+'32'-$/0(4'"-'$
$%'39)'3)M3='"%+'$0-'$-'39)'.2//2%B/2+)'&"$%'<"--7/)+'32
,)'[)*2'$%'39)'3)M3=>';9)'20'"/0J-')11).3$#)%)--'$%'*)W).3B
$%&' .2//2%B/2+)' -$&%"(-' $-' /)"-7*)+' ,4' $3-' GROO5
+)1$%)+'"$.
GROO = QF'(2&' BBBBBBBB
$ 0-
Figure P2.8
A -C = A - ! CBBQB ∆A A -Q = A - + BBCQB ∆A S$%+')M0*)--$2%-'12*'$. 5'$0- 5'"%+'GROO>'A1'$.'$-'cF'+e'"%+
39)' 362' 3*"%-.2%+7.3"%.)-' "*)' /"3.9)+' 32' 6$39$%' F>Cg' 21
)".9'239)*5'."(.7("3)'$0-'"%+'GROO>
Section 2.2: The Inverting
Configuration
2.8 H--7/$%&' $+)"(' 20' "/0-5' 1$%+' 39)' #2(3"&)' &"$%
v 1 ⁄ v ) "%+' $%073' *)-$-3"%.)' ?$%' 21' )".9' 21' 39)' .$*.7$3-' $%
S$&>']Q>c>
2.9 H' 0"*3$.7("*' $%#)*3$%&' .$*.7$3' 7-)-' "%' $+)"(' 20' "/0
"%+' 362' CFB8Ω' *)-$-32*->' Y9"3' .(2-)+B(220' &"$%' 627(+
427' )M0).3\' A1' "' +.' #2(3"&)' 21' +C>FF' `' $-' "00($)+' "3' 39)
$%0735'69"3'273073'*)-7(3\'A1'39)'CFB8Ω'*)-$-32*-'"*)'-"$+'32
,)'^Cg'*)-$-32*-5_'9"#$%&'#"(7)-'-2/)69)*)'$%'39)'*"%&)
<C ±'F>FC='3$/)-'39)'%2/$%"('#"(7)5'69"3'*"%&)'21'273073627(+'427')M0).3'32'".37"((4'/)"-7*)'12*'"%'$%073'21'0*)B
.$-)(4'C>FF'`\
2.10 w27'"*)'0*2#$+)+'6$39'"%'$+)"('20'"/0'"%+'39*))'CFB
8Ω'*)-$-32*->'a-$%&'-)*$)-'"%+'0"*"(()('*)-$-32*'.2/,$%"3$2%-5
926'/"%4'+$11)*)%3'$%#)*3$%&B"/0($1$)*'.$*.7$3'3202(2&$)-'"*)
02--$,()\'Y9"3'$-'39)'("*&)-3'<%2%$%1$%$3)='"#"$(",()'#2(3"&)
!
!
"
"
(a)
(b)
!
!
"
"
(c)
(d)
PROBLEMS
2.6 ;9)'362'6$*)-'()"+$%&'1*2/'39)'273073'3)*/$%"(-'21'"
3*"%-+7.)*'0$.8'70'"%'$%3)*1)*)%.)'-$&%"('39"3'$-'"'EFB![5'CB
`'-$%7-2$+>';9)'273073'-$&%"('21'39)'3*"%-+7.)*'$-'-$%7-2$B
+"(' 21' CFB/`' "/0($37+)' "%+' CFFFB![' 1*)K7)%.4>' i$#)
)M0*)--$2%-' 12*' v0-5' v.5' "%+' 39)' 323"(' -$&%"(' ,)36))%' )".9
6$*)'"%+'39)'-4-3)/'&*27%+>
G2%-$+)*'"%'20'"/0'692-)'$%3)*%"('-3*7.37*)'$-'21'39)'340)
-926%'$%'S$&>'@Q>T')M.)03'12*'"'/$-/"3.9'∆A-',)36))%'39)
3*"%-.2%+7.3"%.)-'21'39)'362'.9"%%)(-X'39"3'$-5
CHAPTER 2
2.5 O)1)*'32'@M)*.$-)'Q>T>';9$-'0*2,()/')M0(2*)-'"%'"(3)*B
%"3$#)' $%3)*%"(' -3*7.37*)' 12*' 39)' 20' "/0>' A%' 0"*3$.7("*5' 6)
6$-9'32'/2+)('39)'$%3)*%"('-3*7.37*)'21'"'0"*3$.7("*'20'"/0
7-$%&'362'3*"%-.2%+7.3"%.)'"/0($1$)*-'"%+'2%)'3*"%-*)-$-3"%.)
"/0($1$)*>' L7&&)-3' "%' "00*20*$"3)' 3202(2&4>' S2*' )K7"(
3*"%-.2%+7.3"%.)-' A-' "%+' "' 3*"%-*)-$-3"%.)' ?-5' 1$%+' "%
)M0*)--$2%'12*'39)'20)%B(220'&"$%'$>'S2*'A-'='CF'/Hd`'"%+
?-'='Q'''CFE' Ω5'69"3'#"(7)'21'$'*)-7(3-\
CHAPTER 2
PROBLEMS
110 Chapter 2 Operational Amplifiers
&"$%\' Y9"3' $-'39)'-/"(()-3'<%2%[)*2=' "#"$(",()' &"$%\' Y9"3
"*)'39)'$%073'*)-$-3"%.)-'$%'39)-)'362'."-)-\'
2.11 S2*' $+)"(' 20' "/0-' 20)*"3$%&' 6$39' 39)' 12((26$%&
1))+,".8'%)362*8-'$%'39)'$%#)*3$%&'.2%1$&7*"3$2%5'69"3'.(2-)+B
(220'&"$%'*)-7(3-\
<"= ? C = CF'8Ω5'? Q = CF'8Ω
<,= ? C = CF'8Ω5'? Q = CFF'8Ω
<.= ? C = CF'8Ω5'? Q = C'8Ω
<+= ? C = CFF'8Ω5'? Q = CF'RΩ
<)= ? C = CFF'8Ω5'? Q = C'RΩ
D 2.12 i$#)%'"%'$+)"('20'"/05'69"3'"*)'39)'#"(7)-'21'39)
*)-$-32*-'?C'"%+'?Q'32',)'7-)+'32'+)-$&%'"/0($1$)*-'6$39'39)
.(2-)+B(220'&"$%-'($-3)+',)(26\'A%'427*'+)-$&%-5'7-)'"3'()"-3
2%)'CFB8Ω'*)-$-32*'"%+'"%239)*')K7"('2*'("*&)*'*)-$-32*>
<"= −C'`d`
<,= −Q'`d`
<.= −F>V'`d`
<+= −CFF'`d`
D 2.13 j)-$&%' "%' $%#)*3$%&' 20B"/0' .$*.7$3' 12*' 69$.9' 39)
&"$%'$-'−U'`d`'"%+'39)'323"('*)-$-3"%.)'7-)+'$-'CFF'8Ω.'
D 2.14 a-$%&'39)'.$*.7$3'21'S$&>'Q>V'"%+'"--7/$%&'"%'$+)"(
20'"/05'+)-$&%'"%'$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'QE'+e
9"#$%&' 39)' ("*&)-3' 02--$,()' $%073' *)-$-3"%.)' 7%+)*' 39)' .2%B
-3*"$%3'21'9"#$%&'32'7-)'*)-$-32*-'%2'("*&)*'39"%'C'RΩ. Y9"3
$-'39)'$%073'*)-$-3"%.)'21'427*'+)-$&%\
2.15 H%' $+)"(' 20' "/0' $-' .2%%).3)+' "-' -926%' $%' S$&>' Q>V
6$39' ?C' =' CF' 8Ω' "%+' ?Q' =' CFF' 8Ω>' H' -4//)3*$."(' -K7"*)B
6"#)' -$&%"(' 6$39' ()#)(-' 21' F' `' "%+' C' `' $-' "00($)+' "3' 39)
$%073>'L8)3.9'"%+'.()"*(4'(",)('39)'6"#)12*/'21'39)'*)-7(3$%&
273073'#2(3"&)>'Y9"3'$-'$3-'"#)*"&)'#"(7)\'Y9"3'$-'$3-'9$&9B
)-3'#"(7)\'Y9"3'$-'$3-'(26)-3'#"(7)\
2.16 S2*' 39)' .$*.7$3' $%' S$&>' ]Q>CE5' "--7/$%&' "%' $+)"(' 20
"/05'1$%+'39)'.7**)%3-'39*27&9'"((',*"%.9)-'"%+'39)'#2(3"&)"3' "((' %2+)->' L$%.)' 39)' .7**)%3' -700($)+' ,4' 39)' 20' "/0' $&*)"3)*'39"%'39)'.7**)%3'+*"6%'1*2/'39)'$%073'-$&%"('-27*.)5
69)*)'+2)-'39)'"++$3$2%"('.7**)%3'.2/)'1*2/\
2.17 H%' $%#)*3$%&' 20B"/0' .$*.7$3' $-' 1",*$."3)+' 6$39' 39)
*)-$-32*-' ?C' "%+' ?Q' 9"#$%&' Cg' 32()*"%.)' <$>)>5' 39)' #"(7)' 21
)".9' *)-$-3"%.)' ."%' +)#$"3)' 1*2/' 39)' %2/$%"(' #"(7)' ,4' "/7.9'"-'± Cg=>'Y9"3'$-'39)'32()*"%.)'2%'39)'*)"($[)+'.(2-)+B
(220' &"$%\' H--7/)' 39)' 20' "/0' 32' ,)' $+)"(>' A1' 39)' %2/$%"(
.(2-)+B(220'&"$%'$-'−CFF'`d`'"%+'C'='C5'69"3'$-'39)'*"%&)'21
&"$%'#"(7)-')M0).3)+'1*2/'-7.9'"'.$*.7$3\'
2.18 H%' $+)"(' 20' "/0' 6$39' VB8Ω' "%+' CVB8Ω' *)-$-32*-' $7-)+' 32' .*)"3)' "' +VB`' -700(4' 1*2/' "' −CVB`' *)1)*)%.)>
L8)3.9'39)'.$*.7$3>'Y9"3'"*)'39)'#2(3"&)-'"3'39)')%+-'21'39)'VB
8Ω' *)-$-32*\' A1' 39)-)' *)-$-32*-' "*)' -2B."(()+' Cg' *)-$-32*-5
692-)'".37"('#"(7)-'"*)'39)'*"%&)',27%+)+',4'39)'%2/$%"(
#"(7)' ±Cg5' 69"3' "*)' 39)' ($/$3-' 21' 39)' 273073' #2(3"&)' 0*2B
+7.)+\'A1'39)'−CVB`'-700(4'."%'"(-2'#"*4',4'±Cg5'69"3'$39)'*"%&)'21'39)'273073'#2(3"&)-'39"3'/$&93',)'127%+\
2.19 H%'$%#)*3$%&'20B"/0'.$*.7$3'12*'69$.9'39)'*)K7$*)+'&"$%
$-' −VF' `d`' 7-)-' "%' 20' "/0' 692-)' 20)%B(220' &"$%' $-' 2%(4
TFF `d`>'A1'39)'("*&)*'*)-$-32*'7-)+'$-'CFF'8Ω5'32'69"3'/7-3'39)
-/"(()*' ,)' "+W7-3)+\' Y$39'69"3' *)-$-32*' /7-3' "' QB8Ω' *)-$-32*
.2%%).3)+'32'39)'$%073',)'-97%3)+'32'".9$)#)'39$-'&2"(\'<P23)
39"3'"'*)-$-32*'?/'$-'-"$+'32',)'-97%3)+',4'*)-$-32*'?5'69)%'?5'$0(".)+'$%'0"*"(()('6$39'?/>=
D 2.20 <"= j)-$&%' "%' $%#)*3$%&' "/0($1$)*' 6$39' "' .(2-)+B
(220'&"$%'21'−CFF'`d`'"%+'"%'$%073'*)-$-3"%.)'21'C'8Ω>
<,= A1'39)'20'"/0'$-'8%26%'32'9"#)'"%'20)%B(220'&"$%'21
QFFF' `d`5' 69"3' +2' 427' )M0).3' 39)' .(2-)+B(220' &"$%' 21
427*' .$*.7$3' 32' ,)' <"--7/$%&' 39)' *)-$-32*-' 9"#)' 0*).$-)
#"(7)-=\
<.= i$#)' 39)' #"(7)' 21' "' *)-$-32*' 427' ."%' 0(".)' $%' 0"*"(()(
<-97%3='6$39'?C'32'*)-32*)'39)'.(2-)+B(220'&"$%'32'$3-'%2/$%"(
#"(7)>' a-)' 39)' .(2-)-3' -3"%+"*+' Cg' *)-$-32*' #"(7)' <-))
H00)%+$M'!=>
2.21 H%' 20' "/0' 6$39' "%' 20)%B(220' &"$%' 21' QFFF' `d`' $7-)+'$%'39)'$%#)*3$%&'.2%1$&7*"3$2%>'A1'$%'39$-'"00($."3$2%'39)
273073' #2(3"&)' *"%&)-' 1*2/' −CF' `' 32' +CF' `5' 69"3' $-' 39)
/"M$/7/' #2(3"&)' ,4' 69$.9' 39)' ^#$*37"(' &*27%+' %2+)_
+)0"*3-'1*2/'$3-'$+)"('#"(7)\
2.22 ;9)'.$*.7$3'$%'S$&>']Q>QQ'$-'1*)K7)%3(4'7-)+'32'0*2#$+)
"%'273073'#2(3"&)'v1'0*202*3$2%"('32'"%'$%073'-$&%"('.7**)%3'))>
10 kV
1 kV
2
20.5 V 1
2
Figure P2.16
1
2 kV
1
vi
2
Figure P2.22
vo
Problems 111
7/8 !&$)&$+,$+$-"9
7:8 !&$)&,$+$-"9
"F
=
" $+ " " B ! ============
!!B
*2.24 @*#&/+&$+%"#-$+5&/<(3$,$"#&4$-.&+*<$+/3&03*)"1=3**(
5/$+& " F ⁄ " B>&,$+1&-."&<$+$<2<&%/32"&-./-&-."&*(=/<(&*("+=
3**(&5/$+&!&<2)-&./%"&7$+&-"#<)&*,& " F ⁄ " B8&)*&-./-&-."&5/$+
"##*#&$)&3$<$-"1&-*&A9BC>&BC>&/+1&BAC9&D+&"/0.&0/)"&,$+1&-."
%/32"& *,& /& #")$)-*#& "#$& )20.& -./-& 4."+& $-& $)& (3/0"1& $+& ).2+4$-.&"% >&-."&5/$+&$)&#")-*#"1&-*&$-)&+*<$+/3&%/32"9
*2.25 @$52#"&EF9FG&).*4)&/+&*(&/<(&-./-&$)&$1"/3&"'0"(-&,*#
./%$+5&/&,$+$-"&*("+=3**(&5/$+&/+1&$)&2)"1&-*&#"/3$H"&/+&$+%"#-=
$+5& /<(3$,$"#& 4.*)"& 5/$+& ./)& /& +*<$+/3& </5+$-21"
' = "F ⁄ " B 9&I*&0*<("+)/-"&,*#&-."&5/$+&#"120-$*+&12"&-*&-."
,$+$-"&!>&/&#")$)-*#&"&&$)&).2+-"1&/0#*))&"B9&;.*4&-./-&("#,"00*<("+)/-$*+&$)&/0.$"%"1&4."+&"&&$)&)"3"0-"1&/00*#1$+5&-*&
"
# '=
=====& = !
=============
"B
B+'
Rc
Vi
R2
2.28 O*+)$1"#& -."& 0$#02$-& $+& @$59& F9P& 4$-.& "B& = "F& =& "Q& =
B RΩ>&/+1&/))2<"&-."&*(&/<(&-*&:"&$1"/39&@$+1&%/32")&,*#&"S
-*&*:-/$+&-."&,*33*4$+5&5/$+)6
7/8 −FAA&TUT
7:8 −FA&TUT
708 −F&TUT
D 2.29 V+&$+%"#-$+5&*(=/<(&0$#02$-&2)$+5&/+&$1"/3&*(&/<(
<2)-&:"&1")$5+"1&-*&./%"&/&5/$+&*,&−BAAA&TUT&2)$+5&#")$)=
-*#)&+*&3/#5"#&-./+&BAA&MΩ.
7/8 @*#& -."& )$<(3"& -4*=#")$)-*#& 0$#02$->& 4./-& $+(2-& #")$)=
-/+0"&4*231&#")23-N
7:8 D,&-."&0$#02$-&$+&@$59&F9P&$)&2)"1&4$-.&-.#""&#")$)-*#)&*,
</'$<2<& %/32">& 4./-& $+(2-& #")$)-/+0"& #")23-)N& W./-& $)
-."&%/32"&*,&-."&)</33")-&#")$)-*#&+""1"1N
2.30 I."&$+%"#-$+5&0$#02$-&4$-.&-."&I&+"-4*#M&$+&-."&,""1=
:/0M&$)&#"1#/4+&$+&@$59&EF9SA&$+&/&4/?&-./-&"<(./)$H")&-."
*:)"#%/-$*+&-./-&"F&/+1&"S&$+&",,"0-&/#"&$+&(/#/33"3&7:"0/2)"
-."& $1"/3& *(& /<(& ,*#0")& /& %$#-2/3& 5#*2+1& /-& -."& $+%"#-$+5
$+(2-&-"#<$+/389&J)"&-.$)&*:)"#%/-$*+&-*&1"#$%"&/+&"'(#"))$*+
,*#&-."&5/$+& ( v , ⁄ v # ) &:?&,$#)-&,$+1$+5& ( v - ⁄ v # )&/+1& ( v , ⁄ v - )9
@*#&-."&3/--"#&2)"&-."&%*3-/5"=1$%$1"#&#23"&/((3$"1&-*&"Q&&/+1
7"F&|| "S89
!
R2
Vo
R1
"
vX
R4
R3
iI
vI
Figure P2.25
*D 2.26 7/8&J)"&KL9&7F9G8&-*&*:-/$+&-."&/<(3$,$"#&*("+=3**(
5/$+& !& #"L2$#"1& -*& #"/3$H"& /& )("0$,$"1& 03*)"1=3**(& 5/$+
( ' +*<$+/3 = # " F ⁄ " B ) &4$-.$+&/&)("0$,$"1&5/$+&"##*#&ε>
# ' +*<$+/3
ε& ≡ & '
===========================
=
R1
0V
!
vO
"
Figure P2.30
' +*<$+/3
7:8&!")$5+&/+&$+%"#-$+5&/<(3$,"#&,*#&/&+*<$+/3&03*)"1=3**(
5/$+&*,&−BAA>&/+&$+(2-&#")$)-/+0"&*,&F&MΩ, /+1&/&5/$+&"##*#&*,
≤BAC9&;("0$,?&"B>&"F >&/+1&-."&<$+$<2<&!&#"L2$#"19
*2.31 I."&0$#02$-&$+&@$59&EF9SB&0/+&:"&0*+)$1"#"1&-*&:"&/+
"'-"+)$*+&*,&-."&0$#02$-&$+&@$59&F9P9
*2.27 7/8&J)"&KL9&7F9G8&-*&).*4&-./-&/&#"120-$*+&∆!&$+&-."&*(=
/<(&5/$+&!&5$%")&#$)"&-*&/&#"120-$*+& ∆ ' &$+&-."&</5+$-21"&*,
-."&03*)"1=3**(&5/$+&'&4$-.&∆ ' &/+1&∆!&#"3/-"1&:?
7/8 @$+1& -."& #")$)-/+0")& 3**M$+5& $+-*& +*1"& B>& "BX& +*1"& F>
"FX&+*1"&S>&"SX&/+1&+*1"&Q>&"Q9
7:8 @$+1&-."&02##"+-)&#B>&#F>&#S>&/+1&#Q>&$+&-"#<)&*,&-."&$+(202##"+-&#9
708 @$+1&-."&%*3-/5")&/-&+*1")&B>&F>&S>&/+1&Q>&-./-&$)>&)B>&)F>
)S>&/+1&)Q&$+&-"#<)&*,&7#"89
B ! "F ⁄ "B
∆ ' ⁄ '=
=====================
" ========================
=
∆! ⁄ !
!
PROBLEMS
2.23 ;.*4& -./-& ,*#& -."& $+%"#-$+5& /<(3$,$"#& $,& -."& *(=/<(
5/$+&$)&!>&-."&$+(2-&#")$)-/+0"&$)&5$%"+&:?
7:8& D,& $+& /& 03*)"1=3**(& /<(3$,$"#& 4$-.& /& +*<$+/3& 5/$+& 7$9">
" F ⁄ " B8&*,&BAA>&!(1"0#"/)")&:?&GAC>&4./-&$)&-."&<$+$<2<
+*<$+/3&!&#"L2$#"1&-*&3$<$-&-."&("#0"+-/5"&0./+5"&$+& ' &-*
A9GCN
CHAPTER 2
!"#$%"& "'(#"))$*+)& ,*#& -."& -#/+)#")$)-/+0"& " * ≡ v + ⁄ % % & /+1
-."&$+(2-&#")$)-/+0"& " % ≡ v % ⁄ % % &,*#&-."&,*33*4$+5&0/)")6
CHAPTER 2
PROBLEMS
112 Chapter 2 Operational Amplifiers
R
R/2
1
I
R
R1
R/2
2
R
R2
4
R
R3
I2
I1
0V
R/2
3
R4
I4
I3
2
1
Ideal
Figure P2.31
2.32 ;9)'.$*.7$3'$%'S$&>']Q>TQ'73$($[)-'"%'$+)"('20'"/0>
<"= S$%+'>C5'>Q5'>T5'>D5'"%+'!C>
<,= A1'!B'$-'%23'32',)'(26)*'39"%'−CT'`5'1$%+'39)'/"M$/7/
"((26)+'#"(7)'12*'?D>
<.= A1'?D'$-'#"*$)+'$%'39)'*"%&)'CFF'Ω'32'C'8Ω5'69"3'$-'39)
.2**)-02%+$%&'.9"%&)'$%'>D'"%+'$%'!B\
I2
10 kV
I3
I1
VX
RL
<.= A1'?D'='C'8Ω'"%+'39)'20'"/0'20)*"3)-'$%'"%'$+)"('/"%B
%)*'"-'(2%&'"-'vB'$-'$%'39)'*"%&)'±CQ'`5'69"3'*"%&)'21')>'$02--$,()\
<+= A1' 39)' "/0($1$)*' $-' 1)+' 6$39' "' .7**)%3' -27*.)' 9"#$%&' "
.7**)%3'21'F>Q'/H'"%+'"'-27*.)'*)-$-3"%.)'21'CF'8Ω5'1$%+')D>
10 kV
IL
iI
100 V
2
vO
1
2
1
RL
R
10 kV
1V
iL
VO
Figure P2.34
Figure P2.32
2.33 a-)' 39)' .$*.7$3' $%' S$&>' ]Q>TQ' "-' "%' $%-0$*"3$2%' 32
+)-$&%'"'.$*.7$3'39"3'-700($)-'"'.2%-3"%3'.7**)%3'>'21'T>C'/H
32' "' #"*$",()' *)-$-3"%.)' ?D>' H--7/)' 39)' "#"$(",$($34' 21' "
C>V `',"33)*4'"%+'+)-$&%'-2'39"3'39)'.7**)%3'+*"6%'1*2/'39)
,"33)*4'$-'F>C'/H>'S2*'39)'-/"(()-3'*)-$-3"%.)'$%'39)'.$*.7$35
7-)' VFF' Ω>' A1' 39)' 20' "/0' -"37*"3)-' "3' xCQ' `5' 69"3' $-' 39)
/"M$/7/' #"(7)' 39"3' ?D' ."%' 9"#)' 69$()' 39)' .7**)%3B-27*.)
-700(4$%&'$3'20)*"3)-'0*20)*(4\
D 2.34 H--7/$%&'39)'20'"/0'32',)'$+)"(5'$3'$-'*)K7$*)+'32
+)-$&%'39)'.$*.7$3'-926%'$%'S$&>']Q>TU'32'$/0()/)%3'"'.7*B
*)%3'"/0($1$)*'6$39'&"$%' ) D ⁄ ) > = CF'HdH>
<"= S$%+'39)'*)K7$*)+'#"(7)'12*'?>
<,= Y9"3' "*)' 39)' $%073' "%+' 39)' 273073' *)-$-3"%.)' 21' 39$.7**)%3'"/0($1$)*\
D 2.35 j)-$&%'39)'.$*.7$3'-926%'$%'S$&>']Q>TV'32'9"#)'"%
$%073' *)-$-3"%.)' 21' CFF' 8Ω' "%+' "' &"$%' 39"3' ."%' ,)' #"*$)+
R3
R2
vI
R1
2
1
Figure P2.35
R4
vO
Problems 113
D 2.37 j)-$&%' "%' 20' "/0' .$*.7$3' 32' 0*2#$+)' "%' 273073
v B = ! [ Qv C + ( v Q ⁄ Q ) ]>' G922-)' *)("3$#)(4' (26' #"(7)-' 21
*)-$-32*-' ,73' 2%)-' 12*' 69$.9' 39)' $%073' .7**)%3' <1*2/' )".9
$%073'-$&%"('-27*.)='+2)-'%23')M.))+'F>C'/H'12*'CB`'$%073
-$&%"(->
D 2.38 a-)'39)'-.9)/)'$((7-3*"3)+'$%'S$&>'Q>CF'32'+)-$&%'"%
20B"/0' .$*.7$3' 6$39' $%073-' vC5' v Q5' "%+' vT5' 692-)' 273073' $vB = −<QvC'+'UvQ'+'cvT='7-$%&'-/"(('*)-$-32*-',73'%2'-/"(()*
39"%'CF'8Ω>
*2.43 S$&7*)']Q>UT'-926-'"'.$*.7$3'12*'"'+$&$3"(B32B"%"(2&
.2%#)*3)*' <jHG=>' ;9)' .$*.7$3' "..)03-' "' UB,$3' $%073' ,$%"*4
62*+'/T/Q/C/F5'69)*)'/F5'/C5'/Q5'"%+'/T'3"8)'39)'#"(7)-'21'F
2*' C5' "%+' $3' 0*2#$+)-' "%' "%"(2&' 273073' #2(3"&)' vB' 0*202*B
3$2%"('32'39)'#"(7)'21'39)'+$&$3"('$%073>'@".9'21'39)',$3-'21
39)' $%073' 62*+' .2%3*2(-' 39)' .2**)-02%+$%&(4' %7/,)*)+
-6$3.9>'S2*'$%-3"%.)5'$1'/Q'$-'F'39)%'-6$3.9'KQ'.2%%).3-'39)
QFB8Ω'*)-$-32*'32'&*27%+5'69$()'$1'/Q'$-'C'39)%'KQ'.2%%).339)'QFB8Ω'*)-$-32*'32'39)'+VB`'026)*'-700(4>'L926'39"3'vB
$-'&$#)%',4
?2 F
C
Q
T
v B = ! BBBBBB [ Q / F + Q / C + Q / Q + Q / T ]
CE
69)*)'?2'$-'$%'8$(29/-.'S$%+'39)'#"(7)'21'?2'-2'39"3'vB'*"%&)1*2/'F'32'−CQ'#2(3->
D 2.39 H%' $+)"(' 20' "/0' $-' .2%%).3)+' $%' 39)' 6)$&93)+
-7//)*' .2%1$&7*"3$2%' 21' S$&>' Q>CF>' ;9)' 1))+,".8' *)-$-32*
?2% % = CF' 8Ω5' "%+' -$M' CFB8Ω' *)-$-32*-' "*)' .2%%).3)+' 32' 39)
$%#)*3$%&'$%073'3)*/$%"('21'39)'20'"/0>'L9265',4'-8)3.9$%&
39)' #"*$27-' .$*.7$3' .2%1$&7*"3$2%-5' 926' 39$-' ,"-$.' .$*.7$3
."%',)'7-)+'32'$/0()/)%3'39)'12((26$%&'17%.3$2%-:
<"= v B = ! ( v C + Qv Q + Tv T )
<,= v B = ! ( v C + v Q + Qv T + Qv U )
<.= v B = ! ( v C + Vv Q )
<+= v B = ! E v C
A%' )".9' ."-)' 1$%+' 39)' $%073' *)-$-3"%.)' -))%' ,4' )".9' 21' 39)
-$&%"('-27*.)-'-700(4$%&'vC5'v Q5'v T5'"%+'v U>'L7&&)-3'"3'()"-3
362'"++$3$2%"('-7//$%&'17%.3$2%-'39"3'427'."%'*)"($[)'6$39
39$-'.$*.7$3>'!26'627(+'427'*)"($[)'"'-7//$%&'.2)11$.$)%3
39"3'$-'F>V\'
D 2.40 i$#)'"'.$*.7$35'.2/0()3)'6$39'.2/02%)%3'#"(7)-5'12*
"'6)$&93)+'-7//)*'39"3'-9$13-'39)'+.'()#)('21'"'-$%)B6"#)'-$&B
%"('21'T'-$%<ω &='`'1*2/'[)*2'32'−T'`>'H--7/)'39"3'$%'"++$3$2%
32' 39)' -$%)B6"#)' -$&%"(' 427' 9"#)' "' +.' *)1)*)%.)' #2(3"&)' 21
C>V `'"#"$(",()>'L8)3.9'39)'273073'-$&%"('6"#)12*/>
D 2.41 a-)'362'$+)"('20'"/0-'"%+'*)-$-32*-'32'$/0()/)%3
39)'-7//$%&'17%.3$2%
v B = v C + Qv Q ! Tv T ! Uv U D *2.42 A%'"%'$%-3*7/)%3"3$2%'-4-3)/5'39)*)'$-'"'%))+'32
3"8)' 39)' +$11)*)%.)' ,)36))%' 362' -$&%"(-5' 2%)' 21' vC' =
Q -$%<Qπ''× EF&='+'F>FC'-$%<Qπ' × CFFF&='#2(3-'"%+'"%239)*
21'vQ'= Q -$%<Qπ' ×'EF&='−'F>FC'-$%<Qπ' × CFFF&='#2(3->'j*"6
"' .$*.7$3' 39"3' 1$%+-' 39)' *)K7$*)+' +$11)*)%.)' 7-$%&' 362' 20
"/0-'"%+'/"$%(4'CFFB8Ω''*)-$-32*->'L$%.)'$3'$-'+)-$*",()'32
"/0($14'39)'CFFFB!['.2/02%)%3'$%'39)'0*2.)--5'"**"%&)'32
0*2#$+)' "%' 2#)*"((' &"$%' 21' CFF' "-' 6)((>' ;9)' 20' "/0-
Figure P2.43
Section 2.3: The Noninverting
Configuration
D 2.44 i$#)%' "%' $+)"(' 20' "/0' 32' $/0()/)%3' +)-$&%-' 12*
39)'12((26$%&'.(2-)+B(220'&"$%-5'69"3'#"(7)-'21'*)-$-32*-'<?C5
?Q='-927(+',)'7-)+\'Y9)*)'02--$,()5'7-)'"3'()"-3'2%)'CFB8Ω
*)-$-32*'"-'39)'-/"(()-3'*)-$-32*'$%'427*'+)-$&%>
PROBLEMS
2.36 H'6)$&93)+'-7//)*'.$*.7$3'7-$%&'"%'$+)"('20'"/0'9"39*))'$%073-'7-$%&'CFFB8Ω'*)-$-32*-'"%+'"'1))+,".8'*)-$-32*'21
VF'8Ω>'H'-$&%"('vC'$-'.2%%).3)+'32'362'21'39)'$%073-'69$()'"
-$&%"( vQ $-' .2%%).3)+' 32' 39)' 39$*+>' @M0*)--' vB' $%' 3)*/-' 21' vC
"%+ vQ>'A1'vC'Z'Q'`'"%+'vQ'Z'nQ'`5'69"3'$-'vB\
"#"$(",()'"*)'$+)"(')M.)03'39"3'39)$*'273073'#2(3"&)'-6$%&'$($/$3)+'32'±CF'`>
CHAPTER 2
1*2/'−C'`d`'32'−CF'`d`'7-$%&'39)'CFB8Ω'023)%3$2/)3)*'?U>
Y9"3' #2(3"&)' &"$%' *)-7(3-' 69)%' 39)' 023)%3$2/)3)*' $-' -)3
)M".3(4'"3'$3-'/$++()'#"(7)\
CHAPTER 2
PROBLEMS
114 Chapter 2 Operational Amplifiers
<"= +C'`d`
<,= +Q'`d`
<.= +CC'`d`
<+= +CFF'`d`
D 2.45 j)-$&%'"'.$*.7$3',"-)+'2%'39)'3202(2&4'21'39)'%2%B
$%#)*3$%&'"/0($1$)*'32'2,3"$%'"'&"$%'21'+C>V'`d`5'7-$%&'2%(4
CFB8Ω'*)-$-32*->'P23)'39"3'39)*)'"*)'362'02--$,$($3$)->'Y9$.9
21'39)-)'."%',)')"-$(4'.2%#)*3)+'32'9"#)'"'&"$%'21')$39)*'+C>F
`d`'2*'+Q>F'`d`'-$/0(4',4'-92*3B.$*.7$3$%&'"'-$%&()'*)-$-32*
$%')".9'."-)\
D 2.46 S$&7*)']Q>UE'-926-'"'.$*.7$3'12*'"%'"%"(2&'#2(3/)B
3)*' 21' #)*4' 9$&9' $%073' *)-$-3"%.)' 39"3' 7-)-' "%' $%)M0)%-$#)
/2#$%&B.2$(' /)3)*>' ;9)' #2(3/)3)*' /)"-7*)-' 39)' #2(3"&)' !
"00($)+' ,)36))%' 39)' 20' "/0J-' 02-$3$#)B$%073' 3)*/$%"(' "%+
&*27%+>'H--7/$%&'39"3'39)'/2#$%&'.2$('0*2+7.)-'17((B-."()
+)1().3$2%' 69)%' 39)' .7**)%3' 0"--$%&' 39*27&9' $3' $-' CFF' µH5
1$%+' 39)' #"(7)' 21' ?' -7.9' 39"3'17((B-."()' *)"+$%&' $-' 2,3"$%)+
69)%'!'$-'+CF'`>'j2)-'39)'/)3)*'*)-$-3"%.)'-926%'"11).3'39)
#2(3/)3)*'."($,*"3$2%\
RP0
Figure P2.47
D 2.48 j)-$&%'"'.$*.7$35'7-$%&'2%)'$+)"('20'"/05'692-)'273B
073'$-'vB'Z'v>C't'Tv>Q'n'Q<v>T't'Tv>U=>% <P)*&Q'a-)'"'-3*7.37*)'-$/B
$("*'32'39"3'-926%'$%'&)%)*"('12*/'$%'S$&>']Q>UI>=
2.49 j)*$#)'"%')M0*)--$2%'12*'39)'#2(3"&)'&"$%5' v B ⁄ v > 5'21
39)'.$*.7$3'$%'S$&>']Q>UD>
R2
R1
V
2
1
Figure P2.46
D *2.47 <"= a-)'-70)*02-$3$2%'32'-926'39"3'39)'273073'21
39)'.$*.7$3'$%'S$&>']Q>UI'$-'&$#)%',4
?2
?2
?2
v B = ! BBBBBBBB v OC + BBBBBBBB v OQ + >'>'> + BBBBBBBB v O*
? OC
? OQ
? O*
?2
+ C + BBBBBB
?O
?
?
?
BBBBBBBEB v EC + BBBBBBBEB v EQ + >'>'> + BBBBBBBEB v E*
? EC
? EQ
? E*
69)*)'?O%%='?OCrr?OQrr'>'>'>'rr?O*'"%+
%%%%%%%%%%%?E% = ?ECrr?EQrr'>'>'>'rr?E*rr?EF
<,= j)-$&%'"'.$*.7$3'32'2,3"$%
v B = ! Tv OC + v EC + Qv EQ
;9)'-/"(()-3'*)-$-32*'7-)+'-927(+',)'CF'8Ω>
1
R3
vI
2
R4
1
vO
2
Figure P2.49
2.50 S2*'39)'.$*.7$3'$%'S$&>']Q>VF5'7-)'-70)*02-$3$2%'32'1$%+
vB'$%'3)*/-'21'39)'$%073'#2(3"&)-'vC'"%+'vQ>'H--7/)'"%'$+)"(
20'"/0>'S2*
v C = CF -$% ( Q π ' × ' EF& ) ! F>C-$% ( Q π ×'CFFF& ), #2(3v Q = CF -$% ( Q π ' × 'EF& ) + F>C-$% ( Q π ×'CFFF& ), #2(31$%+'vB>'
D 2.51 ;9)' .$*.7$3' -926%' $%' S$&>' ]Q>VC' 73$($[)-' "' CFB8Ω
023)%3$2/)3)*'32'*)"($[)'"%'"+W7-3",()B&"$%'"/0($1$)*>'j)*$#)
"%')M0*)--$2%'12*'39)'&"$%'"-'"'17%.3$2%'21'39)'023)%3$2/)3)*
Problems 115
2.55 G2/0()3)'39)'12((26$%&'3",()'12*'1))+,".8'"/0($1$)*.*)"3)+'7-$%&'2%)'$+)"('20'"/0>'P23)'39"3'?$%'-$&%$1$)-'$%073
*)-$-3"%.)' "%+' ?C' "%+' ?Q' "*)' 1))+,".8B%)362*8' *)-$-32*-' "(",)(()+'$%'39)'$%#)*3$%&'"%+'%2%$%#)*3$%&'.2%1$&7*"3$2%->
20R
Figure P2.50
Figure P2.51
-)33$%&'C>'H--7/)'39)'20'"/0'32',)'$+)"(>'Y9"3'$-'39)'*"%&)
21'&"$%-'2,3"$%)+\'L926'926'32'"++'"'1$M)+'*)-$-32*'-2'39"3
39)'&"$%'*"%&)'."%',)'C'32'CC'`d`>'Y9"3'-927(+'39)'*)-$-32*
#"(7)',)\
D 2.52 i$#)%' 39)' "#"$(",$($34' 21' *)-$-32*-' 21' #"(7)' C' 8Ω
"%+'CF'8Ω'2%(45'+)-$&%'"'.$*.7$3',"-)+'2%'39)'%2%$%#)*3$%&
.2%1$&7*"3$2%'32'*)"($[)'"'&"$%'21'+CF'`d`>
2.53 A3'$-'*)K7$*)+'32'.2%%).3'"'CFB`'-27*.)'6$39'"'-27*.)
*)-$-3"%.)'21'CFF'8Ω'32'"'CB8Ω'(2"+>'S$%+'39)'#2(3"&)'39"3
6$(('"00)"*'".*2--'39)'(2"+'$1:'
<"= ;9)'-27*.)'$-'.2%%).3)+'+$*).3(4'32'39)'(2"+>'
<,= H' 7%$34B&"$%' 20B"/0' ,711)*' $-' $%-)*3)+' ,)36))%' 39)
-27*.)'"%+'39)'(2"+>
A%')".9'."-)'1$%+'39)'(2"+'.7**)%3'"%+'39)'.7**)%3'-700($)+
,4' 39)' -27*.)>' Y9)*)' +2)-' 39)' (2"+' .7**)%3' .2/)' 1*2/' $%
."-)'<,=\
2.54 j)*$#)'"%')M0*)--$2%'12*'39)'&"$%'21'39)'#2(3"&)'12(B
(26)*'21'S$&>'Q>CU5'"--7/$%&'39)'20'"/0'32',)'$+)"(')M.)03
12*' 9"#$%&' "' 1$%$3)' &"$%' $>' G"(.7("3)' 39)' #"(7)' 21' 39)
.(2-)+B(220' &"$%' 12*' $' =' CFFF5' CFF5'"%+' CF>' A%' )".9'."-)
1$%+'39)'0)*.)%3"&)')**2*'$%'&"$%'/"&%$37+)'1*2/'39)'%2/$B
%"('#"(7)'21'7%$34>
/
>
*
?
(
@
.
Gain
Rin
−%4-;<;
−%-;<;
−#-;<;
+%-;<;
+#-;<;
+%%-;<;
−4$7-;<;
%4-=Ω
∞
R1
%44-=Ω
%4-=Ω
%4-=Ω
R2
%44-=Ω
%44-=Ω
D 2.56 H'%2%$%#)*3$%&'20B"/0'.$*.7$3'6$39' %2/$%"('&"$%
21'CF'`d`'7-)-'"%'20'"/0'6$39'20)%B(220'&"$%'21'VF'`d`
"%+'"'(26)-3B#"(7)'*)-$-32*'21'CF'8Ω>'Y9"3'.(2-)+B(220'&"$%
".37"((4'*)-7(3-\'Y$39'69"3'#"(7)'*)-$-32*'."%'69$.9'*)-$-32*
,)'-97%3)+'32'".9$)#)'39)'%2/$%"('&"$%\'A1'$%'39)'/"%71".B
37*$%&'0*2.)--5'"%'20'"/0'21'&"$%'CFF'`d`'6)*)'7-)+5'69"3
.(2-)+B(220'&"$%'627(+'*)-7(3'$%')".9'."-)'<39)'7%.2/0)%B
-"3)+'2%)5'"%+'39)'.2/0)%-"3)+'2%)=\'
2.57 a-)' @K>' <Q>CC=' 32' -926' 39"3' $1' 39)' *)+7.3$2%' $%' 39)
.(2-)+B(220'&"$%'A'1*2/'39)'%2/$%"('#"(7)' A F 3 C + ? Q ⁄ ? C
$-' 32' ,)' 8)03' ()--' 39"%' Cg' 21' AF5' 39)%' 39)' 20)%B(220' &"$%
21 39)' 20' "/0' /7-3' )M.))+' AF' ,4' "3' ()"-3' "' 1".32*' J' =
<CFF ⁄ C= ! C '!'CFF ⁄ C >' S$%+' 39)' *)K7$*)+' J' 12*' C' Z' F>FC5
F>C5'C5'"%+'CF>'a3$($[)'39)-)'*)-7(3-'32'1$%+'12*')".9'#"(7)'21'C
39)'/$%$/7/'*)K7$*)+'20)%B(220'&"$%'32'2,3"$%'.(2-)+B(220
&"$%-'21'C5'CF5'CFQ5'CFT5'"%+'CFU'`d`>
2.58 S2*' )".9' 21' 39)' 12((26$%&' .2/,$%"3$2%-' 21' 20B"/0
20)%B(220'&"$%%$'"%+'%2/$%"('.(2-)+B(220'&"$%'AF5'."(.7("3)
39)'".37"('.(2-)+B(220'&"$%'A'39"3'$-'".9$)#)+>'H(-25'."(.7B
("3)'39)'0)*.)%3"&)',4'69$.9' A '1"((-'-92*3'21'39)'%2/$%"(
&"$%'/"&%$37+)' A F >'
Case
G0 (V/V)
"
,
.
+
)
1
&
−C
+C
−C
+CF
−CF
−CF
+C
A (V/V)
CF
CF
CFF
CF
CFF
CFFF
Q
PROBLEMS
Case
CHAPTER 2
20R
2.59 S$&7*)']Q>VD'-926-'"'.$*.7$3'39"3'0*2#$+)-'"%'273073
#2(3"&)'vB'692-)'#"(7)'."%',)'#"*$)+',4'37*%$%&'39)'6$0)*
21'39)'CFFB8Ω'''023)%3$2/)3)*>'S$%+'39)'*"%&)'2#)*'69$.9
vB'."%',)'#"*$)+>'A1'39)'023)%3$2/)3)*'$-'"'^QFB37*%_'+)#$.)5
1$%+'39)'.9"%&)'$%'vB'.2**)-02%+$%&'32')".9'37*%'21'39)'023>
CHAPTER 2
PROBLEMS
116 Chapter 2 Operational Amplifiers
Figure P2.62
.2//2%B/2+)' -$&%"(' -27*.)>' S2*' ? Q ⁄ ? C = ? U ⁄ ? T 5' -926
39"3' 39)' $%073'
.2//2%B/2+)'
*)-$-3"%.)'
$( ? T + ? U ) || ( ? C + ? Q )>
2.64 G2%-$+)*'39)'.$*.7$3'21'S$&>'Q>CE5'"%+'()3')".9'21'39)
v>C'"%+' v>Q'-$&%"(' -27*.)-' 9"#)' "'-)*$)-' *)-$-3"%.)'?4>' Y9"3
.2%+$3$2%' /7-3' "00(4' $%' "++$3$2%' 32' 39)' .2%+$3$2%' $%' @K>
<Q>CV='$%'2*+)*'12*'39)'"/0($1$)*'32'17%.3$2%'"-'"%'$+)"('+$1B
1)*)%.)'"/0($1$)*\
Figure P2.59
Section 2.4: Difference Amplifiers
2.60 S$%+' 39)' #2(3"&)' &"$%' v B ⁄ v >. ' 12*' 39)' +$11)*)%.)
"/0($1$)*'21'S$&>'Q>CE'12*'39)'."-)'?C'= ?T'='CF'8Ω'"%+'?Q'=
?U'='CFF'8Ω>'Y9"3'$-'39)'+$11)*)%3$"('$%073'*)-$-3"%.)'?).\'A1
39)'362'8)4'*)-$-3"%.)'*"3$2-'( ? Q ⁄ ? C )'"%+'( ? U ⁄ ? T )'"*)'+$1B
1)*)%3' 1*2/' )".9' 239)*' ,4' Cg5' 69"3' +2' 427' )M0).3' 39)
.2//2%B/2+)'&"$%'$0-'32',)\'H(-25'1$%+'39)'GROO'$%'39$."-)>'P)&().3'39)')11).3'21'39)'*"3$2'/$-/"3.9'2%'39)'#"(7)
21'$. >
D 2.61 a-$%&' 39)' +$11)*)%.)' "/0($1$)*' .2%1$&7*"3$2%' 21
S$&>'Q>CE'"%+'"--7/$%&'"%'$+)"('20'"/05'+)-$&%'39)'.$*.7$3
32'0*2#$+)'39)'12((26$%&'+$11)*)%3$"('&"$%->'A%')".9'."-)5'39)
+$11)*)%3$"('$%073'*)-$-3"%.)'-927(+',)'QF'8Ω>
<"= C'`d `
<,= Q'`d `
<.= CFF'`d `
<+= F>V'`d `
2.62 S2*' 39)' .$*.7$3' -926%' $%' S$&>' ]Q>EQ5' )M0*)--' vB' "-' "
17%.3$2%'21'vC'"%+'vQ>'Y9"3'$-'39)'$%073'*)-$-3"%.)'-))%',4'vC
"(2%)\'e4'vQ'"(2%)\'e4'"'-27*.)'.2%%).3)+',)36))%'39)'362
$%073'3)*/$%"(-\'e4'"'-27*.)'.2%%).3)+'32',239'$%073'3)*/$B
%"(-'-$/7(3"%)27-(4\
2.63 G2%-$+)*' 39)' +$11)*)%.)' "/0($1$)*' 21' S$&>' Q>CE' 6$39
39)' 362' $%073' 3)*/$%"(-' .2%%).3)+' 32&)39)*' 32' "%' $%073
*2.65 S2*'39)'+$11)*)%.)'"/0($1$)*'-926%'$%'S$&>']Q>EQ5'()3
"((' 39)' *)-$-32*-' ,)' CF' 8Ω' ±' Cg>' S$%+' "%' )M0*)--$2%' 12*' 39)
62*-3B."-)' .2//2%B/2+)' &"$%' 39"3' *)-7(3->' @#"(7"3)' 39$-' 12*
C ='F>C5'C5'"%+'V>'H(-25')#"(7"3)'39)'*)-7(3$%&'GROO'$%')".9
."-)>'P)&().3'39)')11).3'21'*)-$-32*'32()*"%.)-'2%'$. >
2.66 S2*' 39)' +$11)*)%.)' "/0($1$)*' 21' S$&>' Q>CE5' -926' 39"3' $1
)".9'*)-$-32*'9"-'"'32()*"%.)'21'±CFF' ε g'<$>)>5'12*5'-"45'"'Vg
*)-$-32*5' ε = F>FV=' 39)%' 39)' 62*-3B."-)' GROO' $-' &$#)%
"00*2M$/"3)(4',4'
I+C
GROO'!'QF'(2& BBBBBBBBBBBBB
Uε
69)*)'I'$-'39)'%2/$%"('<$+)"(='#"(7)'21'39)'*"3$2-' ( ? Q ⁄ ? C )
"%+' ( ? U ⁄ ? T )>'G"(.7("3)'39)'#"(7)'21'62*-3B."-)'GROO'12*
"%' "/0($1$)*'+)-$&%)+'32'9"#)'"'+$11)*)%3$"('&"$%'21'$+)"((4
CFF' `d`5' "--7/$%&' 39"3' 39)' 20' "/0' $-' $+)"(' "%+' 39"3' Cg
*)-$-32*-'"*)'7-)+>
D *2.67 j)-$&%'39)'+$11)*)%.)'"/0($1$)*'.$*.7$3'21'S$&>'Q>CE
32'*)"($[)'"'+$11)*)%3$"('&"$%'21'CFF5'"'+$11)*)%3$"('$%073'*)-$-B
3"%.)'21'QF'8Ω5'"%+'"'/$%$/7/'GROO'21'cF'+e>'H--7/)'39)
20'"/0'32',)'$+)"(>'L0).$14',239'39)'*)-$-32*'#"(7)-'"%+'39)$*
*)K7$*)+'32()*"%.)'<)>&>5',)33)*'39"%'Cg=>
*2.68 <"= S$%+' $.' "%+'$0-' 12*' 39)' +$11)*)%.)' "/0($1$)*' .$*B
.7$3'-926%'$%'S$&>']Q>Ec>'
<,= A1'39)'20'"/0'$-'-0).$1$)+'32'20)*"3)'0*20)*(4'"-'(2%&
"-'39)'.2//2%B/2+)'#2(3"&)'"3'$3-'02-$3$#)'"%+'%)&"3$#)
$%073-'1"((-'$%'39)'*"%&)'±Q>V'`5'69"3'$-'39)'.2**)-02%+$%&
($/$3"3$2%'2%'39)'*"%&)'21'39)'$%073'.2//2%B/2+)'-$&%"(
v>0-\' <;9$-' $- 8%26%' "-' 39)' 0.++."/+.1$* %,"'$' 21' 39)
+$11)*)%3$"('"/0($1$)*>=
Problems 117
*2.70 S$&7*)']Q>IF'-926-'"'/2+$1$)+'#)*-$2%'21'39)'+$11)*B
)%.)'"/0($1$)*>';9)'/2+$1$)+'.$*.7$3'$%.(7+)-'"'*)-$-32*'?A5
69$.9'."%',)'7-)+'32'#"*4'39)'&"$%>'L926'39"3'39)'+$11)*)%B
3$"('#2(3"&)'&"$%'$-'&$#)%',4
100 kV
v
?
?
BBBBBBB = ! Q BBBBBQ C + BBBBBQB
v >.
?C
?A
vI2
<P)*&Q' ;9)' #$*37"(' -92*3' .$*.7$3' "3' 39)' 20B"/0' $%073' ."7-)39)'.7**)%3'39*27&9'39)'?C'*)-$-32*-'32',)'v >. ⁄ Q? C >=
100 kV
2
A
100 kV
B
vO
1
100 kV
vId
Figure P2.68
**2.69 ;2' 2,3"$%' "' 9$&9B&"$%5' 9$&9B$%073B*)-$-3"%.)' +$11)*B
)%.)'"/0($1$)*5'39)'.$*.7$3'$%'S$&>']Q>ED')/0(24-'02-$3$#)'1))+B
,".85' $%' "++$3$2%' 32' 39)' %)&"3$#)' 1))+,".8' 0*2#$+)+' ,4' 39)
*)-$-32*'?'.2%%).3)+'1*2/'39)'273073'32'39)'%)&"3$#)'$%073'21'39)
20' "/0>' L0).$1$."((45' "' #2(3"&)' +$#$+)*' <?V5' ?E=' .2%%).3)+
".*2--'39)'273073'1))+-'"'1*".3$2%'β'21'39)'2730735'39"3'$-5'"'#2(3B
"&)' β vB5' ,".8' 32' 39)' 02-$3$#)B$%073' 3)*/$%"(' 21' 39)' 20
"/0 39*27&9' "' *)-$-32*' ?>' H--7/)' 39"3' ?V' "%+' ?E' "*)' /7.9
-/"(()*'39"%'?'-2'39"3'39)'.7**)%3'39*27&9'?'$-'/7.9'(26)*'39"%
39)' .7**)%3' $%' 39)' #2(3"&)' +$#$+)*5' 6$39' 39)' *)-7(3' 39"3
β ! ? E ( ? V + ? E )>'L926'39"3'39)'+$11)*)%3$"('&"$%'$-'&$#)%',4
v
C
$ .' ≡ ' BBBBBBB = BBBBBBBBBBBB
v >.
C!β
<P)*&Q'a-)'-70)*02-$3$2%>=
j)-$&%'39)'.$*.7$3'32'2,3"$%'"'+$11)*)%3$"('&"$%'21'CF'`d`'"%+
+$11)*)%3$"('$%073'*)-$-3"%.)'21'Q'RΩ>'L)().3'#"(7)-'12*'?5'?V5
"%+'?E5'-7.9'39"3'( ? V + ? E ) ≤ ? ⁄ CFF>
v1
R
R
2
vO
1
v2
<"= L926'926'39)'.$*.7$3'."%',)'7-)+'32'$/0()/)%3'"'+$1B
1)*)%.)'"/0($1$)*'21'7%$34'&"$%>
<,= L926' 926' 39)' .$*.7$3' ."%' ,)' 7-)+' 32' $/0()/)%3' -$%B
&()B)%+)+'"/0($1$)*-'6$39'&"$%-:
''''''''<$= −C'`d `
'''''''<$$= +C'`d `
''''' <$$$= +Q'`d `
''''''<$#= +CdQ'`d`
A
R
25 kV
C
2
O
bvO
1
R6
B
Figure P2.69
25 kV
R5
1
R
D *2.71 ;9)'.$*.7$3'-926%'$%'S$&>']Q>IC'$-'"'*)0*)-)%3"3$2%
21'"'#)*-"3$()5'.2//)*.$"((4'"#"$(",()'AG5'39)'APHCFV5'/"%7B
1".37*)+',4'e7**Be*26%'"%+'8%26%'"-'"'+$11)*)%3$"('"/0($B
1$)*' /2+7()>' A3' .2%-$-3-' 21' "%' 20' "/0' "%+' 0*).$-$2%5' ("-)*B
3*$//)+5'/)3"(B1$(/'*)-$-32*->';9)'.$*.7$3'."%',)'.2%1$&7*)+
12*'"'#"*$)34'21'"00($."3$2%-',4'39)'"00*20*$"3)'.2%%).3$2%'21
3)*/$%"(-'H5'e5'G5'j5'"%+'?>
H#2$+'()"#$%&'"'3)*/$%"('20)%B.$*.7$3)+5'12*'-7.9'"'3)*/$%"(
/"4'".3'"-'"%'^"%3)%%"5_'0$.8$%&'70'$%3)*1)*)%.)'"%+'%2$-)
2
vId
Figure P2.70
25 kV
Figure P2.71
25 kV
D
PROBLEMS
vI1
CHAPTER 2
<.= ;9)'.$*.7$3'$-'/2+$1$)+',4'.2%%).3$%&'"'CFB8Ω'*)-$-32*
,)36))%' %2+)' H' "%+' &*27%+5' "%+' "%239)*' CFB8Ω' *)-$-32*
,)36))%'%2+)'e'"%+'&*27%+>'Y9"3'6$(('%26',)'39)'#"(7)21'$. 5'$0- 5'"%+'39)'$%073'.2//2%B/2+)'*"%&)\
CHAPTER 2
PROBLEMS
118 Chapter 2 Operational Amplifiers
39*27&9'."0".$3$#)'.270($%&>'O"39)*5'1$%+'"'.2%#)%$)%3'%2+)
32'.2%%).3'-7.9'"'3)*/$%"('$%'"'*)+7%+"%3'6"4>'Y9)%'/2*)
39"%'2%)'.$*.7$3'$/0()/)%3"3$2%'$-'02--$,()5'.2//)%3'2%'39)
*)("3$#)' /)*$3-' 21' )".95' 3"8$%&' $%32' "..27%3' -7.9' .2%-$+)*B
"3$2%-' "-' +)0)%+)%.)' 2%' .2/02%)%3' /"3.9$%&' "%+' $%073
*)-$-3"%.)>
20 k&
2.72 G2%-$+)*'39)'$%-3*7/)%3"3$2%'"/0($1$)*'21'S$&>'Q>QF<,=
6$39'"'.2//2%B/2+)'$%073'#2(3"&)'21'+Q'`'<+.='"%+'"'+$1B
1)*)%3$"(' $%073' -$&%"(' 21' cFB/`' 0)"8' -$%)' 6"#)>' k)3' Q?C' =
Q 8Ω5'?Q'='VF'8Ω5'?T'='?U'= CF'8Ω>'S$%+'39)'#2(3"&)'"3')#)*4
%2+)'$%'39)'.$*.7$3>
2.73 <"= G2%-$+)*'39)'$%-3*7/)%3"3$2%'"/0($1$)*'.$*.7$3'21
S$&>'Q>QF<"=>'A1'39)'20'"/0-'"*)'$+)"(')M.)03'39"3'39)$*'273B
073-' -"37*"3)' "3' ±CU' `5' $%' 39)' /"%%)*' -926%' $%' S$&>' C>CU5
1$%+'39)'/"M$/7/'"((26)+'$%073'.2//2%B/2+)'-$&%"('12*
39)'."-)'?C'='C'8Ω'"%+'?Q'='CFF'8Ω>
<,= O)0)"3'<"='12*'39)'.$*.7$3'$%'S$&>'Q>QF<,=5'"%+'.2//)%3
2%'39)'+$11)*)%.)',)36))%'39)'362'.$*.7$3->
2.74 <"= @M0*)--$%&' v>C' "%+' v>Q' $%' 3)*/-' 21' +$11)*)%3$"(
"%+' .2//2%B/2+)' .2/02%)%3-5' 1$%+' vBC' "%+' vBQ' $%' 39)
.$*.7$3' $% S$&>' Q>QF<"=' "%+' 9)%.)' 1$%+' 39)$*' +$11)*)%3$"(
.2/02%)%3'vBQ'−'vBC'"%+'39)$*'.2//2%B/2+)'.2/02%)%3
CBBB
( v + v BQ )>'P26'1$%+'39)'+$11)*)%3$"('&"$%'"%+'39)'.2//2%B
Q BC
/2+)'&"$%'21'39)'1$*-3'-3"&)'21'39$-'$%-3*7/)%3"3$2%'"/0($B
1$)*'"%+'9)%.)'39)'GROO>
<,= O)0)"3'12*'39)'.$*.7$3'$%'S$&>'Q>QF<,=5'"%+'.2//)%3'2%
39)'+$11)*)%.)',)36))%'39)'362'.$*.7$3->
*2.75 S2*'"%'$%-3*7/)%3"3$2%'"/0($1$)*'21'39)'340)'-926%
$%'S$&>'Q>QF<,=5'"'+)-$&%)*'0*202-)-'32'/"8)'?Q'='?T'='?U'=
CFF' 8Ω5' "%+' Q?C' =' CF' 8Ω>' S2*' $+)"(' .2/02%)%3-5' 69"3
+$11)*)%.)B/2+)' &"$%5' .2//2%B/2+)' &"$%5' "%+' GROO
*)-7(3\'O))#"(7"3)'39)'62*-3B."-)'#"(7)-'12*'39)-)'12*'39)'-$3B
7"3$2%' $%' 69$.9' "((' *)-$-32*-' "*)' -0).$1$)+' "-' ±Cg' 7%$3->
O)0)"3' 39)' ("33)*' "%"(4-$-' 12*' 39)' ."-)' $%' 69$.9' Q?C' $*)+7.)+'32'C'8Ω>'Y9"3'+2'427'.2%.(7+)'",273'39)')11).3'21
39)'&"$%'21'39)'1$*-3'-3"&)'2%'GROO\'<P)*&Q'@K>'<Q>CD='."%
,)'7-)+'32')#"(7"3)'$0-'21'39)'-).2%+'-3"&)>=
30 k&
Figure P2.77
<.= H--7/$%&'39"3'39)'20'"/0-'20)*"3)' 1*2/'±CVB`'026)*
-700($)-'"%+'39"3'39)$*'273073'-"37*"3)-'"3'±CU'`'<$%'39)'/"%B
%)*'-926%'$%'S$&>'C>CU=5'69"3'$-'39)'("*&)-3'-$%)B6"#)'273B
073'39"3'."%',)'"..2//2+"3)+\'L0).$14',239'$3-'0)"8B32B
0)"8'"%+'*/-'#"(7)->
*2.78 ;9)' 362' .$*.7$3-' $%' S$&>' ]Q>Ic' "*)' $%3)%+)+' 32
17%.3$2%' "-' #2(3"&)B32B.7**)%3' .2%#)*3)*-X' 39"3' $-5' 39)4
-700(4'39)'(2"+'$/0)+"%.)'FD'6$39'"'.7**)%3'0*202*3$2%"(
32'v>'"%+'$%+)0)%+)%3'21'39)'#"(7)'21'FD>'L926'39"3'39$-'$$%+))+'39)'."-)5'"%+'1$%+'12*')".9'.$*.7$3')B'"-'"'17%.3$2%
21' v>>' G2//)%3' 2%' 39)' +$11)*)%.)-' ,)36))%' 39)' 362
.$*.7$3->
Section 2.5: Integrators and
Differentiators
2.79 H' R$(()*' $%3)&*"32*' $%.2*02*"3)-' "%' $+)"(' 20' "/05' "
*)-$-32*'?'21'CFF'8Ω5'"%+'"'."0".$32*'"'21'C'%S>'H'-$%)B6"#)
-$&%"('$-'"00($)+'32'$3-'$%073>
*2.77 ;9)'.$*.7$3'-926%'$%'S$&>']Q>II'$-'$%3)%+)+'32
-700(4'"'#2(3"&)'32'1(2"3$%&'(2"+-'<392-)'12*'69$.9',239'3)*B
/$%"(-'"*)'7%&*27%+)+='69$()'/"8$%&'&*)"3)-3'02--$,()'7-)
21'39)'"#"$(",()'026)*'-700(4>
<"= H3' 69"3' 1*)K7)%.4' <$%' ![=' "*)' 39)' $%073' "%+' 273073
-$&%"(-')K7"('$%'"/0($37+)\
<,= H3' 39"3' 1*)K7)%.45' 926' +2)-' 39)' 09"-)' 21' 39)' 273073
-$%)'6"#)'*)("3)'32'39"3'21'39)'$%073\
<.= A1'39)'1*)K7)%.4'$-'(26)*)+',4'"'1".32*'21'CF'1*2/'39"3
127%+' $%' <"=5' ,4' 69"3' 1".32*' +2)-' 39)' 273073' #2(3"&)
.9"%&)5'"%+'$%'69"3'+$*).3$2%'<-/"(()*'2*'("*&)*=\
<+= Y9"3'$-'39)'09"-)'*)("3$2%',)36))%'39)'$%073'"%+'273B
073'$%'-$37"3$2%'<.=\
<"= H--7/$%&' $+)"(' 20' "/0-5' -8)3.9' 39)' #2(3"&)' 6"#)B
12*/-'"3'%2+)-'e'"%+'G'12*'"'CB`'0)"8B32B0)"8'-$%)'6"#)
"00($)+'"3'H>'H(-2'-8)3.9'vB>
<,= Y9"3'$-'39)'#2(3"&)'&"$%'v B ⁄ v > \
D 2.80 j)-$&%' "' R$(()*' $%3)&*"32*' 6$39' "' 3$/)' .2%-3"%3' 21
F>C'-'"%+'"%'$%073'*)-$-3"%.)'21'CFF'8Ω>'H'+.'#2(3"&)'21'−C
#2(3'$-'"00($)+'"3'39)'$%073'"3'3$/)'F5'"3'69$.9'/2/)%3'vB =
−CF'`>'!26'(2%&'+2)-'$3'3"8)'39)'273073'32'*)".9'F'`\'+CF'`\
D 2.76 j)-$&%' 39)' $%-3*7/)%3"3$2%B"/0($1$)*' .$*.7$3' 21
S$&>' Q>QF<,=' 32' *)"($[)' "' +$11)*)%3$"(' &"$%5' #"*$",()' $%' 39)
*"%&)'C'32'CFF5'73$($[$%&'"'CFFB8Ω'023'"-'#"*$",()'*)-$-32*>
<P)*&Q'j)-$&%'39)'-).2%+'-3"&)'12*'"'&"$%'21'F>V>=
Problems 119
CHAPTER 2
R1
"
"
R1
ZL
iO
R
"
vI
!
R1
PROBLEMS
vI
!
"
!
R
R1
!
"
!
"
!
!
ZL
"
(a)
iO
(b)
Figure P2.78
2.81 H%'20B"/0B,"-)+'$%#)*3$%&'$%3)&*"32*'$-'/)"-7*)+'"3
C' 8![' 32' 9"#)' "' #2(3"&)' &"$%' 21' −CFF' `d`>' H3' 69"3' 1*)B
K7)%.4'$-'$3-'&"$%'*)+7.)+'32'−C'`d`\'Y9"3'$-'39)'$%3)&*"32*
3$/)'.2%-3"%3\
D 2.82 j)-$&%'"'R$(()*'$%3)&*"32*'39"3'9"-'"'7%$34B&"$%'1*)B
K7)%.4'21'C'8*"+d-'"%+'"%'$%073'*)-$-3"%.)'21'CFF'8Ω>'L8)3.9
39)'273073'427'627(+')M0).3'12*'39)'-$37"3$2%'$%'69$.95'6$39
273073' $%$3$"((4' "3' F' `5' "' QB`5' QB/-' 07(-)' $-' "00($)+' 32' 39)
$%073>'G9"*".3)*$[)'39)'273073'39"3'*)-7(3-'69)%'"'-$%)'6"#)
Q -$%'CFFF&'$-'"00($)+'32'39)'$%073>
D 2.83 j)-$&%'"'R$(()*'$%3)&*"32*'692-)'$%073'*)-$-3"%.)'$QF'8Ω'"%+'7%$34B&"$%'1*)K7)%.4'$-'CF'8![>'Y9"3'.2/02%)%3"*)' %))+)+\' S2*' (2%&B3)*/' -3",$($345' "' 1))+,".8' *)-$-32*' $$%3*2+7.)+'".*2--'39)'."0".$32*5'($/$3-'39)'+.'&"$%'32'UF'+e>
Y9"3' $-' $3-' #"(7)\' Y9"3' $-' 39)' "--2.$"3)+' (26)*' TB+e' 1*)B
K7)%.4\' L8)3.9' "%+' (",)(' 39)' 273073' 39"3' *)-7(3-' 6$39' "
F>CB/-5'CB`'02-$3$#)B$%073'07(-)'<$%$3$"((4'"3'F'`='6$39'<"='%2
+.' -3",$($["3$2%' <,73' 6$39' 39)' 273073' $%$3$"((4' "3' F' `=' "%+
<,= 39)'1))+,".8'*)-$-32*'.2%%).3)+>
Figure P2.84
*2.84 H'R$(()*'$%3)&*"32*'692-)'$%073'"%+'273073'#2(3"&)"*)'$%$3$"((4'[)*2'"%+'692-)'3$/)'.2%-3"%3'$-'C'/-'$-'+*$#)%
,4'39)'-$&%"('-926%'$%'S$&>']Q>cU>'L8)3.9'"%+'(",)('39)'273B
073'6"#)12*/'39"3'*)-7(3->'A%+$."3)'69"3'9"00)%-'$1'39)'$%073
()#)(-'"*)'±Q'`5'6$39'39)'3$/)'.2%-3"%3'39)'-"/)'<C'/-='"%+
6$39'39)'3$/)'.2%-3"%3'*"$-)+'32'Q'/->
2.85 G2%-$+)*'"'R$(()*'$%3)&*"32*'9"#$%&'"'3$/)'.2%-3"%3'21
C' /-' "%+' "%' 273073' 39"3' $-' $%$3$"((4' [)*25' 69)%' 1)+' 6$39' "
-3*$%&'21'07(-)-'21'CFBµ-'+7*"3$2%'"%+'CB`'"/0($37+)'*$-$%&
1*2/'F'`'<-))'S$&>']Q>cV=>'L8)3.9'"%+'(",)('39)'273073'6"#)
Figure P2.85
12*/'*)-7(3$%&>'!26'/"%4'07(-)-'"*)'*)K7$*)+'12*'"%'273073
#2(3"&)'.9"%&)'21'C'`\
CHAPTER 2
PROBLEMS
120 Chapter 2 Operational Amplifiers
D 2.86 S$&7*)']Q>cE'-926-'"'.$*.7$3'39"3'0)*12*/-'"'(26B
0"--'L;G'17%.3$2%>'L7.9'"'.$*.7$3'$-'8%26%'"-'"'1$*-3B2*+)*5
(26B0"--' ".3$#)' 1$(3)*>' j)*$#)' 39)' 3*"%-1)*' 17%.3$2%' "%+
-926 39"3'39)'+.'&"$%'$-' ( ! ? Q ⁄ ? C )'"%+'39)'TB+e'1*)K7)%.4
ω F = C ⁄ "? Q >' j)-$&%' 39)' .$*.7$3' 32' 2,3"$%' "%' $%073' *)-$-B
3"%.)'21'CF'8Ω5'"'+.'&"$%'21'QF'+e5'"%+'"'TB+e'1*)K7)%.4'21
CF'8![>'H3'69"3'1*)K7)%.4'+2)-'39)'/"&%$37+)'21'39)'3*"%-B
1)*'17%.3$2%'*)+7.)'32'7%$34\
Vo
Figure P2.86
2.87 L926' 39"3' "' R$(()*' $%3)&*"32*' $/0()/)%3)+' 6$39' "%' 20
"/0'6$39'20)%B(220'&"$%'$F'9"-'"'(26B0"--'L;G'3*"%-1)*'17%.B
3$2%>' Y9"3' $-' 39)' 02()' 1*)K7)%.4' 21' 39)' L;G' 17%.3$2%\' !26
+2)-'39$-'.2/0"*)'6$39'39)'02()'1*)K7)%.4'21'39)'$+)"('$%3)&*"B
32*\'A1'"%'$+)"('R$(()*'$%3)&*"32*'$-'1)+'6$39'"'nCB`'07(-)'-$&%"(
6$39'"'6$+39':'Z'"?5'69"3'6$(('39)'273073'#2(3"&)',)'"3'&'Z': \
H--7/)'39"3'"3'&'Z'F5'vB'Z'F>'O)0)"3'12*'"%'$%3)&*"32*'6$39'"%'20
"/0'9"#$%&'$F'Z'CFFF>'
2.88 H'+$11)*)%3$"32*'73$($[)-'"%'$+)"('20'"/05'"'CFB8Ω'*)-$-B
32*5'"%+'"'F>FCBµS'."0".$32*>'Y9"3'$-'39)'1*)K7)%.4'2F'<$% ![=
"3' 69$.9' $3-' $%073' "%+' 273073' -$%)B6"#)' -$&%"(-' 9"#)' )K7"(
/"&%$37+)\'Y9"3'$-'39)'273073'-$&%"('12*'"'CB`'0)"8B32B0)"8
-$%)B6"#)'$%073'6$39'1*)K7)%.4')K7"('32'CF 2F\
2.89 H%' 20B"/0' +$11)*)%3$"32*' 6$39' CB/-' 3$/)' .2%-3"%3' $+*$#)%',4'39)'*"3)B.2%3*2(()+'-3)0'-926%'$%'S$&>']Q>cD>'H--7/B
$%&'vB'32',)'[)*2'$%$3$"((45'-8)3.9'"%+'(",)('$3-'6"#)12*/>
2.90 H%' 20B"/0' +$11)*)%3$"32*5' )/0(24$%&' 39)' .$*.7$3
-926%'$%'S$&>'Q>QI<"=5'9"-'?'='CF'8Ω'"%+'"'='F>C'yS>'Y9)%
"'3*$"%&()'6"#)'21'±CB`'0)"8'"/0($37+)'"3'C'8!['$-'"00($)+
32' 39)' $%0735' 69"3' 12*/' 21' 273073' *)-7(3-\' Y9"3' $-' $3-' 1*)B
K7)%.4\' Y9"3' $-' $3-' 0)"8' "/0($37+)\' Y9"3' $-' $3-' "#)*"&)
#"(7)\'Y9"3'#"(7)'21'?'$-'%))+)+'32'."7-)'39)'273073'32'9"#)
"'CFB`'0)"8'"/0($37+)\
2.91 a-)'"%'$+)"('20'"/0'32'+)-$&%'"'+$11)*)%3$"3$2%'.$*.7$3
12*'69$.9'39)'3$/)'.2%-3"%3'$-'CF−T'-'7-$%&'"'CFB%S'."0".$32*>
Y9"3'"*)'39)'&"$%-'"%+'09"-)'-9$13-'127%+'12*'39$-'.$*.7$3'"3
2%)B3)%39' "%+' CF' 3$/)-' 39)' 7%$34B&"$%' 1*)K7)%.4\' H' -)*$)$%073' *)-$-32*' $-' "++)+' 32' ($/$3' 39)' &"$%' /"&%$37+)' "3' 9$&9
1*)K7)%.$)-' 32' CFF' `d`>' Y9"3' $-' 39)' "--2.$"3)+' TB+e' 1*)B
K7)%.4\' Y9"3' &"$%' "%+' 09"-)' -9$13' *)-7(3' "3' CF' 3$/)-' 39)
7%$34B&"$%'1*)K7)%.4\
D 2.92 S$&7*)' ]Q>DQ' -926-' "' .$*.7$3' 39"3' 0)*12*/-' 39)
9$&9B0"--5' -$%&()B3$/)B.2%-3"%3' 17%.3$2%>' L7.9' "' .$*.7$3' $8%26%' "-' "' 1$*-3B2*+)*' 9$&9B0"--' ".3$#)' 1$(3)*>' j)*$#)' 39)
3*"%-1)*' 17%.3$2%' "%+' -926' 39"3' 39)' 9$&9B1*)K7)%.4' &"$%' $( ! ? Q ⁄ ? C )'"%+'39)'TB+e'1*)K7)%.4'ω F = C ⁄ "? C >'j)-$&%'39)
.$*.7$3'32'2,3"$%'"'9$&9B1*)K7)%.4'$%073'*)-$-3"%.)'21'CF'8Ω5'"
9$&9B1*)K7)%.4' &"$%' 21' UF' +e5' "%+' "' TB+e' 1*)K7)%.4' 21' VFF
![>' H3' 69"3' 1*)K7)%.4' +2)-' 39)' /"&%$37+)' 21' 39)' 3*"%-1)*
17%.3$2%'*)+7.)'32'7%$34\
Vo
Figure P2.92
D **2.93 j)*$#)' 39)' 3*"%-1)*' 17%.3$2%' 21' 39)' .$*.7$3' $%
S$&>' ]Q>DT' <12*' "%' $+)"(' 20' "/0=' "%+' -926' 39"3' $3' ."%' ,)
6*$33)%'$%'39)'12*/
!1
!?Q ⁄ ?C
BBBBB = BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B
!)
[ C + ( ωC ⁄ G ω ) ] [ C + G ( ω ⁄ ωQ ) ]
69)*)'ω C = C ⁄ " C ? C'"%+'ω Q = C ⁄ " Q ? Q >'H--7/$%&'39"3'39)
.$*.7$3' $-' +)-$&%)+' -7.9' 39"3' ωQ' ) ωC5' 1$%+' "00*2M$/"3)
)M0*)--$2%-' 12*' 39)' 3*"%-1)*' 17%.3$2%' $%' 39)' 12((26$%&' 1*)B
K7)%.4'*)&$2%-:
Figure P2.89
<"= ω'$'ω C
<,= ωC'$'ω'$'ω Q
<.= ω'')'ω Q
Problems 121
Figure P2.93
a-)'39)-)'"00*2M$/"3$2%-'32'-8)3.9'"'e2+)'0(23'12*'39)'/"&B
%$37+)' *)-02%-)>' ?,-)*#)' 39"3' 39)' .$*.7$3' 0)*12*/-' "-' "%
"/0($1$)*'692-)'&"$%'*2((-'211'"3'39)'(26B1*)K7)%.4')%+'$%
39)'/"%%)*'21'"'9$&9B0"--'L;G'%)362*85'"%+'"3'39)'9$&9B
1*)K7)%.4' )%+' $%' 39)' /"%%)*' 21' "' (26B0"--' L;G' %)362*8>
j)-$&%'39)'.$*.7$3'32'0*2#$+)'"'&"$%'21'UF'+e'$%'39)'^/$++()
1*)K7)%.4'*"%&)5_'"'(26B1*)K7)%.4'TB+e'02$%3'"3'CFF'![5'"
9$&9B1*)K7)%.4' TB+e' 02$%3' "3' CFF' 8![5' "%+' "%' $%073' *)-$-B
3"%.)'<"3'ω')'ωC='21'C'8Ω>
D *2.99 H'%2%$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'+CF'`d`
7-$%&'CFF'8Ω "-'39)'1))+,".8'*)-$-32*'20)*"3)-'1*2/'"'VB8Ω
-27*.)>'S2*'"%'"/0($1$)*'211-)3'#2(3"&)'21'F'/`5',73'6$39'"
,$"-'.7**)%3'21'C'µH'"%+'"%'211-)3'.7**)%3'21'F>C'yH5'69"3
*"%&)' 21' 273073-' 627(+' 427' )M0).3\' A%+$."3)' 69)*)' 427
627(+'"++'"%'"++$3$2%"('*)-$-32*'32'.2/0)%-"3)'12*'39)',$".7**)%3->' Y9"3' +2)-' 39)' *"%&)' 21' 02--$,()' 273073-' 39)%
,).2/)\'H'+)-$&%)*'6$-9)-'32'7-)'39$-'"/0($1$)*'6$39'"'CVB
8Ω'-27*.)>'A%'2*+)*'32'.2/0)%-"3)'12*'39)',$"-'.7**)%3'$%'39$."-)5'69"3'*)-$-32*'627(+'427'7-)\'H%+'69)*)\
Section 2.6: DC Imperfections
D 2.100 ;9)'.$*.7$3'21'S$&>'Q>TE'$-'7-)+'32'.*)"3)'"%'".B
.270()+' %2%$%#)*3$%&' "/0($1$)*' 6$39' "' &"$%' 21' QFF' `d`
7-$%&'*)-$-32*-'%2'("*&)*'39"%'CFF'8Ω>'Y9"3'#"(7)-'21'?C5'?Q5
"%+'?T '-927(+',)'7-)+\'S2*'"',*)"8'1*)K7)%.4'+7)'32'"C'"3
CFF'![5'"%+'39"3'+7)'32'"Q'"3'CF'![5'69"3'#"(7)-'21'"C'"%+
"Q'"*)'%))+)+\
2.94 H%'20'"/0'6$*)+'$%'39)'$%#)*3$%&'.2%1$&7*"3$2%'6$39
39)'$%073'&*27%+)+5'9"#$%&'?Q'='CFF'8Ω'"%+'?C'='C'8Ω5'9""%'273073'+.'#2(3"&)'21'nF>U'`>'A1'39)'$%073',$"-'.7**)%3'$8%26%'32',)'#)*4'-/"((5'1$%+'39)'$%073'211-)3'#2(3"&)>
*2.101 G2%-$+)*'39)'+$11)*)%.)'"/0($1$)*'.$*.7$3'$%'S$&>'Q>CE>
k)3'?C'='?T'='CF'8Ω'"%+'?Q'='?U'='C'RΩ>'A1'39)'20'"/0'9"!BK'='U'/`5'>L'='F>V'yH5'"%+'>BK'='F>C'yH5'1$%+'39)'62*-3B
."-)'<("*&)-3='+.'211-)3'#2(3"&)'"3'39)'273073>
2.95 H'%2%$%#)*3$%&'"/0($1$)*'6$39'"'&"$%'21'QFF'7-)-'"%
20'"/0'9"#$%&'"%'$%073'211-)3'#2(3"&)'21'±Q'/`>'S$%+'39)
273073'69)%'39)'$%073'$-'F>FC'-$%'ω &5'#2(3->
*2.102 ;9)' .$*.7$3' -926%' $%' S$&>' ]Q>CFQ' 7-)-' "%' 20' "/0
9"#$%&' "' ±UB/`' 211-)3>' Y9"3' $-' $3-' 273073' 211-)3' #2(3"&)\
Y9"3'+2)-'39)'273073'211-)3',).2/)'6$39'39)'$%073'".'.27B
0()+'39*27&9'"'."0".$32*'"\'A15'$%-3)"+5'"'("*&)'."0".$32*'$0(".)+' $%' -)*$)-' 6$39' CB8Ω' *)-$-32*5' 69"3' +2)-' 39)' 273073
211-)3',).2/)\
2.96 H' %2%$%#)*3$%&' "/0($1$)*' 6$39' "' .(2-)+B(220' &"$%
21'CFFF'$-'+)-$&%)+'7-$%&'"%'20'"/0'9"#$%&'"%'$%073'211B
-)3' #2(3"&)' 21' V' /`' "%+' 273073' -"37*"3$2%' ()#)(-' 21
±CT `>'Y9"3'$-'39)'/"M$/7/'"/0($37+)'21'39)'-$%)'6"#)
39"3' ."%' ,)' "00($)+' "3' 39)' $%073' 6$39273' 39)' 273073' .($0B
0$%&\'A1'39)'"/0($1$)*'$-'."0".$3$#)(4'.270()+'$%'39)'/"%B
%)*' $%+$."3)+' $%' S$&>' Q>TE5' 69"3' 627(+' 39)' /"M$/7/
02--$,()'"/0($37+)',)\
2.97 H%'20'"/0'.2%%).3)+'$%'"'.(2-)+B(220'$%#)*3$%&'.2%B
1$&7*"3$2%' 9"#$%&' "' &"$%' 21' CFFF' `d`' "%+' 7-$%&' *)("3$#)(4
-/"((B#"(7)+' *)-$-32*-' $-' /)"-7*)+' 6$39' $%073' &*27%+)+' 32
9"#)'"'+.'273073'#2(3"&)'21'nC>U'`>'Y9"3'$-'$3-'$%073'211-)3
#2(3"&)\']*)0"*)'"%'211-)3B#2(3"&)B-27*.)'-8)3.9'*)-)/,($%&
39"3'$%'S$&>'Q>Qc>'e)'."*)17('21'02("*$3$)->
2.98 H' 0"*3$.7("*' $%#)*3$%&' "/0($1$)*' 6$39' %2/$%"(' &"$%
21'nCFF'`d`'7-)-'"%'$/0)*1).3'20'"/0'$%'.2%W7%.3$2%'6$39
CFFB8Ω'"%+'CFBRΩ'*)-$-32*->';9)'273073'#2(3"&)'$-'127%+'32
,)'+D>TC'`'69)%'/)"-7*)+'6$39'39)'$%073'20)%'"%+'+D>FD'`
6$39'39)'$%073'&*27%+)+>
Figure P2.102
2.103 a-$%&' 211-)3B%7(($%&' 1".$($3$)-' 0*2#$+)+' 12*' 39)' 20
"/05'"'.(2-)+B(220'"/0($1$)*'6$39'&"$%'21'+CFFF'$-'"+W7-3)+
PROBLEMS
Vo
CHAPTER 2
<"= Y9"3' $-' 39)' ,$"-' .7**)%3' 21' 39$-' "/0($1$)*\' A%' 69"3
+$*).3$2%'+2)-'$3'1(26\
<,= @-3$/"3)'39)'#"(7)'21'39)'$%073'211-)3'#2(3"&)>
<.= H'CFBRΩ'*)-$-32*'$-'.2%%).3)+',)36))%'39)'02-$3$#)B
$%073' 3)*/$%"(' "%+' &*27%+>' Y$39' 39)' $%073' ()13' 1(2"3$%&
<+$-.2%%).3)+=5' 39)' 273073' +.' #2(3"&)' $-' /)"-7*)+' 32' ,)'
nF>c'`>'@-3$/"3)'39)'$%073'211-)3'.7**)%3>
CHAPTER 2
PROBLEMS
122 Chapter 2 Operational Amplifiers
"3'QV°G'32'0*2+7.)'[)*2'273073'6$39'39)'$%073'&*27%+)+>'A1
39)'$%073'211-)3B#2(3"&)'+*$13'21'39)'20'"/0'$-'-0).$1$)+'32
,)' CF y`d°G5' 69"3' 273073' 627(+' 427' )M0).3' "3' F°G' "%+' "3
IV°G\'Y9$()'%239$%&'."%',)'-"$+'-)0"*"3)(4'",273'39)'02("*B
$34'21'39)'273073'211-)3'"3')$39)*'F'2*'IV°G5'69"3'627(+'427
)M0).3'39)$*'*)("3$#)'02("*$3$)-'32',)\
2.104 H%'20'"/0'$-'.2%%).3)+'$%'"'.(2-)+'(220'6$39'&"$%
21'+CFF'73$($[$%&'"'1))+,".8'*)-$-32*'21'C'RΩ>
<"= A1'39)'$%073',$"-'.7**)%3'$-'CFF'%H5'69"3'273073'#2(3B
"&)'*)-7(3-'6$39'39)'$%073'&*27%+)+\
<,= A1'39)'$%073'211-)3'#2(3"&)'$-'±C'/`'"%+'39)'$%073',$".7**)%3' "-' $%' <"=5' 69"3' $-' 39)' ("*&)-3' 02--$,()' 273073' 39"3
."%',)'2,-)*#)+'6$39'39)'$%073'&*27%+)+\
<.= A1',$"-B.7**)%3'.2/0)%-"3$2%'$-'7-)+5'69"3'$-'39)'#"(7)
21' 39)' *)K7$*)+' *)-$-32*\' A1' 39)' 211-)3' .7**)%3' $-' %2' /2*)
39"%'2%)B3)%39'39)',$"-'.7**)%35'69"3'$-'39)'*)-7(3$%&'273B
073'211-)3'#2(3"&)'<+7)'32'211-)3'.7**)%3'"(2%)=\
<+= Y$39' ,$"-B.7**)%3' .2/0)%-"3$2%' "-' $%' <.=' $%' 0(".)
69"3'$-'39)'("*&)-3'+.'#2(3"&)'"3'39)'273073'+7)'32'39)'.2/B
,$%)+')11).3'21'211-)3'#2(3"&)'"%+'211-)3'.7**)%3\
*2.105 H%' 20' "/0' $%3)%+)+' 12*' 20)*"3$2%' 6$39' "' .(2-)+B
(220' &"$%' 21' nCFF' `d`' 7-)-' *)-$-32*-' 21' CF' 8Ω' "%+' C RΩ
6$39' "' ,$"-B.7**)%3B.2/0)%-"3$2%' *)-$-32*' ?T>' Y9"3' -927(+
39)' #"(7)'21' ?T' ,)\' Y$39' $%073' &*27%+)+5' 39)' 273073' 211-)3
#2(3"&)'$-'127%+'32',)'+F>QC'`>'@-3$/"3)'39)'$%073'211-)3'.7*B
*)%3' "--7/$%&' [)*2' $%073' 211-)3' #2(3"&)>' A1' 39)' $%073' 211-)3
#2(3"&)'."%',)'"-'("*&)'"-'C'/`'21'7%8%26%'02("*$345'69"3
*"%&)'21'211-)3'.7**)%3'$-'02--$,()\
2.106 H'R$(()*'$%3)&*"32*'6$39'?'='CF'8Ω'"%+'"'='CF'%S'$$/0()/)%3)+' ,4' 7-$%&' "%' 20' "/0' 6$39' !BK =' T' /`5' >L =
F>C µH5'"%+'>BK'='CF'%H>';2'0*2#$+)'"'1$%$3)'+.'&"$%5'"'CBRΩ
*)-$-32*'$-'.2%%).3)+'".*2--'39)'."0".$32*>
<"= ;2' .2/0)%-"3)' 12*' 39)' )11).3' 21' >L5' "' *)-$-32*' $-' .2%B
%).3)+'$%'-)*$)-'6$39'39)'02-$3$#)B$%073'3)*/$%"('21'39)'20
"/0>'Y9"3'-927(+'$3-'#"(7)',)\
<,= Y$39'39)'*)-$-32*'21'<"='$%'0(".)5'1$%+'39)'62*-3B."-)'+.
273073' #2(3"&)' 21' 39)' $%3)&*"32*' 69)%' 39)' $%073' $&*27%+)+>
Section 2.7: Effect of Finite Open-Loop Gain
and Bandwidth on Circuit Performance
2.107 ;9)' +"3"' $%' 39)' 12((26$%&' 3",()' "00(4' 32' $%3)*%"((4
.2/0)%-"3)+'20'"/0->'S$(('$%'39)',("%8')%3*$)->
A0
fb (Hz)
''''''CFV
'''''' CFE
'CFQ
'''''Q'× CFV
CFT'''''
CF−C
CF
ft (Hz)
''''''''CFE
'CFc
''''''''CFE
2.108 H' /)"-7*)/)%3' 21' 39)' 20)%B(220' &"$%' 21' "%' $%3)*B
%"((4'.2/0)%-"3)+'20'"/0'"3'#)*4'(26'1*)K7)%.$)-'-926-'$3
32',)'DQ'+eX'"3'CFF'8![5'39$-'-926-'$3'$-'UF'+e>'@-3$/"3)'#"(B
7)-'12*'$F5'255'"%+'2&>
2.109 R)"-7*)/)%3-' 21' 39)' 20)%B(220' &"$%' 21' "' .2/0)%B
-"3)+'20'"/0'$%3)%+)+'12*'9$&9B1*)K7)%.4'20)*"3$2%'$%+$."3)
39"3'39)'&"$%'$-'V>C'×'CFT'"3'CFF'8!['"%+'c>T'×'CFT'"3'CF'8![>
@-3$/"3)'$3-'TB+e'1*)K7)%.45'$3-'7%$34B&"$%'1*)K7)%.45'"%+'$3+.'&"$%>
2.110 R)"-7*)/)%3-' /"+)' 2%' 39)' $%3)*%"((4' .2/0)%-"3)+
"/0($1$)*-' ($-3)+' ,)(26' 0*2#$+)' 39)' +.' &"$%' "%+' 39)' 1*)B
K7)%.4'"3'69$.9'39)'&"$%'9"-'+*200)+',4'QF'+e>'S2*')".95
69"3'"*)'39)'T'+e'"%+'7%$34B&"$%'1*)K7)%.$)-\
<"= T'×'CFV'`d`'"%+'E'×'CFQ'![
<,= VF'×'CFV'`d`'"%+'CF'![
<.= CVFF'`d`'"%+'F>C'R![
<+= CFF'`d`'"%+'F>C'i![
<)= QV'`d/`'"%+'QV'8![
2.111 H%'$%#)*3$%&'"/0($1$)*'6$39'%2/$%"('&"$%'21'−QF'`d`
)/0(24-'"%'20'"/0'9"#$%&'"'+.'&"$%'21'CFU'"%+'"''7%$34B&"$%
1*)K7)%.4'21'CFE'![>'Y9"3'$-'39)'TB+e'1*)K7)%.4'2T+e'21'39)
.(2-)+B(220' "/0($1$)*\' Y9"3' $-' $3-' &"$%' "3' F>C' 2T+e' "%+' "3' CF
2T+e\
2.112 H' 0"*3$.7("*' 20' "/05' .9"*".3)*$[)+' ,4' "' &"$%n,"%+B
6$+39' 0*2+7.3' 21' CF' R![5' $-' 20)*"3)+' 6$39' "' .(2-)+B(220
&"$%'21'+CFF'`d`>'Y9"3'TB+e',"%+6$+39'*)-7(3-\'H3'69"3
1*)K7)%.4' +2)-' 39)' .(2-)+B(220' "/0($1$)*' )M9$,$3' "' −E°
09"-)'-9$13\'H'−cU°'09"-)'-9$13\
2.113 S$%+' 39)' 2&' *)K7$*)+' 12*' $%3)*%"((4' .2/0)%-"3)+' 20
"/0-' 32' ,)' 7-)+' $%' 39)' $/0()/)%3"3$2%' 21' .(2-)+B(220
"/0($1$)*-'6$39'39)'12((26$%&'%2/$%"('+.'&"$%-'"%+'TB+e
,"%+6$+39-:
<"= −CFF'`d`X'CFF'8![
<,= +CFF'`d`X'CFF'8![
<.= +Q'`d`X'CF'R![
<+= −Q'`d`X'CF'R![
<)= −CFFF'`d`X'QF'8![
<1 = +C'`d`X'C'R![
<&= −C'`d`X'C'R![
2.114 H'%2%$%#)*3$%&'20B"/0'.$*.7$3'6$39'"'&"$%'21'DE'`d`
$-'127%+'32'9"#)'"'TB+e'1*)K7)%.4'21'c'8![>'S2*'"'0"*3$.7("*
-4-3)/'"00($."3$2%5'"',"%+6$+39'21'QU'8!['$-'*)K7$*)+>'Y9"3
$-'39)'9$&9)-3'&"$%'"#"$(",()'7%+)*'39)-)'.2%+$3$2%-\
2.115 G2%-$+)*'"'7%$34B&"$%'12((26)*'73$($[$%&'"%'$%3)*%"((4
.2/0)%-"3)+'20'"/0'6$39'2&'='C'R![>'Y9"3'$-'39)'TB+e'1*)B
K7)%.4'21'39)'12((26)*\'H3'69"3'1*)K7)%.4'$-'39)'&"$%'21'39)
12((26)*' Cg' ,)(26' $3-' (26B1*)K7)%.4' /"&%$37+)\' A1' 39)
$%073'32'39)'12((26)*'$-'"'CB`'-3)05'1$%+'39)'CFg'32'DFg'*$-)
3$/)'21''39)'273073'#2(3"&)>'<O1&(Q';9)'-3)0'*)-02%-)'21'L;G
(26B0"--'%)362*8-'$-'+$-.7--)+'$%'H00)%+$M'@>=
e
x
Problems 123
<"= L926' 39"3' ."-."+$%&' 362' $+)%3$."(' "/0($1$)*' -3"&)-5
)".9'9"#$%&'"'(26B0"--'L;G'1*)K7)%.4'*)-02%-)'6$39'"'TB
+e' 1*)K7)%.4' 2C5' *)-7(3-' $%' "%' 2#)*"((' "/0($1$)*' 6$39' "' TB
+e'1*)K7)%.4'&$#)%',4
2T+e =
Q' ! 'C' 2 C
<,= A3'$-'*)K7$*)+'32'+)-$&%'"'%2%$%#)*3$%&'"/0($1$)*'6$39'"
+.'&"$%'21'UF'+e'73$($[$%&'"'-$%&()'$%3)*%"((4'.2/0)%-"3)+
20' "/0' 6$39' 2&% =' C' R![>' Y9"3' $-' 39)' TB+e' 1*)K7)%.4
2,3"$%)+\
<.= O)+)-$&%'39)'"/0($1$)*'21'<,=',4'."-."+$%&'362'$+)%3$."(
%2%$%#)*3$%&'"/0($1$)*-')".9'6$39'"'+.'&"$%'21'QF'+e>'Y9"3
$-'39)'TB+e'1*)K7)%.4'21'39)'2#)*"(('"/0($1$)*\'G2/0"*)'39$32'39)'#"(7)'2,3"$%)+'$%'<,='",2#)>'''
D **2.118 H'+)-$&%)*5'6"%3$%&'32'".9$)#)'"'-3",()'&"$%'21
CFF'`d`'"3'V'R![5'.2%-$+)*-'9)*'.92$.)'21'"/0($1$)*'3202(2B
&$)->' Y9"3' 7%$34B&"$%' 1*)K7)%.4' 627(+' "' -$%&()' 20)*"3$2%"(
"/0($1$)*'*)K7$*)'32'-"3$-14'9)*'%))+\'a%12*37%"3)(45'39)',)-3
"#"$(",()' "/0($1$)*' 9"-' "%' 2&' 21' UF' R![>' !26' /"%4' -7.9
"/0($1$)*-' .2%%).3)+' $%' "' ."-."+)' 21' $+)%3$."(' %2%$%#)*3$%&
-3"&)-'627(+'-9)'%))+'32'".9$)#)'9)*'&2"(\'Y9"3'$-'39)'TB+e
1*)K7)%.4'21')".9'-3"&)'-9)'."%'7-)\'Y9"3'$-'39)'2#)*"(('TB+e
1*)K7)%.4\
2.119 G2%-$+)*'39)'7-)'21'"%'20'"/0'6$39'"'7%$34B&"$%'1*)B
K7)%.4'2&'$%'39)'*)"($["3$2%'21:
<"= H%'$%#)*3$%&'"/0($1$)*'6$39'+.'&"$%'21'/"&%$37+)'I>
<,= H'%2%$%#)*3$%&'"/0($1$)*'6$39'"'+.'&"$%'21'I>'
A%')".9'."-)'1$%+'39)'TB+e'1*)K7)%.4'"%+'39)'&"$%B,"%+6$+39
0*2+7.3'<ie]'≡ |i"$%|'× 25?A&$-B1CC(+,-1+-,D(-)(EFG,E$
*2.120 G2%-$+)*' "%' $%#)*3$%&' -7//)*' 6$39' 362' $%073-' !C
"%+'!Q'"%+'6$39'!1'='−<!C '+'Q!Q=>'S$%+'39)'TB+e'1*)K7)%.4
21')".9'21'39)'&"$%'17%.3$2%-'!1 ⁄ !C "%+'!1 ⁄ !Q $%'3)*/-'21'39)
20'"/0'2&>'<P)*&Q'A%')".9'."-)5'39)'239)*'$%073'32'39)'-7//)*
."%',)'-)3'32'[)*2f"%'"00($."3$2%'21'-70)*02-$3$2%>=
Section 2.8: Large-Signal Operation
of Op Amps
2.121 H' 0"*3$.7("*' 20' "/0' 7-$%&' ±CVB`' -700($)-' 20)*"3)($%)"*(4'12*'273073-'$%'39)'*"%&)'−CQ'`'32'+CQ'`>'A1'7-)+'$%
2.122 G2%-$+)*'"%'20'"/0'.2%%).3)+'$%'39)'$%#)*3$%&'.2%1$&7B
*"3$2%'32'*)"($[)'"'.(2-)+B(220'&"$%'21'nCFF'`d`'73$($[$%&'*)-$-B
32*-' 21' C' 8Ω "%+' CFF' 8Ω>' H' (2"+' *)-$-3"%.)' ?D' $-' .2%%).3)+
1*2/'39)'273073'32'&*27%+5'"%+'"'(26B1*)K7)%.4'-$%)B6"#)'-$&B
%"('21'0)"8'"/0($37+)'!+'$-'"00($)+'32'39)'$%073>'k)3'39)'20'"/0
,)'$+)"(')M.)03'39"3'$3-'273073'#2(3"&)'-"37*"3)-'"3'±CF'`'"%+'$3273073'.7**)%3'$-'($/$3)+'32'39)'*"%&)'±QF'/H>
<"= S2*'?D'='C'8Ω5'69"3'$-'39)'/"M$/7/'02--$,()'#"(7)'21
!+'69$()'"%'7%+$-32*3)+'273073'-$%7-2$+'$-'2,3"$%)+\
<,= O)0)"3'<"='12*'?D'='CFF Ω>
<.= A1' $3' $-' +)-$*)+' 32' 2,3"$%' "%' 273073' -$%7-2$+' 21' CFB`
0)"8'"/0($37+)5'69"3'/$%$/7/'#"(7)'21'?D'$-'"((26)+\
2.123 H%' 20' "/0' 9"#$%&' "' -()6' *"3)' 21' CF' `dy-' $-' 32' ,)
7-)+' $%' 39)' 7%$34B&"$%' 12((26)*' .2%1$&7*"3$2%5' 6$39' $%073
07(-)-'39"3'*$-)'1*2/'F'32'V'`>'Y9"3'$-'39)'-92*3)-3'07(-)'39"3
."%',)'7-)+'69$()')%-7*$%&'17((B"/0($37+)'273073\'S2*'-7.9
"'07(-)5'+)-.*$,)'39)'273073'*)-7(3$%&>
2.124 S2*'20)*"3$2%'6$39'CFB`'273073'07(-)-'6$39'39)'*)K7$*)B
/)%3'39"3'39)'-7/'21'39)'*$-)'"%+'1"(('3$/)-'*)0*)-)%3'2%(4'QFg
21' 39)' 07(-)' 6$+39' <"3' 9"(1'"/0($37+)=5' 69"3' $-' 39)' -()6B*"3)
*)K7$*)/)%3' 12*' "%' 20' "/0' 32' 9"%+()' 07(-)-' Q' y-' 6$+)\
<O1&(Q';9)'*$-)'"%+'1"(('3$/)-'21'"'07(-)'-$&%"('"*)'7-7"((4'/)"B
-7*)+',)36))%'39)'CFgB'"%+'DFgB9)$&93'02$%3->=
2.125 Y9"3'$-'39)'9$&9)-3'1*)K7)%.4'21'"'3*$"%&()'6"#)'21'QFB
`'0)"8B32B0)"8'"/0($37+)'39"3'."%',)'*)0*2+7.)+',4'"%'20
"/0' 692-)' -()6' *"3)' $-' CF' `dy-\' S2*' "' -$%)' 6"#)' 21' 39)
-"/)'1*)K7)%.45'69"3'$-'39)'/"M$/7/'"/0($37+)'21'273073
-$&%"('39"3'*)/"$%-'7%+$-32*3)+\
2.126 S2*'"%'"/0($1$)*'9"#$%&'"'-()6'*"3)'21'EF'`dy-5'69"3
$-'39)'9$&9)-3'1*)K7)%.4'"3'69$.9'"'QFB`'0)"8B32B0)"8'-$%)
6"#)'."%',)'0*2+7.)+'"3'39)'273073\
D *2.127 A%'+)-$&%$%&'6$39'20'"/0-'2%)'9"-'32'.9).8'39)
($/$3"3$2%-'2%'39)'#2(3"&)'"%+'1*)K7)%.4'*"%&)-'21'20)*"3$2%
21'39)'.(2-)+B(220'"/0($1$)*5'$/02-)+',4'39)'20B"/0'1$%$3)
,"%+6$+39'< 2&=5'-()6'*"3)'<LO=5'"%+'273073'-"37*"3$2%'<!1/"M=>
;9$-'0*2,()/'$((7-3*"3)-'39)'02$%3',4'.2%-$+)*$%&'39)'7-)'21
"%'20'"/0'6$39'2&'='Q'R![5'LO'='C'`dy-5'"%+'!1/"M'='CF'`'$%
39)'+)-$&%'21'"'%2%$%#)*3$%&'"/0($1$)*'6$39'"'%2/$%"('&"$%
21'CF>'H--7/)'"'-$%)B6"#)'$%073'6$39'0)"8'"/0($37+)'!)>
<"= A1'!)'='F>V'`5'69"3'$-'39)'/"M$/7/'1*)K7)%.4',)12*)
39)'273073'+$-32*3-\
<,= A1'2'='QF'8![5'69"3'$-'39)'/"M$/7/'#"(7)'21'!)',)12*)
39)'273073'+$-32*3-\
<.= A1' !)' =' VF' /`5' 69"3' $-' 39)' 7-)17(' 1*)K7)%.4' *"%&)' 21
20)*"3$2%\
<+= A1'2'='V'8![5'69"3'$-'39)'7-)17('$%073'#2(3"&)'*"%&)\
PROBLEMS
D *2.117 ;9$-' 0*2,()/' $((7-3*"3)-' 39)' 7-)' 21' ."-."+)+
.(2-)+B(220' "/0($1$)*-' 32' 2,3"$%' "%' 2#)*"((' ,"%+6$+39
&*)"3)*'39"%'."%',)'".9$)#)+'7-$%&'"'-$%&()B-3"&)'"/0($1$)*
6$39'39)'-"/)'2#)*"(('&"$%>
"%' $%#)*3$%&' "/0($1$)*' .2%1$&7*"3$2%' 21' &"$%' nCFF5' 69"3' $39)'*/-'#"(7)'21'39)'("*&)-3'02--$,()'-$%)'6"#)'39"3'."%',)
"00($)+'"3'39)'$%073'6$39273'273073'.($00$%&\
CHAPTER 2
D *2.116 A3' $-' *)K7$*)+' 32' +)-$&%' "' %2%$%#)*3$%&' "/0($1$)*
6$39' "' +.' &"$%' 21' CF>' Y9)%' "' -3)0' #2(3"&)' 21' CFF' /`' $"00($)+'"3'39)'$%0735'$3'$-'*)K7$*)+'39"3'39)'273073',)'6$39$%
Cg'21'$3-'1$%"('#"(7)'21'C'`'$%'"3'/2-3'CFF'%->'Y9"3'/7-3'39)
2&'21'39)'20'"/0',)\'<O1&(Q';9)'-3)0'*)-02%-)'21'L;G'(26B
0"--'%)362*8-'$-'+$-.7--)+'$%'H00)%+$M'@>=
CHAPTER 3
Semiconductors
Introduction
3.1
3.5 The pn!Junction with Applied
Voltage 145
125
Intrinsic Semiconductors
126
3.2 Doped Semiconductors
129
3.3 Current Flow in Semiconductors
3.6 Capacitive Effects in the pn
Junction 154
132
3.4 The pn!Junction with Open-Circuit
Terminals (Equilibrium) 138
Summary
157
Problems
159
IN THIS CHAPTER YOU WILL LEARN
1. The basic properties of semiconductors and in particular silicon, which
is the material used to make most of today’s electronic circuits.
2. How doping a pure silicon crystal dramatically changes its electrical conductivity, which is the fundamental idea underlying the use of semiconductors in the implementation of electronic devices.
3. The two mechanisms by which current flows in semiconductors: drift
and diffusion of charge carriers.
4. The structure and operation of the "#!junction; a basic semiconductor structure that implements the diode and plays a dominant role in transistors.
Introduction
!"#$%&'(%)*%"'+*%,*'-.%)/."%*-*0.(12/0%0/(0#/.$3%'2,%21.'4-5%'67-/&/*($3%'$%$5$.*6%4#/-,/28
4-109$:%;1(%/2$.'20*3%/2%<"'7.*(%=%)*%-*'(2*,%"1)%.1%#$*%17%'67$%.1%,*$/82%/2.*(*$./28%'2,
#$*&#-%0/(0#/.$3%.'9/28%',+'2.'8*%1&%."*%.*(6/2'-%0"'('0.*(/$./0$%1&%."*%17%'67%'2,%)/."1#.
'25%921)-*,8*%1&%)"'.%/$%/2$/,*%."*%17%'67%7'09'8*:%!"1#8"%/2.*(*$./28%'2,%61./+'./283
."/$% '77(1'0"% "'$% /.$% -/6/.'./12$:% >2,**,3% .1% '0"/*+*% 1#(% 81'-% 1&% 7(*7'(/28% ."*% (*',*(% .1
4*016*%'%7(1&/0/*2.%0/(0#/.%,*$/82*(3%)*%"'+*%.1%81%4*512,%."/$%4-'09?41@%1(%$5$.*6?-*+*'4$.('0./12%'2,%-*'(2%'41#.%."*%4'$/0%,*+/0*$%&(16%)"/0"%*-*0.(12/0%0/(0#/.$%'(*%'$$*64-*,3
2'6*-53%,/1,*$%A<"'7.*(%BC%'2,%.('2$/$.1($%A<"'7.*($%D%'2,%EC:%!"*$*%$1-/,?$.'.*%,*+/0*$%'(*
6',*%#$/28%$*6/012,#0.1(%6'.*(/'-$3%7(*,16/2'2.-5%$/-/012:
>2% ."/$% 0"'7.*(3% )*% 4(/*&-5% /2.(1,#0*% ."*% 7(17*(./*$% '2,% 7"5$/0$% 1&% $*6/012,#0.1($:% !"*
14F*0./+*%/$%.1%7(1+/,*%'%4'$/$%&1(%#2,*($.'2,/28%."*%7"5$/0'-%17*('./12%1&%,/1,*$%'2,%.('2$/$.1($
/2%1(,*(%.1%*2'4-*%."*/(%*&&*0./+*%#$*%/2%."*%,*$/82%1&%0/(0#/.$:%G-."1#8"%6'25%1&%."*%0120*7.$
$.#,/*,% /2% ."/$% 0"'7.*(% '77-5% .1% $*6/012,#0.1(% 6'.*(/'-$% /2% 8*2*('-3% 1#(% .(*'.6*2.% /$% "*'+/-5
4/'$*,%.1)'(,%$/-/0123%$/67-5%4*0'#$*%/.%/$%."*%6'.*(/'-%#$*,%/2%."*%+'$.%6'F1(/.5%1&%6/0(1*-*0?
.(12/0%0/(0#/.$:%!1%0167-*6*2.%."*%6'.*(/'-%7(*$*2.*,%"*(*3%G77*2,/@%G%7(1+/,*$%'%,*$0(/7./12%1&
."*%/2.*8('.*,?0/(0#/.%&'4(/0'./12%7(10*$$:%G$%,/$0#$$*,%/2%G77*2,/@%G3%)"*."*(%1#(%0/(0#/.%012?
$/$.$%1&%'%$/28-*%.('2$/$.1(%1(%/$%'2%!"#$%&'#$()*!&*+!#%012.'/2/28%61(*%."'2%=%4/--/12%.('2$/$.1($3%/.
/$%&'4(/0'.*,%/2%'%$/28-*%$/-/012%0(5$.'-3%)"/0"%8/+*$%(/$*%.1%."*%2'6*%,-"-.!#/!*)*!&*+!#:%!"/$
0"'7.*(%."*(*&1(*%4*8/2$%)/."%'%$.#,5%1&%."*%0(5$.'-%$.(#0.#(*%1&%$*6/012,#0.1($%'2,%/2.(1,#0*$
."*%.)1%.57*$%1&%0"'(8*%0'((/*($%'+'/-'4-*%&1(%0#((*2.%012,#0./12H%*-*0.(12$%'2,%"1-*$:%!"*%61$.
$/82/&/0'2.%7(17*(.5%1&%$*6/012,#0.1($%/$%."'.%."*/(%012,#0./+/.5%0'2%4*%+'(/*,%1+*(%'%+*(5%)/,*
('28*%."(1#8"%."*%/2.(1,#0./12%1&%012.(1--*,%'61#2.$%1&%/67#(/.5%'.16$%/2.1%."*%$*6/012,#0.1(
0(5$.'-%/2%'%7(10*$$%0'--*,%(-0!"%:%I17*,%$*6/012,#0.1($%'(*%,/$0#$$*,%/2%J*0./12%K:=:%!"/$%/$
125
126 Chapter 3 Semiconductors
&1--1)*,%45%."*%$.#,5%/2%J*0./12%K:K%1&%."*%.)1%6*0"'2/$6$%&1(%0#((*2.%&-1)%/2%$*6/012,#0.1($3
2'6*-53%0'((/*(%,(/&.%'2,%0'((/*(%,/&&#$/12:
G(6*,%)/."%."*$*%4'$/0%$*6/012,#0.1(%0120*7.$3%)*%$7*2,%."*%(*6'/2,*(%1&%."*%0"'7.*(%12%."*
$.#,5%1&%'2%/671(.'2.%$*6/012,#0.1(%$.(#0.#(*L%."*%"#%F#20./12:%>2%',,/./12%.1%4*/28%*$$*2./'--5%'
,/1,*3%."*%"#%F#20./12%/$%."*%4'$/0%*-*6*2.%1&%."*%4/71-'(%F#20./12%.('2$/$.1(%AMN!3%<"'7.*(%EC%'2,
7-'5$%'2%/671(.'2.%(1-*%/2%."*%17*('./12%1&%&/*-,?*&&*0.%.('2$/$.1($%A;O!$3%<"'7.*(%DC:
3.1 Intrinsic Semiconductors
G$%."*/(%2'6*%/67-/*$3%$*6/012,#0.1($%'(*%6'.*(/'-$%)"1$*%012,#0./+/.5%-/*$%4*.)**2%."'.%1&
012,#0.1($3%$#0"%'$%0177*(3%'2,%/2$#-'.1($3%$#0"%'$%8-'$$:%!"*(*%'(*%.)1%9/2,$%1&%$*6/012?
,#0.1($H%$/28-*?*-*6*2.%$*6/012,#0.1($3%$#0"%'$%8*(6'2/#6%'2,%$/-/0123%)"/0"%'(*%/2%8(1#7
>P%/2%."*%7*(/1,/0%.'4-*L%'2,%01671#2,%$*6/012,#0.1($3%$#0"%'$%8'--/#6?'($*2/,*3%)"/0"%'(*
&1(6*,%45%0164/2/28%*-*6*2.$%&(16%8(1#7$%>>>%'2,%P%1(%8(1#7$%>>%'2,%P>:%<1671#2,%$*6/?
012,#0.1($%'(*%#$*&#-%/2%$7*0/'-%*-*0.(12/0%0/(0#/.%'77-/0'./12$%'$%)*--%'$%/2%'77-/0'./12$%."'.
/2+1-+*%-/8".3%$#0"%'$%-/8".?*6/../28%,/1,*$%AQOI$C:%R&%."*%.)1%*-*6*2.'-%$*6/012,#0.1($3
8*(6'2/#6%)'$%#$*,%/2%."*%&'4(/0'./12%1&%+*(5%*'(-5%.('2$/$.1($%A-'.*%STBU$3%*'(-5%STDU$C:%>.
)'$%V#/09-5%$#77-'2.*,3%"1)*+*(3%)/."%$/-/0123%12%)"/0"%.1,'5W$%/2.*8('.*,?0/(0#/.%.*0"21-?
185% /$% '-61$.% *2./(*-5% 4'$*,:% ;1(% ."/$% (*'$123% )*% )/--% ,*'-% 61$.-5% )/."% $/-/012% ,*+/0*$
."(1#8"1#.%."/$%4119:S
G%$/-/012%'.16%"'$%&1#(%+'-*20*%*-*0.(12$3%'2,%."#$%/.%(*V#/(*$%'21."*(%&1#(%.1%0167-*.*
/.$%1#.*(61$.%$"*--:%!"/$%/$%'0"/*+*,%45%$"'(/28%12*%1&%/.$%+'-*20*%*-*0.(12$%)/."%*'0"%1&%/.$
&1#(%2*/8"41(/28%'.16$:%O'0"%7'/(%1&%$"'(*,%*-*0.(12$%&1(6$%'%*-1'.$"#)2-"(:%!"*%(*$#-.%/$
."'.%'%0(5$.'-%1&%7#(*%1(%/2.(/2$/0%$/-/012%"'$%'%(*8#-'(%-'../0*%$.(#0.#(*3%)"*(*%."*%'.16$%'(*
"*-,%/2%."*/(%71$/./12%45%."*%01+'-*2.%412,$:%;/8#(*%K:S%$"1)$%'%.)1?,/6*2$/12'-%(*7(*$*2.'?
./12%1&%$#0"%'%$.(#0.#(*:
G.% $#&&/0/*2.-5% -1)% .*67*('.#(*$3% '77(1'0"/28% '4$1-#.*% X*(1% AU% YC3% '--% ."*% 01+'-*2.
412,$%'(*%/2.'0.%'2,%21%*-*0.(12$%'(*%'+'/-'4-*%.1%012,#0.%*-*0.(/0%0#((*2.:%!"#$3%'.%$#0"%-1)
.*67*('.#(*$3%."*%/2.(/2$/0%$/-/012%0(5$.'-%4*"'+*$%'$%'2%/2$#-'.1(:
G.%(116%.*67*('.#(*3%$#&&/0/*2.%."*(6'-%*2*(85%*@/$.$%.1%4(*'9%$16*%1&%."*%01+'-*2.%412,$3
'%7(10*$$%921)2%'$%."*(6'-%8*2*('./12:%G$%$"1)2%/2%;/8:%K:=3%)"*2%'%01+'-*2.%412,%/$%4(19*23
'2%*-*0.(12%/$%&(**,:%!"*%3&$$)$.$*#&-"%0'2%)'2,*(%')'5%&(16%/.$%7'(*2.%'.163%'2,%/.%4*016*$
'+'/-'4-*%.1%012,#0.%*-*0.(/0%0#((*2.%/&%'2%*-*0.(/0%&/*-,%/$%'77-/*,%.1%."*%0(5$.'-:%G$%."*%*-*0.(12
-*'+*$%/.$%7'(*2.%'.163%/.%-*'+*$%4*"/2,%'%2*.%71$/./+*%0"'(8*3%*V#'-%.1%."*%6'82/.#,*%1&%."*%*-*0?
.(12%0"'(8*:%!"#$3%'2%*-*0.(12%&(16%'%2*/8"41(/28%'.16%6'5%4*%'..('0.*,%.1%."/$%71$/./+*%0"'(8*3
'2,%-*'+*$%/.$%7'(*2.%'.16:%!"/$%'0./12%&/--$%#7%."*%Z"1-*[%."'.%*@/$.*,%/2%."*%/12/X*,%'.16%4#.
0(*'.*$% '% 2*)%"1-*% /2% ."*%1."*(% '.16:%!"/$%7(10*$$% 6'5%(*7*'.% /.$*-&3% )/."%."*% (*$#-.%."'.% )*
*&&*0./+*-5%"'+*%'%71$/./+*-5%0"'(8*,%0'((/*(3%1(%/-.$3%61+/28%."(1#8"%."*%$/-/012%0(5$.'-%$.(#0?
.#(*%'2,%4*/28%'+'/-'4-*%.1%012,#0.%*-*0.(/0%0#((*2.:%!"*%0"'(8*%1&%'%"1-*%/$%*V#'-%/2%6'82/.#,*
.1%."*%0"'(8*%1&%'2%*-*0.(12:%\*%0'2%."#$%$**%."'.%'$%.*67*('.#(*%/20(*'$*$3%61(*%01+'-*2.%412,$
'(*%4(19*2%'2,%*-*0.(12]"1-*%7'/($%'(*%8*2*('.*,:%!"*%/20(*'$*%/2%."*%2#64*($%1&%&(**%*-*0.(12$
'2,%"1-*$%(*$#-.$%/2%'2%/20(*'$*%/2%."*%012,#0./+/.5%1&%$/-/012:
S
G2%*@0*7./12%/$%."*%$#4F*0.%1&%8'--/#6%'($*2/,*%A^'G$C%0/(0#/.$3%)"/0"%."1#8"%21.%01+*(*,%/2%."/$%*,/?
./12% 1&% ."*% 41193% /$% $.#,/*,% /2% $16*% ,*.'/-% /2% 6'.*(/'-% 7(1+/,*,% 12% ."*% .*@.% )*4$/.*% '2,% 12% ."*% ,/$0
'00167'25/28%."*%.*@.:
3.1 Intrinsic Semiconductors
Valence
electrons
Covalent
bonds
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
Silicon atoms
Figure 3.1 !)1?,/6*2$/12'-%(*7(*$*2.'./12%1&%."*%$/-/012%0(5$.'-:%!"*%0/(0-*$%(*7(*$*2.%."*%/22*(%01(*%1&
$/-/012%'.16$3%)/."%+B%/2,/0'./28%/.$%71$/./+*%0"'(8*%1&%+B$3%)"/0"%/$%2*#.('-/X*,%45%."*%0"'(8*%1&%."*%&1#(
+'-*20*%*-*0.(12$:%R4$*(+*%"1)%."*%01+'-*2.%412,$%'(*%&1(6*,%45%$"'(/28%1&%."*%+'-*20*%*-*0.(12$:%G.%U%Y3
'--%412,$%'(*%/2.'0.%'2,%21%&(**%*-*0.(12$%'(*%'+'/-'4-*%&1(%0#((*2.%012,#0./12:
Valence
electrons
Broken
covalent
bond
Covalent
bond
Free
electron
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
"
!
! "4 !
!
! "4 !
!
! "4 !
!
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
Hole
Silicon atoms
Figure 3.2 G.%(116%.*67*('.#(*3%$16*%1&%."*%01+'-*2.%412,$%'(*%4(19*2%45%."*(6'-%8*2*('./12:%O'0"%4(1?
9*2%412,%8/+*$%(/$*%.1%'%&(**%*-*0.(12%'2,%'%"1-*3%41."%1&%)"/0"%4*016*%'+'/-'4-*%&1(%0#((*2.%012,#0./12:
!"*(6'-%8*2*('./12%(*$#-.$%/2%&(**%*-*0.(12$%'2,%"1-*$%/2%*V#'-%2#64*($%'2,%"*20*%*V#'0120*2.('./12$3%)"*(*%0120*2.('./12%(*&*($%.1%."*%2#64*(%1&%0"'(8*%0'((/*($%7*(%#2/.%+1-#6*
A06KC:%!"*%&(**%*-*0.(12$%'2,%"1-*$%61+*%('2,16-5%."(1#8"%."*%$/-/012%0(5$.'-%$.(#0.#(*3%'2,
/2%."*%7(10*$$%$16*%*-*0.(12$%6'5%&/--%$16*%1&%."*%"1-*$:%!"/$%7(10*$$3%0'--*,%&$*-,2!"'#!-"3
(*$#-.$% /2% ."*% ,/$'77*'('20*% 1&% &(**% *-*0.(12$% '2,% "1-*$:% !"*% (*0164/2'./12% ('.*% /$
127
128 Chapter 3 Semiconductors
7(171(./12'-%.1%."*%2#64*(%1&% &(**%*-*0.(12$%'2,%"1-*$3%)"/0"%/2%.#(2%/$%,*.*(6/2*,%45%."*
."*(6'-%%$"$&'#!-")('.*:%!"*%-'..*(%/$%'%$.(128%&#20./12%1&%.*67*('.#(*:%>2%."*(6'-%*V#/-/4?
(/#63%."*%(*0164/2'./12%('.*%/$%*V#'-%.1%."*%8*2*('./12%('.*3%'2,%12*%0'2%0120-#,*%."'.%."*
0120*2.('./12%1&%&(**%*-*0.(12$%#%/$%*V#'-%.1%."*%0120*2.('./12%1&%"1-*$%"3%
AK:SC
# ! " ! #+
)"*(*% # + %,*21.*$%."*%2#64*(%1&%&(**%*-*0.(12$%'2,%"1-*$%/2%'%#2/.%+1-#6*%A06KC%1&%/2.(/2$/0
$/-/012%'.%'%8/+*2%.*67*('.#(*:%_*$#-.$%&(16%$*6/012,#0.1(%7"5$/0$%8/+*$% # + %'$
# + ! *)
K ⁄ = ]&'`=()
%
AK:=C
SD
"K
"K ⁄ =
)"*(*% *% /$% '% 6'.*(/'-?,*7*2,*2.% 7'('6*.*(% ."'.% /$% b:K × SU 06 Y % &1(% $/-/012L% &' 3% '
7'('6*.*(%921)2%'$%."*% 2'"(%'0)$"$&%43%/$%S:S=%*-*0.(12%+1-.%A*PC%&1(%$/-/012=L%'2,% (%/$
M1-.X6'22W$%012$.'2.%A c:E= × SU "D %*P`YC:%>.%/$%/2.*(*$./28%.1%921)%."'.%."*%4'2,8'7%*2*(85
&'%/$%."*%6/2/6#6%*2*(85%(*V#/(*,%.1%4(*'9%'%01+'-*2.%412,%'2,%."#$%8*2*('.*%'2%*-*0.(12?
"1-*%7'/(:%
Example 3.1
<'-0#-'.*%."*%+'-#*%1&% # + %&1(%$/-/012%'.%(116%.*67*('.#(*%A) ! KUU%YC:
Solution
J#4$./.#./28%."*%+'-#*$%8/+*2%'41+*%/2%OV:%AK:SC%7(1+/,*$%
SD
# + ! b:K × SU ( KUU )
SU
K ⁄ = " S:S= ⁄ ( = × c:E= × SU
%
! S:D × SU 0'((/*($ ⁄ 06
"D
× KUU )
K
==
G-."1#8"%."/$%2#64*(%$**6$%-'(8*3%.1%7-'0*%/.%/2.1%012.*@.%21.*%."'.%$/-/012%"'$% D × SU %'.16$`06K:%!"#$
S=
'.%(116%.*67*('.#(*%12-5%12*%/2%'41#.% D × SU %'.16$%/$%/12/X*,%'2,%012.(/4#./28%'%&(**%*-*0.(12%'2,%'
"1-*d
;/2'--53%/.%/$%#$*&#-%&1(%&#.#(*%7#(71$*$%.1%*@7(*$$%."*%7(1,#0.%1&%."*%"1-*%'2,%&(**?*-*0.(12
0120*2.('./12%'$
=
AK:KC
"# ! # +
SU
K
)"*(*% &1(% $/-/012% '.% (116% .*67*('.#(*3% # + ! S:D × SU ⁄ 06 :% G$% )/--% 4*% $**2% $"1(.-53% ."/$
(*-'./12$"/7%*@.*2,$%.1%*@.(/2$/0%1(%,17*,%$/-/012%'$%)*--:
a1.*%."'.%S%*P% ! S:E × SU
=%
" ST
%N:
3.2 Doped Semiconductors 129
EXERCISE
3.1 <'-0#-'.*%."*%/2.(/2$/0%0'((/*(%,*2$/.5% # + %&1(%$/-/012%'.%)%e%DU%Y%'2,%KDU%Y:
" KT
K
K
Ans. T:E × SU ⁄ 06 L% B:SD × SU SS ⁄ 06
3.2 Doped Semiconductors
!"*%/2.(/2$/0%$/-/012%0(5$.'-%,*$0(/4*,%'41+*%"'$%*V#'-%0120*2.('./12$%1&%&(**%*-*0.(12$%'2,
"1-*$3%8*2*('.*,%45%."*(6'-%8*2*('./12:%!"*$*%0120*2.('./12$%'(*%&'(%.11%$6'--%&1(%$/-/012%.1
012,#0.%'77(*0/'4-*%0#((*2.%'.%(116%.*67*('.#(*:%G-$13%."*%0'((/*(%0120*2.('./12$%'2,%"*20*
."*% 012,#0./+/.5% '(*% $.(128% &#20./12$% 1&% .*67*('.#(*3% 21.% '% ,*$/('4-*% 7(17*(.5% /2% '2% *-*0?
.(12/0%,*+/0*:%;1(.#2'.*-53%'%6*."1,%)'$%,*+*-17*,%.1%0"'28*%."*%0'((/*(%0120*2.('./12%/2%'
$*6/012,#0.1(% 0(5$.'-% $#4$.'2./'--5% '2,% /2% '% 7(*0/$*-5% 012.(1--*,% 6'22*(:% !"/$% 7(10*$$% /$
921)2%'$%,17/283%'2,%."*%(*$#-./28%$/-/012%/$%(*&*((*,%.1%'$%(-0$()5!.!*-":
I17/28%/2+1-+*$%/2.(1,#0/28%/67#(/.5%'.16$%/2.1%."*%$/-/012%0(5$.'-%/2%$#&&/0/*2.%2#6?
4*($%.1%$#4$.'2./'--5%/20(*'$*%."*%0120*2.('./12%1&%*/."*(%&(**%*-*0.(12$%1(%"1-*$%4#.%)/."%-/..-*
1(%21%0"'28*%/2%."*%0(5$.'-%7(17*(./*$%1&%$/-/012:%!1%/20(*'$*%."*%0120*2.('./12%1&%&(**%*-*0?
.(12$3%#3%$/-/012%/$%,17*,%)/."%'2%*-*6*2.%)/."%'%+'-*20*%1&%D3%$#0"%'$%7"1$7"1(#$:%!"*%(*$#-.?
/28%,17*,%$/-/012%/$%."*2%$'/,%.1%4*%1&%!)#40$:%!1%/20(*'$*%."*%0120*2.('./12%1&%"1-*$3%"3%$/-/012
/$%,17*,%)/."%'2%*-*6*2.%"'+/28%'%+'-*20*%1&%K3%$#0"%'$%41(123%'2,%."*%(*$#-./28%,17*,%$/-/012
/$%$'/,%.1%4*%1&%")#40$:
;/8#(*%K:K%$"1)$%'%$/-/012%0(5$.'-%,17*,%)/."%7"1$7"1(#$%/67#(/.5:%!"*%,17'2.%A7"1$?
7"1(#$C%'.16$%(*7-'0*%$16*%1&%."*%$/-/012%'.16$%/2%."*%0(5$.'-%$.(#0.#(*:%J/20*%."*%7"1$7"1(#$
'.16%"'$%&/+*%*-*0.(12$%/2%/.$%1#.*(%$"*--3%&1#(%1&%."*$*%*-*0.(12$%&1(6%01+'-*2.%412,$%)/."%."*
Covalent
bonds
Valence
electrons
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
!
!
! "4 !
!
! "5 !
!
! "4 !
!
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
Free electron donated
by impurity atom
Pentavalent impurity
atom (donor)
Silicon atoms
Figure 3.3 G%$/-/012%0(5$.'-%,17*,%45%'%7*2.'+'-*2.%*-*6*2.:%O'0"%,17'2.%'.16%,12'.*$%'%&(**%*-*0.(12
'2,%/$%."#$%0'--*,%'%,121(:%!"*%,17*,%$*6/012,#0.1(%4*016*$%#%.57*:
130 Chapter 3 Semiconductors
2*/8"41(/28% '.16$3% '2,% ."*% &/&."% *-*0.(12% 4*016*$% '% &(**% *-*0.(12:% !"#$% *'0"% 7"1$7"1(#$
'.16%,-#./%0%'%&(**%*-*0.(12%.1%."*%$/-/012%0(5$.'-3%'2,%."*%7"1$7"1(#$%/67#(/.5%/$%0'--*,%'
(-"-&:%>.%$"1#-,%4*%0-*'(3%."1#8"3%."'.%21%"1-*$%'(*%8*2*('.*,%45%."/$%7(10*$$:%!"*%71$/./+*
0"'(8*%'$$10/'.*,%)/."%."*%7"1$7"1(#$%'.16%/$%'%2-+"()*/'&%$%."'.%,1*$%21.%61+*%."(1#8"
."*%0(5$.'-:
>&%."*%0120*2.('./12%1&%,121(%'.16$%/$% 1 2 3%)"*(*% 1 2 %/$%#$#'--5%6#0"%8(*'.*(%."'2%#+ 3%."*
0120*2.('./12%1&%&(**%*-*0.(12$%/2%."*%#?.57*%$/-/012%)/--%4*
## ! 12
AK:BC
)"*(*%."*%$#4$0(/7.%#!,*21.*$%#?.57*%$/-/012:%!"#$% # # %/$%,*.*(6/2*,%45%."*%,17/28%0120*2?
.('./12%'2,%21.%45%.*67*('.#(*:%!"/$%/$%21.%."*%0'$*3%"1)*+*(3%&1(%."*%"1-*%0120*2.('./12:%G-."*%"1-*$%/2%."*%#?.57*%$/-/012%'(*%."1$*%8*2*('.*,%45%."*(6'-%/12/X'./12:%!"*/(%0120*2.('./12
" # %0'2%4*%&1#2,%45%21./28%."'.%."*%(*-'./12$"/7%/2%OV:%AK:KC%'77-/*$%*V#'--5%)*--%&1(%,17*,
$/-/0123%7(1+/,*,%."*(6'-%*V#/-/4(/#6%/$%'0"/*+*,:%!"#$%&1(%#?.57*%$/-/012
=
"# ## % ! #+
J#4$./.#./28%&1(% # # %&(16%OV:%AK:BC3%)*%14.'/2%&1(% " #
=
#
" # ! ??????+?
12
AK:DC
=
!"#$% " # %)/--%"'+*%."*%$'6*%,*7*2,*20*%12%.*67*('.#(*%'$%."'.%1&% # + :%;/2'--53%)*%21.*
."'.%/2%#?.57*%$/-/012%."*%0120*2.('./12%1&%&(**%*-*0.(12$% # # %)/--%4*%6#0"%-'(8*(%."'2%."'.%1&
"1-*$:% f*20*% *-*0.(12$% '(*% $'/,% .1% 4*% ."*% ,'6-&!#4% 0"'(8*% 0'((/*($% '2,% "1-*$% ."*% ,!"-&!#4
0"'(8*%0'((/*($%/2%#?.57*%$/-/012:
!1%14.'/2%"?.57*%$/-/012%/2%)"/0"%"1-*$%'(*%."*%6'F1(/.5%0"'(8*%0'((/*($3%'%.(/+'-*2.%/67#?
(/.5%$#0"%'$%41(12%/$%#$*,:%;/8#(*%K:B%$"1)$%'%$/-/012%0(5$.'-%,17*,%)/."%41(12:%a1.*%."'.%."*
41(12% '.16$% (*7-'0*% $16*% 1&% ."*% $/-/012% '.16$% /2% ."*% $/-/012% 0(5$.'-% $.(#0.#(*:% J/20*% *'0"
Covalent
bonds
Valence
electrons
Silicon atom
!
!
!
! "4 !
!
! "4 !
!
! "4 !
!
!
!
!
! "4 !
!
! "3 !
!
! "4 !
!
!
!
"
! "4 !
!
! "4 !
!
! "4 !
!
Trivalent impurity
atom (acceptor)
Electron accepted from
this atom, thus creating
a hole
Figure 3.4 G%$/-/012%0(5$.'-%,17*,%)/."%'%.(/+'-*2.%/67#(/.5:%O'0"%,17'2.%'.16%8/+*$%(/$*%.1%'%"1-*3%'2,
."*%$*6/012,#0.1(%4*016*$%"%.57*:
3.2 Doped Semiconductors
41(12%'.16%"'$%."(**%*-*0.(12$%/2%/.$%1#.*(%$"*--3%/.%'**$0#5%'2%*-*0.(12%&(16%'%2*/8"41(/28
'.163%."#$%&1(6/28%01+'-*2.%412,$:%!"*%(*$#-.%/$%'%"1-*%/2%."*%2*/8"41(/28%'.16%'2,%'%41#2,
2*8'./+*%0"'(8*%'.%."*%'**$0#-&%A41(12C%'.16:%>.%&1--1)$%."'.%*'0"%'00*7.1(%'.16%7(1+/,*$%'
"1-*:% >&% ."*% '00*7.1(% ,17/28% 0120*2.('./12% /$% 1 3 3% )"*(*% 1 3 # # + L % ."*% "1-*% 0120*2.('./12
4*016*$
AK:EC
" " %! 1 3
)"*(*%."*%$#4$0(/7.%"!,*21.*$%"?.57*%$/-/012:%!"#$3%"*(*%."*%6'F1(/.5%0'((/*($%'(*%"1-*$%'2,
."*/(% 0120*2.('./12% /$% ,*.*(6/2*,% 45% 13:% !"*% 0120*2.('./12% 1&% 6/21(/.5% *-*0.(12$% 0'2% 4*
&1#2,%45%#$/28%."*%(*-'./12$"/7%
=
"" #" % ! #+
'2,%$#4$./.#./28%&1(% " " %&(16%OV:%AK:EC3
=
#
# " ! ?????+?
13
AK:bC
!"#$3% ."*% 0120*2.('./12% 1&% ."*% 6/21(/.5% *-*0.(12$% )/--% "'+*% ."*% $'6*% .*67*('.#(*% ,*7*2?
=
,*20*%'$%."'.%1&% # + :
>.%$"1#-,%4*%*67"'$/X*,%."'.%'%7/*0*%1&%#?.57*%1(%"?.57*%$/-/012%/$%*-*0.(/0'--5%2*#.('-L%."*
0"'(8*%1&%."*%6'F1(/.5%&(**%0'((/*($%A*-*0.(12$%/2%."*%#?.57*%'2,%"1-*$%/2%."*%"?.57*%$/-/012C%'(*
2*#.('-/X*,%45%."*%41#2,%0"'(8*$%'$$10/'.*,%)/."%."*%/67#(/.5%'.16$:
Example 3.2
Sb
K
<12$/,*(% '2%#?.57*% $/-/012% &1(% )"/0"% ."*% ,17'2.% 0120*2.('./12% 1 2 ! SU ⁄ 06 :% ;/2,% ."*% *-*0.(12% '2,
"1-*%0120*2.('./12$%'.%)%%e%KUU%Y:
Solution
!"*%0120*2.('./12%1&%."*%6'F1(/.5%*-*0.(12$%/$
Sb
# # ! 1 2 ! SU ⁄ 06
K
!"*%0120*2.('./12%1&%."*%6/21(/.5%"1-*$%/$
=
#
" # ! ??????+?
12
SU
K
>2%O@'67-*%K:S%)*%&1#2,%."'.%'.%)%e%KUU%Y3% # + ! S:D × SU ⁄ 06 :%!"#$3
SU =
S:D × SU )
" # ! (??????????????????????????????
?
Sb
SU
K
! =:=D × SU ⁄ 06
R4$*(+*%."'.% # # # # + %'2,%."'.% # # %/$%+'$.-5%"/8"*(%."'2% " #:
K
131
132 Chapter 3 Semiconductors
EXERCISES
3.2 ;1(%."*%$/.#'./12%/2%O@'67-*%K:=3%&/2,%."*%*-*0.(12%'2,%"1-*%0120*2.('./12$%'.%KDU%Y:%g1#%6'5%#$*
."*%+'-#*%1&% # + %'.%)!e%KDU%Y%&1#2,%/2%O@*(0/$*%K:S:
Sb
K
E
K
Ans. # # ! SU ⁄ 063 % " # ! S:b= × SU ⁄ 06
3.3 ;1(%'%$/-/012%0(5$.'-%,17*,%)/."%41(123%)"'.%6#$.% 1 3 %4*%/&%'.%)%e%KUU%Y%."*%*-*0.(12%0120*2.('./12
E
,(17$%4*-1)%."*%/2.(/2$/0%-*+*-%45%'%&'0.1(%1&% SU h
SE
K
Ans. 1 3 ! S:D × SU ⁄ 06
3.3 Current Flow in Semiconductors
!"*(*% '(*% .)1% ,/$./20.-5% ,/&&*(*2.% 6*0"'2/$6$% &1(% ."*% 61+*6*2.% 1&% 0"'(8*% 0'((/*($% '2,
"*20*%&1(%0#((*2.%&-1)%/2%$*6/012,#0.1($H%,(/&.%'2,%,/&&#$/12:
3.3.1 Drift Current
\"*2%'2%*-*0.(/0'-%&/*-,%&%/$%*$.'4-/$"*,%/2%'%$*6/012,#0.1(%0(5$.'-3%"1-*$%'(*%'00*-*('.*,%/2
."*%,/(*0./12%1&%&3%'2,%&(**%*-*0.(12$%'(*%'00*-*('.*,%/2%."*%,/(*0./12%1771$/.*%.1%."'.%1&%&:
!"/$%$/.#'./12%/$%/--#$.('.*,%/2%;/8:%K:D:%!"*%"1-*$%'0V#/(*%'%+*-10/.5%4"?,(/&.%8/+*2%45
4"?,(/&.%e%µ"&
AK:cC
)"*(*% µ"%/$%'%012$.'2.%0'--*,%."*%/-.$),-2!.!#4H%>.%(*7(*$*2.$%."*%,*8(**%1&%*'$*%45%)"/0"
"1-*$%61+*%."(1#8"%."*%$/-/012%0(5$.'-%/2%(*$712$*%.1%."*%*-*0.(/0'-%&/*-,%&:%J/20*%+*-10/.5%"'$
."*%#2/.$%1&%0*2./6*.*($%7*(%$*012,%'2,!&%"'$%."*%#2/.$%1&%+1-.$%7*(%0*2./6*.*(3%)*%$**%&(16
OV:% AK:cC% ."'.% ."*% 614/-/.5% µ"% 6#$.% "'+*% ."*% #2/.$% 1&% 0*2./6*.*($% $V#'(*,% 7*(% +1-.?$*012,
A06=`P:$C:%;1(%/2.(/2$/0%$/-/012% µ " ! BcU %06=`P : $:
!"*%&(**%*-*0.(12$%'0V#/(*%'%,(/&.%+*-10/.5% 4 #?,(/&. %8/+*2%45
4#?,(/&. %e %]µ# &
AK:TC
)"*(*%."*%(*$#-.%/$%2*8'./+*%4*0'#$*%."*%*-*0.(12$%61+*%/2%."*%,/(*0./12%1771$/.*%.1%&:%f*(*
µ # %/$%."*%$.$*#&-"),-2!.!#43%)"/0"%&1(%/2.(/2$/0%$/-/012%/$%'41#.%SKDU%06=`P:$:%a1.*%."'.% µ #
/$%'41#.%=:D%./6*$%µ" 3%$/82/&5/28%."'.%*-*0.(12$%61+*%)/."%6#0"%8(*'.*(%*'$*%."(1#8"%."*%$/-?
/012%0(5$.'-%."'2%,1%"1-*$:
E
Holes
Electrons
"
!
x
V
Figure 3.5 G2% *-*0.(/0% &/*-,% &% *$.'4-/$"*,% /2% '
4'(%1&%$/-/012%0'#$*$%."*%"1-*$%.1%,(/&.%/2%."*%,/(*0?
./12%1&%&%'2,%."*%&(**%*-*0.(12$%.1%,(/&.%/2%."*%1771?
$/.*% ,/(*0./12:% M1."% ."*% "1-*% '2,% *-*0.(12% ,(/&.
0#((*2.$%'(*%/2%."*%,/(*0./12%1&%&:
3.3 Current Flow in Semiconductors
Q*.W$%21)%(*.#(2%.1%."*%$/28-*?0(5$.'-%$/-/012%4'(%$"1)2%/2%;/8:%K:D:%Q*.%."*%0120*2.('./12
1&%"1-*$%4*%"!'2,%."'.%1&%&(**%*-*0.(12$%#:%\*%)/$"%.1%0'-0#-'.*%."*%0#((*2.%016712*2.%,#*%.1
."*%&-1)%1&%"1-*$:%<12$/,*(%'%7-'2*%7*(7*2,/0#-'(%.1%."*%5%,/(*0./12:%>2%12*%$*012,3%."*%"1-*
0"'(8*% ."'.% 0(1$$*$% ."'.% 7-'2*% )/--% 4*% A3$"v"?,(/&.C% 01#-164$3% )"*(*% 3% /$% ."*% 0(1$$?$*0./12''(*'%1&%."*%$/-/012%4'(%'2,%$!/$%."*%6'82/.#,*%1&%*-*0.(12%0"'(8*:%!"/$%."*2%6#$.%4*%."*%"1-*
016712*2.%1&%."*%,(/&.%0#((*2.%&-1)/28%."(1#8"%."*%4'(3
6"% e% 3$"4"?,7+8/
AK:SUC
J#4$./.#./28%&1(%v"?,(/&.%&(16%OV:%AK:TC3%)*%14.'/2
6 " ! 3$" µ " &
\*% '(*% #$#'--5% /2.*(*$.*,% /2% ."*% 0#((*2.% ,*2$/.5% 9" 3% )"/0"% /$% ."*% 0#((*2.% 7*(% #2/.% 0(1$$?
$*0./12'-%'(*'3
6"
9 " ! ???? ! $" µ " &
AK:SSC
3
!"*% 0#((*2.% 016712*2.% ,#*% .1% ."*% ,(/&.% 1&%&(**%*-*0.(12$% 0'2% 4*%&1#2,% /2% '% $/6/-'(% 6'22*(:
a1.*3%"1)*+*(3%."'.%*-*0.(12$%,(/&./28%&(16%(/8".%.1%-*&.%(*$#-.%/2%'%0#((*2.%016712*2.%&(16%-*&.
.1%(/8".:%!"/$%/$%4*0'#$*%1&%."*%012+*2./12%1&%.'9/28%."*%,/(*0./12%1&%0#((*2.%&-1)%'$%."*%,/(*0?
./12%1&%&-1)%1&%71$/./+*%0"'(8*%'2,%1771$/.*%.1%."*%,/(*0./12%1&%&-1)%1&%2*8'./+*%0"'(8*:%!"#$3
6#% e% ]3$#4#?,(/&.
J#4$./.#./28%&1(%v#?,(/&.%&(16%OV:%AK:TC3%)*%14.'/2%."*%0#((*2.%,*2$/.5% 9 # ! 6 # ⁄ 3 %'$%
9 # ! $# µ # &
AK:S=C
!"*%.1.'-%,(/&.%0#((*2.%,*2$/.5%0'2%21)%4*%&1#2,%45%$#66/28% 9 " %'2,% 9 # %&(16%OV$:%AK:SSC
'2,%AK:S=C3
9 ! 9 " # 9 # ! $ ( " µ : # # µ # )&
AK:SKC
!"/$%(*-'./12$"/7%0'2%4*%)(/..*2%'$
9 ! σ&
AK:SBC
9 ! &⁄ρ
AK:SDC
σ ! $ ( " µ" # # µ# )
AK:SEC
S
S
?
ρ ≡ ??? ! ???????????????????????????????
σ $ ( " µ" # # µ# )
AK:SbC
1(
)"*(*%."*%*-"(+*#!1!#4% σ %/$%8/+*2%45
'2,%."*%&$5!5#!1!#4% ρ %/$%8/+*2%45
R4$*(+*%."'.%OV:%AK:SDC%/$%'%&1(6%1&%R"6W$%-')%'2,%0'2%4*%)(/..*2%'-.*(2'.*-5%'$%
ρ ! &
???
9
P ⁄ 06 :
!"#$%."*%#2/.$%1&%ρ%'(*%1"6:0*2./6*.*($% Ω ⋅ 06 ! ?????????????????
=
G ⁄ 06
AK:ScC
133
134 Chapter 3 Semiconductors
Example 3.3
SE
K
;/2,% ."*% (*$/$./+/.5% 1&% A'C% /2.(/2$/0% $/-/012% '2,% A4C% "?.57*% $/-/012% )/."% 1 3 % ! SU ⁄ 06 :% i$*
SU
=
# + % ! S:D × SU ⁄ 06 K3% '2,% '$$#6*% ."'.% &1(% /2.(/2$/0% $/-/012% µ # % ! SKDU 06 ⁄ P : $% '2,
=
=
=
µ " % ! BcU 06 ⁄ P : $3% '2,% &1(% ."*% ,17*,% $/-/012% µ # % ! SSSU 06 ⁄ P : $% '2,% µ " % ! BUU 06 ⁄ P : $:
Aa1.*%."'.%,17/28%(*$#-.$%/2%(*,#0*,%0'((/*(%614/-/./*$C:
Solution
A'C%;1(%/2.(/2$/0%$/-/0123
SU
" ! # ! # + ! S:D × SU ⁄ 06
K
!"#$3
S
ρ ! ???????????????????????????????
?
$ ( " µ" # # µ# )
S
ρ ! ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
" ST
SU
SU
S:E × SU ( S:D × SU × BcU # S:D × SU × SKDU )
D
! =:=c × SU Ω :%%06
A4C%;1(%."*%"?.57*%$/-/012
SE
" " ! 1 3 ! SU ⁄ 06
K
=
SU =
#
S:D × SU )
# " ! ?????+? ! (??????????????????????????????
? ! =:=D × SUB `06K
SE
13
SU
!"#$3
S
ρ ! ???????????????????????????????
?
$ ( " µ" # # µ# )
S
! ??????????????????????????????????????????????????????????????????????????????????????????????????????????
?
" ST
SE
B
S:E × SU ( SU × BUU # =:=D × SU × SSSU )
S
? ! S:DE Ω :%%06
! ?????????????????????????????????????????????????????????
" ST
SE
S:E × SU × SU × BUU
R4$*(+*%."'.%."*%(*$/$./+/.5%1&%."*%"?.57*%$/-/012%/$%,*.*(6/2*,%'-61$.%*2./(*-5%45%."*%,17/28%0120*2?
D
.('./12:%G-$1%14$*(+*%."'.%,17/28%."*%$/-/012%(*,#0*$%/.$%(*$/$./+/.5%45%'%&'0.1(%1&%'41#.% SU 3%'%.(#-5
(*6'(9'4-*%0"'28*:
3.3 Current Flow in Semiconductors 135
EXERCISE
3.4 G% #2/&1(6% 4'(% 1&% #?.57*% $/-/012% 1&% =% µ6% -*28."% "'$% '% +1-.'8*% 1&% S% P% '77-/*,% '0(1$$% /.:% >&
SE
K
=
1 2 ! SU ⁄ 06 %'2,% µ # ! SKDU 06 ⁄ P :$3%&/2,%A'C%."*%*-*0.(12%,(/&.%+*-10/.53%A4C%."*%./6*%/.%.'9*$%'2
*-*0.(12%.1%0(1$$%."*%=?µ6%-*28."3%A0C%."*%,(/&.?0#((*2.%,*2$/.53%'2,%A,C%."*%,(/&.%0#((*2.%/2%."*%0'$*
=
."*%$/-/012%4'(%"'$%'%0(1$$%$*0./12'-%'(*'%1&% U:=D µ6 :
E
B
=
Ans. E:bD × SU %06`$L%KU%7$L%S:Uc × SU G ⁄ 06 L%=b%µG
3.3.2 Diffusion Current
<'((/*(%,/&&#$/12%100#($%)"*2%."*%,*2$/.5%1&%0"'(8*%0'((/*($%/2%'%7/*0*%1&%$*6/012,#0.1(%/$
21.%#2/&1(6:%;1(%/2$.'20*3%/&%45%$16*%6*0"'2/$6%."*%0120*2.('./12%1&3%$'53%"1-*$3%/$%6',*
"/8"*(% /2% 12*% 7'(.% 1&% '% 7/*0*% 1&% $/-/012% ."'2% /2% '21."*(3% ."*2% "1-*$% )/--% ,/&&#$*% &(16% ."*
(*8/12%1&%"/8"%0120*2.('./12%.1%."*%(*8/12%1&%-1)%0120*2.('./12:%J#0"%'%,/&&#$/12%7(10*$$%/$
-/9*%."'.%14$*(+*,%/&%12*%,(17$%'%&*)%/29%,(17$%/2%'%)'.*(?&/--*,%.'29:%!"*%,/&&#$/12%1&%0"'(8*
0'((/*($%8/+*$%(/$*%.1%'%2*.%&-1)%1&%0"'(8*3%1(%(!33+5!-")*+&&$"#:
G$%'2%*@'67-*3%012$/,*(%."*%4'(%1&%$/-/012%$"1)2%/2%;/8:%K:EA'CH%M5%$16*%#2$7*0/&/*,
7(10*$$3% )*% "'+*% '(('28*,% .1% /2F*0.% "1-*$% /2.1% /.$% -*&.% $/,*:% !"/$% 012./2#1#$% "1-*% /2F*0./12
8/+*$%(/$*%.1%'2,%6'/2.'/2$%'%"1-*%*-"*$"#&'#!-")0&-3!.$%$#0"%'$%."'.%$"1)2%/2%;/8:%K:EA4C:
!"/$%7(1&/-*%/2%.#(2%0'#$*$%"1-*$%.1%,/&&#$*%&(16%-*&.%.1%(/8".%'-128%."*%$/-/012%4'(3%(*$#-./28%/2
'%"1-*%0#((*2.%/2%."*%5%,/(*0./12:%!"*%6'82/.#,*%1&%."*%0#((*2.%'.%'25%71/2.%/$%7(171(./12'-%.1
."*%$-17*%1&%."*%0120*2.('./12%7(1&/-*3%1(%."*%*-"*$"#&'#!-")%&'(!$"#3%'.%."'.%71/2.3%
," ( 5 )
9 " ! " $2 " ??????????????
,5
"
Hole
injection
AK:STC
" "" "
" " " "
"
" "" " "
"
" "
" " " "
" " " " " " "
" " "
"
(a)
x
Hole concentration, p
Hole diffusion
Hole current
x
0
(b)
Figure 3.6 G% 4'(% 1&% $/-/012) 7'8% /2.1
)"/0"% "1-*$% '(*% /2F*0.*,3% ."#$% 0(*'./28% ."*
"1-*%0120*2.('./12%7(1&/-*%'-128%."*%5%'@/$3
$"1)2%/2%728:%!"*%"1-*$%,/&&#$*%/2%."*%71$/?
./+*% ,/(*0./12% 1&% 5% '2,% 8/+*% (/$*% .1% '% "1-*?
,/&&#$/12% 0#((*2.% /2% ."*% $'6*% ,/(*0./12:
a1.*%."'.%)*%'(*%21.%$"1)/28%."*%0/(0#/.%.1
)"/0"%."*%$/-/012%4'(%/$%0122*0.*,:
136 Chapter 3 Semiconductors
=
)"*(*% 9 "%/$%."*%"1-*?0#((*2.%,*2$/.5%A G ⁄ 06 C3%$%/$%."*%6'82/.#,*%1&%*-*0.(12%0"'(8*3% 2 "%/$%'
012$.'2.% 0'--*,% ."*% (!33+5!-") *-"5#'"#% 1(% (!33+5!1!#4% 1&% "1-*$L% '2,% " ( 5 )% /$% ."*% "1-*
0120*2.('./12%'.%71/2.%5:%a1.*%."'.%."*%8(',/*2.% ( ," ⁄ ,5 ) %/$%2*8'./+*3%(*$#-./28%/2%'%71$/./+*
0#((*2.%/2%."*%5%,/(*0./123%'$%$"1#-,%4*%*@7*0.*,:
>2%."*%0'$*%1&%*-*0.(12%,/&&#$/12%(*$#-./28%&(16%'2%*-*0.(12%0120*2.('./12%8(',/*2.%A$**
;/8:%K:bC3%'%$/6/-'(%(*-'./12$"/7%'77-/*$3%8/+/28%."*%*-*0.(12?0#((*2.%,*2$/.53
,# ( 5 )
9 # ! $2 # ??????????????
,5
AK:=UC
)"*(*% 2 # %/$%."*%,/&&#$/12%012$.'2.%1(%,/&&#$/+/.5%1&%*-*0.(12$:%R4$*(+*%."'.%'%2*8'./+*%A,#`,5C
8/+*$%(/$*%.1%'%2*8'./+*%0#((*2.3%'%(*$#-.%1&%."*%012+*2./12%."'.%."*%71$/./+*%,/(*0./12%1&%0#((*2.
/$%.'9*2%.1%4*%."'.%1&%."*%&-1)%1&%71$/./+*%0"'(8*%A'2,%1771$/.*%.1%."'.%1&%."*%&-1)%1&%2*8'./+*
0"'(8*C:%;1(%"1-*$%'2,%*-*0.(12$%,/&&#$/28%/2%/2.(/2$/0%$/-/0123%.57/0'-%+'-#*$%&1(%."*%,/&&#$/12
012$.'2.$%'(*%2"%e%S=%06=`$%%'2,%2#%e%KD%06=`$:
G.%."/$%71/2.%."*%(*',*(%/$%7(14'4-5%)12,*(/28%)"*(*%."*%,/&&#$/12%0#((*2.%/2%."*%$/-/012
4'(%/2%;/8:%K:EA'C%81*$:%G%811,%V#*$./12%'$%)*%'(*%21.%$"1)/28%"1)%."*%(/8".?$/,*%*2,%1&%."*
4'(%/$%0122*0.*,%.1%."*%(*$.%1&%."*%0/(0#/.:%\*%)/--%',,(*$$%."/$%'2,%(*-'.*,%V#*$./12$%/2%,*.'//2%1#(%,/$0#$$/12%1&%."*%"#%F#20./12%/2%-'.*(%$*0./12$:%
Electron concentration, n
Electron diffusion
Electron current
x
0
Figure 3.7 >&%."*%*-*0.(12?0120*2.('./12%7(1&/-*
$"1)2%/$%*$.'4-/$"*,%/2%'%4'(%1&%$/-/0123%*-*0.(12$
,/&&#$*%/2%."*%5%,/(*0./123%8/+/28%(/$*%.1%'2%*-*0.(12?
,/&&#$/12%0#((*2.%/2%."*%2*8'./+*%?5%,/(*0./12:
Example 3.4
<12$/,*(%'%4'(%1&%$/-/012%/2%)"/0"%'%"1-*%0120*2.('./12%7(1&/-*%,*$0(/4*,%45
" ( 5 ) ! "U %
"5 ⁄ ;:
SE
K
/$%*$.'4-/$"*,:%;/2,%."*%"1-*?0#((*2.%,*2$/.5%'.%5!e%U:%Q*.% " U ! SU ⁄ 06 %'2,% ; " ! S % µ6:%>&%."*
0(1$$?$*0./12'-%'(*'%1&%."*%4'(%/$%SUU%µ6=3%&/2,%."*%0#((*2.%6":
3.3 Current Flow in Semiconductors
Solution
," ( 5 )
9 " % ! " $2 " ??????????????
,5
"5 ⁄ ;:
,
! " $2 " ?????? [ " U %
]
,5
!"#$3
2"
9 " ( U )% ! $ ?????? " U
;"
! S:E × SU
" ST
S=
? × SU SE
× ??????????????????
"B
S × SU
! ST= G ⁄ 06
=
!"*%0#((*2.%6 "%0'2%4*%&1#2,%&(16
6" % ! 9" × 3
! ST= × SUU × SU
"c
e%ST=%%µG
EXERCISE
3.5 !"*%-/2*'(%*-*0.(12?0120*2.('./12%7(1&/-*%$"1)2%/2%;/8:%OK:D%"'$%4**2%*$.'4-/$"*,%/2%'%7/*0*%1&%$/-/?
Sb
K
012:% >&% # U ! SU ⁄ 06 % '2,% <% e% S% µ63% &/2,% ."*% *-*0.(12?0#((*2.% ,*2$/.5% /2% 6/0(1% '67*(*$% 7*(
6/0(12%$V#'(*,%AµG`µ6=C:%>&%'%,/&&#$/12%0#((*2.%1&%S%6G%/$%(*V#/(*,%)"'.%6#$.%."*%0(1$$?$*0./12''(*'%7/2%'%,/(*0./12%7*(7*2,/0#-'(%.1%."*%7'8*C%4*h
n(x)
n0
0
Ans. $%&µ'(µ)*+&,-&µ)*
W
x
Figure E3.5
137
138 Chapter 3 Semiconductors
3.3.3 Relationship between D and m
G%$/67-*%4#.%71)*(&#-%(*-'./12$"/7%./*$%."*%,/&&#$/12%012$.'2.%)/."%."*%614/-/.53
2"
2#
?????? ! ?????? ! = )
µ#
AK:=SC
µ"
)"*(*% = ) ! () ⁄ $ :%!"*%7'('6*.*(% = ) %/$%921)2%'$%."*%#/$&,'.)1-.#'%$:%G.%(116%.*67*('?
.#(*3%) ! KUU%Y%'2,% = ) %%e%=D:T %6P:%\*%)/--%*201#2.*(% = ) %(*7*'.*,-5%."(1#8"1#.%."/$%4119:
!"*%(*-'./12$"/7%/2%OV:%AK:=SC%/$%921)2%'$%."*%9!"5#$!")&$.'#!-"5/!0:
EXERCISE
=
3.6 i$*%."*% O/2$.*/2% (*-'./12$"/7%.1%&/2,% 2 # %'2,% 2 " %&1(%/2.(/2$/0%$/-/012%#$/28% µ # ! SKDU%06 ⁄ P⋅ $
=
'2,% µ " ! BcU%06 ⁄ P ⋅ $ :
=
Ans. KD%06 `$L%S=:B%06= `$
3.4 The pn Junction with Open-Circuit Terminals
(Equilibrium)
f'+/28%-*'(2*,%/671(.'2.%$*6/012,#0.1(%0120*7.$3%)*%'(*%21)%(*',5%.1%012$/,*(%1#(%&/($.
7('0./0'-%$*6/012,#0.1(%$.(#0.#(*j."*%"#%F#20./12:%G$%6*2./12*,%7(*+/1#$-53%."*%"#%F#20?
./12%/67-*6*2.$%."*%,/1,*%A<"'7.*(%BC%'2,%7-'5$%."*%,16/2'2.%(1-*%/2%."*%$.(#0.#(*%'2,%17*(?
'./12%1&%."*%4/71-'(%F#20./12%.('2$/$.1(%AMN!C:%G$%)*--3%#2,*($.'2,/28% "#%F#20./12$%/$%+*(5
/671(.'2.%.1%."*%$.#,5%1&%."*%kRJ;O!%17*('./12%A<"'7.*(%DC:
3.4.1 Physical Structure
;/8#(*% K:c% $"1)$% '% $/67-/&/*,% 7"5$/0'-% $.(#0.#(*% 1&% ."*% "#% F#20./12:% >.% 012$/$.$% 1&% "?.57*
$*6/012,#0.1(%A*:8:3%$/-/012C%4(1#8".%/2.1%0-1$*%012.'0.%)/."%'2%#?.57*%$*6/012,#0.1(%6'.*?
(/'-%A'-$1%$/-/012C:%>2%'0.#'-%7('0./0*3%41."%."*%"%'2,%#%(*8/12$%'(*%7'(.%1&%."*%$'6*%$/-/012
0(5$.'-L%."'.%/$3%."*%"#%F#20./12%/$%&1(6*,%)/."/2%'%$/28-*%$/-/012%0(5$.'-%45%0(*'./28%(*8/12$%1&
,/&&*(*2.%,17/28$%A"%'2,%#%(*8/12$C:%G77*2,/@%G%7(1+/,*$%'%,*$0(/7./12%1&%."*%&'4(/0'./12
7(10*$$%1&%/2.*8('.*,%0/(0#/.$%/20-#,/28%"#%F#20./12$:%G$%/2,/0'.*,%/2%;/8:%K:c3%*@.*(2'-%)/(*
0122*0./12$%'(*%6',*%.1%."*%"%'2,%#%(*8/12$%."(1#8"%6*.'-%A'-#6/2#6C%012.'0.$:%>&%."*%"#
F#20./12% /$% #$*,% '$% '% ,/1,*3% ."*$*% 012$./.#.*% ."*% ,/1,*% .*(6/2'-$% '2,% '(*% ."*(*&1(*% -'4*-*,
Z'21,*[%'2,%Z0'."1,*[%/2%9**7/28%)/."%,/1,*%.*(6/21-185:K
K
!"/$%.*(6/21-185%/2%&'0.%/$%'%0'((51+*(%&(16%."'.%#$*,%)/."%+'0##6?.#4*%.*0"21-1853%)"/0"%)'$%."*
.*0"21-185%&1(%6'9/28%,/1,*$%'2,%1."*(%*-*0.(12/0%,*+/0*$%#2./-%."*%/2+*2./12%1&%."*%.('2$/$.1(%/2%STBb:
!"/$%*+*2.%#$"*(*,%/2%."*%*('%1&%$1-/,?$.'.*%*-*0.(12/0$3%)"/0"%0"'28*,%21.%12-5%*-*0.(12/0$3%0166#2/?
0'./12$3%'2,%0167#.*($%4#.%/2,**,%."*%)1(-,d
3.5 The pn Junction with an Applied Voltage
Metal contact
Anode
Metal contact
p-type
silicon
n-type
silicon
Cathode
Figure 3.8 J/67-/&/*,%7"5$/0'-%$.(#0.#(*%1&%."*%"#%F#20./12:%AG0.#'-%8*16*.(/*$%'(*%8/+*2%/2%G77*2,/@%G:C
G$%."*!"#%F#20./12%/67-*6*2.$%."*%F#20./12%,/1,*3%/.$%.*(6/2'-$%'(*%-'4*-*,%'21,*%'2,%0'."1,*:
3.4.2 Operation with Open-Circuit Terminals
;/8#(*%K:T%$"1)$%'%"#%F#20./12%#2,*(%17*2?0/(0#/.%012,/./12$j."'.%/$3%."*%*@.*(2'-%.*(6/?
2'-$% '(*% -*&.% 17*2:% !"*% Z+[% $/82$% /2% ."*% "?.57*% 6'.*(/'-% ,*21.*% ."*% 6'F1(/.5% "1-*$:% !"*
0"'(8*%1&%."*$*%"1-*$%/$%2*#.('-/X*,%45%'2%*V#'-%'61#2.%1&%41#2,%2*8'./+*%0"'(8*%'$$10/?
'.*,% )/."% ."*% '00*7.1(% '.16$:% ;1(% $/67-/0/.53% ."*$*% 41#2,% 0"'(8*$% '(*% 21.% $"1)2% /2% ."*
,/'8('6:%G-$1%21.% $"1)2%'(*%."*%6/21(/.5%*-*0.(12$% 8*2*('.*,% /2%."*% "?.57*% 6'.*(/'-%45
."*(6'-%/12/X'./12:%
>2%."*%#?.57*%6'.*(/'-%."*%6'F1(/.5%*-*0.(12$%'(*%/2,/0'.*,%45%Z][%$/82$:%f*(*%'-$13%."*
41#2,%71$/./+*%0"'(8*3%)"/0"%2*#.('-/X*$%."*%0"'(8*%1&%."*%6'F1(/.5%*-*0.(12$3%/$%21.%$"1)2
/2%1(,*(%.1%9**7%."*%,/'8('6%$/67-*:%!"*%#?.57*%6'.*(/'-%'-$1%012.'/2$%6/21(/.5%"1-*$%8*2*(?
'.*,%45%."*(6'-%/12/X'./12%4#.%21.%$"1)2%/2%."*%,/'8('6:
The Diffusion Current ID M*0'#$*%."*%0120*2.('./12%1&%"1-*$%/$%"/8"%/2%."*%"%(*8/12%'2,
-1)%/2%."*%#%(*8/123%"1-*$%,/&&#$*%'0(1$$%."*%F#20./12%&(16%."*%"%$/,*%.1%."*%#%$/,*L%$/6/-'(-53
*-*0.(12$%,/&&#$*%'0(1$$%."*%F#20./12%&(16%."*%#%$/,*%.1%."*%"%$/,*:%!"*$*%.)1%0#((*2.%01671?
2*2.$%',,%.18*."*(%.1%&1(6%."*%,/&&#$/12%0#((*2.%62 3%)"1$*%,/(*0./12%/$%&(16%."*%"%$/,*%.1%."*
#%$/,*3%'$%/2,/0'.*,%/2%;/8:%K:T:
The Depletion Region !"*% "1-*$% ."'.% ,/&&#$*% '0(1$$% ."*% F#20./12% /2.1% ."*% #% (*8/12
V#/09-5%(*0164/2*%)/."%$16*%1&%."*%6'F1(/.5%*-*0.(12$%7(*$*2.%."*(*%'2,%."#$%,/$'77*'(%&(16
."*%$0*2*:%!"/$%(*0164/2'./12%7(10*$$%(*$#-.$%'-$1%/2%."*%,/$'77*'('20*%1&%$16*%&(**%*-*0.(12$
&(16%."*%#?.57*%6'.*(/'-:%!"#$%$16*%1&%."*%41#2,%71$/./+*%0"'(8*%)/--%21%-128*(%4*%2*#.('-?
/X*,%45%&(**%*-*0.(12$3%'2,%."/$%0"'(8*%/$%$'/,%.1%"'+*%4**2%+"*-1$&$(:%J/20*%(*0164/2'./12
.'9*$%7-'0*%0-1$*%.1%."*%F#20./123%."*(*%)/--%4*%'%(*8/12%0-1$*%.1%."*%F#20./12%."'.%/$ ,%">%/%,!-8
87%%!%>%?/7-#0%'2,%012.'/2$%#201+*(*,%41#2,%71$/./+*%0"'(8*3%'$%/2,/0'.*,%/2%;/8:%K:T:
!"*%*-*0.(12$%."'.%,/&&#$*%'0(1$$%."*%F#20./12%/2.1%."*%"%(*8/12%V#/09-5%(*0164/2*%)/."
$16*%1&%."*%6'F1(/.5%"1-*$%."*(*3%'2,%."#$%,/$'77*'(%&(16%."*%$0*2*:%!"/$%(*$#-.$%'-$1%/2%."*
,/$'77*'('20*% 1&% $16*% 6'F1(/.5% "1-*$3% 0'#$/28% $16*% 1&% ."*% 41#2,% 2*8'./+*% 0"'(8*% .1% 4*
#201+*(*,%A/:*:3%21%-128*(%2*#.('-/X*,%45%"1-*$C:%!"#$3%/2%."*%"%6'.*(/'-%0-1$*%.1%."*%F#20./123
."*(*%)/--%4*%'%(*8/12%,%">%/%,!-8!@->%0%'2,%012.'/2/28%#201+*(*,%41#2,%2*8'./+*%0"'(8*3%'$
/2,/0'.*,%/2%;/8:%K:T:%
;(16%."*%'41+*%/.%&1--1)$%."'.%'%*'&&!$&:($0.$#!-")&$%!-"%)/--%*@/$.%12%41."%$/,*$%1&%."*
F#20./123%)/."%."*%#%$/,*%1&%."/$%(*8/12%71$/./+*-5%0"'(8*,%'2,%."*%"%$/,*%2*8'./+*-5%0"'(8*,:
!"/$%0'((/*(?,*7-*./12%(*8/12j1(3%$/67-53%($0.$#!-")&$%!-"j/$%'-$1%0'--*,%."*%50'*$:*/'&%$
&$%!-":% !"*% 0"'(8*$% 12% 41."% $/,*$% 1&% ."*% ,*7-*./12% (*8/12% 0'#$*% '2% *-*0.(/0% &/*-,% &% .1% 4*
139
140 Chapter 3 Semiconductors
E
(b)
Figure 3.9 7'8%!"*%"#%F#20./12%)/."%21%'77-/*,%+1-.'8*%A17*2?0/(0#/.*,%.*(6/2'-$C:%728%!"*%71.*2./'-%,/$.(/?
4#./12%'-128%'2%'@/$%7*(7*2,/0#-'(%.1%."*%F#20./12:
*$.'4-/$"*,%'0(1$$%."*%(*8/12%/2%."*%,/(*0./12%/2,/0'.*,%/2%;/8:%K:T:%f*20*%'%71.*2./'-%,/&&*(*20*
(*$#-.$%'0(1$$%."*%,*7-*./12%(*8/123%)/."%."*%#%$/,*%'.%'%71$/./+*%+1-.'8*%(*-'./+*%.1%."*%"%$/,*3%'$
$"1)2%/2%;/8:%K:TA4C:%!"#$%."*%(*$#-./28%*-*0.(/0%&/*-,%1771$*$%."*%,/&&#$/12%1&%"1-*$%/2.1%."*%#
(*8/12%'2,%*-*0.(12$%/2.1%."*%"%(*8/12:%>2%&'0.3%."*%+1-.'8*%,(17%'0(1$$%."*%,*7-*./12%(*8/12%'0.$
'$%'%2'&&!$&%."'.%"'$%.1%4*%1+*(016*%&1(%"1-*$%.1%,/&&#$*%/2.1%."*%#%(*8/12%'2,%*-*0.(12$%.1%,/&?
&#$*%/2.1%."*%" (*8/12:%!"*%-'(8*(%."*%4'((/*(%+1-.'8*3%."*%$6'--*(%."*%2#64*(%1&%0'((/*($%."'.
)/--%4*%'4-*%.1%1+*(016*%."*%4'((/*(%'2,%"*20*%."*%-1)*(%."*%6'82/.#,*%1&%,/&&#$/12%0#((*2.:
!"#$%/.%/$%."*%'77*'('20*%1&%."*%4'((/*(%+1-.'8*%=U%."'.%-/6/.$%."*%0'((/*(%,/&&#$/12%7(10*$$:%>.
&1--1)$%."'.%."*%,/&&#$/12%0#((*2.%62%,*7*2,$%$.(128-5%12%."*%+1-.'8*%,(17%=U%'0(1$$%."*%,*7-*?
./12%(*8/12:
The Drift Current IS and Equilibrium >2% ',,/./12% .1% ."*% 0#((*2.% 016712*2.% 62% ,#*% .1
6'F1(/.5?0'((/*(%,/&&#$/123%'%016712*2.%,#*%.1%6/21(/.5%0'((/*(%,(/&.%*@/$.$%'0(1$$%."*%F#20?
./12:%J7*0/&/0'--53%$16*%1&%."*%."*(6'--5%8*2*('.*,%"1-*$%/2%."*%#%6'.*(/'-%61+*%.1)'(,%."*
F#20./12%'2,%(*'0"%."*%*,8*%1&%."*%,*7-*./12%(*8/12:%!"*(*3%."*5%*@7*(/*20*%."*%*-*0.(/0%&/*-,
/2%."*%,*7-*./12%(*8/123%)"/0"%$)**7$%."*6%'0(1$$%."'.%(*8/12%/2.1%."*%"%$/,*:%J/6/-'(-53%$16*
1&%."*%6/21(/.5%."*(6'--5%8*2*('.*,%*-*0.(12$%/2%."*%"%6'.*(/'-%61+*%.1%."*%*,8*%1&%."*%,*7-*?
./12%(*8/12%'2,%8*.%$)*7.%45%."*%*-*0.(/0%&/*-,%/2%."*%,*7-*./12%(*8/12%'0(1$$%."'.%(*8/12%/2.1
."*%#%$/,*:%!"*$*%.)1%0#((*2.%016712*2.$j*-*0.(12$%61+*,%45%,(/&.%&(16%"%.1%#%'2,%"1-*$
61+*,%45%,(/&.%&(16%#%.1%"j',,%.18*."*(%.1%&1(6%."*%,(/&.%0#((*2.%6A 3%)"1$*%,/(*0./12%/$%&(16
."*%#%$/,*%.1%."*%"%$/,*%1&%."*%F#20./123%'$%/2,/0'.*,%/2%;/8:%K:T:%J/20*%."*%0#((*2.%6A%/$%0'((/*,
3.5 The pn Junction with an Applied Voltage 141
45% ."*(6'--5% 8*2*('.*,% 6/21(/.5% 0'((/*($3% /.$% +'-#*% /$% $.(128-5% ,*7*2,*2.% 12% .*67*('.#(*L
"1)*+*(3%/.%/$%/2,*7*2,*2.%1&%."*%+'-#*%1&%."*%,*7-*./12?-'5*(%+1-.'8*%=U:%!"/$%/$%,#*%.1%."*
&'0.%."'.%."*%,(/&.%0#((*2.%/$%,*.*(6/2*,%45%."*%2#64*(%1&%6/21(/.5%0'((/*($%."'.%6'9*%/.%.1%."*
*,8*%1&%."*%,*7-*./12%(*8/12L%'25%6/21(/.5%0'((/*($%."'.%6'2'8*%.1%8*.%.1%."*%*,8*%1&%."*%,*7-*?
./12%(*8/12%)/--%4*%$)*7.%'0(1$$%45%&%/((*$7*0./+*%1&%."*%+'-#*%1&%&%1(3%01((*$712,/28-53%1&%=U:
i2,*(%17*2?0/(0#/.%012,/./12$%A;/8:%K:TC%21%*@.*(2'-%0#((*2.%*@/$.$L%."#$%."*%.)1%1771$/.*
0#((*2.$%'0(1$$%."*%F#20./12%6#$.%4*%*V#'-%/2%6'82/.#,*H
62 = 6A
B
!"/$%*V#/-/4(/#6%012,/./12 %/$%6'/2.'/2*,%45%."*%4'((/*(%+1-.'8*%=U:%!"#$3%/&%&1(%$16*%(*'$12%62
*@0**,$%6A 3%."*2%61(*%41#2,%0"'(8*%)/--%4*%#201+*(*,%12%41."%$/,*$%1&%."*%F#20./123%."*%,*7-*?
./12% -'5*(% )/--% )/,*23% '2,% ."*% +1-.'8*% '0(1$$% /.% A=U C% )/--% /20(*'$*:% !"/$% /2% .#(2% 0'#$*$% 62% .1
,*0(*'$*%#2./-%*V#/-/4(/#6%/$%'0"/*+*,%)/."%62%=%6A:%R2%."*%1."*(%"'2,3%/&%6A%*@0**,$%623%."*2%."*
'61#2.%1&%#201+*(*,%0"'(8*%)/--%,*0(*'$*3%."*%,*7-*./12%-'5*(%)/--%2'((1)3%'2,%."*%+1-.'8*
'0(1$$%/.%A=UC%)/--%,*0(*'$*:%!"/$%0'#$*$%62%.1%/20(*'$*%#2./-%*V#/-/4(/#6%/$%'0"/*+*,%)/."%62%=%6A:
The Junction Built-In Voltage \/."%21%*@.*(2'-%+1-.'8*%'77-/*,3%."*%4'((/*(%+1-.'8*%=U
'0(1$$%."*%"#%F#20./12%0'2%4*%$"1)2%.1%4*%8/+*2%45D
1 3 1 2
?
= U = = ) -2 ????????????
# +=
AK:==C
)"*(*% 13% '2,% 12% '(*% ."*% ,17/28% 0120*2.('./12$% 1&% ."*% "% $/,*% '2,% #% $/,*% 1&% ."*% F#20./123
(*$7*0./+*-5:% !"#$% =U% ,*7*2,$% 41."% 12% ,17/28% 0120*2.('./12$% '2,% 12% .*67*('.#(*:% >.% /$
921)2%'$%."*%6+"*#!-")2+!.#:!")1-.#'%$:%!57/0'--53%&1(%$/-/012%'.%(116%.*67*('.#(*3%=U%/$%/2
."*%('28*%1&%U:E%P%.1%U:T%P:
\"*2%."*%"#%F#20./12%.*(6/2'-$%'(*%-*&.%17*2?0/(0#/.*,3%."*%+1-.'8*%6*'$#(*,%4*.)**2
."*6%)/--%4*%X*(1:%!"'.%/$3%."*%+1-.'8*%=U%'0(1$$%."*%,*7-*./12%(*8/12%,-%0!#-/%'77*'(%4*.)**2
."*% F#20./12% .*(6/2'-$:% !"/$% /$% 4*0'#$*% 1&% ."*% 012.'0.% +1-.'8*$% *@/$./28% '.% ."*% 6*.'-?
$*6/012,#0.1(%F#20./12$%'.%."*%.*(6/2'-$3%)"/0"%01#2.*(%'2,%*@'0.-5%4'-'20*%."*%4'((/*(%+1-.?
'8*:%>&%."/$%)*(*%21.%."*%0'$*3%)*%)1#-,%"'+*%4**2%'4-*%.1%,(')%*2*(85%&(16%."*%/$1-'.*,%"#
F#20./123%)"/0"%)1#-,%0-*'(-5%+/1-'.*%."*%7(/20/7-*%1&%012$*(+'./12%1&%*2*(85:
Width of and Charge Stored in the Depletion Region ;/8#(*% K:SU% 7(1+/,*$% &#(?
."*(%/--#$.('./12%1&%."*%$/.#'./12%."'.%14.'/2$%/2%."*%"#%F#20./12%)"*2%."*%F#20./12%/$%/2%*V#/?
-/4(/#6:%>2%;/8:%K:SUA'C%)*%$"1)%'%F#20./12%/2%)"/0"% 1 3 > 1 23%'%.57/0'-%$/.#'./12%/2%7('0./0*:
!"/$%/$%41(2*%1#.%45%."*%0'((/*(%0120*2.('./12%12%41."%$/,*$%1&%."*%F#20./123%'$%$"1)2%/2%;/8
K:SUA4C:%a1.*%."'.%)*%"'+*%,*21.*,%."*%6/21(/.5%0'((/*(%0120*2.('./12$%/2%41."%$/,*$%45% # "U
'2,%"#U3%)/."%."*%',,/./12'-%$#4$0(/7.%ZU[%$/82/&5/28%*V#/-/4(/#6%A/:*:3%4*&1(*%*@.*(2'-%+1-.?
'8*$% '(*% '77-/*,% '$% )/--% 4*% $**2% /2% ."*% 2*@.% $*0./12C:% R4$*(+*% ."'.% ."*% ,*7-*./12% (*8/12
*@.*2,$%/2%41."%."*%"%'2,%#%6'.*(/'-$%'2,%."'.%*V#'-%'61#2.$%1&%0"'(8*%*@/$.%12%41."%$/,*$
A B l %'2,% B " /2%;/8:%K:SU0C:%f1)*+*(3%$/20*%#$#'--5%#2*V#'-%,17/28$% 13%'2,% 12%'(*%#$*,3%'$
/2%."*%0'$*%/--#$.('.*,%/2%;/8:%K:SU3%."*%)/,."%1&%."*%,*7-*./12%-'5*(%)/--%21.%4*%."*%$'6*%12
."*%.)1%$/,*$:%_'."*(3%.1%#201+*(%."*%$'6*%'61#2.%1&%0"'(8*3%."*%,*7-*./12%-'5*(%)/--%*@.*2,
,**7*(% /2.1% ."*% 61(*% -/8".-5% ,17*,% 6'.*(/'-:% J7*0/&/0'--53% /&% )*% ,*21.*% ."*% )/,."% 1&% ."*
B
>2%&'0.3%/2%*V#/-/4(#6%."*%*V#'-/.5%1&%,(/&.%'2,%,/&&#$/12%0#((*2.$%'77-/*$%21.%F#$.%.1%."*%.1.'-%0#((*2.$%4#.
'-$1%.1%."*/(%/2,/+/,#'-%016712*2.$:%!"'.%/$3%."*%"1-*%,(/&.%0#((*2.%6#$.%*V#'-%."*%"1-*%,/&&#$/12%0#((*2.
'2,3%$/6/-'(-53%."*%*-*0.(12%,(/&.%0#((*2.%6#$.%*V#'-%."*%*-*0.(12%,/&&#$/12%0#((*2.:
D
!"*%,*(/+'./12%1&%."/$%&1(6#-'%'2,%1&%'%2#64*(%1&%1."*($%/2%."/$%0"'7.*(%0'2%4*%&1#2,%/2%.*@.4119$%,*'-?
/28%)/."%,*+/0*$3%$#0"%'$%."'.%45%J.(**.6'2%'2,%M'22*(F**%A$**%."*%(*',/28%-/$.%/2%G77*2,/@%^C:
142 Chapter 3 Semiconductors
ID
IS
"
"
"
"
"
"
"
"
"
"
"
"
p
"
"
"
"
"
"
!
"
"
"
"
"
"
!
!
!
!
"
"
! ! ! !
"
"
! ! ! !
! !n! !
"
"
! ! ! !
! ! ! !
!
!xp
xn
0
E
(a)
np0 $
Carrier concentration
pp $ NA
ni2
nn $ ND
W
ni2
ND
pn0 $
NA
xn
0
(b)
Change
density
!xp
x
" Q" " $ Aq ND xn
xn
!xp
x
" Q! " $ Aq NAxp
W
Voltage
(c)
!xp
0
(d)
VO
xn
Figure 3.10 7'8%G%"#%F#20./12%)/."%."*%.*(6/2'-$%17*2%0/(0#/.*,:% 728%<'((/*(%0120*2.('./12$L%21.*%."'.
13 # 12:% 7*8% !"*% 0"'(8*% $.1(*,% /2% 41."% $/,*$% 1&% ."*% ,*7-*./12% (*8/12L% B9% e% mBlm% e% mB]m:% 7(8)!"*% 4#/-.?/2
+1-.'8*%=U:
3.5 The pn Junction with an Applied Voltage 143
,*7-*./12%(*8/12%/2%."*%"%$/,*%45% 5 " %'2,%/2%."*%#%$/,*%45%5#3%)*%0'2%*@7(*$$%."*%6'82/.#,*%1&
."*%0"'(8*%12%."*%#%$/,*%1&%."*%F#20./12%'$
AK:=KC
B l % ! $35 # 1 2
'2,%."'.%12%."*%"%$/,*%1&%."*%F#20./12%'$
AK:=BC
B " % ! $35 " 1 3
)"*(*%3%/$%."*%0(1$$?$*0./12'-%'(*'%1&%."*%F#20./12%/2%."*%7-'2*%7*(7*2,/0#-'(%.1%."*%7'8*:
!"*%0"'(8*%*V#'-/.5%012,/./12%0'2%21)%4*%)(/..*2%'$
$35 # 1 2 % ! $35 " 1 3
)"/0"%0'2%4*%(*'(('28*,%.1%5/*-,
5#
1
???? % ! ??????3?
5" 12
AK:=DC
>2%'0.#'-%7('0./0*3%/.%/$%#$#'-%&1(%12*%$/,*%1&%."*%F#20./12%.1%4*%6#0"%61(*%"*'+/-5%,17*,%."'2
."*% 1."*(3% )/."% ."*% (*$#-.% ."'.% ."*% ,*7-*./12% (*8/12% *@/$.$% '-61$.% *2./(*-5% 12% 12*% $/,*% A."*
-/8".-5%,17*,%$/,*C:
!"*%)/,."%<%1&%."*%,*7-*./12%-'5*(%0'2%4*%$"1)2%.1%4*%8/+*2%45%
<% ! 5 # # 5 " % !
=ε 0 S
S? =
??????? ?????? # ??????
$ 13 12 U
AK:=EC
" SB
)"*(*% ε 0 % /$% ."*% *-*0.(/0'-% 7*(6/../+/.5% 1&% $/-/012 ! SS:bε U % ! SS:b × c:cD × SU ;`06 e
" S=
S:UB × SU ;`06:%!57/0'--5%<%/$%/2%."*%('28*%U:S%µ6%.1%S%µ6:%OV$: AK:=DC%'2,%AK:=EC%0'2%4*
#$*,%.1%14.'/2% 5#%'2,% 5"%/2%.*(6$%1&%<%'$%
13
?
5 # % ! < ???????????????????
13 # 12
AK:=bC
12
?
5 " % ! < ???????????????????
13 # 12
AK:=cC
!"*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&%."*%,*7-*./12%(*8/12%0'2%4*%*@7(*$$*,%/2%.*(6$%1&%<%45
#./-/X/28%OV$:%AK:=KC%'2,%AK:=bC%.1%14.'/2
B9 % ! Bl % ! B]
13 12 ? <
B 9 % ! 3$ ???????????????????
13 # 12
AK:=TC
;/2'--53%)*%0'2%$#4$./.#.*%&1(%<%&(16%OV:%AK:=EC%.1%14.'/2%
13 12 ? =
B 9 % ! 3 =ε 0 $ ???????????????????
13 # 12 U
!"*$*%*@7(*$$/12$%&1(% B 9 %)/--%7(1+*%#$*&#-%/2%$#4$*V#*2.%$*0./12$:
AK:KUC
144 Chapter 3 Semiconductors
Example 3.5
<12$/,*(%'%"#%F#20./12%/2%*V#/-/4(/#6%'.%(116%.*67*('.#(*%A)%e%KUU%YC%&1(%)"/0"%."*%,17/28%0120*2?
Sc
K
SE
K
.('./12$%'(*% 1 3 % ! SU ⁄ 06 %'2,% 1 2 % ! SU ⁄ 06 %'2,%."*%0(1$$?$*0./12'-%'(*'%3%e%SU]B%06=:%<'-0#-'.*
SU
K
"" 3% #"U3% ## 3% "#U3% =U3%<3% 5#3% 5" 3%'2,% B 9 :%i$*% # + % ! S:D × SU ⁄ 06 :
Solution
Sc
" " ! 1 3 ! SU %06
=
"K
=
SU =
#
#
( S:D × SU )
=
"K
# "U % ! ????+? ! ?????+? ! ????????????????????????????
! =:=D × SU %06
Sc
"" 13
SU
SE
"K
# # ! 1 2 % ! SU %06
=
=
SU =
#
#
( S:D × SU )
? % ! =:=D × SU B %06 "K
" #U % ! ????+? ! ??????+? % ! ??????????????????????????????
SE
## 12
SU
!1%&/2,% = U %)*%#$*%OV:%AK:==C3
1 3 1 2
?
=C ! = ) -2 ?????????????
=
#+
)"*(*
"D
() c:E= × SU × KUU% ( *P )
= ) % ! ?????? ! ???????????????????????????????????????????????????????
?
$
$
(*)
"K
! =D:T × SU %P
!"#$3
Sc
SE
" K SU × SU ?
= U % ! =D:T × SU -2 ??????????????????????????
=U
=:=D × SU
! U:cSB%P
!1%,*.*(6/2*%<%)*%#$*%OV:%AK:=ECH
" S=
= × S:UB × SU S
S ? × U:cSB
?????????????????????????????????????
? ?????????? # ?????????
" ST
Sc
SE
S:E × SU
SU
SU
"D
! K:=b × SU %06 ! U:K=b %µ6
<!
!1%,*.*(6/2*% 5 # %'2,% 5 " %)*%#$*%OV:%AK:=bC%'2,%AK:=cC3%(*$7*0./+*-5H
13
?
5 # % ! < ???????????????????
13 # 12
Sc
SU
? ! U:K=B %µ6
! U:K=b ??????????????????????????
Sc
SE
SU # SU
12
?
5 " % ! < ???????????????????
13 # 12
SE
SU
? ! U:UUK%µ6
! U:K=b ??????????????????????????
Sc
SE
SU # SU
;/2'--53%.1%,*.*(6/2*%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&%."*%,*7-*./12%(*8/123%)*%#$*%OV:%AK:=TC
B 9 % ! SU
"B
× S:E × SU
! D:Sc × SU
" S=
" ST SU
Sc
SE
× SU ? × U:K=b × SU "B
??????????????????????????
Sc
SE
SU # SU
%<%e%D:Sc%7<
3.5 The pn Junction with an Applied Voltage 145
EXERCISES
3.7 J"1)%."'.
13 12 =
S $
? <
= U % ! ??? ???? ???????????????????
= ε0 13 # 12
3.8 J"1)%."'.%&1(%'%"#%F#20./12%/2%)"/0"%."*%"%$/,*%/$%6#0"%61(*%"*'+/-5%,17*,%."'2%."*%#!$/,*3%A/:*:
l
1 3 # 1 2 C3%(*&*((*,%.1%'$%'% " # %,/1,*3%OV$:%AK:=EC3%AK:=bC3%AK:=cC3%AK:=TC3%'2,%AK:KUC%0'2%4*%$/67-/?
&/*,%'$%&1--1)$H
=ε
< ! ?????????0? = U
AK:=E′C
$1 2
5# ! <
AK:=b′C
5" ! ( < ⁄ ( 13 ⁄ 12 ) )
AK:=c′C
B 9 ! 3$1 2 <
AK:=T′C
B 9 ! 3 =ε 0 $1 2 = U
AK:KU′C
3.9 >&%/2%."*%&'4(/0'./12%1&%."*%"#%F#20./12%/2%O@'67-*%K:D3%/.%/$%(*V#/(*,%.1%/20(*'$*%."*%6/21(/.5%0'((/*(
0120*2.('./12%/2%."*%#%(*8/12%45%'%&'0.1(%1&%=3%)"'.%6#$.%4*%,12*h
Ans. ./012& 1 2 &34&5&6578/2&/6&*9
3.5 The pn Junction with an Applied Voltage
f'+/28%$.#,/*,%."*%17*2?0/(0#/.*,%"#%F#20./12%/2%,*.'/-3%)*%'(*%21)%(*',5%.1%'77-5%'%,0%+1-.?
'8*%4*.)**2%/.$%.)1%.*(6/2'-$%.1%&/2,%/.$%*-*0.(/0'-%012,#0./12%7(17*(./*$:%>&%."*%+1-.'8*%/$
'77-/*,%$1%."'.%."*%"%$/,*%/$%6',*%61(*%71$/./+*%."'2%."*%#%$/,*3%/.%/$%(*&*((*,%.1%'$%'%&1()'(,?
4/'$E%+1-.'8*:%<12+*($*-53%/&%1#(%'77-/*,%,0%+1-.'8*%/$%$#0"%."'.%/.%6'9*$%."*%#%$/,*%61(*%71$?
/./+*%."'2%."*%"%$/,*3%/.%/$%$'/,%.1%4*%'%(*+*($*?4/'$%+1-.'8*:%G$%)/--%4*%$**23%."*%"#%F#20./12
*@"/4/.$%+'$.-5%,/&&*(*2.%012,#0./12%7(17*(./*$%/2%/.$%&1()'(,%'2,%(*+*($*%,/(*0./12$:
R#(%7-'2%/$%'$%&1--1)$:%\*%4*8/2%45%'%$/67-*%V#'-/.'./+*%,*$0(/7./12%/2%J*0./12%K:D:S
'2,% ."*2% 012$/,*(% '2% '2'-5./0'-% ,*$0(/7./12% 1&% ."*% + " v % 0"'('0.*(/$./0% 1&% ."*% F#20./12% /2
J*0./12%K:D:=:
3.5.1 Qualitative Description of Junction Operation
;/8#(*%K:SS%$"1)$%."*%"#%F#20./12%#2,*(%."(**%,/&&*(*2.%012,/./12$H%A'C%."*%17*2?0/(0#/.%1(
*V#/-/4(/#6%012,/./12%$.#,/*,%/2%."*%7(*+/1#$%$*0./12L%A4C%."*%(*+*($*?4/'$%012,/./123%)"*(*%'
,0%+1-.'8*%= E%/$%'77-/*,L%'2,%A0C%."*%&1()'(,?4/'$%012,/./12%)"*(*%'%,0%+1-.'8*%= F %/$%'77-/*,:
R4$*(+*%."'.%/2%."*%17*2?0/(0#/.%0'$*3%'%4'((/*(%+1-.'8*%= U%,*+*-17$3%6'9/28%#!61(*%71$/./+*
."'2%"3%'2,%-/6/./28%."*%,/&&#$/12%0#((*2.% 6 2%.1%'%+'-#*%*@'0.-5%*V#'-%.1%."*%,(/&.%0#((*2.% 6 A 3
E
;1(%."*%./6*%4*/283%)*%.'9*%."*%.*(6%D+.0%.1%(*&*(%$/67-5%.1%."*%'77-/0'./12%1&%'%,0%+1-.'8*:%\*%)/--%$**
/2%-'.*(%0"'7.*($%."'.%/.%"'$%'%,**7*(%6*'2/28%/2%."*%,*$/82%1&%*-*0.(12/0%0/(0#/.$:
(a) Open-circuit
(Equilibrium)
n
(b) Reverse Bias
(V0 " VR)
p
IS
ID
Figure 3.11 !"*%"#%F#20./12%/2H)7'8)*V#/-/4(/#6L)728%(*+*($*%4/'$L%7*8)&1()'(,%4/'$:%
V0
p
ID
IS
VR
n
p
IS
(c) Forward Bias
(V0 ! VF)
ID
VF
n
146 Chapter 3 Semiconductors
3.5 The pn Junction with an Applied Voltage
."#$%(*$#-./28%/2%'%X*(1%0#((*2.%'.%."*%F#20./12%.*(6/2'-$3%'$%$"1#-,%4*%."*%0'$*%$/20*%."*%.*(?
6/2'-$%'(*%17*2%0/(0#/.*,:%G-$13%'$%6*2./12*,%7(*+/1#$-53%."*%4'((/*(%+1-.'8*% = U3%."1#8"%/.
*$.'4-/$"*$%."*%0#((*2.%*V#/-/4(/#6%'0(1$$%."*%F#20./123%,1*$%#-/%/2%&'0.%'77*'(%4*.)**2%."*
F#20./12%.*(6/2'-$:
<12$/,*(%21)%."*%(*+*($*?4/'$%0'$*%/2%A4C:%!"*%*@.*(2'--5%'77-/*,%(*+*($*?4/'$%+1-.'8*
= E %/$%/2%."*%,/(*0./12%.1%',,%.1%."*%4'((/*(%+1-.'8*3%'2,%/.%,1*$3%."#$%/20(*'$/28%."*%*&&*0./+*
4'((/*(%+1-.'8*%.1% ( = U # = E ) %'$%$"1)2:%!"/$%(*,#0*$%."*%2#64*(%1&%"1-*$%."'.%,/&&#$*%/2.1%."*
#%(*8/12%'2,%."*%2#64*(%1&%*-*0.(12$%."'.%,/&&#$*%/2.1%."*%"%(*8/12:%!"*%*2,%(*$#-.%/$%."'.%."*
,/&&#$/12%0#((*2.% 6 2 %/$%,('6'./0'--5%(*,#0*,:%G$%)/--%4*%$**2%$"1(.-53%'%(*+*($*?4/'$%+1-.'8*%1&
'%+1-.%1(%$1%/$%$#&&/0/*2.%.1%0'#$*% 6 2 ! U3%'2,%."*%0#((*2.%'0(1$$%."*%F#20./12%'2,%."(1#8"%."*
*@.*(2'-%0/(0#/.%)/--%4*%*V#'-%.1% 6 A :%_*0'--/28%."'.% 6 A %/$%."*%0#((*2.%,#*%.1%."*%,(/&.%'0(1$$%."*
,*7-*./12%(*8/12%1&%."*%."*(6'--5%8*2*('.*,%6/21(/.5%0'((/*($3%)*%*@7*0.% 6 A %.1%4*%+*(5%$6'-'2,%.1%4*%$.(128-5%,*7*2,*2.%12%.*67*('.#(*:%\*%)/--%$"1)%."/$%.1%4*%."*%0'$*%+*(5%$"1(.-5:
\*% ."#$% 0120-#,*% ."'.% /2% ."*% (*+*($*% ,/(*0./123% ."*% "#% F#20./12% 012,#0.$% '% +*(5% $6'--% '2,
'-61$.?012$.'2.%0#((*2.%*V#'-%.1% 6 A :
M*&1(*%-*'+/28%."*%(*+*($*?4/'$%0'$*3%14$*(+*%."'.%."*%/20(*'$*%/2%4'((/*(%+1-.'8*%)/--%4*
'00167'2/*,%45%'%01((*$712,/28%/20(*'$*%/2%."*%$.1(*,%#201+*(*,%0"'(8*%12%41."%$/,*$%1&%."*
,*7-*./12%(*8/12:%!"/$%/2%.#(2%6*'2$%'%)/,*(%,*7-*./12%(*8/123%2**,*,%.1%#201+*(%."*%',,/./12'0"'(8*%(*V#/(*,%.1%$#771(.%."*%-'(8*(%4'((/*(%+1-.'8*% ( = U # = E ):%G2'-5./0'--53%."*$*%(*$#-.$%0'2
4*%14.'/2*,%*'$/-5%45%'%$/67-*%*@.*2$/12%1&%."*%(*$#-.$%1&%."*%*V#/-/4(/#6%0'$*:%!"#$%."*%)/,."
1&%."*%,*7-*./12%(*8/12%0'2%4*%14.'/2*,%45%(*7-'0/28% = U %/2%OV:%AK:=EC%45% ( = U # = E )3
<% ! 5 # # 5 " % !
S S
=ε 0 ?????
??????? ? # ??????? ( = U # = E )
$ 13 12
AK:KSC
'2,%."*%6'82/.#,*%1&%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&%."*%,*7-*./12%(*8/12%0'2%4*%,*.*(?
6/2*,%45%(*7-'0/28% = U %/2%OV:%AK:KUC%45% ( = U # = E )3
13 12 ? ( =U # =E )
B 9 % ! 3 =ε 0 $ ???????????????????
13 # 12
AK:K=C
\*%2*@.%012$/,*(%."*%&1()'(,?4/'$%0'$*%$"1)2%/2%;/8:%K:SSA0C:%f*(*%."*%'77-/*,%+1-.'8*%=F %/$
/2%."*%,/(*0./12%."'.%$#4.('0.$%&(16%."*%4#/-.?/2%+1-.'8*% =U3%(*$#-./28%/2%'%(*,#0*,%4'((/*(%+1-.?
'8*% ( =U " =F ) %'0(1$$%."*%,*7-*./12%(*8/12:%!"/$%(*,#0*,%4'((/*(%+1-.'8*%)/--%4*%'00167'2/*,
45% (*,#0*,% ,*7-*./12?(*8/12% 0"'(8*% '2,% 01((*$712,/28-5% 2'((1)*(% ,*7-*./12?(*8/12% )/,."
<:%k1$.%/671(.'2.-53%."*%-1)*(/28%1&%."*%4'((/*(%+1-.'8*%)/--%*2'4-*%61(*%"1-*$%.1%,/&&#$*
&(16% "% .1% #! '2,% 61(*% *-*0.(12$% .1% ,/&&#$*% &(16% #% .1% ":% !"#$% ."*% ,/&&#$/12% 0#((*2.% 6 2
/20(*'$*$%$#4$.'2./'--5%'2,3%'$%)/--%4*%$**2%$"1(.-53%0'2%4*016*%6'25%1(,*($%1&%6'82/.#,*
-'(8*(%."'2%."*%,(/&.%0#((*2.% 6 A : %!"*%0#((*2.%6%/2%."*%*@.*(2'-%0/(0#/.%/$%1&%01#($*%."*%,/&&*(*20*
4*.)**2% 6 2 %'2,% 6 A 3
6%% ! 6 2 " 6 A
'2,%/.%&-1)$%/2%."*%&1()'(,%,/(*0./12%1&%."*%F#20./123%&(16%"%.1%#:%\*%."#$%0120-#,*%."'.%."*
"#%F#20./12%0'2%012,#0.%'%$#4$.'2./'-%0#((*2.%/2%."*%&1()'(,?4/'$%(*8/12%'2,%."'.%0#((*2.%/$
61$.-5%'%,/&&#$/12%0#((*2.%)"1$*%+'-#*%/$%,*.*(6/2*,%45%."*%&1()'(,?4/'$%+1-.'8*% =F :
3.5.2 The Current–Voltage Relationship of the Junction
\*%'(*%21)%(*',5%.1%&/2,%'2%'2'-5./0'-%*@7(*$$/12%."'.%,*$0(/4*$%."*%0#((*2.]+1-.'8*%(*-'?
./12$"/7% 1&% ."*% "#% F#20./12:% >2% ."*% &1--1)/28% )*% 012$/,*(% '% F#20./12% 17*('./28% )/."% '
147
148 Chapter 3 Semiconductors
&1()'(,%'77-/*,%+1-.'8*%=!'2,%,*(/+*%'2%*@7(*$$/12%&1(%."*%0#((*2.%6!."'.%&-1)$%/2%."*%&1(?
)'(,%,/(*0./12%A&(16%"%.1%#C:%f1)*+*(3%1#(%,*(/+'./12%/$%8*2*('-%'2,%)/--%4*%$**2%.1%5/*-,
."*%(*+*($*%0#((*2.%)"*2%."*%'77-/*,%+1-.'8*%=%/$%6',*%2*8'./+*:
;(16%."*%V#'-/.'./+*%,*$0(/7./12%'41+*%)*%921)%."'.%'%&1()'(,?4/'$%+1-.'8*%=%$#4.('0.$
&(16%."*%4#/-.?/2%+1-.'8*%= U 3%."#$%(*$#-./28%/2%'%-1)*(%4'((/*(%+1-.'8*% ( = U " = ):%!"*%-1)*(*,
4'((/*(%/2%.#(2%6'9*$%/.%71$$/4-*%&1(%'%8(*'.*(%2#64*(%1&%"1-*$%.1%1+*(016*%."*%4'((/*(%'2,%,/&?
&#$*%/2.1%."*%#%(*8/12:%G%$/6/-'(%$.'.*6*2.%0'2%4*%6',*%'41#.%*-*0.(12$%&(16%."*%#!(*8/12%,/&?
&#$/28%/2.1%."*%"%(*8/12:%
Q*.%#$%21)%012$/,*(%."*%"1-*$%/2F*0.*,%/2.1%."*%#%(*8/12:%!"*%0120*2.('./12%1&%"1-*$%/2
."*%#%(*8/12%'.%."*%*,8*%1&%."*%,*7-*./12%(*8/12%)/--%/20(*'$*%012$/,*('4-5:%>2%&'0.3%'2%/671(?
.'2.%(*$#-.%&(16%,*+/0*%7"5$/0$%$"1)$%."'.%."*%$.*',5?$.'.*%0120*2.('./12%'.%."*%*,8*%1&%."*
,*7-*./12%(*8/12%)/--%4*%
" # ( 5 # )% ! " #U %
= ⁄ =)
AK:KKC
!"'.%/$3%."*%0120*2.('./12%1&%."*%6/21(/.5%"1-*$%/20(*'$*$%&(16%."*%*V#/-/4(/#6%+'-#*%1&% " #U
A$**%;/8:%K:SUC%.1%."*%6#0"%-'(8*(%+'-#*%,*.*(6/2*,%45%."*%+'-#*%1&%=3%8/+*2%45%OV:%AK:KKC:
\*%,*$0(/4*%."/$%$/.#'./12%'$%&1--1)$H%!"*%&1()'(,?4/'$%+1-.'8*!=%(*$#-.$%/2%'2%$;*$55
*-"*$"#&'#!-"%1&%6/21(/.5%"1-*$%'.% 5%%! 5 # 3 %8/+*2%45
O@0*$$%0120*2.('./12%e% " #U %
%
= ⁄ =)
! " #U ( %
" " #U
= ⁄ =)
" S)
AK:KBC
!"*%/20(*'$*%/2%6/21(/.5%0'((/*(%0120*2.('./12%/2%OV$:%AK:KKC%'2,%AK:KBC%100#($%'.%."*%*,8*%1&
."*%,*7-*./12%(*8/12% ( 5% ! 5 # ):%G$%."*%/2F*0.*,%"1-*$%,/&&#$*%/2.1%."*%#%6'.*(/'-3%$16*%)/-(*0164/2*%)/."%."*%6'F1(/.5%*-*0.(12$%'2,%,/$'77*'(:%!"#$3%."*%*@0*$$%"1-*%0120*2.('./12
)/--%,*0'5%*@712*2./'--5%)/."%,/$.'20*:%G$%'%(*$#-.3%/2%."*%.1.'-%"1-*%0120*2.('./12%/2%."*%#
6'.*(/'-%)/--%4*%8/+*2%45%
" # ( 5 )% ! " #U # ( O@0*$$%0120*2.('./12 )%
"( 5 " 5# ) ⁄ ;"
J#4$./.#./28%&1(%."*%ZO@0*$$%0120*2.('./12[%&(16%OV:%AK:KBC%8/+*$
" # ( 5 ) ! " #U # " #U ( %
= ⁄ =)
" S )%
"( 5 " 5# ) ⁄ ;"
AK:KDC
!"*%*@712*2./'-%,*0'5%/$%0"'('0.*(/X*,%45%."*%012$.'2.%;"3%)"/0"%/$%0'--*,%."*%(!33+5!-").$"%#/%1&
"1-*$%/2%."*%#%6'.*(/'-:%!"*%$6'--*(%."*%+'-#*%1&%;"3%."*%&'$.*(%."*%/2F*0.*,%"1-*$%)/--%(*0164/2*
)/."%."*%6'F1(/.5%*-*0.(12$3%(*$#-./28%/2%'%$.**7*(%,*0'5%1&%6/21(/.5%0'((/*(%0120*2.('./12:
;/8#(*%K:S=%$"1)$%."*%$.*',5?$.'.*%6/21(/.5%0'((/*(%0120*2.('./12%7(1&/-*$%12%41."%$/,*$%1&%'%"#
F#20./12%/2%)"/0"% 1 3 # 1 2 :%Q*.W$%$.'5%'%-/..-*%-128*(%)/."%."*%,/&&#$/12%1&%"1-*$%/2.1%."*%#!(*8/12:
a1.*%."'.%."*%$"',*,%(*8/12%#2,*(%."*%*@712*2./'-%(*7(*$*2.$%."*%*@0*$$%6/21(/.5%0'((/*($%A"1-*$C:
;(16%1#(%$.#,5%1&%,/&&#$/12%/2%J*0./12%K:K3%)*%921)%."'.%."*%*$.'4-/$"6*2.%1&%'%0'((/*(%0120*2.('?
./12%7(1&/-*%$#0"%'$%."'.%/2%;/8:%K:S=%/$%*$$*2./'-%.1%$#771(.%'%$.*',5?$.'.*%,/&&#$/12%0#((*2.:%>2%&'0.3
)*%0'2%21)%&/2,%."*%+'-#*%1&%."*%"1-*],/&&#$/12%0#((*2.%,*2$/.5%45%'77-5/28%OV:%AK:STC3
," # ( 5 )
?
9 " ( 5 )% ! " $2 " ???????????????
,5
J#4$./.#./28%&1(% " # ( 5 ) %&(16%OV:%AK:KDC%8/+*$
2"
= ⁄ =)
"( 5 " 5# ) ⁄ ;:
9 " ( 5 )% ! $ ?????? " #U ( %
" S )%
;:
AK:KEC
3.5 The pn Junction with an Applied Voltage
pn , np
p region
Depletion
region
pn (xn)
n region
Excess
concentration
pn (x)
np (!xp)
np(x)
pn0
Thermal equilibrium
value
np0
!xp 0
xn
x
Figure 3.12 k/21(/.5?0'((/*(%,/$.(/4#./12%/2%'%&1()'(,?4/'$*,%"#%F#20./12:%>.%/$%'$$#6*,%."'.%."*%"%(*8/12%
/$%61(*%"*'+/-5%,17*,%."'2%."*%#%(*8/12L%13%#%12:
G$%*@7*0.*,3% 9 " ( 5 ) %/$%"/8"*$.%'.% 5 ! 5 #3
2
= ⁄ =)
9 " ( 5 # ) ! $ ?????"? " #U ( %
" S)
;"
AK:KbC
'2,%,*0'5$%*@712*2./'--5%&1(% 5 > 5 # 3%'$%."*%6/21(/.5%"1-*$%(*0164/2*%)/."%."*%6'F1(/.5%*-*0?
.(12$:%!"/$%(*0164/2'./123%"1)*+*(3%6*'2$%."'.%."*%6'F1(/.5%*-*0.(12$%)/--%"'+*%.1%4*%(*7-*2?
/$"*,% 45% '% 0#((*2.% ."'.% /2F*0.$% *-*0.(12$% &(16% ."*% *@.*(2'-% 0/(0#/.% /2.1% ."*% #% (*8/12% 1&% ."*
F#20./12:%!"/$%-'..*(%0#((*2.%016712*2.%"'$%."*%$'6*%,/(*0./12%'$%."*%"1-*%0#((*2.%A4*0'#$*
*-*0.(12$%61+/28%&(16%(/8".%.1%-*&.%8/+*%(/$*%.1%0#((*2.%/2%."*%,/(*0./12%&(16%-*&.%.1%(/8".C:%>.
&1--1)$%."'.%'$% 9 " ( 5 ) %,*0(*'$*$3%."*%*-*0.(12%0#((*2.%016712*2.%/20(*'$*$%45%*@'0.-5%."*%$'6*
'61#2.3%6'9/28%."*%.1.'-%0#((*2.%/2%."*!#%6'.*(/'-%012$.'2.%'.%."*%+'-#*%8/+*2%45%OV:%AK:KbC:
G2%*@'0.-5%7'('--*-%,*+*-176*2.%0'2%4*%'77-/*,%.1%."*%*-*0.(12$%."'.%'(*%/2F*0.*,%&(16%."*%#
.1% ."*% "% (*8/123% (*$#-./28% /2% '2% *-*0.(12% ,/&&#$/12% 0#((*2.% 8/+*2% 45% '% $/67-*% ','7.'./12% 1&% OV:
AK:KbC3
2
= ⁄ =)
AK:KcC
" S)
9 # ( " 5 " ) ! $ ?????#? # "U ( %
;#
a1)3%'-."1#8"%."*%0#((*2.$%/2%OV$:%AK:KbC%'2,%AK:KcC%'(*%&1#2,%'.%."*%.)1%*,8*$%1&%."*%,*7-*?
./12%(*8/123%."*/(%+'-#*$%,1%21.%0"'28*%/2%."*%,*7-*./12%(*8/12:%!"#$%)*%0'2%,(17%."*%-10'./12
,*$0(/7.1($% ( 5 # )3% ( " 5 " )3%',,%."*%.)1%0#((*2.%,*2$/./*$3%'2,%6#-./7-5%45%."*%F#20./12%'(*'%3%.1
14.'/2%."*%.1.'-%0#((*2.%6!'$%
6 ! 3 ( 9" # 9# )
2
2
= ⁄ =)
" S)
6 ! 3$ ?????"? " #U # ?????#? # :U ( %
;"
;#
149
150 Chapter 3 Semiconductors
=
=
J#4$./.#./28%&1(% " #U % ! # + ⁄ 1 2 %'2,%&1(% # "U ! # + ⁄ 1 3 %8/+*$
2 # = ⁄ =)
= 2"
" S)
6 ! 3$# + ????????????? # ???????????? ( %
;
1
;
# 13
" 2
AK:KTC
;(16%."/$%*V#'./12%)*%21.*%."'.%&1(%'%2*8'./+*%=%A(*+*($*%4/'$C%)/."%'%6'82/.#,*%1&%'%&*)
./6*$% = ) %A=D:T%6PC3%."*%*@712*2./'-%.*(6%4*016*$%*$$*2./'--5%X*(13%'2,%."*%0#((*2.%'0(1$$
."*% F#20./12% 4*016*$% 2*8'./+*% '2,% 012$.'2.:% ;(16% 1#(% V#'-/.'./+*% ,*$0(/7./12% /2% J*0./12
K:D:S3%)*%921)%."'.%."/$%0#((*2.%6#$.%4*% 6 A : %!"#$3
6% ! 6 A ( %
= ⁄ =)
" S)
AK:BUC
)"*(*
2# = 2"
6 A% % ! 3$# + ????????????? # ????????????
;
1
;
# 13
" 2
AK:BSC
;/8#(*%AK:SKC%$"1)$%."*%6G=%0"'('0.*(/$./0%1&%."*%"#%F#20./12%AOV:%K:BUC:%R4$*(+*%."'.%/2
."*%(*+*($*%,/(*0./12%."*%0#((*2.%$'.#('.*$%'.%'%+'-#*%*V#'-%.1%G6A:%;1(%."/$%(*'$123% 6 A %/$%8/+*2
."*%2'6*%5'#+&'#!-")*+&&$"#:%;(16%OV:%AK:BSC%)*%$**%."'.%6A%/$%,/(*0.-5%7(171(./12'-%.1%."*
0(1$$?$*0./12'-%'(*'%3%1&%."*%F#20./12:%!"#$3%'21."*(%2'6*%&1(%6A 3%12*%)*%7(*&*(%.1%#$*%/2%."/$
41193%/$%."*%F#20./12)5*'.$)*+&&$"#:%!57/0'-%+'-#*$%&1(%6A 3%&1(%F#20./12$%1&%+'(/1#$%'(*'$3%('28*
" Sc
" S=
&(16% SU %.1% SU %G:%
M*$/,*$% 4*/28% 7(171(./12'-% .1% ."*% F#20./12% '(*'% 33% ."*% *@7(*$$/12% &1(% 6 A % /2% OV:% AK:BSC
=
/2,/0'.*$%."'.% 6 A %/$% 7(171(./12'-%.1% # + %)"/0"%/$%'%+*(5%$.(128% &#20./12%1&% .*67*('.#(*%A$**
OV: K:=C:
I
0
IS
Figure 3.13 !"*%"#%F#20./12%6G=%0"'('0.*(/$./0:
V
3.5 The pn Junction with an Applied Voltage
Example 3.6
Sc
K
SE
K
;1(% ."*% "#! F#20./12% 012$/,*(*,% /2% O@'67-*% K:D% &1(% )"/0"% 1 3 % ! SU ⁄ 06 3% 1 2 % ! SU ⁄ 06 3
"B
=
SU
K
=
3% ! SU 06 3% # + % ! S:D × SU ⁄ 06 3%-*.% ; " % ! D %µ63% ; # ! SU %µ63% 2 " %A/2%."*%#%(*8/12C%e SU%06 ⁄ P : $3
=
'2,% 2 # %A/2%."*%"%(*8/12C% ! Sc%06 ⁄ P: $:%!"*%"#%F#20./12%/$%&1()'(,%4/'$*,%'2,%012,#0./28%'%0#((*2.
6%e%U:S%6G:%<'-0#-'.*H%A'C% 6 A L%A4C%."*%&1()'(,?4/'$%+1-.'8*%=L%'2,%A0C%."*%016712*2.%1&%."*%0#((*2.%6
,#*%.1%"1-*%/2F*0./12%'2,%."'.%,#*%.1%*-*0.(12%/2F*0./12%'0(1$$%."*%F#20./12:
Solution
A'C%i$/28%OV:%AK:BSC3%)*%&/2,% 6 A %'$%
"B
SU =
" ST
6 A% % ! SU × S:E × SU × ( S:D × SU ) ×
SU
Sc
? # ??????????????????????????????????????
?
???????????????????????????????????
"B
SE
"B
Sc
SU × SU × SU
D × SU × SU
! b:K × SU
" SD
%G
A4C%>2%."*%&1()'(,%,/(*0./123
6% ! 6 A ( %
! 6A %
= ⁄ =)
" S)
= ⁄ =)
!"#$3
;1(%6!e%U:S%6G3
6
=% ! = ) %-2 ????
6A
U:S × SU " K "K
?
=% ! =D:T × SU %-2 ?????????????????????????
" SD
b:K × SU
e%U:EUD%P
A0C%!"*%"1-*?/2F*0./12%016712*2.%1&%6!0'2%4*%&1#2,%#$/28%OV:%AK:KbC
2"
= ⁄ =)
6 " % ! 3$ ?????? " #U ( %
" S)
;"
=
2" #
= ⁄ =)
! 3$ ?????? ??????+? ( %
" S)
;" 12
J/6/-'(-5% 6 # %0'2%4*%&1#2,%#$/28%OV:%AK:KTC3%
=
2 # =⁄=
6 # ! 3$ ?????#? ?????+? ( % ) " S )
;# 13
!"#$3
;1(%1#(%0'$*3
2" ;
6"
1
???? ! ?????? ????#? ??????3? 2# ;" 12
6#
Sc
6"
SU ?
=
???? % ! SU
?????? × SU
?????? × ?????????
! S:SS × SU ! SSS
6 # Sc D SU SE
151
152 Chapter 3 Semiconductors
Example 3.6 continued
!"#$%61$.%1&%."*%0#((*2.%/$%012,#0.*,%45%"1-*$%/2F*0.*,%/2.1%."*%#%(*8/12:
J7*0/&/0'--53
SSS
6 " % ! ????????? × U:S ! U:UTTS %6G
SS=
S
6 # % ! ????????? × U:S ! U:UUUT %6G
SS=
!"/$%$.'2,$%.1%(*'$123%$/20*%."*%"%6'.*(/'-%"'$%'%,17/28%0120*2.('./12%SUU%./6*$%."'.%1&%."*%#%6'.*(/'-:
EXERCISES
3.10 J"1)%."'.%/&% 1 3 # 1 2 3%
= 2"
?
6 A% ! 3$# + ????????????
;" 12
3.11 ;1(%."*%"#%F#20./12%/2%O@'67-*%K:E3%&/2,%."*%+'-#*%1&% 6 A %'2,%."'.%1&%."*%0#((*2.%6%'.%=%e%U:EUD%P%A$'6*
+1-.'8*%&1#2,%/2%O@'67-*%K:E%'.%'%0#((*2.%6%e%U:S%6GC%/&% 1 2 %/$%(*,#0*,%45%'%&'0.1(%1&%=:
" SB
Ans. S:BE × SU %GL%U:=%6G
3.12 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,%."*%)/,."%1&%."*%,*7-*./12%(*8/12%<%01(?
(*$712,/28%.1%."*%&1()'(,?4/'$%+1-.'8*%&1#2,%/2%O@'67-*%K:E:%AI+#/H%i$*%."*%&1(6#-'%/2%OV: AK:KSC
)/."% = E %(*7-'0*,%)/."% " = F :C
Ans. U:SEE%µ6
3.13 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,%."*%)/,."%1&%."*%,*7-*./12%(*8/12%<%'2,
."*%0"'(8*%$.1(*,%/2%."*%,*7-*./12%(*8/12% B 9 %)"*2%'%=?P%(*+*($*%4/'$%/$%'77-/*,:%G-$1%&/2,%."*%+'-#*
1&%."*%(*+*($*%0#((*2.%6:
" SD
Ans. U:EUc%µ6L%T:EK%7<L% b:K × SU %G
3.5.3 Reverse Breakdown
!"*% ,*$0(/7./12% 1&% ."*% 17*('./12% 1&% ."*% "#% F#20./12% /2% ."*% (*+*($*% ,/(*0./123% '2,% ."*% 6 " =
(*-'./12$"/7% 1&% ."*% F#20./12% /2% OV:% AK:BUC3% /2,/0'.*% ."'.% '.% '% (*+*($*?4/'$% +1-.'8*% ]=3% )/."
= # = ) 3%."*%(*+*($*%0#((*2.%."'.%&-1)$%'0(1$$%."*%F#20./12%/$%'77(1@/6'.*-5%*V#'-%.1% 6 A !'2,
."#$%/$% +*(5% $6'--:% f1)*+*(3%'$% ."*% 6'82/.#,*% 1&% ."*% (*+*($*?4/'$%+1-.'8*%=% /$% /20(*'$*,3% '
+'-#*%/$%(*'0"*,%'.%)"/0"%'%+*(5%-'(8*%(*+*($*%0#((*2.%&-1)$%'$%$"1)2%/2%;/8:%K:SB:%R4$*(+*%."'.
'$%=%(*'0"*$%."*%+'-#*%=H 3%."*%,('6'./0%/20(*'$*%/2%(*+*($*%0#((*2.%/$%'00167'2/*,%45%'%+*(5
$6'--%/20(*'$*%/2%."*%(*+*($*%+1-.'8*L%."'.%/$3%."*%(*+*($*%+1-.'8*%'0(1$$%."*%F#20./12%(*6'/2$
+*(5% 0-1$*% .1% ."*% +'-#*% =H:% !"*% 7"*216*212% ."'.% 100#($% '.% = ! = H % /$% 921)2% '$% 6+"*#!-"
2&$'<(-=":% >.% /$% 21.% '% ,*$.(#0./+*% 7"*216*212:% !"'.%/$3% ."*%"#% F#20./12% 0'2% 4*% (*7*'.*,-5
17*('.*,%/2%."*%4(*'9,1)2%(*8/12%)/."1#.%'%7*(6'2*2.%*&&*0.%12%/.$%0"'('0.*(/$./0$:%!"/$3%"1)?
*+*(3%/$%7(*,/0'.*,%12%."*%'$$#67./12%."'.%."*%6'82/.#,*%1&%."*%(*+*($*?4(*'9,1)2%0#((*2.%/$
3.5 The pn Junction with an Applied Voltage 153
I
!VZ
0
V
Figure 3.14 !"*%6?=%0"'('0.*(/$./0%1&%."*%"#%F#20./12%$"1)/28%."*%('7/,%/20(*'$*%/2%(*+*($*%0#((*2.%/2%."*
4(*'9,1)2%(*8/12:
-/6/.*,%45%."*%*@.*(2'-%0/(0#/.%.1%'%Z$'&*[%+'-#*:%!"*%Z$'&*[%+'-#*%/$%12*%."'.%(*$#-.$%/2%."*%-/6/?
.'./12%1&%."*%71)*(%,/$$/7'.*,%/2%."*%F#20./12%.1%'%$'&*3%'--1)'4-*%-*+*-:
!"*(*%'(*%.)1%71$$/4-*%6*0"'2/$6$%&1(%"#%F#20./12%4(*'9,1)2H%."*%>$"$&)$33$*#b%'2,%."*
'1'.'"*/$)$33$*#:%>&%'%"#%F#20./12%4(*'9$%,1)2%)/."%'%4(*'9,1)2%+1-.'8*% = H < D %P3%."*%4(*'9?
,1)2%6*0"'2/$6%/$%#$#'--5%."*%X*2*(%*&&*0.:%G+'-'20"*%4(*'9,1)2%100#($%)"*2% = H %/$%8(*'.*(
."'2%'77(1@/6'.*-5%b%P:%;1(%F#20./12$%."'.%4(*'9%,1)2%4*.)**2%D%P%'2,%b%P3%."*%4(*'9,1)2
6*0"'2/$6%0'2%4*%*/."*(%."*%X*2*(%1(%."*%'+'-'20"*%*&&*0.%1(%'%0164/2'./12%1&%."*%.)1:
n*2*(%4(*'9,1)2%100#($%)"*2%."*%*-*0.(/0%&/*-,%/2%."*%,*7-*./12%-'5*(%/20(*'$*$%.1%."*
71/2.%1&%4(*'9/28%01+'-*2.%412,$%'2,%8*2*('./28%*-*0.(12?"1-*%7'/($:%!"*%*-*0.(12$%8*2*('.*,
/2%."/$%)'5%)/--%4*%$)*7.%45%."*%*-*0.(/0%&/*-,%/2.1%."*%#%$/,*%'2,%."*%"1-*$%/2.1%."*%"%$/,*:%!"#$
."*$*% *-*0.(12$% '2,% "1-*$% 012$./.#.*% '% (*+*($*% 0#((*2.% '0(1$$% ."*% F#20./12:% R20*% ."*% X*2*(
*&&*0.% $.'(.$3% '%-'(8*% 2#64*(%1&% 0'((/*($%0'2% 4*% 8*2*('.*,3%)/."% '%2*8-/8/4-*%/20(*'$*% /2%."*
F#20./12%+1-.'8*:%!"#$%."*%(*+*($*%0#((*2.%/2%."*%4(*'9,1)2%(*8/12%)/--%4*%-'(8*%'2,%/.$%+'-#*
6#$.%4*%,*.*(6/2*,%45%."*%*@.*(2'-%0/(0#/.3%)"/-*%."*%(*+*($*%+1-.'8*%'77*'(/28%4*.)**2%."*
,/1,*%.*(6/2'-$%)/--%(*6'/2%0-1$*%.1%."*%$7*0/&/*,%4(*'9,1)2%+1-.'8*%=H:
!"*% 1."*(% 4(*'9,1)2% 6*0"'2/$63% '+'-'20"*% 4(*'9,1)23% )"/0"% 100#($% )"*2% ."*
6/21(/.5%0'((/*($%."'.%0(1$$%."*%,*7-*./12%(*8/12%#2,*(%."*%/2&-#*20*%1&%."*%*-*0.(/0%&/*-,%8'/2
$#&&/0/*2.%9/2*./0%*2*(85%.1%4*%'4-*%.1%4(*'9%01+'-*2.%412,$%/2%'.16$%)/."%)"/0"%."*5%01--/,*:
!"*%0'((/*($%-/4*('.*,%45%."/$%7(10*$$%6'5%"'+*%$#&&/0/*2.-5%"/8"%*2*(85%.1%4*%'4-*%.1%0'#$*
1."*(%0'((/*($%.1%4*%-/4*('.*,%/2%'21."*(%/12/X/28%01--/$/12:%!"/$%7(10*$$%9**7$%(*7*'./28%/2%."*
&'$"/12%1&%'2%'+'-'20"*3%)/."%."*%(*$#-.%."'.%6'25%0'((/*($%'(*%0(*'.*,%."'.%'(*%'4-*%.1%$#771(.
'25%+'-#*%1&%(*+*($*%0#((*2.3%'$%,*.*(6/2*,%45%."*%*@.*(2'-%0/(0#/.3%)/."%'%2*8-/8/4-*%0"'28*%/2
."*%+1-.'8*%,(17%'0(1$$%."*%F#20./12:
a'6*,%'&.*(%'2%*'(-5%)1(9*(%/2%."*%'(*':%a1.*%."'.%."*%$#4$0(/7.!H%/2%=H%,*21.*$%J%#%7:%\*%)/--%#$*%=H
.1%,*21.*%."*%4(*'9,1)2%+1-.'8*%)"*."*(%."*%4(*'9,1)2%6*0"'2/$6%/$%."*%X*2*(%*&&*0.%1(%."*%'+'-'20"*
*&&*0.:
b%
154 Chapter 3 Semiconductors
G$%)/--%4*%$**2%/2%<"'7.*(%B3%$16*%"#!F#20./12%,/1,*$%'(*%&'4(/0'.*,%.1%17*('.*%$7*0/&/?
0'--5%/2%."*%4(*'9,1)2%(*8/123%)"*(*%#$*%/$%6',*%1&%."*%2*'(-5%012$.'2.%+1-.'8*%=H:
3.6 Capacitive Effects in the pn Junction
!"*(*%'(*%.)1%0"'(8*%$.1('8*%6*0"'2/$6$%/2%."*%"#%F#20./12:%R2*%/$%'$$10/'.*,%)/."%."*%0"'(8*
$.1(*,% /2% ."*% ,*7-*./12% (*8/123% '2,% ."*% 1."*(% '$$10/'.*,% )/."% ."*% 6/21(/.5% 0'((/*(% 0"'(8*
$.1(*,%/2%."*%#%'2,%"%6'.*(/'-$%'$%'%(*$#-.%1&%."*%0120*2.('./12%7(1&/-*$%*$.'4-/$"*,%45%%0'(?
(/*(%/2F*0./12:%\"/-*%."*%&/($.%/$%*'$/*(%.1%$**%)"*2%."*%"#%F#20./12%/$%(*+*($*%4/'$*,3%."*%$*0?
12,%/$%/2%*&&*0.%12-5%)"*2%."*%F#20./12%/$%&1()'(,%4/'$*,:
3.6.1 Depletion or Junction Capacitance
\"*2%'%"#%F#20./12%/$%(*+*($*%4/'$*,%)/."%'%+1-.'8*%=E 3%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&
."*%,*7-*./12%(*8/12%/$%8/+*2%45%OV:%AK:K=C3
13 12
? ( = # =E )
B 9 %% ! 3 =ε 0 $ ???????????????????
13 # 12 U
!"#$3%&1(%'%8/+*2%"#%F#20./123
B9 ! α =U # =E
AK:B=C
13 12
?
α% ! 3 =ε 0 $ ???????????????????
13 # 12
AK:BKC
Charge stored in depletion layer, QJ
)"*(*% α %/$%8/+*2%45
Slope $ CJ
Q
Bias point
0
VQ
Reverse voltage,VR
Figure 3.15 !"*% 0"'(8*% $.1(*,% 12% */."*(% $/,*% 1&% ."*% ,*7-*./12% -'5*(% '$% '% &#20./12% 1&% ."*% (*+*($*
+1-.'8* =E:
3.6 Capacitive Effects in the pn Junction 155
!"#$% B 9 %/$%212-/2*'(-5%(*-'.*,%.1%=E 3%'$%$"1)2%/2%;/8:%AK:SDC:%!"/$%212-/2*'(%(*-'./12$"/7
6'9*$%/.%,/&&/0#-.%.1%,*&/2*%'%0'7'0/.'20*%."'.%'001#2.$%&1(%."*%2**,%.1%0"'28*% B 9 %)"*2*+*(
= E %/$%0"'28*,:%\*%0'23%"1)*+*(3%'$$#6*%."'.%."*%F#20./12%/$%17*('./28%'.%'%71/2.%$#0"%'$%B3
'$%/2,/0'.*,%/2%;/8:%K:SD3%'2,%,*&/2*%'%0'7'0/.'20*% L M %."'.%(*-'.*$%."*%0"'28*%/2%."*%0"'(8*
B 9 %.1%'%0"'28*%/2%."*%+1-.'8*% = E 3
,B
L M%% ! ?????????9
,= E
AK:BBC
= E != B
!"/$% /20(*6*2.'-?0'7'0/.'20*% '77(1'0"% .#(2$% 1#.% .1% 4*% V#/.*% #$*&#-% /2% *-*0.(12/0% 0/(0#/.
,*$/823%'$%)*%$"'--%$**%."(1#8"1#.%."/$%4119:
i$/28%OV:%AK:BBC%.18*."*(%)/."%OV:%AK:B=C%5/*-,$%
α
L M % ! ??????????????????????????
= =U # =E
!"*%+'-#*%1&% L M %'.%X*(1%(*+*($*?4/'$%0'2%4*%14.'/2*,%&(16%OV: AK:BDC%'$
α ?
L MU ! ????????????
= =U
)"/0"%*2'4-*$%#$%.1%*@7(*$$% L M %'$%
L MU
L M ! ????????????????????
=
S # ?????E?
=U
AK:BDC
AK:BEC
AK:BbC
)"*(*% L MU %/$%8/+*2%45%OV:%AK:BEC%1(%'-.*(2'./+*-5%/&%)*%$#4$./.#.*%&1(% α %&(16%OV:%AK:BKC%45
ε 0 $ 1 3 1 2 S ???????????????????? ??????
L MU ! 3 ???????
= 13 # 12 =U
AK:BcC
M*&1(*%-*'+/28%."*%$#4F*0.%1&%,*7-*./12?(*8/12%1(%F#20./12%0'7'0/.'20*%)*%71/2.%1#.%."'.%/2
."*%"#%F#20./12%)*%"'+*%4**2%$.#,5/283%."*%,17/28%0120*2.('./12%/$%6',*%.1%0"'28*%'4(#7.-5
'.%."*%F#20./12%41#2,'(5:%J#0"%'%F#20./12%/$%921)2%'$%'2%'2&+0#)6+"*#!-":%!"*(*%/$%'21."*(
.57*%1&%"#%F#20./12%/2%)"/0"%."*%0'((/*(%0120*2.('./12%/$%6',*%.1%0"'28*%8(',#'--5%&(16%12*
$/,*%1&%."*%F#20./12%.1%."*%1."*(:%!1%'--1)%&1(%$#0"%'%%&'($()6+"*#!-"3%."*%&1(6#-'%&1(%."*
F#20./12%0'7'0/.'20*%AOV:%K:BbC%0'2%4*%)(/..*2%/2%."*%61(*%8*2*('-%&1(6
L MU
L M ! ????????????????????????
?
=E K
S # ?????
?
=U
AK:BTC
)"*(*%K%/$%'%012$.'2.%0'--*,%."*%%&'(!"%)*-$33!*!$"#3%)"1$*%+'-#*%('28*$%&(16%S`K%.1%S`=
,*7*2,/28%12%."*%6'22*(%/2%)"/0"%."*%0120*2.('./12%0"'28*$%&(16%."*%"%.1%."*%#%$/,*:%
EXERCISE
3.12 ;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E3%&/2,% L MU %'2,% L M %'.% = E % ! = %P:%_*0'--%."'.
Sc
K
SE
K
"B
=
= U % ! U:cSB %P3% 1 3 % ! SU ⁄ 06 3% 1 2 % ! SU ⁄ 06 %'2,% 3% ! SU 06 :
Ans. K:=%7;L%S:b%7;
156 Chapter 3 Semiconductors
3.6.2 Diffusion Capacitance
<12$/,*(% '% &1()'(,?4/'$*,% "#% F#20./12:% >2% $.*',5?$.'.*3% 6/21(/.5% 0'((/*(% ,/$.(/4#./12$% /2
."*%"%'2,%#%6'.*(/'-$%'(*%*$.'4-/$"*,3%'$%$"1)2%/2%;/8:%K:S=:%!"#$%'%0*(.'/2%'61#2.%1&%*@0*$$
6/21(/.5%0'((/*(%0"'(8*%/$%$.1(*,%/2%*'0"%1&%."*%"%'2,%#%4#-9%(*8/12$%A1#.$/,*%."*%,*7-*./12
(*8/12C:% >&% ."*% .*(6/2'-% +1-.'8*% =% 0"'28*$3% ."/$% 0"'(8*% )/--% "'+*% .1% 0"'28*% 4*&1(*% '% 2*)
$.*',5%$.'.*%/$%'0"/*+*,:%!"/$%0"'(8*?$.1('8*%7"*216*212%8/+*$%(/$*%.1%'21."*(%0'7'0/./+*
*&&*0.3%,/$./20.-5%,/&&*(*2.%&(16%."'.%,#*%.1%0"'(8*%$.1('8*%/2%."*%,*7-*./12%(*8/12:
!1%0'-0#-'.*%."*%*@0*$$%6/21(/.5%0'((/*(%0"'(8*3%(*&*(%.1%;/8:%K:S=:%!"*%*@0*$$%"1-*%0"'(8*
$.1(*,%/2%."*%#%(*8/12%0'2%4*%&1#2,%&(16%."*%$"',*,%'(*'%#2,*(%."*%*@712*2./'-%'$%&1--1)$Hc
B " ! 3$ × $"',*,%'(*'%#2,*(%."*% " # ( 5 ) %0#(+*
! 3$ [ " # ( 5 # ) " " #U ]; "
$#4$./.#./28%&1(% " # ( 5 # ) %&(16%OV:%AK:KKC%'2,%#$/28%OV:%AK:KbC%*2'4-*$%#$%.1%*@7(*$$% B " %'$
=
;"
B " % ! ?????? 6 "
2"
AK:DUC
=
!"*%&'0.1(% ( ; " ⁄ 2 " ) %."'.%(*-'.*$% B " %.1% 6 " %/$%'%#$*&#-%,*+/0*%7'('6*.*(%."'.%"'$%."*%,/6*2$/12
1&%./6*%A$C%'2,%/$%,*21.*,% τ "
=
;"
τ " % ! ??????
2"
AK:DSC
B" ! τ" 6"
AK:D=C
!"#$3
!"*%./6*%012$.'2.% τ "%/$%921)2%'$%."*%*@0*$$%,!"-&!#4)*'&&!$&)7/-.$8).!3$#!,$:%6/!+0!/@%
.4%7.'%!/+K%!+/!/.(%0!8-7!.!@->%!+#M%?/%,!+#/-!/@%!#!7%'+-#!/-!7%?-KD+#%!N+/@!.!K.M-7+/O!%>%?P
/7-#:%!"/$%,*&/2/./12%1&% τ "%/67-/*$%."'.%."*%*2./(*%0"'(8*% B "%,/$'77*'($%'2,%"'$%.1%4*%(*7-*2?
/$"*,%*+*(5%τ "%$*012,$:%!"*%0#((*2.%."'.%'00167-/$"*$%."*%(*7-*2/$"/28%/$% 6 " ! B " ⁄ τ " :%!"/$%/$
'2%'-.*(2'.*%,*(/+'./12%&1(%OV:%AK:D=C:
G%(*-'./12$"/7%$/6/-'(%.1%."'.%/2%OV:%AK:D=C%0'2%4*%,*+*-17*,%&1(%."*%*-*0.(12%0"'(8*%$.1(*,%/2
."*%"%(*8/123
B# % ! τ# 6#
AK:DKC
)"*(*% τ # %/$%."*%*-*0.(12%-/&*./6*%/2%."*%"%(*8/12:%!"*%.1.'-%*@0*$$%6/21(/.5%0'((/*(%0"'(8*%0'2
4*%14.'/2*,%45%',,/28%.18*."*(% B " %'2,% B # 3
B% ! τ " 6 " # τ # 6 #
AK:DBC
!"/$%0"'(8*%0'2%4*%*@7(*$$*,%/2%.*(6$%1&%."*%,/1,*%0#((*2.% 6% ! 6 " # 6 # %'$%
B% ! τ ) 6
AK:DDC
)"*(*% τ ) %/$%0'--*,%."*%,$'")#&'"5!#)#!,$%1&%."*%F#20./12:%R4+/1#$-53% τ ) %/$%(*-'.*,%.1% τ " %'2,
τ #:%;#(."*(61(*3%&1(%61$.%7('0./0'-%,*+/0*$3%12*%$/,*%1&%."*%F#20./12%/$%6#0"%61(*%"*'+/-5
,17*,% ."'2% ."*% 1."*(:% ;1(% /2$.'20*3% /&% 1 3 # 1 2 3% 12*% 0'2% $"1)% ."'.% 6 " # 6 # 3% 6 ! 6 " 3
B " # B # 3%B ! B " 3%'2,%."#$% τ )% ! τ " :%
_*0'--%."'.%."*%'(*'%#2,*(%'2%*@712*2./'-%0#(+*% 3%
c
"5 ⁄ *
%/$%*V#'-%.1%3*:
3.6 Capacitive Effects in the pn Junction 157
;1(% $6'--% 0"'28*$% '(1#2,% '% 4/'$% 71/2.3% )*% 0'2% ,*&/2*% '2% !"*&$,$"#'.) (!33+5!-"
*'0'*!#'"*$% L , %'$%
,B
AK:DEC
L , % ! ???????
,=
'2,%0'2%$"1)%."'.
τ
L , % ! ??????)? 6
=)
AK:DbC
)"*(*%6!/$%."*%&1()'(,?4/'$%0#((*2.:%a1.*%."'.% L , %/$%,/(*0.-5%7(171(./12'-%.1%."*%&1()'(,%0#(?
(*2.%6%'2,%."#$%/$%2*8-/8/4-5%$6'--%)"*2%."*%,/1,*%/$%(*+*($*%4/'$*,:%G-$1%21.*%."'.%.1%9**7
L , %$6'--3%."*%.('2$/.%./6*% τ ) %6#$.%4*%6',*%$6'--3%'2%/671(.'2.%(*V#/(*6*2.%&1(%'%"#!F#20?
./12%/2.*2,*,%&1(%"/8"?$7**,%1(%"/8"?&(*V#*205%17*('./12:
EXERCISES
3.15
i$*%."*%,*&/2/./12%1&% L , %/2%OV:%AK:DEC%.1%,*(/+*%."*%*@7(*$$/12%/2%OV:%AK:DbC%45%6*'2$%1&%OV$:%AK:DDC
'2,%AK:BUC:
3.16
;1(%."*%"#%F#20./12%012$/,*(*,%/2%O@'67-*$%K:D%'2,%K:E%&1(%)"/0"% 2 " % ! SU%06 ⁄ P ⋅ $ 3%'2,% ; " ! D
µ63%&/2,% τ " %'2,% L , %'.%'%&1()'(,?4/'$%0#((*2.%1&%U:S%6G:%_*0'--%."'.%&1(%."/$%F#20./123% 6 " ! 6 :
=
Ans. =D%2$L%TE:D%7;
158 Chapter 3 Semiconductors
Summary
!1,'5W$% 6/0(1*-*0.(12/0$% .*0"21-185% /$% '-61$.% *2./(*-5
4'$*,%12%."*%$*6/012,#0.1(%6'.*(/'-%$/-/012:%>&%'%0/(0#/.%/$
.1%4*%&'4(/0'.*,%'$%'%6121-/."/0%/2.*8('.*,%0/(0#/.%A><C%/.%/$
6',*%#$/28%'%$/28-*%$/-/012%0(5$.'-3%21%6'..*(%"1)%-'(8*
."*% 0/(0#/.% /$% o'% (*0*2.% 0"/7% A=UUTC% 012.'/2$% =:K% 4/--/12
.('2$/$.1($p:
>2%'%0(5$.'-%1&%/2.(/2$/0%1(%7#(*%$/-/0123%."*%'.16$%'(*%"*-,
/2%71$/./12%45%01+'-*2.%412,$:%G.%+*(5%-1)%.*67*('.#(*$3
'--%."*%412,$%'(*%/2.'0.3%'2,%21%0"'(8*%0'((/*($%'(*%'+'/-?
'4-*%.1%012,#0.%*-*0.(/0'-%0#((*2.:%!"#$3%'.%$#0"%-1)%.*6?
7*('.#(*$3%$/-/012%4*"'+*$%'$%'2%/2$#-'.1(:
G.%(116%.*67*('.#(*3%."*(6'-%*2*(85%0'#$*$%$16*%1&%."*
01+'-*2.% 412,$% .1% 4(*'93% ."#$% 8*2*('./28% &(**% *-*0.(12$
'2,%"1-*$%."'.%4*016*%'+'/-'4-*%&1(%0#((*2.%012,#0./12:
<#((*2.%/2%$*6/012,#0.1($%/$%0'((/*,%45%&(**%*-*0.(12$%'2,
"1-*$:% !"*/(% 2#64*($% '(*% *V#'-% '2,% (*-'./+*-5% $6'--% /2
/2.(/2$/0%$/-/012:
!"*%012,#0./+/.5%1&%$/-/012%0'2%4*%/20(*'$*,%,('6'./0'--5
45% /2.(1,#0/28% $6'--% '61#2.$% 1&% '77(17(/'.*% /67#(/.5
6'.*(/'-$%/2.1%."*%$/-/012%0(5$.'-%/2%'%7(10*$$%0'--*,%,17/28:
!"*(*%'(*%.)1%9/2,$%1&%,17*,%$*6/012,#0.1(H!#?.57*3%/2
)"/0"%*-*0.(12$%'(*%'4#2,'2.3%'2,%"?.57*3%/2%)"/0"%"1-*$
'(*%'4#2,'2.:
!"*(*%'(*%.)1%6*0"'2/$6$%&1(%."*%.('2$71(.%1&%0"'(8*%0'(?
(/*($%/2%$*6/012,#0.1(H%,(/&.%'2,%,/&&#$/12:
<'((/*(% ,(/&.% (*$#-.$% )"*2% '2% *-*0.(/0% &/*-,% &! /$% '77-/*,
'0(1$$%'%7/*0*%1&%$/-/012:%!"*%*-*0.(/0%&/*-,%'00*-*('.*%."*
"1-*$%/2%."*%,/(*0./12%1&%&%'2,%."*%*-*0.(12$%/2%."*%,/(*0?
./12% 1771$/.*% .1% &:% !"*$*% .)1% 0#((*2.% 016712*2.$% ',,
.18*."*(%.1%7(1,#0*%'%,(/&.%0#((*2.%/2%."*%,/(*0./12%1&%&:
<'((/*(%,/&&#$/12%100#($%)"*2%."*%0120*2.('./12%1&%0"'(8*
0'((/*($%/$%6',*%"/8"*(%/2%12*%7'(.%1&%."*%$/-/012%0(5$.'."'2% /2% 1."*(% 7'(.$:% !1% *$.'4-/$"% '% $.*',5?$.'.*% ,/&&#$/12
0#((*2.3% '% 0'((/*(% 0120*2.('./12% 8(',/*2.% 6#$.% 4*% 6'/2?
.'/2*,%/2%."*%$/-/012%0(5$.'-:
G%4'$/0%$*6/012,#0.1(%$.(#0.#(*%/$%."*!"#%F#20./12:%>.%/$
&'4(/0'.*,% /2% '% $/-/012% 0(5$.'-% 45% 0(*'./28% '% "% (*8/12% /2
0-1$*%7(1@/6/.5%.1%'2%#!(*8/12:%!"*%"#%F#20./12%/$%'%,/1,*
'2,%7-'5$%'%,16/2'2.%(1-*%/2%."*%$.(#0.#(*%'2,%17*('./12%1&
.('2$/$.1($:
\"*2%."*%.*(6/2'-$%1&%."*%"#%F#20./12%'(*%-*&.%17*23%21
0#((*2.% &-1)$% *@.*(2'--5:% f1)*+*(3% .)1% *V#'-% '2,
1771$/.*% 0#((*2.$3% 6 2%'2,% 6 A 3% &-1)% '0(1$$% ."*% F#20./123
'2,%*V#/-/4(/#6%/$%6'/2.'/2*,%45%'%4#/-.?/2%+1-.'8*% = U
."'.%,*+*-17$%'0(1$$%."*%F#20./123%)/."%."*%#%$/,*%71$/./+*
(*-'./+*% .1% ."*% "% $/,*:% a1.*3% "1)*+*(3% ."'.% ."*% +1-.'8*
'0(1$$%'2%17*2%F#20./12%/$%U P3%$/20*%=U%/$%0'20*--*,%45
71.*2./'-$%'77*'(/28%'.%."*%6*.'-?.1?$*6/012,#0.1(%012?
2*0./12%/2.*(&'0*$:
!"*%+1-.'8*%= U%'77*'($%'0(1$$%."*%,*7-*./12%(*8/123%)"/0"
*@.*2,$%12%41."%$/,*$%1&%."*%F#20./12:
!"*% ,/&&#$/12% 0#((*2.% 6 2 % /$% 0'((/*,% 45% "1-*$% ,/&&#$/28
&(16%"%.1%#%'2,%*-*0.(12$%,/&&#$/28%&(16%#%.1%":% 6 2 %&-1)$
&(16%"%.1%#3%)"/0"%/$%."*%&1()'(,%,/(*0./12%1&%."*%F#20./12:
>.$%+'-#*%,*7*2,$%12%=U:
!"*%,(/&.%0#((*2.% 6 A %/$%0'((/*,%45%."*(6'--5%8*2*('.*,
6/21(/.5% *-*0.(12$% /2% ."*% "% 6'.*(/'-% ."'.% '(*% $)*7.
'0(1$$%."*%,*7-*./12%-'5*(%/2.1%."*%#%$/,*3%'2,%45%."*(?
6'--5% 8*2*('.*,% 6/21(/.5% "1-*$% /2% ."*! #% $/,*% ."'.% '(*
$)*7.% '0(1$$% ."*% ,*7-*./12% (*8/12% /2.1% ."*% "% $/,*:% 6 A
&-1)$%&(16%#!.1%"3%/2%."*%(*+*($*%,/(*0./12%1&%."*%F#20?
./123%'2,% /.$% +'-#*%/$% '% $.(128%&#20./12%1&%.*67*('.#(*
4#.%/2,*7*2,*2.%1&%=U:
;1()'(,%4/'$/28%."*%"#%F#20./123%."'.%/$3%'77-5/28%'2%*@.*(?
2'-%+1-.'8*%=%."'.%6'9*$%"%61(*%71$/./+*%."'2%#3%(*,#0*$
."*%4'((/*(%+1-.'8*%.1% = U " = %'2,%(*$#-.$%/2%'2%*@712*2./'/20(*'$*%/2% 6 2 %)"/-*%6 A%(*6'/2$%#20"'28*,:%!"*%2*.%(*$#-.
/$%'%$#4$.'2./'-%0#((*2.% 6% ! 6 2 " 6 A %."'.%&-1)$%'0(1$$%."*
F#20./12%'2,%."(1#8"%."*%*@.*(2'-%0/(0#/.:%
G77-5/28% '% 2*8'./+*% =% (*+*($*?4/'$*$% ."*% F#20./12% '2,
/20(*'$*$% ."*% 4'((/*(% +1-.'8*3% )/."% ."*% (*$#-.% ."'.% 6 2 % /$
(*,#0*,%.1%'-61$.%X*(1%'2,%."*%2*.%0#((*2.%'0(1$$%."*%F#20?
./12%4*016*$%."*%+*(5%$6'--%(*+*($*%0#((*2.%6A :
>&%."*%(*+*($*%+1-.'8*%/$%/20(*'$*,%/2%6'82/.#,*%.1%'%+'-#*
= H %$7*0/&/0%.1%."*%7'(./0#-'(%F#20./123%."*%F#20./12%4(*'9$
,1)23%'2,%'%-'(8*%(*+*($*%0#((*2.%&-1)$:%!"*%+'-#*%1&%."*
(*+*($*%0#((*2.%6#$.%4*%-/6/.*,%45%."*%*@.*(2'-%0/(0#/.:
\"*2*+*(% ."*% +1-.'8*% '0(1$$% '% "#% F#20./12% /$% 0"'28*,3
$16*%./6*%"'$%.1%7'$$%4*&1(*%$.*',5%$.'.*%/$%(*'0"*,:%!"/$
/$%,#*%.1%."*%0"'(8*?$.1('8*%*&&*0.$%/2%."*%F#20./123%)"/0"
'(*%61,*-*,%45%.)1%0'7'0/.'20*$H%."*%F#20./12%0'7'0/.'20*
L M %'2,%."*%,/&&#$/12%0'7'0/.'20*% L, :
;1(%&#.#(*%(*&*(*20*3%)*%7(*$*2.%/2%!'4-*%K:S%'%$#66'(5
1&% 7*(./2*2.% (*-'./12$"/7$% '2,% ."*% +'-#*$% 1&% 7"5$/0'012$.'2.$:
3.6 Capacitive Effects in the pn Junction
159
Table 3.1 Summary of Important Equations
P'-#*$%1&%<12$.'2.$%'2,%r'('6*.*($%
A&1(%>2.(/2$/0%J/%'.%)%e%KUU%YC
q#'2./.5
_*-'./12$"/7
<'((/*(%0120*2.('./12%/2%
/2.(/2$/0%$/-/012%A06]KC
# + = *)
I/&&#$/12%0#((*2.%
,*2$/.5%AG`06=C
,"
9 " = " $2 " ??????
,5
K`= " & ' ⁄ =()
%
,#
9 # = $2 # ??????
,5
"K
SD
* = b:K × SU 06 Y
& ' = S:S=%*P
"D
( = c:E= × SU *P`Y
SU
K
# + = S:D × SU `06
$ = S:EU × SU
" ST
" K`=
%01#-164
=
2 " = S=%06 `$
=
2 # = KB%06 `$
=
I(/&.%0#((*2.%,*2$/.5%
AG`06=C
9 ,7+8/ = $ ( " µ " + # µ # )&
µ " = BcU%06 `P⋅$
_*$/$./+/.5%AΩ⋅06C
ρ = S ⁄ [ $ ( " µ" + # µ# ) ]
µ"%'2,%µ#%,*0(*'$*%)/."%."*%/20(*'$*
_*-'./12$"/7%4*.)**2%
614/-/.5%'2,%,/&&#$/+/.5
2
2#
?????? = ?????"? = = )
= ) = () ⁄ $ ! =D:c%6P
<'((/*(%0120*2.('./12%/2%
#?.57*%$/-/012%A06%]K C
# #U %! 1 2
<'((/*(%0120*2.('./12%/2%
"?.57*%$/-/012%A06%%]K C
" "U% ! 1 3
N#20./12%4#/-.?/2%
+1-.'8*%APC
1 3 1 2
?
= U = = ) -2 ?????????????
=
#+
\/,."%1&%,*7-*./12%
(*8/12%A06C
5#
1
???? = ??????3?
5"
12
=
µ # = SKDU%06 `P⋅$
µ#
µ"
/2%,17/28%0120*2.('./12
=
" #U = # + ⁄ 1 2
=
# "U = # + ⁄ 1 3
ε 0 = SS:b ε U
< = 5# + 5"
=
= ε0 S
S?
??????? ?????? + ??????
( =U + =E )
$ 1 3 12
<"'(8*%$.1(*,%/2%,*7-*./12%
-'5*(%A01#-164C
13 12
? 3<
B 9 = $ ???????????????????
13 + 12
;1()'(,%0#((*2.%AGC
6 = 6" + 6#
= ⁄ =)
= 2"
6 " = 3$ # + ????????????? ( %
" S)
;" 12
=⁄=
= 2#
? (% ) " S)
6 # = 3$ # + ???????????
;# 13
J'.#('./12%0#((*2.%AGC
2"
2# =
? + ???????????
?
6 A = 3$ # + ????????????
;" 12 ;# 13
6?=%_*-'./12$"/7
6 ! 6A ( %
= ⁄ =)
" S)
ε U = c:cDB% × SU
" SB
%;`06
160 Chapter 3 Semiconductors
Table 3.1 continued
P'-#*$%1&%<12$.'2.$%'2,%r'('6*.*($%
A&1(%>2.(/2$/0%J/%'.%)%e%KUU%YC
q#'2./.5
_*-'./12$"/7
k/21(/.5?0'((/*(%
-/&*./6*%A$C
τ " = ;" ⁄ 2"
k/21(/.5?0'((/*(%
0"'(8*%$.1('8*%
A01#-164C
B" = τ" 6"
I*7-*./12%0'7'0/.'20*%A;C
ε 0 $ 1 3 1 2 S
? ???????????????????? ?????
L MU = 3 ??????
= 13 # 12 =U
=
; ", ; # = S%µ6%.1%SUU%µ6
=
τ# = ;# ⁄ 2#
B
τ ", τ # = S%2$%.1%SU %2$
B# = τ# 6#
B = B" + B# = τ) 6
= K
L M = L MU %% S + ?????E?
=U
I/&&#$/12%
0'7'0/.'20*%A;C
S S
K = ??? %.1% ???
K =
τ
L , = ?????)? 6
=)
PROBLEMS
r(14-*6$%'(*%6'(9*,%)/."%'$.*(/$9$%.1%,*$0(/4*%."*/(%,*8(**
1&%,/&&/0#-.5:%I/&&/0#-.%7(14-*6$%'(*%6'(9*,%)/."%'2%'$.*(/$9
AsCL% 61(*% ,/&&/0#-.% 7(14-*6$% )/."% .)1% '$.*(/$9$% AssCL% '2,
+*(5% 0"'--*28/28% '2,`1(% ./6*?012$#6/28% 7(14-*6$% )/."
."(**%'$.*(/$9$%AsssC:%G-$13%/&%/2%."*%&1--1)/28%7(14-*6$%."*
2**,% '(/$*$% &1(% ."*% +'-#*$% 1&% 7'(./0#-'(% 7'('6*.*($% 1(
7"5$/0'-% 012$.'2.$% ."'.% '(*% 21.% $.'.*,3% 7-*'$*% 012$#-.
!'4-* K:S:
Section 3.1: Intrinsic Semiconductors
3.1 ;/2,% +'-#*$% 1&% ."*% /2.(/2$/0% 0'((/*(% 0120*2.('./12% # +
&1(% $/-/012% '.% " bU°<3% U° <3% =U°<3% SUU°<3% '2,% S=D°<:% G.
*'0"% .*67*('.#(*3% )"'.% &('0./12% 1&% ."*% '.16$% /$% /12/X*,h
==
_*0'--% ."'.% '% $/-/012% 0(5$.'-% "'$% '77(1@/6'.*-5% D × SU
K
'.16$`06 :%
3.2 <'-0#-'.*% ."*% +'-#*% 1&% # + % &1(% 8'--/#6% '($*2/,*
SB
A^'G$C% '.% )% e% KUU% Y:% !"*% 012$.'2.% *% ! K:DE × SU
"K "K ⁄ =
( 06 Y
)%'2,%."*%4'2,8'7%+1-.'8*%&' e S:B=%*P:
Section 3.2: Doped Semiconductors
3.3
;1(%'%"?.57*%$/-/012%/2%)"/0"%."*%,17'2.%0120*2.('./12
1 3 % ! SU Sc ⁄ 06 K3% &/2,% ."*% "1-*% '2,% *-*0.(12% 0120*2.('./12$
'.%)%e%KUU%Y:
3.4 ;1(% '% $/-/012% 0(5$.'-% ,17*,% )/."% 7"1$7"1(#$3% )"'.
6#$.% 1 2 % 4*% /&% '.% )% e% KUU% Y% ."*% "1-*% 0120*2.('./12% ,(17$
b
4*-1)%."*%/2.(/2$/0%-*+*-%45%'%&'0.1(%1&% SU h
3.5 >2% '% 7"1$7"1(#$?,17*,% $/-/012% -'5*(% )/."% /67#(/.5
SE
K
0120*2.('./12% 1&%SU ⁄ 06 3% &/2,% ."*% "1-*% '2,% *-*0.(12% 012?
0*2.('./12$%'.% =b°< %'2,%S=D°<:
Section 3.3: Current Flow in Semiconductors
3.6 G% 51#28% ,*$/82*(3% '/6/28% .1% ,*+*-17% /2.#/./12% 012?
0*(2/28%012,#0./28%7'."$%)/."/2%'2%/2.*8('.*,%0/(0#/.3%*@'6?
/2*$%."*%*2,?.1?*2,%(*$/$.'20*%1&%'%0122*0./28%4'(%SU%µ6
-1283%K%µ6%)/,*3%'2,%S%µ6%."/093%6',*%1&%+'(/1#$%6'.*(/'-$:
!"*%,*$/82*(%012$/,*($H
Problems
SE
K
Sc
K
SE
K
A4C%#?,17*,%$/-/012%)/."% 1 2 ! SU ⁄ 06
A0C%#?,17*,%$/-/012%)/."% 1 2 ! SU ⁄ 06
A,C%"?,17*,%$/-/012%)/."% 1 3 ! SU ⁄ 06
pn(x)
108 pn0
CHAPTER 3 P R O B L E M S
A'C%/2.(/2$/0%$/-/012
161
n region
A*C%'-#6/2#6%)/."%(*$/$./+/.5%1&%=:c% µΩ : 06
;/2,%."*%(*$/$.'20*%/2%*'0"%0'$*:%;1(%/2.(/2$/0%$/-/0123%#$*%."*
,'.'% /2% !'4-*% K:S:% ;1(% ,17*,% $/-/0123% '$$#6*
=
µ #% ! =:D µ " % ! S=UU%06 ⁄ P:$:%A_*0'--%."'.% E ! ρ ; ⁄ 3 C
3.7 <12.('$.%."*%*-*0.(12%'2,%"1-*%,(/&.%+*-10/./*$%."(1#8"
'%SU?µ6%-'5*(%1&%/2.(/2$/0%$/-/012%'0(1$$%)"/0"%'%+1-.'8*%1&
=
D P% /$% /671$*,:% Q*.% µ # ! SKDU %06 ⁄ P:$% '2,
=
µ " ! BcU%06 ⁄ P:$:
3.8 ;/2,%."*%0#((*2.%."'.%&-1)$%/2%'%$/-/012%4'(%1&%SU?µ6
-*28."% "'+/28% '% D?µ6 × B?µ6 % 0(1$$% $*0./12% '2,% "'+/28
D
K
SD
K
&(**%*-*0.(12%'2,%"1-*%,*2$/./*$%1&% SU ⁄ %06 %'2,%SU ⁄ 06 3
(*$7*0./+*-53% )"*2% '% S% P% /$% '77-/*,% *2,?.1?*2,:% i$*
=
=
µ # ! S=UU%06 ⁄ P:$%'2,% µ " ! DUU%06 ⁄ P:$:
3.9 >2% '% SU?µ6% -128% 4'(% 1&% ,121(?,17*,% $/-/0123% )"'.
,121(%0120*2.('./12%/$%2**,*,%.1%(*'-/X*%'%0#((*2.%,*2$/.5%1&
=
S%6G ⁄ µ6 %/2%(*$712$*%.1%'2%'77-/*,%+1-.'8*%1&%S%P:%A1-/%H
G-."1#8"%."*%0'((/*(%614/-/./*$%0"'28*%)/."%,17/28%0120*2?
.('./123% '$% '% &/($.% '77(1@/6'./12% 51#% 6'5% '$$#6*% µ # % .1% 4*
012$.'2.% '2,% #$*% ."*% +'-#*% &1(% /2.(/2$/0% $/-/0123
=
SKDU%06 ⁄ P:$C:
3.10 f1-*$% '(*% 4*/28% $.*',/-5% /2F*0.*,% /2.1% '% (*8/12% 1&% #?
.57*%$/-/012%A0122*0.*,%.1%1."*(%,*+/0*$3%."*%,*.'/-$%1&%)"/0"
'(*%21.%/671(.'2.%&1(%."/$%V#*$./12C:%>2%."*%$.*',5%$.'.*3%."*
*@0*$$?"1-*% 0120*2.('./12% 7(1&/-*% $"1)2% /2% ;/8:% rK:SU% /$
*$.'4-/$"*,% /2% ."*% #?.57*% $/-/012% (*8/12:% f*(*% Z*@0*$$[
6*'2$% 1+*(% '2,% '41+*% ."*% ."*(6'-?*V#/-/4(/#6% 0120*2.('?
./12% A/2% ."*% '4$*20*% 1&% "1-*% /2F*0./12C3% ,*21.*,% " #U:% >&
1 2 ! SU SE ⁄ 06 K3% # + ! S:D × SU SU ⁄ 06 K 3% 2 # ! S=%06 = ⁄ $3
'2,%<!e%U:S%µ63%&/2,%."*%,*2$/.5%1&%."*%0#((*2.%."'.%)/--%&-1)
/2%."*%5%,/(*0./12:%
Doping Concentration
(carriers/cm3)
>2.(/2$/0
SU
SE
SU
Sb
SU
Sc
Table P3.11
pn0
0
W
x
Figure P3.10
3.11 M1."%."*%0'((/*(% 614/-/.5% '2,% ,/&&#$/+/.5% ,*0(*'$*% '$
."*% ,17/28% 0120*2.('./12% 1&% $/-/012% /$% /20(*'$*,:% !"*% .'4-*
4*-1)%7(1+/,*$%'%&*)%,'.'%71/2.$%&1(% µ #%'2,%µ "%+*($#$%,17?
/28%0120*2.('./12:%i$*%."*%O/2$.*/2%(*-'./12$"/7%.1%14.'/2%."*
01((*$712,/28%+'-#*$%&1(% 2 # %'2,% 2 ":
Section 3.4: The pn Junction with Open-Circuit
Terminals (Equilibrium)
3.12 <'-0#-'.*% ."*% 4#/-.?/2% +1-.'8*% 1&% '% F#20./12% /2% )"/0"
SE
."*%"%'2,%#%(*8/12$%'(*%,17*,%*V#'--5%)/."% SU %'.16$`06K:
SU
K
G$$#6*% # + % ! S:D × SU ⁄ 06 :%\/."%."*%.*(6/2'-$%-*&.%17*23
)"'.%/$%."*%)/,."%1&%."*%,*7-*./12%(*8/123%'2,%"1)%&'(%,1*$%/.
*@.*2,%/2.1%."*%"%'2,%#%(*8/12$h%>&%."*%0(1$$?$*0./12'-%'(*'%1&
."*% F#20./12% /$% SUU% µ6=3% &/2,% ."*% 6'82/.#,*% 1&% ."*% 0"'(8*
$.1(*,%12%*/."*(%$/,*%1&%."*%F#20./12:
3.13 >&3%&1(%'%7'(./0#-'(%F#20./123%."*%'00*7.1(%0120*2.('?
./12%/$% SU SE⁄ 06 K %'2,%."*%,121(%0120*2.('./12%/$%SU SD⁄ 06 K3
&/2,% ."*% F#20./12% 4#/-.?/2% +1-.'8*:% G$$#6*% #+ e
SU
K
S:D × SU ⁄ 06 :% G-$13% &/2,% ."*% )/,."% 1&% ."*% ,*7-*./12
(*8/12% A<C% '2,% /.$% *@.*2.% /2% *'0"% 1&% ."*% "% '2,% #% (*8/12$
)"*2% ."*% F#20./12% .*(6/2'-$% '(*% -*&.% 17*2:% <'-0#-'.*% ."*
6'82/.#,*%1&%."*%0"'(8*%$.1(*,%12%*/."*(%$/,*%1&%."*%F#20?
./12:%G$$#6*%."'.%."*%F#20./12%'(*'%/$%BUU%µ6=:
mn (cm2/V·s)
mp (cm2/V·s)
SKDU
BcU
SSUU
BUU
bUU
=EU
KEU
SDU
Dn (cm2/s)
Dp (cm2/s)
CHAPTER 3 P R O B L E M S
162 Chapter 3 Semiconductors
3.14 O$./6'.*%."*%.1.'-%0"'(8*%$.1(*,%/2%'%U:S?µ6%,*7-*./12
-'5*(%12%12*%$/,*%1&%'% SU?µ6 × SU?µ6 %F#20./12:%!"*%,17?
SE
K
/28%0120*2.('./12%12%."'.%$/,*%1&%."*%F#20./12%/$% SU ⁄ 06 :
3.15 >2%'%"#%F#20./12%&1(%)"/0"% 1 3 # 1 2 3%'2,%."*%,*7-*?
./12%-'5*(%*@/$.$%61$.-5%12%."*%$"'--1)-5%,17*,%$/,*%)/."%<%e
SE
K
U:K%µ63%&/2,% = U %/&% 1 2 ! SU ⁄ 06 :%G-$1%0'-0#-'.*% B 9 :
)/--%4*%'77(1@/6'.*-5%."*%$'6*%&'0.1(%45%)"/0"% 6 A %0"'28*$
&1(%'%D°<%(/$*%/2%.*67*('.#(*:%\"'.%/$%."*%&'0.1(h
l
3.22 G% " # %F#20./12%/$%12*%/2%)"/0"%."*%,17/28%0120*2.('?
./12%/2%."*%"%(*8/12%/$%6#0"%8(*'.*(%."'2%."'.%/2%."*%#!(*8/12:
>2%$#0"%'%F#20./123%."*%&1()'(,%0#((*2.%/$%61$.-5%,#*%.1%"1-*
/2F*0./12%'0(1$$%."*%F#20./12:%J"1)%."'.%
3.16 M5% "1)% 6#0"% ,1*$% = U % 0"'28*% /&% 1 3 % 1(% 1 2 % /$
/20(*'$*,%45%'%&'0.1(%1&%SUh
=⁄=
= 2"
?(% ) " S)
6 ! 6 " ! 3$# + ????????????
;" 12
Section 3.5: The pn Junction with an Applied
Voltage
;1(% ."*% $7*0/&/0% 0'$*% /2% )"/0"% 1 2 ! SU ⁄ 06 3
=
B
2 " ! SU%06 ⁄ $3% ; " ! SU% µ63% '2,% 3 ! SU % µ6=3% &/2,
6 A % '2,% ."*% +1-.'8*% =% 14.'/2*,% )"*2% 6% e% U:D% 6G:% G$$#6*
SU
K
17*('./12%'.%KUU%Y%)"*(*% # + ! S:D × SU ⁄ 06 :
SE
3.17 >&% '% D?P% (*+*($*?4/'$% +1-.'8*% /$% '77-/*,% '0(1$$% ."*
F#20./12%$7*0/&/*,%/2%r(14-*6%K:SK3%&/2,%<%'2,% B 9 :
3.18 J"1)% ."'.% &1(% '! "#% F#20./12% (*+*($*?4/'$*,% )/."% '
+1-.'8*% = E 3% ."*% ,*7-*./12?-'5*(% )/,."% <% '2,% ."*% 0"'(8*
$.1(*,%12%*/."*(%$/,*%1&%."*%F#20./123%B 9 3%0'2%4*%*@7(*$$*,%'$%
=
<% ! < U S # ?????E?
=U
B 9% ! B 9U
K
3.23%G%"#%F#20./12%&1(%)"/0"%."*%4(*'9,1)2%+1-.'8*%/$%S=%P
"'$%'%('.*,%A/:*:3%6'@/6#6%'--1)'4-*C%71)*(%,/$$/7'./12%1&
U:=D% \:% \"'.% 012./2#1#$%0#((*2.%/2%."*%4(*'9,1)2%(*8/12
)/--% ('/$*% ."*% ,/$$/7'./12% .1% "'-&% ."*% ('.*,% +'-#*h% >&% 4(*'9?
,1)2%100#($%&1(%12-5%SU%6$%/2%*+*(5%=U%6$3%)"'.%'+*('8*
4(*'9,1)2%0#((*2.%/$%'--1)*,h
Section 3.6: Capacitive Effects in the pn
Junction
=
S # ?????E?
=U
3.24% ;1(% ."*% "#% F#20./12% $7*0/&/*,% /2% r(14-*6% K:SK3% &/2,
L MU%'2,% L M %'.% = E % ! D %P:
)"*(*% < U %'2,% B 9U %'(*%."*%+'-#*$%/2%*V#/-/4(/#6:
3.19 >2%'%&1()'(,?4/'$*,%"#%F#20./12%$"1)%."'.%."*%('./1%1&
."*%0#((*2.%016712*2.%,#*%.1%"1-*%/2F*0./12%'0(1$$%."*%F#20?
./12%.1%."*%016712*2.%,#*%.1%*-*0.(12%/2F*0./12%/$%8/+*2%45%
3.25 ;1(% '% 7'(./0#-'(% F#20./12% &1(% )"/0"% L MU ! U:E% 7;3
= U ! U:bD%P3%'2,%K%e%S`K3%&/2,% L M %'.%(*+*($*?4/'$%+1-.'8*$
6" 2" ;# 13
???? % ! ?????? ????? ???????
6# 2# ;" 12
3.26%!"*%F#20./12%0'7'0/.'20*%L M%0'2%4*%."1#8".%1&%'$%."'.
1&%'%7'('--*-?7-'.*%0'7'0/.1(%'2,%."#$%8/+*2%45
Sc
K
O+'-#'.*% ."/$% ('./1% &1(% ."*% 0'$*% 1 3 ! SU ⁄ 06 3
SE
K
1 2 ! SU ⁄ 06 3% ; " ! D µ63% ; # ! SU µ63% 2" e
=
SU%06 ⁄ $ 3%'2,% 2 # ! =U%06 = ⁄ $ 3%'2,%"*20*%&/2,% 6 " %'2,
6 # %&1(%."*%0'$*%/2%)"/0"%."*%"#%F#20./12%/$%012,#0./28%'%&1(?
)'(,%0#((*2.%6!e%S%6G:
3.20%<'-0#-'.*% 6 A %'2,%."*%0#((*2.%6!&1(%=%e%bUU%6P%&1(%'%"#
Sb
K
SE
K
F#20./12% &1(% )"/0"% 1 3 % ! SU ⁄ 06 3% 1 2 ! SU ⁄ 06 3%3 e
SU
K
=
=UU µ6 3% # + % ! S:D × SU ⁄ 06 3% ; " % ! D µ63% ; # ! SU µ63
=
=
2 " % ! SU%06 ⁄ $ 3%'2,% 2 #% ! Sc%06 ⁄ $ :
3.21 G$$#6/28% ."'.% ."*% .*67*('.#(*% ,*7*2,*20*% 1&% 6 A
=
'(/$*$% 61$.-5% 4*0'#$*% 6 A % /$% 7(171(./12'-% .1% # + 3% #$*% ."*
*@7(*$$/12% &1(% # + % /2% OV:% AK:=C% .1% ,*.*(6/2*% ."*% &'0.1(% 45
=
)"/0"% # + %0"'28*$%'$%)!0"'28*$%&(16%KUU%Y%.1%KUD%Y:%!"/$
1&%S%P%'2,%SU%P:
??????
L M % ! ε3
<
J"1)%."'.%."/$%'77(1'0"%-*',$%.1%'%&1(6#-'%/,*2./0'-%.1%."'.
14.'/2*,% 45% 0164/2/28% OV$: AK:BKC% '2,% AK:BDC% o1(% *V#/+'?
-*2.-53%45%0164/2/28%OV$: AK:BbC%'2,%AK:BcCp:
3.27 G% "#% F#20./12% 17*('./28% /2% ."*% &1()'(,?4/'$% (*8/12
)/."%'%0#((*2.%6%1&%S%6G%/$%&1#2,%.1%"'+*%'%,/&&#$/12%0'7'0/?
.'20*% 1&% SU% 7;:% \"'.% ,/&&#$/12% 0'7'0/.'20*% ,1% 51#% *@7*0.
."/$%F#20./12%.1%"'+*%'.%6!e%U:S%6Gh%\"'.%/$%."*%6*'2%.('2$/.
./6*%&1(%."/$%F#20./12h
3.28 ;1(% ."*% "l#% F#20./12% $7*0/&/*,% /2% r(14-*6% K:==3% &/2,
τ " %'2,%0'-0#-'.*%."*%*@0*$$%6/21(/.5%0'((/*(%0"'(8*%'2,%."*
+'-#*%1&%."*%,/&&#$/12%0'7'0/.'20*%'.%6%e%U:=%6G:
Problems
=
./+*-5:%G$%'%(*$#-.3%."*%*@0*$$%6/21(/.5%0'((/*(%,/$.(/4#./12%/2
*'0"% (*8/12% /$% '% $.('/8".% -/2*% ('."*(% ."'2% ."*% *@712*2./'-$
$"1)2%/2%;/8:%K:S=:
2"
2#
= ⁄ =)
=
6 ! 3$# + ?????????????????????????????? # ?????????????????????????????
? (%
" S)
( < # " 5 # )1 2 ( < " " 5 " )1 3
'2,
=
S<
! ??? ???????#? 6 " 3%&1(% < # # 5 #
= 2"
A0C%G-$13%'$$#6/28% B ! B " 3% 6 ! 6 " 3%$"1)%."'.
τ
L , % ! ?????)? 6
=)
)"*(*
=
S<
τ ) % ! ??? ??????#?
= 2"
A,C% >&% '% ,*$/82*(% )/$"*$% .1% -/6/.% L , % .1% c% 7;% '.% 6% e% S% 6G3
)"'.%$"1#-,%< # %4*h%G$$#6*% 2 " ! SU%06=⁄ $ :
CHAPTER 3 P R O B L E M S
S ( <# " 5# ) ?
6"
B " % ! ??? ????????????????????????
=
2"
3.29 G%5/-&#:2'5$)(!-($%/$%12*%)"*(*%."*%)/,."$%1&%."*%"
'2,% #% (*8/12$% '(*% 6#0"% $6'--*(% ."'2% ; # % '2,% ; " 3% (*$7*0?
A'C%;1(%."*%$"1(.?4'$*%,/1,*3%$9*.0"%'%&/8#(*%01((*$712,/28
.1%;/8:%K:S=%'2,%'$$#6*%'$%/2%;/8:%K:S=%."'.% 1 3 # 1 2 :
A4C% ;1--1)/28% '% ,*(/+'./12% $/6/-'(% .1% ."'.% 8/+*2% /2% J*0./12
K:D:=3% $"1)% ."'.% /&% ."*% )/,."$% 1&% ."*% "% '2,% #! (*8/12$% '(*
,*21.*,% < " %'2,% < # %."*2
163
CHAPTER 4
Diodes
Introduction
4.1
4.5 Rectifier Circuits
165
The Ideal Diode
166
4.2 Terminal Characteristics of Junction
Diodes 173
4.3 Modeling the Diode Forward
Characteristic 179
4.4 Operation in the Reverse Breakdown
Region—Zener Diodes 189
194
4.6 Limiting and Clamping Circuits
4.7 Special Diode Types
Summary
215
Problems
216
213
207
IN THIS CHAPTER YOU WILL LEARN
1. The characteristics of the ideal diode and how to analyze and design circuits containing multiple ideal diodes together with resistors and dc
sources to realize useful and interesting nonlinear functions.
2. The details of the !"v characteristic of the junction diode (which was derived in Chapter 3) and how to use it to analyze diode circuits operating
in the various bias regions: forward, reverse, and breakdown.
3. A simple but effective model of the diode !"v characteristic in the forward direction; the constant-voltage-drop model.
4. A powerful technique for the application and modeling of the diode (and
in later chapters, transistors): dc-biasing the diode and modeling its operation for small signals around the dc operating point by means of the
small-signal model.
5. The use of a string of forward-biased diodes and of diodes operating in
the breakdown region (zener diodes), to provide constant dc voltages
(voltage regulators).
6. Application of the diode in the design of rectifier circuits, which convert
ac voltages to dc as needed for powering electronic equipment.
7. A number of other practical and important applications of diodes.
Introduction
!"#$%&'()*+#,#&"-#.#/)#-)&0(#&012+(#)"(3*)04#/3(%#03")&*#53*563(+7#&"4#"2"03")&*3(48#+65%#&+
(%&(#3"(*2-65)-#94#&1'03:3)*#26('6(#+&(6*&(32"8#/&+#(*)&()-#&+#&#'*290)1#(2#9)#+20;)-#94#(%)
53*563(# -)+3<")*=# >2/);)*8# (%)*)# &*)# 1&"4# 2(%)*# +3<"&0?'*25)++3"<# :6"5(32"+# (%&(# 5&"# 9)
31'0)1)"()-# 2"04# 94# "2"03")&*# 53*563(+=# @A&1'0)+# 3"506-)# (%)# <)")*&(32"# 2:# -5# ;20(&<)+
:*21# (%)# &5# '2/)*# +6''048# &"-# (%)# <)")*&(32"# 2:# +3<"&0+# 2:# ;&*326+# /&;):2*1+# B)=<=8
+3"6+23-+8#+C6&*)#/&;)+8#'60+)+D=#E0+28#-3<3(&0#02<35#&"-#1)12*4#53*563(+#52"+(3(6()#&#+')53&0
50&++#2:#"2"03")&*#53*563(+=
F%)# +31'0)+(# &"-# 12+(# :6"-&1)"(&0# "2"03")&*# 53*563(# )0)1)"(# 3+# (%)# -32-)=# G6+(# 03H)# &
*)+3+(2*8#(%)#-32-)#%&+#(/2#()*13"&0+7#96(#6"03H)#(%)#*)+3+(2*8#/%35%#%&+#&#03")&*#B+(*&3<%(?03")D
*)0&(32"+%3'#9)(/))"#(%)#56**)"(#:02/3"<#(%*26<%#3(#&"-#(%)#;20(&<)#&'')&*3"<#&5*2++#3(8#(%)
-32-)#%&+#&#"2"03")&*#!"v#5%&*&5()*3+(35=
165
166 Chapter 4 Diodes
F%3+#5%&'()*#3+#52"5)*")-#/3(%#(%)#+(6-4#2:#-32-)+=#!"#2*-)*#(2#6"-)*+(&"-#(%)#)++)"5)#2:
(%)#-32-)#:6"5(32"8#/)#9)<3"#/3(%#&#:35(3(326+#)0)1)"(8#(%)#3-)&0#-32-)=#I)#(%)"#3"(*2-65)#(%)
+30352"# J6"5(32"# -32-)8# )A'0&3"# 3(+# ()*13"&0# 5%&*&5()*3+(35+8# &"-# '*2;3-)# ()5%"3C6)+# :2*# (%)
&"&04+3+#2:#-32-)#53*563(+=#F%)#0&(()*#(&+H#3";20;)+#(%)#31'2*(&"(#+69J)5(#2:#-);35)#12-)03"<=
K6*#+(6-4#2:#12-)03"<#(%)#-32-)#5%&*&5()*3+(35+#/300#0&4#(%)#:26"-&(32"#:2*#26*#+(6-4#2:#12-?
)03"<#(*&"+3+(2*#2')*&(32"#3"#(%)#")A(#(/2#5%&'()*+=
K:#(%)#1&"4#&''035&(32"+#2:#-32-)+8#(%)3*#6+)#3"#(%)#-)+3<"#2:#*)5(3:3)*+#B/%35%#52";)*(#&5
(2# -5D# 3+# (%)# 12+(# 52112"=# F%)*):2*)# /)# +%&00# +(6-4# *)5(3:3)*# 53*563(+# 3"# +21)# -)(&30# &"9*3):04# 022H# &(# &# "619)*# 2:# 2(%)*# -32-)# &''035&(32"+=# L6*(%)*# "2"03")&*# 53*563(+# (%&(# 6(303M)
-32-)+#&"-#2(%)*#-);35)+#/300#9)#:26"-#(%*26<%26(#(%)#922H8#96(#'&*(3560&*04#3"#$%&'()*#,N=
F%)#J6"5(32"#-32-)#3+#"2(%3"<#12*)#(%&"#(%)##$#J6"5(32"#/)#+(6-3)-#3"#$%&'()*#O8#&"12+(#2:#(%3+#5%&'()*#3+#52"5)*")-#/3(%#(%)#+(6-4#2:#+30352"##$?J6"5(32"#-32-)+=#!"#(%)#0&+(#+)5?
(32"8# %2/);)*8#/)#9*3):04#52"+3-)*#+21)# +')53&03M)-#-32-)#(4')+8#3"506-3"<#(%)# '%2(2-32-)
&"-#(%)#03<%(?)13((3"<#-32-)=
4.1 The Ideal Diode
4.1.1 Current–Voltage Characteristic
F%)#3-)&0#-32-)#1&4#9)#52"+3-)*)-#(2#9)#(%)#12+(#:6"-&1)"(&0#"2"03")&*#53*563(#)0)1)"(=#!(
3+#&#(/2?()*13"&0#-);35)#%&;3"<#(%)#53*563(#+41920#2:#L3<=#P=,B&D#&"-#(%) !"v 5%&*&5()*3+(35
+%2/"#3"#L3<=#P=,B9D=#F%)#()*13"&0#5%&*&5()*3+(35#2:#(%)#3-)&0#-32-)#5&"#9)#3"()*'*)()-#&+#:20?
02/+Q# !:# &# ")<&(3;)# ;20(&<)# B*)0&(3;)# (2# (%)# *):)*)"5)# -3*)5(32"# 3"-35&()-# 3"# L3<=# P=,&D# 3+
&''03)-#(2#(%)#-32-)8#"2#56**)"(#:02/+#&"-#(%)#-32-)#9)%&;)+#&+#&"#2')"#53*563(#BL3<=#P=,5D=
R32-)+#2')*&()-#3"#(%3+#12-)#&*)#+&3-#(2#9)#!"#"!$"%&'($")8#2*#2')*&()-#3"#(%)#*);)*+)#-3*)5?
(32"=#E"#3-)&0#-32-)#%&+#M)*2#56**)"(#/%)"#2')*&()-#3"#(%)#*);)*+)#-3*)5(32"#&"-#3+#+&3-#(2#9)
*+,%-..8#2*#+31'04#-..=
K"#(%)#2(%)*#%&"-8#3:#&#'2+3(3;)#56**)"(#B*)0&(3;)#(2#(%)#*):)*)"5)#-3*)5(32"#3"-35&()-#3"#L3<=
P=,&D#3+#&''03)-#(2#(%)#3-)&0#-32-)8#M)*2#;20(&<)#-*2'#&'')&*+#&5*2++#(%)#-32-)=#!"#2(%)*#/2*-+8
(%)#3-)&0#-32-)#9)%&;)+#&+#&#+%2*(#53*563(#3"#(%)#%&'()'*#-3*)5(32"#BL3<=#P=,-D7#3(#'&++)+#&"4#56*?
*)"(#/3(%#M)*2#;20(&<)#-*2'=#E#.-!/(!)0&'($")#-32-)#3+#+&3-#(2#9)#,+!1")%-18#2*#+31'04#-1=
L*21#(%)#&92;)#-)+5*3'(32"#3(#+%260-#9)#"2()-#(%&(#(%)#)A()*"&0#53*563(#16+(#9)#-)+3<")-#(2
0313(# (%)# :2*/&*-# 56**)"(# (%*26<%# &# 52"-65(3"<# -32-)8# &"-# (%)# *);)*+)# ;20(&<)# &5*2++# &# 56(2::
-32-)8#(2#'*)-)()*13")-#;&06)+=#L3<6*)#P=.#+%2/+#(/2#-32-)#53*563(+#(%&(#3006+(*&()#(%3+#'23"(=#!"
(%)#53*563(#2:#L3<=#P=.B&D#(%)#-32-)#3+#29;326+04#52"-65(3"<=#F%6+#3(+#;20(&<)#-*2'#/300#9)#M)*28#&"(%)#56**)"(#(%*26<%#3(#/300#9)#-)()*13")-#94#(%)#+,S?T#+6''04#&"-#(%)#,?HΩ#*)+3+(2*#&+#,S#1E=
F%)#-32-)#3"#(%)#53*563(#2:#L3<=#P=.B9D#3+#29;326+04#56(#2::8#&"-#(%6+#3(+#56**)"(#/300#9)#M)*28#/%35%
3"#(6*"#1)&"+#(%&(#(%)#)"(3*)#,S?T#+6''04#/300#&'')&*#&+#*);)*+)#93&+#&5*2++#(%)#-32-)=
F%)# '2+3(3;)# ()*13"&0# 2:# (%)# -32-)# 3+# 5&00)-# (%)# (1-)"# &"-# (%)# ")<&(3;)# ()*13"&0# (%)
*(,2-)"8# &# 5&**42;)*# :*21# (%)# -&4+# 2:# ;&5661?(69)# -32-)+=# F%)# !"v# 5%&*&5()*3+(35# 2:# (%)
3-)&0#-32-)#B52"-65(3"<#3"#2")#-3*)5(32"#&"-#"2(#3"#(%)#2(%)*D#+%260-#)A'0&3"#(%)#5%235)#2:#3(+
&**2/#03H)#53*563(#+41920=
###E+#+%260-#9)#);3-)"(#:*21#(%)#'*)5)-3"<#-)+5*3'(32"8#(%)#!"v#5%&*&5()*3+(35#2:#(%)#3-)&0
-32-)#3+#%3<%04#"2"03")&*7#&0(%26<%#3(#52"+3+(+#2:#(/2#+(*&3<%(?03")#+)<1)"(+8#(%)4#&*)#&(#US°#(2
2")#&"2(%)*=#E#"2"03")&*#56*;)#(%&(#52"+3+(+#2:#+(*&3<%(?03")#+)<1)"(+#3+#+&3-#(2#9)#3'"*"/'$"
4'1"(!=#!:#&#-);35)#%&;3"<#&#'3)5)/3+)?03")&*#5%&*&5()*3+(35#3+#6+)-#3"#&#'&*(3560&*#&''035&(32"
3"# +65%# &# /&4# (%&(# (%)# +3<"&0# &5*2++# 3(+# ()*13"&0+# +/3"<+# &02"<# 2"04# 2")# 2:# (%)# 03")&*
4.1 The Ideal Diode
i
"
v
!
Figure 4.1 F%)#3-)&0#-32-)Q#5(6#-32-)#53*563(#+419207#5&6# !"v 5%&*&5()*3+(357#5*6#)C63;&0)"(#53*563(#3"#(%)
*);)*+)#-3*)5(32"7#5)6#)C63;&0)"(#53*563(#3"#(%)#:2*/&*-#-3*)5(32"=
(a)
(b)
Figure 4.2 F%)# (/2# 12-)+# 2:# 2')*&(32"# 2:# 3-)&0# -32-)+
&"-# (%)# 6+)# 2:# &"# )A()*"&0# 53*563(# (2# 0313(# 5(6# (%)# :2*/&*56**)"(#&"-#5&6%(%)#*);)*+)#;20(&<)=
+)<1)"(+8#(%)"#(%)#-);35)#5&"#9)#52"+3-)*)-#&#03")&*#53*563(#)0)1)"(#&+#:&*#&+#(%&(#'&*(3560&*
53*563(#&''035&(32"#3+#52"5)*")-=#K"#(%)#2(%)*#%&"-8#3:#+3<"&0+#+/3"<#'&+(#2")#2*#12*)#2:#(%)
9*)&H#'23"(+#3"#(%)#5%&*&5()*3+(358#03")&*#&"&04+3+#3+#"2#02"<)*#'2++390)=
4.1.2 A Simple Application: The Rectifier
E#:6"-&1)"(&0#&''035&(32"#2:#(%)#-32-)8#2")#(%&(#1&H)+#6+)#2:#3(+#+);)*)04#"2"03")&*#!"v#56*;)8#3+
(%)#*)5(3:3)*#53*563(#+%2/"#3"#L3<=#P=OB&D=#F%)#53*563(#52"+3+(+#2:#(%)#+)*3)+#52"")5(32"#2:#&#-32-)#+
&"-#&#*)+3+(2*#,=#V)(#(%)#3"'6(#;20(&<)#v-#9)#(%)#+3"6+23-#+%2/"#3"#L3<=#P=OB9D8#&"-#&++61)#(%)
167
168 Chapter 4 Diodes
-32-)#(2#9)#3-)&0=#R6*3"<#(%)#'2+3(3;)#%&0:?5450)+#2:#(%)#3"'6(#+3"6+23-8#(%)#'2+3(3;)#v-#/300#5&6+)
56**)"(#(2#:02/#(%*26<%#(%)#-32-)#3"#3(+#:2*/&*-#-3*)5(32"=#!(#:2002/+#(%&(#(%)#-32-)#;20(&<)
v+# /300# 9)# ;)*4# +1&00W3-)&004# M)*2=# F%6+# (%)# 53*563(# /300# %&;)# (%)# )C63;&0)"(# +%2/"# 3"
L3<=#P=OB5D8#&"-#(%)#26('6(#;20(&<)#v.#/300#9)#)C6&0#(2#(%)#3"'6(#;20(&<)#v-=#K"#(%)#2(%)*
%&"-8#-6*3"<#(%)#")<&(3;)#%&0:?5450)+#2:# v- 8#(%)#-32-)#/300#"2(#52"-65(=#F%6+#(%)#53*563(
/300#%&;)#(%)#)C63;&0)"(#+%2/"#3"#L3<=#P=OB-D8#&"-#v.#/300#9)#M)*2=#F%6+#(%)#26('6(#;20(&<)
/300#%&;)#(%)#/&;):2*1#+%2/"#3"#L3<=#P=OB)D=#X2()#(%&(#/%30)#v-#&0()*"&()+#3"#'20&*3(4#&"%&+#&#M)*2#&;)*&<)#;&06)8#v.#3+#6"3-3*)5(32"&0#&"-#%&+#&#:3"3()#&;)*&<)#;&06)#2*#&#*/0/&1#&2
$3$4=#F%6+#(%)#53*563(#2:#L3<=#P=OB&D#!"*,'.'"$#(%)#+3<"&0#&"-#%)"5)#3+#5&00)-#&#!"*,'.'"!=#!(
5&"#9)#6+)-#(2#<)")*&()#-5#:*21#&5=#I)#/300#+(6-4#*)5(3:3)*#53*563(+#3"#Y)5(32"#P=Z=
D
(a)
(b)
vI $ 0
vI # 0
(c)
(d)
(e)
Figure 4.3 5(6#[)5(3:3)*#53*563(=#5&6#!"'6(#/&;):2*1=#5*6#@C63;&0)"(#53*563(#/%)"# v-# ≥# S=#5)6#@C63;&0)"(
53*563(#/%)"#v-#≤#S=#5"6#K6('6(#/&;):2*1=
4.1 The Ideal Diode 169
EXERCISES
4.1# L2*#(%)#53*563(#3"#L3<=#P=OB&D8#+H)(5%#(%)#(*&"+:)*#5%&*&5()*3+(35#v.#;)*+6+#v-=
Ans. Y))#L3<=#@P=,=
Figure E4.1
4.2# L2*#(%)#53*563(#3"#L3<=#P=OB&D8#+H)(5%#(%)#/&;):2*1#2:#v+=
Ans. v+#\#v-#]#v. 8#*)+60(3"<#3"#(%)#/&;):2*1#3"#L3<=#@P=.
Figure E4.2
4.3# !"#(%)#53*563(#2:#L3<=#P=OB&D8#0)(#v-#%&;)#&#')&H#;&06)#2:#,S#T#&"-#,#=#,#HΩ=#L3"-#(%)#')&H#;&06)#2:#!+
&"-#(%)#-5#521'2")"(#2:#v.=
Ans. ,S#1E7#O=,^#T
Example 4.1
L3<6*)#P=PB&D#+%2/+#&#53*563(#:2*#5%&*<3"<#&#,.?T#9&(()*4=#!:#v5#3+#&#+3"6+23-#/3(%#.P?T#')&H#&1'03?
(6-)8#:3"-#(%)#:*&5(32"#2:#)&5%#5450)#-6*3"<#/%35%#(%)#-32-)#52"-65(+=#E0+28#:3"-#(%)#')&H#;&06)#2:
(%)#-32-)#56**)"(#&"-#(%)#1&A3161#*);)*+)?93&+#;20(&<)#(%&(#&'')&*+#&5*2++#(%)#-32-)=
170 Chapter 4 Diodes
Example 4.1 continued
(b)
(a)
Figure 4.4 $3*563(#&"-#/&;):2*1+#:2*#@A&1'0)#P=,=
Solution
F%)# -32-)# 52"-65(+# /%)"# v5# )A5))-+# ,.# T8# &+# +%2/"# 3"# L3<=# P=PB9D=# F%)# 52"-65(32"# &"<0)# 3+# .θ8
/%)*)#θ#3+#<3;)"#94
.P#52+ θ = ,.
F%6+#θ#=#`S°#&"-#(%)#52"-65(32"#&"<0)#3+#,.S°8#2*#2")?(%3*-#2:#&#5450)=
F%)#')&H#;&06)#2:#(%)#-32-)#56**)"(#3+#<3;)"#94
! ,.? " S=,.#E
- * " .P
?????????????????
,SS
F%)#1&A3161#*);)*+)#;20(&<)#&5*2++#(%)#-32-)#2556*+#/%)"#v5 3+#&(#3(+#")<&(3;)#')&H#&"-#3+#)C6&0#(2
.P#+#,.#=#O`#T=
4.1.3 Another Application: Diode Logic Gates
R32-)+#(2<)(%)*#/3(%#*)+3+(2*+#5&"#9)#6+)-#(2#31'0)1)"(#-3<3(&0#02<35#:6"5(32"+=#L3<6*)#P=Z
+%2/+#(/2#-32-)#02<35#<&()+=#F2#+))#%2/#(%)+)#53*563(+#:6"5(32"8#52"+3-)*#&#'2+3(3;)?02<35
+4+()1#3"#/%35%#;20(&<)#;&06)+#502+)#(2#S#T#52**)+'2"-#(2#02<35#S#B2*#02/D#&"-#;20(&<)#;&06)+
502+)#(2#+Z#T#52**)+'2"-#(2#02<35#,#B2*#%3<%D=#F%)#53*563(#3"#L3<=#P=ZB&D#%&+#(%*))#3"'6(+8#v6 8
v78#&"-#v8=#!(#3+#)&+4#(2#+))#(%&(#-32-)+#52"")5()-#(2#+Z?T#3"'6(+#/300#52"-65(8#(%6+#50&1'3"<
(%)# 26('6(# v9# (2# &# ;&06)# )C6&0# (2# +Z# T=# F%3+# '2+3(3;)# ;20(&<)# &(# (%)# 26('6(# /300# H))'# (%)
-32-)+# /%2+)# 3"'6(+#&*)#02/#B&*26"-#S#TD#56(# 2::=#F%6+# 4:30&;4#;40(!<<0=30:!>:0!%0&$30&'
1&'30&%04:30!$#;4?0)'30:!>:=#F%)#53*563(#(%)*):2*)#31'0)1)"(+#(%)#4-7'*%89%.+1*,'-18#/%35%
3"#_220)&"#"2(&(32"#3+#)A'*)++)-#&+
9 = 6+7+8
Y3130&*048#(%)#*)&-)*#3+#)"526*&<)-#(2#+%2/#(%&(#6+3"<#(%)#+&1)#02<35#+4+()1#1)"(32")&92;)8#(%)#53*563(#2:#L3<=#P=ZB9D#31'0)1)"(+#(%)#4-7'*%:;<%.+1*,'-18
9 = 6⋅7⋅8
4.1 The Ideal Diode 171
(a)
(b)
Figure 4.5 R32-)#02<35#<&()+Q#5(6#K[#<&()7#5&6#EXR#<&()#B3"#&#'2+3(3;)?02<35#+4+()1D=
Example 4.2
E++613"<#(%)#-32-)+#(2#9)#3-)&08#:3"-#(%)#;&06)+#2:#-#&"-#@#3"#(%)#53*563(+#2:#L3<=#P=`=
D
D
(a)
D
D
(b)
Figure 4.6 $3*563(+#:2*#@A&1'0)#P=.=
Solution
!"#(%)+)#53*563(+#3(#13<%(#"2(#9)#29;326+#&(#:3*+(#+3<%(#/%)(%)*#"2")8#2")8#2*#92(%#-32-)+#&*)#52"-65(3"<=
!"#+65%#&#5&+)8#(301)A30)0#<);?!=<30)??;1#4!&$B0#'&/33*0(!4:04:30)$)<C?!?B0)$*04:3$0/:3/A0(:34:3'0(3
3$*0;#0(!4:0)0/&$?!?43$40?&<;4!&$=#L2*#(%)#53*563(#3"#L3<=#P=`B&D8#/)#+%&00#&++61)#(%&(#92(%#-32-)+#&*)
52"-65(3"<=#!(#:2002/+#(%&(#@7#=#S#&"-#@#=#S=#F%)#56**)"(#(%*26<%#+.#5&"#"2/#9)#-)()*13")-#:*21
172 Chapter 4 Diodes
Example 4.2 continued
,S ! S
- +. = ??????????????? = ,#1E
,S
I*3(3"<#&#"2-)#)C6&(32"#&(#_8
S ! ( ! ,S )
- + , = ???????????????????????
Z
*)+60(+#3"#-#=#,#1E=#F%6+#+,#3+#52"-65(3"<#&+#2*3<3"&004#&++61)-8#&"-#(%)#:3"&0#*)+60(#3+#-#= ,
1E#&"-#@#=#S#T=
L2*# (%)# 53*563(# 3"# L3<=# P=`B9D8# 3:# /)# &++61)# (%&(# 92(%# -32-)+# &*)# 52"-65(3"<8# (%)"
@7 = S#&"-#@#=#S=#F%)#56**)"(#3"#+.#3+#29(&3")-#:*21
,S ! S
- +. = ??????????????? = .#1E
Z
F%)#"2-)#)C6&(32"#&(#_#3+
S ! ( ! ,S )
- + . = ???????????????????????
,S
/%35%#43)0-+#-0=#−,#1E=#Y3"5)#(%3+#3+#"2(#'2++390)8#26*#2*3<3"&0#&++61'(32"#3+#$&4#52**)5(=#I)
+(&*(#&<&3"8#&++613"<#(%&(#+,#3+#2::#&"-#+.#3+#2"=#F%)#56**)"(#-+.#3+#<3;)"#94
,S ! ( ! ,S )
- +. = ?????????????????????????? = ,=OO#1E
,Z
&"-#(%)#;20(&<)#&(#"2-)#_#3+
@ 7 = ],S + ,S × ,=OO = +O=O#T
F%6+#+,#3+#*);)*+)#93&+)-#&+#&++61)-8#&"-#(%)#:3"&0#*)+60(#3+#-0=#S#&"-#@#=#O=O#T=
EXERCISES
4.4# L3"-#(%)#;&06)+#2:#-#&"-#@#3"#(%)#53*563(+#+%2/"#3"#L3<=#@P=P=
(a)
Figure E4.4
(b)
(c)
(d)
4.2 Terminal Characteristics of Junction Diodes 173
(f)
(e)
Figure E4.4 B$2"(3"6)-D
Ans. B&D#.#1E8#S#T7#B9D#S#1E8#Z#T7#B5D#S#1E8#Z#T7#B-D#.#1E8#S#T7#B)D#O#1E8#+O#T7#B:D#P#1E8#+,#T
4.5# L3<6*)#@P=Z#+%2/+#&#53*563(#:2*#&"#&5#;20(1)()*=#!(#6(303M)+#&#12;3"<?5230#1)()*#(%&(#<3;)+#&#:600?+5&0)#*)&-?
3"<#/%)"#(%)#)D3')>3#56**)"(#:02/3"<#(%*26<%#3(#3+#,#1E=#F%)#12;3"<?5230#1)()*#%&+#&#ZS?Ω#*)+3+(&"5)=
Moving-coil
meter
Figure E4.5
L3"-# (%)# ;&06)# 2:# ,# (%&(# *)+60(+# 3"# (%)# 1)()*# 3"-35&(3"<# &# :600?+5&0)# *)&-3"<# /%)"# (%)# 3"'6(# +3")?/&;)
;20(&<)#vI#3+#.S#T#')&H?(2?')&H=#BE!$4F#F%)#&;)*&<)#;&06)#2:#%&0:?+3")#/&;)+#3+#@# aπ=D#
Ans. #O=,OO#HΩ
4.2 Terminal Characteristics of Junction Diodes
F%)#12+(#52112"#31'0)1)"(&(32"#2:#(%)#-32-)#6(303M)+#&##$#J6"5(32"=#I)#%&;)#+(6-3)-#(%)
'%4+35+#2:#(%)##$#J6"5(32"#&"-#-)*3;)-#3(+#!]v#5%&*&5()*3+(35#3"#$%&'()*#O=#F%&(#(%)##$#J6"5?
(32"#3+#6+)-#(2#31'0)1)"(#(%)#-32-)#:6"5(32"#+%260-#521)#&+#"2#+6*'*3+)Q#(%)##$#J6"5(32"#5&"
52"-65(# +69+(&"(3&0# 56**)"(# 3"# (%)# :2*/&*-# -3*)5(32"# &"-# &012+(# "2# 56**)"(# 3"# (%)# *);)*+)
-3*)5(32"=#!"#(%3+#+)5(32"#/)#+(6-4#(%)#!]v#5%&*&5()*3+(35#2:#(%)##$#J6"5(32"#-32-)#3"#-)(&30#3"
2*-)*#(2#'*)'&*)#26*+)0;)+#:2*#-32-)#53*563(#&''035&(32"+=
L3<6*)#P=N#+%2/+#(%)#!]v#5%&*&5()*3+(35#2:#&#+30352"#J6"5(32"#-32-)=#F%)#+&1)#5%&*&5()*3+?
(35#3+#+%2/"#3"#L3<=#P=^#/3(%#+21)#+5&0)+#)A'&"-)-#&"-#2(%)*+#521'*)++)-#(2#*);)&0#-)(&30+=
X2()#(%&(#(%)#+5&0)#5%&"<)+#%&;)#*)+60()-#3"#(%)#&''&*)"(#-3+52"(3"63(4#&(#(%)#2*3<3"=
174 Chapter 4 Diodes
Figure 4.7 F%)#!]v##5%&*&5()*3+(35#2:#&#+30352"#J6"5(32"#-32-)=
Figure 4.8 F%)# -32-)# !]v# # *)0&(32"+%3'# /3(%# +21)# +5&0)+# )A'&"-)-# &"-# 2(%)*+# 521'*)++)-# 3"# 2*-)*# (2
*);)&0#-)(&30+=
E+#3"-35&()-8#(%)#5%&*&5()*3+(35#56*;)#52"+3+(+#2:#(%*))#-3+(3"5(#*)<32"+Q
1. F%)#:2*/&*-?93&+#*)<32"8#-)()*13")-#94#v#b#S
2. F%)#*);)*+)?93&+#*)<32"8#-)()*13")-#94#v#c#S
3. F%)#9*)&H-2/"#*)<32"8#-)()*13")-#94#v#c#]@GH
F%)+)#(%*))#*)<32"+#2:#2')*&(32"#&*)#-)+5*39)-#3"#(%)#:2002/3"<#+)5(32"+=
4.2 Terminal Characteristics of Junction Diodes 175
4.2.1 The Forward-Bias Region
F%)# :2*/&*-?93&+W2*# +31'04# :2*/&*-W*)<32"# 2:# 2')*&(32"# 3+# )"()*)-# /%)"# (%)# ()*13"&0
;20(&<)#v#3+#'2+3(3;)=#!"#(%)#:2*/&*-#*)<32"#(%)#!]v#*)0&(32"+%3'#3+#502+)04#&''*2A31&()-#94#
v⁄@
BP=,D
! = -5 ( 3 I ! , )
!"#(%3+#)C6&(32",#-5#3+#&#52"+(&"(#:2*#&#<3;)"#-32-)#&(#&#<3;)"#()1')*&(6*)=#E#:2*160&#:2*#-5#3"
()*1+#2:#(%)#-32-)d+#'%4+35&0#'&*&1)()*+#&"-#()1')*&(6*)#/&+#<3;)"#3"#@C=BO=P,D=#F%)#56*?
*)"(# -5# 3+# 6+6&004# 5&00)-# (%)# $(,+!(,'-1% *+!!"1,# B:2*# *)&+2"+# (%&(# /300# 9)521)# &''&*)"(
+%2*(04D=#E"2(%)*#"&1)#:2*#-5 8#&"-#2")#(%&(#/)#/300#255&+32"&004#6+)8#3+#(%)#$*(4"%*+!!"1,=
F%3+#"&1)#&*3+)+#:*21#(%)#:&5(#(%&(#-5#3+#-3*)5(04#'*2'2*(32"&0#(2#(%)#5*2++?+)5(32"&0#&*)&#2:
(%)#-32-)=#F%6+#-26903"<#2:#(%)#J6"5(32"#&*)&#*)+60(+#3"#&#-32-)#/3(%#-2690)#(%)#;&06)#2:#-5
&"-8#&+#(%)#-32-)#)C6&(32"#3"-35&()+8#-2690)#(%)#;&06)#2:#56**)"(#!#:2*#&#<3;)"#:2*/&*-#;20(&<)
v=#L2*#e+1&00?+3<"&0f#-32-)+8#/%35%#&*)#+1&00?+3M)#-32-)+#3"()"-)-#:2*#02/?'2/)*#&''035&?
(32"+8#-5#3+#2"#(%)#2*-)*#2:#,S],Z#E=#F%)#;&06)#2:#-5#3+8#%2/);)*8#&#;)*4#+(*2"<#:6"5(32"#2:#()1?
')*&(6*)=#E+#&#*60)#2:#(%6198#-5#-2690)+#3"#;&06)#:2*#);)*4#Z°$#*3+)#3"#()1')*&(6*)=
F%)#;20(&<)#@I#3"#@C=#BP=,D#3+#&#52"+(&"(#5&00)-#(%)#,2"!=(4%#-4,(7"#&"-#3+#<3;)"#94
AI
@I = ??????
J
BP=.D
/%)*)
A0=#_20(M1&""d+#52"+(&"(#=#^=`.#× ,S]Z#)Tag#=#,=O^#× ,S].O#J260)+aH)0;3"
I0=#(%)#&9+206()#()1')*&(6*)#3"#H)0;3"+#=#.NO#+#()1')*&(6*)#3"#°$
J#=#(%)#1&<"3(6-)#2:#)0)5(*2"35#5%&*<)#=#,=`S#×#,S],U#5260219#
Y69+(3(6(3"<#A#\#^=`.#× ,S]Z#)Tag#3"(2#@C=#BP=.D#<3;)+
@I = S=S^`.I8 1@
BP=.&D
F%6+8#&(#*221#()1')*&(6*)#B.S°$D#(%)#;&06)#2:#@I#3+#.Z=O#1T=#!"#*&'3-#&''*2A31&()#53*563(
&"&04+3+#/)#+%&00#6+)#@I#!#.Z#1T#&(#*221#()1')*&(6*)=.
L2*#&''*)53&90)#56**)"(#!#3"#(%)#:2*/&*-#-3*)5(32"8#+')53:35&004#:2*#!#%#-5 8#@C=#BP=,D#5&"#9)
&''*2A31&()-#94#(%)#)A'2")"(3&0#*)0&(32"+%3'
!0! -5 3
vK @
I
BP=OD
F%3+#*)0&(32"+%3'#5&"#9)#)A'*)++)-#&0()*"&(3;)04#3"#(%)#02<&*3(%135#:2*1
!
-5
v = @I 0" ????
BP=PD
/%)*)#0"#-)"2()+#(%)#"&(6*&0#B9&+)#3D#02<&*3(%1=
,
@C6&(32"#BP=,D8#(%)#-32-)#)C6&(32"8#3+#+21)(31)+#/*3(()"#(2#3"506-)#&#52"+(&"(#$#3"#(%)#)A'2")"(3&08
va$A4
#! \ -5 B3
],D
/3(%#$#%&;3"<#&#;&06)#9)(/))"#,#&"-#.8#-)')"-3"<#2"#(%)#1&()*3&0#&"-#(%)#'%4+35&0#+(*65(6*)#2:#(%)#-32-)=
R32-)+#6+3"<#(%)#+(&"-&*-#3"()<*&()-?53*563(#:&9*35&(32"#'*25)++#)A%393(#$#\#,#/%)"#2')*&()-#6"-)*#"2*?
1&0#52"-3(32"+=#L2*#+31'0353(48#/)#+%&00#6+)#$#\#,#(%*26<%26(#(%3+#922H8#6"0)++#2(%)*/3+)#+')53:3)-=
.
E#+03<%(04#%3<%)*#&193)"(#()1')*&(6*)#B.Z°$#2*#+2D#3+#6+6&004#&++61)-#:2*#)0)5(*2"35#)C63'1)"(#2')*?
&(3"<#3"+3-)#&#5&93")(=#E(#(%3+#()1')*&(6*)8#@I##!#.Z=^#1T=#X);)*(%)0)++8#:2*#(%)#+&H)#2:#+31'0353(4#&"(2#'*212()#*&'3-#53*563(#&"&04+3+8#/)#+%&00#6+)#(%)#12*)#&*3(%1)(35&004#52";)"3)"(#;&06)#2:#@I#!#.Z#1T
(%*26<%26(#(%3+#922H=
176 Chapter 4 Diodes
F%)#)A'2")"(3&0#*)0&(32"+%3'#2:#(%)#56**)"(#!#(2#(%)#;20(&<)#v#%20-+#2;)*#1&"4#-)5&-)+#2:
56**)"(#B&#+'&"#2:#&+#1&"4#&+# +);)"#-)5&-)+W3=)=8#&#:&5(2*#2:#,SNW5&"#9)#:26"-D=#F%3+#3+
C63()#&#*)1&*H&90)#'*2')*(4#2:#J6"5(32"#-32-)+8#2")#(%&(#3+#&0+2#:26"-#3"#93'20&*#J6"5(32"#(*&"?
+3+(2*+#&"-#(%&(#%&+#9))"#)A'023()-#3"#1&"4#3"()*)+(3"<#&''035&(32"+=
V)(# 6+# 52"+3-)*# (%)# :2*/&*-# !"v0 *)0&(32"+%3'# 3"# @C=# BP=OD# &"-# );&06&()# (%)# 56**)"(# -,
52**)+'2"-3"<#(2#&#-32-)#;20(&<)#@,Q
@ ⁄ @I
-, = -5 3 ,
Y3130&*048#3:#(%)#;20(&<)#3+#@.8#(%)#-32-)#56**)"(#-.#/300#9)
@ ⁄ @I
- . = -5 3 .
F%)+)#(/2#)C6&(32"+#5&"#9)#52193")-#(2#'*2-65)
(@ ! @ ) ⁄ @
????. = 3 . , I
-,
/%35%#5&"#9)#*)/*3(()"#&+
@ . ! @ , = @ I 0" ????.
-,
2*8#3"#()*1+#2:#9&+)?,S#02<&*3(%1+8
@ . ! @ , = .=O@I 02< ????.
-,
BP=ZD
F%3+#)C6&(32"#+31'04#+(&()+#(%&(#:2*#&#-)5&-)#B:&5(2*#2:#,SD#5%&"<)#3"#56**)"(8#(%)#-32-)#;20(?
&<)#-*2'#5%&"<)+#94#.=O@I 8#/%35%#3+#&''*2A31&()04#`S#1T=#F%3+#&0+2#+6<<)+(+#(%&(#(%)#-32-)
!"v# *)0&(32"+%3'# 3+# 12+(# 52";)"3)"(04# '02(()-# 2"# +)1302<# '&')*=# h+3"<# (%)# ;)*(35&08# 03")&*
&A3+#:2*#v#&"-#(%)#%2*3M2"(&08#02<#&A3+#:2*#!8#2")#29(&3"+#&#+(*&3<%(#03")#/3(%#&#+02')#2:#`S 1T
')*#-)5&-)#2:#56**)"(=
E#<0&"5)#&(#(%)#!"v#5%&*&5()*3+(35#3"#(%)#:2*/&*-#*)<32"#BL3<=#P=^D#*);)&0+#(%&(#(%)#56**)"(
3+#")<03<3904#+1&00#:2*#v#+1&00)*#(%&"#&926(#S=Z#T=#F%3+#;&06)#3+#6+6&004#*):)**)-#(2#&+#(%)#*+,0
'1%#-4,(7"=#!(#+%260-#9)#)1'%&+3M)-8#%2/);)*8#(%&(#(%3+#&''&*)"(#(%*)+%20-#3"#(%)#5%&*&5()*3+?
(35#3+#+31'04#&#52"+)C6)"5)#2:#(%)#)A'2")"(3&0#*)0&(32"+%3'=#E"2(%)*#52"+)C6)"5)#2:#(%3+#*)0&?
(32"+%3'#3+#(%)#*&'3-#3"5*)&+)#2:#!=#F%6+8#:2*#&#e:6004#52"-65(3"<f#-32-)8#(%)#;20(&<)#-*2'#03)+
3"#&#"&**2/#*&"<)8#&''*2A31&()04#S=`#T#(2#S=^#T=#F%3+#<3;)+#*3+)#(2#&#+31'0)#e12-)0f#:2*#(%)
-32-)#/%)*)#3(#3+#&++61)-#(%&(#&#52"-65(3"<#-32-)#%&+#&''*2A31&()04#&#S=N?T#-*2'#&5*2++#3(=
R32-)+# /3(%# -3::)*)"(# 56**)"(# *&(3"<+# B3=)=8# -3::)*)"(# &*)&+# &"-# 52**)+'2"-3"<04# -3::)*)"(# -5D
/300#)A%393(#(%)#S=N?T#-*2'#&(#-3::)*)"(#56**)"(+=#L2*#3"+(&"5)8#&#+1&00?+3<"&0#-32-)#1&4#9)
52"+3-)*)-#(2#%&;)#&#S=N?T#-*2'#&(#!0=#,#1E8#/%30)#&#%3<%)*?'2/)*#-32-)#1&4#%&;)#&#S=N?T
-*2'#&(#! =#,#E=#I)#/300#+(6-4#(%)#(2'35+#2:#-32-)?53*563(#&"&04+3+#&"-#-32-)#12-)0+#3"#(%)
")A(#+)5(32"=
Example 4.3
E#+30352"#-32-)#+&3-#(2#9)#&#,?1E#-);35)#-3+'0&4+#&#:2*/&*-#;20(&<)#2:#S=N#T#&(#&#56**)"(#2:#,#1E=
@;&06&()#(%)#J6"5(32"#+5&03"<#52"+(&"(#-5=#I%&(#+5&03"<#52"+(&"(+#/260-#&''04#:2*#&#,?E#-32-)#2:#(%)
+&1)#1&"6:&5(6*)#(%&(#52"-65(+#,#E#&(#S=N#Ti
4.2 Terminal Characteristics of Junction Diodes 177
Solution
Y3"5)#
! = -5 3
v ⁄ @I
(%)"
- 5 = !3
!v ⁄ @I
L2*#(%)#,?1E#-32-)Q
-5#=#,S−O3−NSSa.Z#=#`=U#×#,S−,`#E
F%)#-32-)#52"-65(3"<#,#E#&(#S=N#T#52**)+'2"-+#(2#2")?(%26+&"-#,?1E#-32-)+#3"#'&*&00)0#/3(%#&#(2(&0
J6"5(32"#&*)&#,SSS#(31)+#<*)&()*=#F%6+#-5#3+#&0+2#,SSS#(31)+#<*)&()*8#
-5#=##`=U#×#,S−,O#E
Y3"5)#92(%#-5#&"-#@I#&*)#:6"5(32"+#2:#()1')*&(6*)8#(%)#:2*/&*-#!"v#5%&*&5()*3+(35#;&*3)+#/3(%#()1?
')*&(6*)8#&+#3006+(*&()-#3"#L3<=#P=U=#E(#&#<3;)"#52"+(&"(#-32-)#56**)"(8#(%)#;20(&<)#-*2'#&5*2++#(%)#-32-)
-)5*)&+)+#94#&''*2A31&()04#.#1T#:2*#);)*4#,°$#3"5*)&+)#3"#()1')*&(6*)=#F%)#5%&"<)#3"#-32-)#;20(?
&<)#/3(%#()1')*&(6*)#%&+#9))"#)A'023()-#3"#(%)#-)+3<"#2:#)0)5(*2"35#(%)*121)()*+=
Figure 4.9 F)1')*&(6*)# -)')"-)"5)# 2:# (%)
-32-)# :2*/&*-# 5%&*&5()*3+(35=# E(# &# 52"+(&"(
56**)"(8#(%)#;20(&<)#-*2'#-)5*)&+)+#94#&''*2A3?
1&()04#.#1T#:2*#);)*4#,°$#3"5*)&+)#3"#()1')*&?
(6*)=
EXERCISES
4.6# L3"-#(%)#5%&"<)#3"#-32-)#;20(&<)#3:#(%)#56**)"(#5%&"<)+#:*21#S=,#1E#(2#,S#1E=
Ans. ,.S#1T
4.7# E#+30352"#J6"5(32"#-32-)#%&+#v#= #S=N#T#&(#!0=#,#1E=#L3"-#(%)#;20(&<)#-*2'#&(#!#=#S=,#1E#&"-#
! =#,S#1E=
Ans. #S=`P#T7#S=N`#T
4.8# h+3"<#(%)#:&5(#(%&(#&#+30352"#-32-)#%&+#-5#=#,S−,P#E#&(#.Z°$#&"-#(%&(#-5#3"5*)&+)+#94#,Zj#')*#°$#*3+)#3"
()1')*&(6*)8#:3"-#(%)#;&06)#2:#-5#&(#,.Z°$=##
Ans. ,=,N#×#,S−^#E
178 Chapter 4 Diodes
4.2.2 The Reverse-Bias Region
F%)#*);)*+)?93&+#*)<32"#2:#2')*&(32"#3+#)"()*)-#/%)"#(%)#-32-)#;20(&<)#v#3+#1&-)#")<&(3;)=#@C6&?
(32"#BP=,D#'*)-35(+#(%&(#3:#v#3+#")<&(3;)#&"-#&#:)/#(31)+#0&*<)*#(%&"#@I#B.Z#1TD#3"#1&<"3(6-)8#(%)
)A'2")"(3&0#()*1#9)521)+#")<03<3904#+1&00#521'&*)-#(2#6"3(48#&"-#(%)#-32-)#56**)"(#9)521)+
!#! ]-5
F%&(#3+8#(%)#56**)"(#3"#(%)#*);)*+)#-3*)5(32"#3+#52"+(&"(#&"-#)C6&0#(2#-5=#F%3+#52"+(&"54#3+#(%)
*)&+2"#9)%3"-#(%)#()*1#?)4;')4!&$0/;''3$4=
[)&0#-32-)+#)A%393(#*);)*+)#56**)"(+#(%&(8#(%26<%#C63()#+1&008#&*)#165%#0&*<)*#(%&"#-5=#L2*
3"+(&"5)8#&#+1&00?+3<"&0#-32-)#/%2+)#-5#3+#2"#(%)#2*-)*#2:#,S−,P#E#(2#,S−,Z#E#5260-#+%2/#&
*);)*+)#56**)"(#2"#(%)#2*-)*#2:#,#"E=#F%)#*);)*+)#56**)"(#&0+2#3"5*)&+)+#+21)/%&(#/3(%#(%)
3"5*)&+)#3"#1&<"3(6-)#2:#(%)#*);)*+)#;20(&<)=#X2()#(%&(#9)5&6+)#2:#(%)#;)*4#+1&00#1&<"3(6-)
2:#(%)#56**)"(8#(%)+)#-)(&30+#&*)#"2(#50)&*04#);3-)"(#2"#(%)#-32-)#!]v#5%&*&5()*3+(35#2:#L3<=#P=^=#
E#0&*<)#'&*(#2:#(%)#*);)*+)#56**)"(#3+#-6)#(2#0)&H&<)#)::)5(+=#F%)+)#0)&H&<)#56**)"(+#&*)
'*2'2*(32"&0#(2#(%)#J6"5(32"#&*)&8#J6+(#&+#-5#3+=#F%)3*#-)')"-)"5)#2"#()1')*&(6*)8#%2/);)*8#3+
-3::)*)"(#:*21#(%&(#2:#-5=#F%6+8#/%)*)&+#-5#-2690)+#:2*#);)*4#Z°$#*3+)#3"#()1')*&(6*)8#(%)#52**)?
+'2"-3"<#*60)#2:#(%619#:2*#(%)#()1')*&(6*)#-)')"-)"5)#2:#(%)#*);)*+)#56**)"(#3+#(%&(#3(#-26?
90)+#:2*#);)*4#,S°$#*3+)#3"#()1')*&(6*)=
EXERCISE
4.9# F%)#-32-)#3"#(%)#53*563(#2:#L3<=#@P=U#3+#&#0&*<)#%3<%?56**)"(#-);35)#/%2+)#*);)*+)#0)&H&<)#3+#*)&+2"&904
3"-)')"-)"(#2:#;20(&<)=#!:#@#=#,#T#&(#.0°$8#:3"-#(%)#;&06)#2:#@#&(#PS°$#&"-#&(#S°$=
Figure E4.9
Ans. P#T7#S=.Z#T
4.2.3 The Breakdown Region
F%)#(%3*-#-3+(3"5(#*)<32"#2:#-32-)#2')*&(32"#3+#(%)#9*)&H-2/"#*)<32"8#/%35%#5&"#9)#)&+304
3-)"(3:3)-#2"#(%)#-32-)#!]v#5%&*&5()*3+(35#3"#L3<=#P=^=#F%)#9*)&H-2/"#*)<32"#3+#)"()*)-#/%)"#(%)
1&<"3(6-)#2:#(%)#*);)*+)#;20(&<)#)A5))-+#&#(%*)+%20-#;&06)#(%&(#3+#+')53:35#(2#(%)#'&*(3560&*#-32-)8
5&00)-#(%)#&!"(>)-/1%#-4,(7"=#F%3+#3+#(%)#;20(&<)#&(#(%)#eH"))f#2:#(%)#!]v#56*;)#3"#L3<=#P=^#&"-#3+
-)"2()-#@GH8#/%)*)#(%)#+69+5*3'(#G#+(&"-+#:2*#M)")*#B+))#Y)5(32"#O=Z=OD#&"-#H#-)"2()+#H"))=
4.3 Modeling the Diode Forward Characteristic 179
E+#5&"#9)#+))"#:*21#L3<=#P=^8#3"#(%)#9*)&H-2/"#*)<32"#(%)#*);)*+)#56**)"(#3"5*)&+)+#*&'?
3-048#/3(%#(%)#&++253&()-#3"5*)&+)#3"#;20(&<)#-*2'#9)3"<#;)*4#+1&00=#R32-)#9*)&H-2/"#3+#"2*?
1&004# "2(# -)+(*65(3;)8# '*2;3-)-# (%)# '2/)*# -3++3'&()-# 3"# (%)# -32-)# 3+# 0313()-# 94# )A()*"&0
53*563(*4#(2#&#e+&:)f#0);)0=#F%3+#+&:)#;&06)#3+#"2*1&004#+')53:3)-#2"#(%)#-);35)#-&(&#+%))(+=#!(
(%)*):2*)#3+#")5)++&*4#(2#0313(#(%)#*);)*+)#56**)"(#3"#(%)#9*)&H-2/"#*)<32"#(2#&#;&06)#52"+3+?
()"(#/3(%#(%)#')*13++390)#'2/)*#-3++3'&(32"=
F%)#:&5(#(%&(#(%)#-32-)#!]v#5%&*&5()*3+(35#3"#9*)&H-2/"#3+#&012+(#&#;)*(35&0#03")#)"&90)+#3(
(2#9)#6+)-#3"#;20(&<)#*)<60&(32"=#F%3+#+69J)5(#/300#9)#+(6-3)-#3"#Y)5(32"#P=Z=
4.3 Modeling the Diode Forward Characteristic
>&;3"<#+(6-3)-#(%)#-32-)#()*13"&0#5%&*&5()*3+(35+#/)#&*)#"2/#*)&-4#(2#52"+3-)*#(%)#&"&04+3+#2:
53*563(+#)1'0243"<#:2*/&*-?52"-65(3"<#-32-)+=#L3<6*)#P=,S#+%2/+#+65%#&#53*563(=#!(#52"+3+(+#2:#&
-5#+26*5)#@++8#&#*)+3+(2*#,8#&"-#&#-32-)=#I)#/3+%#(2#&"&04M)#(%3+#53*563(#(2#-)()*13")#(%)#-32-)
;20(&<)#@+#&"-#56**)"(#-+=#F2/&*-#(%&(#)"-#/)#52"+3-)*#-);)02'3"<#&#;&*3)(4#2:#12-)0+#:2*#(%)
2')*&(32"#2:#(%)#-32-)=#I)#&0*)&-4#H"2/#2:#(/2#+65%#12-)0+Q#(%)#3-)&0?-32-)#12-)08#&"-#(%)
)A'2")"(3&0#12-)0=#!"#(%)#:2002/3"<#-3+56++32"#/)#+%&00#&++)++#(%)#+63(&9303(4#2:#(%)+)#(/2#12-?
)0+#3"#;&*326+#&"&04+3+#+3(6&(32"+=#E0+28#/)#+%&00#-);)02'#&"-#5211)"(#2"#2(%)*#12-)0+=#F%3+
1&()*3&08#9)+3-)+#9)3"<#6+):60#3"#(%)#&"&04+3+#&"-#-)+3<"#2:#-32-)#53*563(+8#)+(&903+%)+#&#:26"-&?
(32"#:2*#(%)#12-)03"<#2:#(*&"+3+(2*#2')*&(32"#(%&(#/)#/300#+(6-4#3"#(%)#")A(#(/2#5%&'()*+=
4.3.1 The Exponential Model
F%)#12+(#&556*&()#-)+5*3'(32"#2:#(%)#-32-)#2')*&(32"#3"#(%)#:2*/&*-#*)<32"#3+#'*2;3-)-#94
(%)# )A'2")"(3&0# 12-)0=# h":2*(6"&()048# %2/);)*8# 3(+# +);)*)04# "2"03")&*# "&(6*)# 1&H)+# (%3+
12-)0#(%)#12+(#-3::3560(#(2#6+)=#F2#3006+(*&()8#0)(d+#&"&04M)#(%)#53*563(#3"#L3<=#P=,S#6+3"<#(%)
)A'2")"(3&0#-32-)#12-)0=
E++613"<#(%&(#@++#3+#<*)&()*#(%&"#S=Z#T#2*#+28#(%)#-32-)#56**)"(#/300#9)#165%#<*)&()*#(%&"
-5 8#&"-#/)#5&"#*)'*)+)"(#(%)#-32-)#!]v#5%&*&5()*3+(35#94#(%)#)A'2")"(3&0#*)0&(32"+%3'8#*)+60(3"<#3"
@ ⁄ @I
-+ = -5 3 +
BP=`D
F%)# 2(%)*# )C6&(32"# (%&(# <2;)*"+# 53*563(# 2')*&(32"# 3+# 29(&3")-# 94# /*3(3"<# &# g3*5%%2::# 022'
)C6&(32"8#*)+60(3"<#3"
@++ ! @+
-+ = ?????????????????????
,
BP=ND
E++613"<#(%&(#(%)#-32-)#'&*&1)()*#-5#3+#H"2/"8#@C+=#BP=`D#&"-#BP=ND#&*)#(/2#)C6&(32"+#3"#(%)
(/2# 6"H"2/"# C6&"(3(3)+# -+# &"-# @+=# F/2# &0()*"&(3;)# /&4+# :2*# 29(&3"3"<# (%)# +206(32"# &*)
<*&'%35&0#&"&04+3+#&"-#3()*&(3;)#&"&04+3+=
Figure 4.10 E#+31'0)#53*563(#6+)-#(2#3006+(*&()#(%)#&"&04+3+#2:
53*563(+#3"#/%35%#(%)#-32-)#3+#:2*/&*-#52"-65(3"<=
180 Chapter 4 Diodes
4.3.2 Graphical Analysis Using the Exponential Model
k*&'%35&0#&"&04+3+#3+#')*:2*1)-#94#'02((3"<#(%)#*)0&(32"+%3'+#2:#@C+=#BP=`D#&"-#BP=ND#2"#(%)
!]v#'0&")=#F%)#+206(32"#5&"#(%)"#9)#29(&3")-#&+#(%)#522*-3"&()+#2:#(%)#'23"(#2:#3"()*+)5(32"#2:
(%)#(/2#<*&'%+=#E#+H)(5%#2:#(%)#<*&'%35&0#52"+(*65(32"#3+#+%2/"#3"#L3<=#P=,,=#F%)#56*;)#*)'?
*)+)"(+#(%)#)A'2")"(3&0#-32-)#)C6&(32"#B@C=#P=`D8#&"-#(%)#+(*&3<%(#03")#*)'*)+)"(+#@C=#BP=ND=
Y65%#&#+(*&3<%(#03")#3+#H"2/"#&+#(%)#4-()%4'1"8#&#"&1)#(%&(#/300#9)521)#12*)#1)&"3"<:60
3"#0&()*#5%&'()*+=#F%)#02&-#03")#3"()*+)5(+#(%)#-32-)#56*;)#&(#'23"(#L8#/%35%#*)'*)+)"(+#(%)
-3"!(,'17%3-'1,#2:#(%)#53*563(=#!(+#522*-3"&()+#<3;)#(%)#;&06)+#2:#-+#&"-#@+=
k*&'%35&0# &"&04+3+# &3-+# 3"# (%)# ;3+6&03M&(32"# 2:# 53*563(# 2')*&(32"=# >2/);)*8# (%)# )::2*(
3";20;)-#3"#')*:2*13"<#+65%#&"#&"&04+3+8#'&*(3560&*04#:2*#521'0)A#53*563(+8#3+#(22#<*)&(#(2#9)#J6+(3?
:3)-#3"#'*&5(35)=
Figure 4.11 k*&'%35&0#&"&04+3+#2:#(%)#53*563(#3"#L3<=#P=,S#6+3"<#(%)#)A'2")"(3&0#-32-)#12-)0=
4.3.3 Iterative Analysis Using the Exponential Model
@C6&(32"+#BP=`D#&"-#BP=ND#5&"#9)#+20;)-#6+3"<#&#+31'0)#3()*&(3;)#'*25)-6*)8#&+#3006+(*&()-#3"
(%)#:2002/3"<#)A&1'0)=
Example 4.4
R)()*13")#(%)#56**)"(#-+#&"-#(%)#-32-)#;20(&<)#@+#:2*#(%)#53*563(#3"#L3<=#P=,S#/3(%#@++#=#Z#T#&"-#
,#=#,#HΩ=#E++61)#(%&(#(%)#-32-)#%&+#&#56**)"(#2:#,#1E#&(#&#;20(&<)#2:#S=N#T=
Solution
F2#9)<3"#(%)#3()*&(32"8#/)#&++61)#(%&(#@+#=#S=N#T#&"-#6+)#@C=#BP=ND#(2#-)()*13")#(%)#56**)"(8
@++ ! @+
?
-+ = ?????????????????????
,
Z ! S=N
= ???????????????? = P=O#1E
,
4.3 Modeling the Diode Forward Characteristic 181
I)#(%)"#6+)#(%)#-32-)#)C6&(32"#(2#29(&3"#&#9)(()*#)+(31&()#:2*#@+=#F%3+#5&"#9)#-2")#94#)1'0243"<
@C=#BP=ZD8#"&1)048
@ . ! @ , = .=O@I 02< ???.?
-,
Y69+3(6(3"<#.=O@I#=#`S#1T8#/)#%&;)
@. = @ , + S=S` 02< ???.?
-,
Y69+(3(6(3"<#@,#=#S=N#T8#-,#=#,#1E8#&"-#-.#=#P=O#1E#*)+60(+#3"#@.#=#S=NO^#T=#F%6+#(%)#*)+60(+#2:#(%)#:3*+(#3()*?
&(32"#&*)#-+#=#P=O#1E#&"-#@+#=#S=NO^#T=#F%)#+)52"-#3()*&(32"#'*25))-+#3"#&#+3130&*#1&"")*Q
Z ! S=NO^
-+ = ?????????????????????? = P=.`.#1E
,
P=.`.
@. = S=NO^ + S=S`#02< ?????????????
P=O
= S=NO^#T
F%6+#(%)#+)52"-#3()*&(32"#43)0-+#-+#=#P=.`.#1E#&"-#@+#=#S=NO^#T=#Y3"5)#(%)+)#;&06)+#&*)#;)*4#502+)
(2#(%)#;&06)+#29(&3")-#&:()*#(%)#:3*+(#3()*&(32"8#"2#:6*(%)*#3()*&(32"+#&*)#")5)++&*48#&"-#(%)#+206(32"#3+
-+#=#P=.`.#1E#&"-#@+#=#S=NO^#T=
4.3.4 The Need for Rapid Analysis
F%)#3()*&(3;)#&"&04+3+#'*25)-6*)#6(303M)-#3"#(%)#)A&1'0)#&92;)#3+#+31'0)#&"-#43)0-+#&556*&()
*)+60(+#&:()*#(/2#2*#(%*))#3()*&(32"+=#X);)*(%)0)++8#(%)*)#&*)#+3(6&(32"+#3"#/%35%#(%)#)::2*(#&"(31)#*)C63*)-#&*)#+(300#<*)&()*#(%&"#5&"#9)#J6+(3:3)-=#Y')53:35&0048#3:#2")#3+#-23"<#&#')"530?&"-?
'&')*#-)+3<"#2:#&#*)0&(3;)04#521'0)A#53*563(8#*&'3-#53*563(#&"&04+3+#3+#&#")5)++3(4=#F%*26<%
C635H# &"&04+3+8# (%)# -)+3<")*# 3+# &90)# (2# );&06&()# ;&*326+# '2++39303(3)+# 9):2*)# -)53-3"<# 2"# &
+63(&90)#53*563(#-)+3<"=#F2#+'))-#6'#(%)#&"&04+3+#'*25)++#2")#16+(#9)#52"()"(#/3(%#0)++#'*)53+)
*)+60(+=#F%3+8#%2/);)*8#3+#+)0-21#&#'*290)18#9)5&6+)#(%)#12*)#&556*&()#&"&04+3+#5&"#9)#'2+(?
'2")-#6"(30#&#:3"&0#2*#&012+(?:3"&0#-)+3<"#3+#29(&3")-=#E556*&()#&"&04+3+#2:#(%)#&012+(?:3"&0
-)+3<"#5&"#9)#')*:2*1)-#/3(%#(%)#&3-#2:#&#521'6()*#53*563(?&"&04+3+#'*2<*&1#+65%#&+#Yl!$@
B+))#E'')"-3A#_#&"-#(%)#-3+5D=#F%)#*)+60(+#2:#+65%#&"#&"&04+3+#5&"#(%)"#9)#6+)-#(2#:6*(%)*
*):3")#2*#e:3")?(6")f#(%)#-)+3<"=
F2#+'))-#6'#(%)#&"&04+3+#'*25)++8#/)#16+(#:3"-#&#+31'0)*#12-)0#:2*#(%)#-32-)#:2*/&*5%&*&5()*3+(35=
4.3.5 The Constant-Voltage-Drop Model
F%)#+31'0)+(#&"-#12+(#/3-)04#6+)-#-32-)#12-)0#3+#(%)#52"+(&"(?;20(&<)?-*2'#12-)0=#F%3+
12-)0#3+#9&+)-#2"#(%)#29+)*;&(32"#(%&(#&#:2*/&*-?52"-65(3"<#-32-)#%&+#&#;20(&<)#-*2'#(%&(
;&*3)+#3"#&#*)0&(3;)04#"&**2/#*&"<)8#+&4#S=`#(2#S=^#T=#F%)#12-)0#&++61)+#(%3+#;20(&<)#(2#9)
52"+(&"(#&(#&#;&06)8#+&48#S=N#T=#F%3+#-);)02'1)"(#3+#3006+(*&()-#3"#L3<=#P=,.=
182 Chapter 4 Diodes
i
i
0
0.7 V v
0
(a)
0.7 V v
(b)
i
"
vD
!
i & 0, vD ' 0.7 V
(c)
Figure 4.12 R);)02'1)"(#2:#(%)#-32-)#52"+(&"(?;20(&<)?-*2'#12-)0Q#5(6#(%)#)A'2")"(3&0#5%&*&5()*?
+(357# 5&6# &''*2A31&(3"<# (%)# )A'2")"(3&0# 5%&*&5()*3+(35# 94# &# 52"+(&"(# ;20(&<)8# 6+6&004# &926(# S=N# T37
5*6 (%)#*)+60(3"<#12-)0#2:#(%)#:2/&*-]52"-65(3"<#-32-)+=
F%)#52"+(&"(?;20(&<)?-*2'#12-)0#3+#(%)#2")#12+(#:*)C6)"(04#)1'024)-#3"#(%)#3"3(3&0#'%&+)+
2:#&"&04+3+#&"-#-)+3<"=#F%3+#3+#)+')53&004#(*6)#3:#&(#(%)+)#+(&<)+#2")#-2)+#"2(#%&;)#-)(&30)3":2*1&(32"#&926(#(%)#-32-)#5%&*&5()*3+(35+8#/%35%#3+#2:()"#(%)#5&+)=
L3"&0048#"2()#(%&(#3:#/)#)1'024#(%)#52"+(&"(?;20(&<)?-*2'#12-)0#(2#+20;)#(%)#'*290)1#3"
@A&1'0)#P=P8#/)#29(&3"
@+ = S=N#T
&"-
@++ ! S=N
?
- + = ?????????????????????
,
Z ! S=N
= ???????????????? = P=O#1E
,
/%35%#&*)#"2(#;)*4#-3::)*)"(#:*21#(%)#;&06)+#29(&3")-#9):2*)#/3(%#(%)#12*)#)0&92*&()#)A'2?
")"(3&0#12-)0=
4.3 Modeling the Diode Forward Characteristic
4.3.6 The Ideal-Diode Model
!"#&''035&(32"+#(%&(#3";20;)#;20(&<)+#165%#<*)&()*#(%&"#(%)#-32-)#;20(&<)#-*2'#BS=`#T]S=^#TD8
/)#1&4#")<0)5(#(%)#-32-)#;20(&<)#-*2'#&0(2<)(%)*#/%30)#5&0560&(3"<#(%)#-32-)#56**)"(=#F%)#*)+60(
3+# (%)# 3-)&0?-32-)# 12-)08# /%35%# /)# +(6-3)-# 3"# Y)5(32"# P=,=# L2*# (%)# 53*563(# 3"# @A&1'0)+# P=P
B3=)=8 L3<=#P=,S#/3(%#@++#=#Z#T#&"-#,#=#,#HΩD8#6(303M&(32"#2:#(%)#3-)&0?-32-)#12-)0#0)&-+#(2#
@ + = S#T
Z!S
- + = ???????????? = Z#1E
,
/%35%#:2*#&#;)*4#C635H#&"&04+3+#/260-#"2(#9)#9&-#&+#&#<*2++#)+(31&()=#>2/);)*8#/3(%#&012+(
"2#&--3(32"&0#/2*H8#(%)#S=N?T?-*2'#12-)0#43)0-+#165%#12*)#*)&03+(35#*)+60(+=#I)#"2()8#%2/?
);)*8#(%&(#(%)#<*)&()+(#6(303(4#2:#(%)#3-)&0?-32-)#12-)0#3+#3"#-)()*13"3"<#/%35%#-32-)+#&*)#2"
&"-#/%35%#&*)#2::#3"#&#160(3-32-)#53*563(8#+65%#&+#(%2+)#52"+3-)*)-#3"#Y)5(32"#P=,=
EXERCISES
4.10#L2*#(%)#53*563(#3"#L3<=#P=,S8#:3"-#-+#&"-#@+#:2*#(%)#5&+)#@++#=#Z#T#&"-#,#=#,S#HΩ=#E++61)#(%&(#(%)
-32-)#%&+#&#;20(&<)#2:#S=N#T#&(#,?1E#56**)"(=#h+)#B&D#3()*&(32"#&"-#B9D#(%)#52"+(&"(?;20(&<)?-*2'
12-)0#/3(%#@+#=#S=N#T=
Ans. B&D#S=PO#1E8#S=`^#T7#B9D#S=PO#1E8#S=N#T
D4.11#R)+3<"#(%)#53*563(#3"#L3<=#@P=,,#(2#'*2;3-)#&"#26('6(#;20(&<)#2:#.=P#T=#E++61)#(%&(#(%)#-32-)+#&;&30&90)
%&;)#S=N?T#-*2'#&(#,#1E=
Figure E4.11
Ans. ,#=#,OU#Ω
4.12# [)')&(#@A)*53+)#P=P#6+3"<#(%)#S=N?T?-*2'#12-)0#(2#29(&3"#9)(()*#)+(31&()+#2:#-#&"-#@#(%&"#(%2+)#:26"3"#@A)*53+)#P=P#B6+3"<#(%)#3-)&0?-32-)#12-)0D=
Ans. B&D#,=N.#1E8#S=N#T7#B9D#S#1E8#Z#T7#B5D#S#1E8#Z#T7#B-D#,=N.#1E8#S=N#T7#B)D#.=O#1E8#+.=O#T7#
B:D#O=O#1E8#+,=N#T
183
184 Chapter 4 Diodes
4.3.7 The Small-Signal Model
F%)*)#&*)#&''035&(32"+#3"#/%35%#&#-32-)#3+#93&+)-#(2#2')*&()#&(#&#'23"(#2"#(%)#:2*/&*-#!]v
5%&*&5()*3+(35#&"-#&#+1&00#&5#+3<"&0#3+#+6')*31'2+)-#2"#(%)#-5#C6&"(3(3)+=#L2*#(%3+#+3(6&(32"8
/)# :3*+(# %&;)# (2# -)()*13")# (%)# -5# 2')*&(3"<# '23"(# B@+# &"-# -+D# 2:# (%)# -32-)# 6+3"<# 2")# 2:
(%) 12-)0+# -3+56++)-# &92;)=# m2+(# :*)C6)"(048# (%)# S=N?T?-*2'# 12-)0# 3+# 6(303M)-=# F%)"8# :2*
+1&00?+3<"&0#2')*&(32"#&*26"-#(%)#-5#93&+#'23"(8#(%)#-32-)#3+#12-)0)-#94#&#*)+3+(&"5)#)C6&0#(2
(%)#3";)*+)#2:#(%)#+02')#2:#(%)#(&"<)"(#(2#(%)#)A'2")"(3&0#!]v#5%&*&5()*3+(35#&(#(%)#93&+#'23"(=
F%)# ()5%"3C6)# 2:# 93&+3"<# &# "2"03")&*# -);35)# &"-# *)+(*35(3"<# +3<"&0# )A56*+32"# (2# &# +%2*(8
&012+(?03")&*#+)<1)"(#2:#3(+#5%&*&5()*3+(35#&*26"-#(%)#93&+#'23"(#3+#5)"(*&0#(2#-)+3<"3"<#03")&*
&1'03:3)*+# 6+3"<# (*&"+3+(2*+8# &+# /300# 9)# +))"# 3"# (%)# ")A(# (/2# 5%&'()*+=# !"# (%3+# +)5(32"8# /)
-);)02'#+65%#&#+1&00?+3<"&0#12-)0#:2*#(%)#J6"5(32"#-32-)#&"-#3006+(*&()#3(+#&''035&(32"=#
Figure 4.13 R);)02'1)"(#2:#(%)#-32-)#+1&00?+3<"&0#12-)0=
4.3 Modeling the Diode Forward Characteristic 185
$2"+3-)*#(%)#52"5)'(6&0#53*563(#3"#L3<=#P=,OB&D#&"-#(%)#52**)+'2"-3"<#<*&'%35&0#*)'*)+)"?
(&(32"#3"#L3<=#P=,OB9D=#E#-5#;20(&<)#@+8#*)'*)+)"()-#94#&#9&(()*48#3+#&''03)-#(2#(%)#-32-)8#&"-#&
(31)?;&*43"<# +3<"&0# v* B4D8# &++61)-# B&*93(*&*304D# (2# %&;)# &# (*3&"<60&*# /&;):2*18# 3+
+6')*31'2+)-#2"#(%)#-5#;20(&<)#@+=#!"#(%)#&9+)"5)#2:#(%)#+3<"&0# v* B4D8#(%)#-32-)#;20(&<)#3+
)C6&0#(2#@+8#&"-#52**)+'2"-3"<048#(%)#-32-)#/300#52"-65(#&#-5#56**)"(#-+#<3;)"#94
@ ⁄ @I
-+ = -5 3 +
BP=^D
I%)"#(%)#+3<"&0#v* B4D#3+#&''03)-8#(%)#(2(&0#3"+(&"(&")26+#-32-)#;20(&<)#v+ B4D#/300#9)#<3;)"#94
v + ( 4 ) = @+ + v * ( 4 )
$2**)+'2"-3"<048#(%)#(2(&0#3"+(&"(&")26+#-32-)#56**)"(#!+ B4D#/300#9)
v+ ⁄ @I
!+ ( 4 ) = -5 3
BP=UD
BP=,SD
Y69+(3(6(3"<#:2*#v+#:*21#@C=#BP=UD#<3;)+
( @ + v* ) ⁄ @I
!+ ( 4 ) = -5 3 +
BP=,,D
/%35%#5&"#9)#*)/*3(()"
@ ⁄ @I
!+ ( 4 ) = -5 3 +
3
v* ⁄ @I
h+3"<#@C=#BP=^D#/)#29(&3"
!+ ( 4 ) = -+ 3
v* ⁄ @I
BP=,.D
X2/#3:#(%)#&1'03(6-)#2:#(%)#+3<"&0#v* B4D#3+#H)'(#+6::353)"(04#+1&00#+65%#(%&(
v
?????* (,
@I
BP=,OD
(%)"#/)#1&4#)A'&"-#(%)#)A'2")"(3&0#2:#@C=#BP=,.D#3"#&#+)*3)+#&"-#(*6"5&()#(%)#+)*3)+#&:()*#(%)
:3*+(#(/2#()*1+#(2#29(&3"#(%)#&''*2A31&()#)A'*)++32"
v
! + ( 4 )# ! #- + , + ?????* @I
BP=,PD
F%3+#3+#(%)#$=(440$'71(4%(33!-?'=(,'-1=#!(#3+#;&03-#:2*#+3<"&0+#/%2+)#&1'03(6-)+#&*)#+1&00)*
(%&"#&926(#Z#1T#B+))#@C=#P=,O8#&"-#*)5&00#(%&(#@I#=#.Z 1TD=O
L*21#@C=#BP=,PD#/)#%&;)
-+
! + ( 4 ) = - + + ?????
v
@I *
BP=,ZD
F%6+8#+6')*31'2+)-#2"#(%)#-5#56**)"(#-+8#/)#%&;)#&#+3<"&0#56**)"(#521'2")"(#-3*)5(04#'*2?
'2*(32"&0#(2#(%)#+3<"&0#;20(&<)#v*=#F%&(#3+8
/%)*)
!+ = -+ + !*
BP=,`D
-+
! * = ?????
v
@I *
BP=,ND
L2*#v*#=#Z#1T8# v * ⁄ @ I = S=.=#F%6+#(%)#")A(#()*1#3"#(%)#+)*3)+#)A'&"+32"#2:#(%)#)A'2")"(3&0#/300#9)# ,??.? #×
S=.. = S=S.8#&#:&5(2*#2:#,S#02/)*#(%&"#(%)#03")&*#()*1#/)#H)'(=
O
186 Chapter 4 Diodes
F%)#C6&"(3(4#*)0&(3"<#(%)#+3<"&0#56**)"(#!*#(2#(%)#+3<"&0#;20(&<)#v*#%&+#(%)#-31)"+32"+#2:#52"?
-65(&"5)8#1%2+#B )8#&"-#3+#5&00)-#(%)#)'-)"%$=(440$'71(4%*-1)+*,(1*"=#F%)#3";)*+)#2:#(%3+
'&*&1)()*#3+#(%)#)'-)"%$=(440$'71(4%!"$'$,(1*"8#2*#'1*!"="1,(4%!"$'$,(1*"8#'* 8
Ω
@
'* = ?????I
-+
BP=,^D
X2()#(%&(#(%)#;&06)#2:#'*#3+#3";)*+)04#'*2'2*(32"&0#(2#(%)#93&+#56**)"(#-+=
V)(#6+#*)(6*"#(2#(%)#<*&'%35&0#*)'*)+)"(&(32"#3"#L3<=#P=,OB9D=#!(#3+#)&+4#(2#+))#(%&(#6+3"<#(%)
+1&00?+3<"&0#&''*2A31&(32"#3+#)C63;&0)"(#(2#&++613"<#(%&(#4:30?!>$)<0)1#<!4;*30!?0?;%%!/!3$4<C
?1)<<0?;/:04:)404:303M/;'?!&$0)<&$>04:30!]v#/;'D30!?0<!1!43*04&0)0?:&'40)<1&?42<!$3)'0?3>13$4N
F%)#+02')#2:#(%3+#+)<1)"(8#/%35%#3+#)C6&0#(2#(%)#+02')#2:#(%)#(&"<)"(#(2#(%)#!]v#56*;)#&(#(%)
2')*&(3"<# '23"(# L8# 3+# )C6&0# (2# (%)# +1&00?+3<"&0# 52"-65(&"5)=# F%)# *)&-)*# 3+# )"526*&<)-# (2
'*2;)#(%&(#(%)#+02')#2:#(%)#!]v#56*;)#&(#!#=#-+#3+#)C6&0#(2# - + ⁄ @ I 8 #/%35%#3+# , ⁄ ' * 7#(%&(#3+8#
∂!
' * = ,## ????????+?
∂ v + !+ =-+
BP=,UD
L*21#(%)#'*)5)-3"<#/)#52"506-)#(%&(#+6')*31'2+)-#2"#(%)#C6&"(3(3)+#@+#&"-#-+#(%&(#-):3")
(%)#-5#93&+#'23"(8#2*#@+'"$*"1,%3-'1,8#2:#(%)#-32-)#/300#9)#(%)#+1&00?+3<"&0#C6&"(3(3)+#v* B4D#&"!* B4D8#/%35%#&*)#*)0&()-#94#(%)#-32-)#+1&00?+3<"&0#*)+3+(&"5)#'*#);&06&()-#&(#(%)#93&+#'23"(#B@C=
P=,^D=#F%6+#(%)#+1&00?+3<"&0#&"&04+3+#5&"#9)#')*:2*1)-#+)'&*&()04#:*21#(%)#-5#93&+#&"&04+3+8#&
<*)&(#52";)"3)"5)#(%&(#*)+60(+#:*21#(%)#03")&*3M&(32"#2:#(%)#-32-)#5%&*&5()*3+(35+#3"%)*)"(#3"#(%)
+1&00?+3<"&0#&''*2A31&(32"=# Y')53:35&0048#&:()*#(%)#-5#&"&04+3+# 3+# ')*:2*1)-8# (%)# +1&00?+3<"&0
)C63;&0)"(#53*563(#3+#29(&3")-#94#)0313"&(3"<#&00#-5#+26*5)+#B3=)=8#+%2*(?53*563(3"<#-5#;20(&<)
+26*5)+#&"-#2')"?53*563(3"<#-5#56**)"(#+26*5)+D#&"-#*)'0&53"<#(%)#-32-)#94#3(+#+1&00?+3<"&0#*)+3+?
(&"5)=#F%)#:2002/3"<#)A&1'0)#+%260-#3006+(*&()#(%)#&''035&(32"#2:#(%)#+1&00?+3<"&0#12-)0=
Example 4.5
$2"+3-)*#(%)#53*563(#+%2/"#3"#L3<=#P=,PB&D#:2*#(%)#5&+)#3"#/%35%#,#=#,S#HΩ=#F%)#'2/)*#+6''04#@ +#%&+#&#-5
;&06)#2:#,S#T#2"#/%35%#3+#+6')*31'2+)-#&#`S?>M#+3"6+23-#2:#,?T#')&H#&1'03(6-)=#BF%3+#e+3<"&0f#521'2?
")"(# 2:# (%)# '2/)*?+6''04# ;20(&<)# 3+# &"# 31')*:)5(32"# 3"# (%)# '2/)*?+6''04# -)+3<"=# !(# 3+# H"2/"# &+# (%)
3-/"!0$+334A%!'334"=#m2*)#2"#(%3+#0&()*=D#$&0560&()#92(%#(%)#-5#;20(&<)#2:#(%)#-32-)#&"-#(%)#&1'03(6-)#2:
(%)#+3")?/&;)#+3<"&0#&'')&*3"<#&5*2++#3(=#E++61)#(%)#-32-)#(2#%&;)#&#S=N?T#-*2'#&(#,?1E#56**)"(=
10 V
ID
R
R
"
VD
"
vs
"
!
rd
!
(a)
(b)
vd
!
(c)
Figure 4.14 5(6# $3*563(# :2*# @A&1'0)# P=Z=# 5&6# $3*563(# :2*# 5&0560&(3"<# (%)# -5# 2')*&(3"<# '23"(=# 5*6# Y1&00?+3<"&0
)C63;&0)"(#53*563(=
4.3 Modeling the Diode Forward Characteristic
187
Solution
$2"+3-)*3"<#-5#C6&"(3(3)+#2"048#/)#&++61)#@+#!#S=N#T#&"-#5&0560&()#(%)#-32-)#-5#56**)"(
,S ! S=N
- + = ??????????????????? = S=UO#1E
,S
Y3"5)#(%3+#;&06)#3+#;)*4#502+)#(2#,#1E8#(%)#-32-)#;20(&<)#/300#9)#;)*4#502+)#(2#(%)#&++61)-#;&06)#2:
S=N#T=#E(#(%3+#2')*&(3"<#'23"(8#(%)#-32-)#3"5*)1)"(&0#*)+3+(&"5)#'*#3+#
@
.Z
' * = ?????I? = ?????????? = .`=U#Ω
S=UO
-+
F%)# +3<"&0# ;20(&<)# &5*2++# (%)# -32-)# 5&"# 9)# :26"-# :*21# (%)# +1&00?+3<"&0# )C63;&0)"(# 53*563(# 3"
L3<= P=,PB5D=# >)*)# v?# -)"2()+# (%)# `S?>M# ,?T# ')&H# +3"6+23-&0# 521'2")"(# 2:# @ +8# &"-# v*# 3+# (%)# 52*?
*)+'2"-3"<#+3<"&0#&5*2++#(%)#-32-)=#h+3"<#(%)#;20(&<)?-3;3-)*#*60)#'*2;3-)+#(%)#')&H#&1'03(6-)#2:#v*
&+#:2002/+Q
'*
?
v * # ( ')&H ) = @n? ?????????????
, + '*
S=S.`U
= , ???????????????????????????? = .=`^ 1T #
,S + S=S.`U
L3"&004#/)#"2()#(%&(#+3"5)#(%3+#;&06)#3+#C63()#+1&008#26*#6+)#2:#(%)#+1&00?+3<"&0#12-)0#2:#(%)#-32-)#3+
J6+(3:3)-=
L3"&0048#/)#"2()#(%&(#/%30)#'*#12-)0+#(%)#+1&00?+3<"&0#2')*&(32"#2:#(%)#-32-)#&(#02/#:*)C6)"?
53)+8#3(+#-4"&135#2')*&(32"#3+#12-)0)-#94#(%)#5&'&53(&"5)+#8O#&"-#8* 8#/%35%#/)#+(6-3)-#3"#Y)5?
(32"#O=`#&"-#/%35%#&0+2#&*)#+1&00?+3<"&0#'&*&1)()*+=#E#521'0)()#12-)0#2:#(%)#-32-)#3"506-)+#8O
&"-#8*03"#'&*&00)0#/3(%0'* =
4.3.8 Use of the Diode Forward Drop in Voltage Regulation
E#:6*(%)*#&''035&(32"#2:#(%)#-32-)#+1&00?+3<"&0#12-)0#3+#:26"-#3"#&#'2'60&*#-32-)#&''035&(32"8
"&1)048#(%)#6+)#2:#-32-)+#(2#5*)&()#&#*)<60&()-#;20(&<)=#E##-4,(7"%!"7+4(,-!#3+#&#53*563(#/%2+)
'6*'2+)#3+#(2#'*2;3-)#&#52"+(&"(#-5#;20(&<)#9)(/))"#3(+#26('6(#()*13"&0+=#F%)#26('6(#;20(&<)#3+
*)C63*)-#(2#*)1&3"#&+#52"+(&"(#&+#'2++390)#3"#+'3()#2:#B&D#5%&"<)+#3"# (%)#02&-#56**)"(#-*&/"
:*21#(%)#*)<60&(2*#26('6(#()*13"&0#&"-#B9D#5%&"<)+#3"#(%)#-5#'2/)*?+6''04#;20(&<)#(%&(#:))-+
(%)#*)<60&(2*#53*563(=#Y3"5)#(%)#:2*/&*-?;20(&<)#-*2'#2:#(%)#-32-)#*)1&3"+#&012+(#52"+(&"(#&(
&''*2A31&()04#S=N#T#/%30)#(%)#56**)"(#(%*26<%#3(#;&*3)+#94#*)0&(3;)04#0&*<)#&126"(+8#&#:2*/&*-?
93&+)-#-32-)#5&"#1&H)#&#+31'0)#;20(&<)#*)<60&(2*=#L2*#3"+(&"5)8#/)#%&;)#+))"#3"#@A&1'0)#P=Z
(%&(#/%30)#(%)#,S?T#-5#+6''04#;20(&<)#%&-#&#*3''0)#2:#.#T#')&H?(2?')&H#B&#±,Sj#;&*3&(32"D8#(%)
52**)+'2"-3"<#*3''0)#3"#(%)#-32-)#;20(&<)#/&+#2"04#&926(#±.=N#1T#B&#±S=Pj#;&*3&(32"D=#[)<6?
0&()-#;20(&<)+#<*)&()*#(%&"#S=N#T#5&"#9)#29(&3")-#94#52"")5(3"<#&#"619)*#2:#-32-)+#3"#+)*3)+=
L2*#)A&1'0)8#(%)#6+)#2:#(%*))#:2*/&*-?93&+)-#-32-)+#3"#+)*3)+#'*2;3-)+#&#;20(&<)#2:#&926(#.#T=
K")#+65%#53*563(#3+#3";)+(3<&()-#3"#(%)#:2002/3"<#)A&1'0)8#/%35%#6(303M)+#(%)#-32-)#+1&00?+3<"&0
12-)0#(2#C6&"(3:4#(%)#)::35&54#2:#(%)#;20(&<)#*)<60&(2*#(%&(#3+#*)&03M)-=
188 Chapter 4 Diodes
Example 4.6
$2"+3-)*#(%)#53*563(#+%2/"#3"#L3<=#P=,Z=#E#+(*3"<#2:#(%*))#-32-)+#3+#6+)-#(2#'*2;3-)#&#52"+(&"(#;20(&<)
2:#&926(#.=,#T=#I)#/&"(#(2#5&0560&()#(%)#')*5)"(&<)#5%&"<)#3"#(%3+#*)<60&()-#;20(&<)#5&6+)-#94#B&D#&
±,Sj#5%&"<)#3"#(%)#'2/)*?+6''04#;20(&<)#&"-#B9D#52"")5(32"#2:#&#,?HΩ#02&-#*)+3+(&"5)=
10) 1 V
R = 1 k*
"
vO
RL = 1 k*
!
Figure 4.15 $3*563(#:2*#@A&1'0)#P=`=
Solution
I3(%#"2#02&-8#(%)#"213"&0#;&06)#2:#(%)#56**)"(#3"#(%)#-32-)#+(*3"<#3+#<3;)"#94#
,S ! .=,
- = ??????????????????? = N=U#1E
ID
,
F%6+#)&5%#-32-)#/300#%&;)#&"#3"5*)1)"(&0#*)+3+(&"5)#2:
@
' * = ?????I? I
D
F%6+8
.Z
' * = ??????? = O=.#Ω
N=U
F%)#(%*))#-32-)+#3"#+)*3)+#/300#%&;)#&#(2(&0#3"5*)1)"(&0#*)+3+(&"5)#2:#
' = O' * = U=`#Ω
F%3+#*)+3+(&"5)8#&02"<#/3(%#(%)#*)+3+(&"5)#,8#:2*1+#&#;20(&<)#-3;3-)*#/%2+)#*&(32#5&"#9)#6+)-#(2#5&0?
560&()#(%)#5%&"<)#3"#26('6(#;20(&<)#-6)#(2#&#±,Sj#B3=)=8#±,?TD#5%&"<)#3"#+6''04#;20(&<)=#F%6+#(%)
')&H?(2?')&H#5%&"<)#3"#26('6(#;20(&<)#/300#9)#
'
S=SSU`
this is ans to q cuz 3*
∆ v . = . ???????????? = . ????????????????????????? = ,U#1T ')&H?(2?')&H
0.7 voltage wont change
'+,
S=SSU` + ,
anyway
19mV /2 =
9.5
F%&(#3+8#52**)+'2"-3"<#(2#(%)#±,?T#B±,SjD#5%&"<)#3"#+6''04#;20(&<)8#(%)#26('6(#;20(&<)#/300#5%&"<)
94#±U=Z#1T#2*#±S=Zj=#Y3"5)#(%3+#31'03)+#&#5%&"<)#2:#&926(#±O=.#1T#')*#-32-)8#26*#6+)#2:#(%)#+1&00?
+3<"&0#12-)0#3+#J6+(3:3)-=
I%)"# &# 02&-# *)+3+(&"5)# 2:# ,# HΩ# 3+# 52"")5()-# &5*2++# (%)# -32-)# +(*3"<8# 3(# -*&/+# &# 56**)"(# 2:
&''*2A31&()04#.=,#1E=#F%6+#(%)#56**)"(#3"#(%)#-32-)+#-)5*)&+)+#94#.=,#1E8#*)+60(3"<#3"#&#-)5*)&+)
3"#;20(&<)#&5*2++#(%)#-32-)#+(*3"<#<3;)"#94
∆ v . = ! .=, × ' = ! .=, × U=` = ! .S#1T
e
x
4.4 Operation in the Reverse Breakdown Region—Zener Diodes
Y3"5)# (%3+# 31'03)+# (%&(# (%)# ;20(&<)# &5*2++# )&5%# -32-)# -)5*)&+)+# 94# &926(# `=N# 1T8# 26*# 6+)# 2:# (%)
+1&00?+3<"&0# 12-)0# 3+# "2(# )"(3*)04# J6+(3:3)-=# X);)*(%)0)++8# &# -)(&30)-# 5&0560&(32"# 2:# (%)# ;20(&<)
5%&"<)#6+3"<#(%)#)A'2")"(3&0#12-)0#*)+60(+#3"# ∆ v . = ! .O#1T8 #/%35%#3+#"2(#(22#-3::)*)"(#:*21#(%)
&''*2A31&()#;&06)#29(&3")-#6+3"<#(%)#3"5*)1)"(&0#12-)0=
EXERCISES
4.13# L3"-#(%)#;&06)#2:#(%)#-32-)#+1&00?+3<"&0#*)+3+(&"5)#'*#&(#93&+#56**)"(+#2:#S=,#1E8#,#1E8#&"-#,S#1E=
Ans. .ZS#Ω7#.Z#Ω7#.=Z#Ω
4.14# $2"+3-)*#&#-32-)#93&+)-#&(#,#1E=#L3"-#(%)#5%&"<)#3"#56**)"(#&+#&#*)+60(#2:#5%&"<3"<#(%)#;20(&<)
94#B&D#−,S#1T8#B9D#−Z#1T8#B5D#+Z#1T8#&"-#B-D#+,S#1T=#!"#)&5%#5&+)8#-2#(%)#5&0560&(32"+#B3D#6+3"<
(%)#+1&00?+3<"&0#12-)0#&"-#B33D#6+3"<#(%)#)A'2")"(3&0#12-)0=
Ans. B&D#−S=PS8#−S=OO#1E; B9D#−S=.S8#−S=,^#1E; B5D#+S=.S8#+S=..#1E; B-D#+S=PS8#+S=PU#1E
D4.15# R)+3<"#(%)#53*563(#2:#L3<=#@P=,Z#+2#(%&(#@.#=#O#T#/%)"#-P#=#S8#&"-#@.#5%&"<)+#94#.S#1T#')*#,#1E
2:#02&-#56**)"(=#
B&D#h+)#(%)#+1&00?+3<"&0#12-)0#2:#(%)#-32-)#(2#:3"-#(%)#;&06)#2:#,=
B9D#Y')53:4#(%)#;&06)#2:#-5002:#)&5%#2:#(%)#-32-)+=
B5D#L2*#(%3+#-)+3<"8#6+)#(%)#-32-)#)A'2")"(3&0#12-)0#(2#-)()*13")#(%)#&5(6&0#5%&"<)#3"#@.#/%)"#&
56**)"(#-P#\#,#1E#3+#-*&/"#:*21#(%)#*)<60&(2*=
"15 V
R
VO
IL
Figure E4.15
Ans. B&D%,#=#.=P#HΩ7#B9D%-5#\#P=N#+#,S!,`#E7%B5D%!..=O#1T%
4.4 Operation in the Reverse Breakdown
Region—Zener Diodes
F%)#;)*4#+())'#!]v#56*;)#(%&(#(%)#-32-)#)A%393(+#3"#(%)#9*)&H-2/"#*)<32"#BL3<=#P=^D#&"-#(%)
&012+(?52"+(&"(#;20(&<)#-*2'#(%&(#(%3+#3"-35&()+8#+6<<)+(#(%&(#-32-)+#2')*&(3"<#3"#(%)#9*)&H-2/"
*)<32"#5&"#9)#6+)-#3"#(%)#-)+3<"#2:#;20(&<)#*)<60&(2*+=#L*21#(%)#'*);326+#+)5(32"8#(%)#*)&-)*
189
190 Chapter 4 Diodes
/300#*)5&00#(%&(#;20(&<)#*)<60&(2*+#&*)#53*563(+#(%&(#'*2;3-)#&#52"+(&"(#-5#26('6(#;20(&<)#3"#(%)
:&5)#2:#5%&"<)+#3"#(%)3*#02&-#56**)"(#&"-#3"#(%)#+4+()1#'2/)*?+6''04#;20(&<)=#F%3+#3"#:&5(#(6*"+
26(#(2#9)#&"#31'2*(&"(#&''035&(32"#2:#-32-)+#2')*&(3"<#3"#(%)#*);)*+)?9*)&H-2/"#*)<32"8#&"+')53&0#-32-)+#&*)#1&"6:&5(6*)-#(2#2')*&()#+')53:35&004#3"#(%)#9*)&H-2/"#*)<32"=#Y65%#-32-)+
&*)#5&00)-#&!"(>)-/1%)'-)"$#2*8#12*)#52112"048#&+#"2()-#)&*03)*8#B"1"!%)'-)"$=
L3<6*)#P=,`#+%2/+#(%)#53*563(#+41920#2:#(%)#M)")*#-32-)=#!"#"2*1&0#&''035&(32"+#2:#M)")*
-32-)+8#56**)"(#:02/+#3"(2#(%)#5&(%2-)8#&"-#(%)#5&(%2-)#3+#'2+3(3;)#/3(%#*)+')5(#(2#(%)#&"2-)=
F%6+#-G#&"-#@G#3"#L3<=#P=,`#%&;)#'2+3(3;)#;&06)+=
IZ
"
VZ
! Figure 4.16 $3*563(# +41920# :2*# &
M)")*#-32-)=
4.4.1 Specifying and Modeling the Zener Diode
L3<6*)# P=,N# +%2/+# -)(&30+# 2:# (%)# -32-)# !]v# 5%&*&5()*3+(35# 3"# (%)# 9*)&H-2/"# *)<32"=# I)
29+)*;)#(%&(#:2*#56**)"(+#<*)&()*#(%&"#(%)#>1""%*+!!"1,#-GH#B+')53:3)-#2"#(%)#-&(&#+%))(#2:
(%) M)")*# -32-)D8# (%)# !]v# 5%&*&5()*3+(35# 3+# &012+(# &# +(*&3<%(# 03")=# F%)# 1&"6:&5(6*)*# 6+6&004
+')53:3)+#(%)#;20(&<)#&5*2++#(%)#M)")*#-32-)#@G#&(#&#+')53:3)-#()+(#56**)"(8#-GI=#I)#%&;)#3"-3?
5&()-#(%)+)#'&*&1)()*+#3"#L3<=#P=,N#&+#(%)#522*-3"&()+#2:#(%)#'23"(#0&9)0)-#L=#F%6+#&#`=^?T
i
!VZ
!VZ 0
!VZK
0
!IZK
Slope '
,V
1
rz
Q
v
!IZT (test current)
,I
,V ' ,I rz
Figure 4.17 F%)#-32-)#!]v#5%&*&5()*3+(35#/3(%#(%)#9*)&H-2/"#*)<32"#+%2/"#3"#+21)#-)(&30=
4.4 Operation in the Reverse Breakdown Region—Zener Diodes 191
M)")*#-32-)#/300#)A%393(#&#`=^?T#-*2'#&(#&#+')53:3)-#()+(#56**)"(#2:8#+&48#,S#1E=#E+#(%)#56*?
*)"(# (%*26<%# (%)# M)")*# -);3&()+# :*21# -GI 8# (%)# ;20(&<)# &5*2++# 3(# /300# 5%&"<)8# (%26<%# 2"04
+03<%(04=#L3<6*)#P=,N#+%2/+#(%&(#52**)+'2"-3"<#(2#56**)"(#5%&"<)#∆-#(%)#M)")*#;20(&<)#5%&"<)+
94#∆@8#/%35%#3+#*)0&()-#(2#∆-#94
∆@ = ' Q ∆/%)*)#'Q#3+#(%)#3";)*+)#2:#(%)#+02')#2:#(%)#&012+(?03")&*#!]v#56*;)#&(#'23"(#L=#[)+3+(&"5)#'Q#3+
(%)#'1*!"="1,(4%!"$'$,(1*"#2:#(%)#M)")*#-32-)#&(#2')*&(3"<#'23"(#L=#!(#3+#&0+2#H"2/"#&+#(%)
)A1(='*%!"$'$,(1*"#2:#(%)#M)")*8#&"-#3(+#;&06)#3+#+')53:3)-#2"#(%)#-);35)#-&(&#+%))(=#F4'3?
5&0048#'Q#3+#3"#(%)#*&"<)#2:#&#:)/#2%1+#(2#&#:)/#()"+#2:#2%1+=#K9;326+048#(%)#02/)*#(%)#;&06)
2:#'Q#3+8#(%)#12*)#52"+(&"(#(%)#M)")*#;20(&<)#*)1&3"+#&+#3(+#56**)"(#;&*3)+8#&"-#(%6+#(%)#12*)
3-)&0#3(+#')*:2*1&"5)#9)521)+#3"#(%)#-)+3<"#2:#;20(&<)#*)<60&(2*+=#!"#(%3+#*)<&*-8#/)#29+)*;)
:*21#L3<=#P=,N#(%&(#/%30)#'Q#*)1&3"+#02/#&"-#&012+(#52"+(&"(#2;)*#&#/3-)#*&"<)#2:#56**)"(8#3(+
;&06)# 3"5*)&+)+# 52"+3-)*&904# 3"# (%)# ;353"3(4# 2:# (%)# H"))=# F%)*):2*)8# &+ &# <)")*&0# -)+3<"
<63-)03")8#2")#+%260-#&;23-#2')*&(3"<#(%)#M)")*#3"#(%3+#02/?56**)"(#*)<32"=
o)")*#-32-)+#&*)#:&9*35&()-#/3(%#;20(&<)+#@G#3"#(%)#*&"<)#2:#&#:)/#;20(+#(2#&#:)/#%6"-*);20(+=#!"#&--3(32"#(2#+')53:43"<#@G#B&(#&#'&*(3560&*#56**)"(#-GID8#'Q8#&"-#-GH8#(%)#1&"6:&5(6*)*
&0+2#+')53:3)+#(%)#1&A3161#'2/)*#(%&(#(%)#-);35)#5&"#+&:)04#-3++3'&()=#F%6+#& S=Z?I8#`=^?T
M)")*# -32-)# 5&"# 2')*&()# +&:)04# &(# 56**)"(+# 6'# (2# &# 1&A3161# 2:# &926(# NS 1E=
F%)# &012+(?03")&*# !]v# 5%&*&5()*3+(35# 2:# (%)# M)")*# -32-)# +6<<)+(+# (%&(# (%)# -);35)# 5&"# 9)
12-)0)-#&+#3"-35&()-#3"#L3<=#P=,^=#>)*)#@G S#-)"2()+#(%)#'23"(#&(#/%35%#(%)#+(*&3<%(#03")#2:
+02')#, ⁄ ' Q#3"()*+)5(+#(%)#;20(&<)#&A3+#B*):)*#(2#L3<=#P=,ND=#E0(%26<%#@GS#3+#+%2/"#3"#L3<= P=,N
(2#9)#+03<%(04#-3::)*)"(#:*21#(%)#H"))#;20(&<)#@GH8#3"#'*&5(35)#(%)3*#;&06)+#&*)#&012+(#)C6&0=
F%)#)C63;&0)"(#53*563(#12-)0#2:#L3<=#P=,^#5&"#9)#&"&04(35&004#-)+5*39)-#94
@ G = @ GS + ' Q - G
BP=.SD
&"-#3(#&''03)+#:2*#-G#>#-GH#&"-8#29;326+048#@G#>#@G S=
Figure 4.18 m2-)0#:2*#(%)#M)")*#-32-)=
4.4.2 Use of the Zener as a Shunt Regulator
I)#"2/#3006+(*&()8#94#/&4#2:#&"#)A&1'0)8#(%)#6+)#2:#M)")*#-32-)+#3"#(%)#-)+3<"#2:#+%6"(#*)<?
60&(2*+8#+2#"&1)-#9)5&6+)#(%)#*)<60&(2*#53*563(#&'')&*+#3"#'&*&00)0#B+%6"(D#/3(%#(%)#02&-=
192 Chapter 4 Diodes
Example 4.7
F%)# `=^?T# M)")*#-32-)#3"#(%)#53*563(#2:#L3<=#P=,UB&D#3+# +')53:3)-#(2#%&;)# @G#=#`=^#T#&(# -G#=#Z#1E8
'Q = .S#Ω8#&"-#-GH#=#S=.#1E=#F%)#+6''04#;20(&<)#@ +#3+#"213"&004#,S#T#96(#5&"#;&*4#94#±,#T=
1 V)
I
IZ
6.8V Vz, ;IZ =
0.005mA;
to calculate Vzo
"
IL
VO
!
(b)
(a)
Figure 4.19 5(6#$3*563(#:2*#@A&1'0)#P=N=#5&6#F%)#53*563(#/3(%#(%)#M)")*#-32-)#*)'0&5)-#/3(%#3(+#)C63;&0)"(#53*563(
12-)0=
B&D L3"-#@.#/3(%#"2#02&-#&"-#/3(%#@ +#&(#3(+#"213"&0#;&06)=
+
B9D L3"-# (%)# 5%&"<)# 3"# @.# *)+60(3"<# :*21# (%)# ±,?T# 5%&"<)# 3"# @ +=# X2()# (%&(# ( ∆@ . ⁄ ∆ @ ) 8# 6+6&004
)A'*)++)-#3"#1T/T8#3+#H"2/"#&+#4'1"%!"7+4(,'-1=
B5D L3"-#(%)#5%&"<)#3"#@.#*)+60(3"<#:*21#52"")5(3"<#&#02&-#*)+3+(&"5)#,P#(%&(#-*&/+#&#56**)"(#-P#=
, 1E8#&"-#%)"5)#:3"-#(%)#4-()%!"7+4(,'-1# ( ∆@ . ⁄ ∆- P ) #3"#1T/1E=
B-D L3"-#(%)#5%&"<)#3"#@.#/%)"#,P#=#.#HΩ=
B)D L3"-#(%)#;&06)#2:#@.#/%)"#,P#=#S=Z#HΩ=
B:D I%&(#3+#(%)#13"3161#;&06)#2:#,P#:2*#/%35%#(%)#-32-)#+(300#2')*&()+#3"#(%)#9*)&H-2/"#*)<32"i
Solution
Vz and
IZ
change
depend
on
supply
L3*+(#/)#16+(#-)()*13")#(%)#;&06)#2:#(%)#'&*&1)()*#@G S#2:#(%)#M)")*#-32-)#12-)0=#Y69+(3(6(3"<#@G#=
`=^#T8#-G#=#Z#1E8#&"-#'Q#=#.S#Ω#3"#@C=#BP=.SD#43)0-+# @ GS = `=N#T= #L3<6*)#P=,UB9D#+%2/+#(%)#53*563(
/3(%#(%)#M)")*#-32-)#*)'0&5)-#/3(%#3(+#12-)0=
B&D I3(%#"2#02&-#52"")5()-8#(%)#56**)"(#(%*26<%#(%)#M)")*#3+#<3;)"#94
+
@ ! @ GS
?
- G = - = ???????????????????
consider
, + 'Q
,S ! `=N
Text
= ???????????????????????? = `=OZ#1E
S=Z + S=S.
F%6+8
Vz=
@ . = @ GS + - G ' Q
= `=N + `=OZ × S=S. = `=^O#T
this as
ID in
amp
biais,
even the
rz exist
already
4.4 Operation in the Reverse Breakdown Region—Zener Diodes 193
B9D L2*#&#±,?T#5%&"<)#3"#@ +8#(%)#5%&"<)#3"#26('6(#;20(&<)#5&"#9)#:26"-#:*21
+ 'Q
?
∆@ . = ∆@ ?????????????
, + 'Q
.S
= ± , × ????????????????????? = ± O^=Z#1T
ZSS + .S
F%6+8
V3")#*)<60&(32"#=#O^=Z#1TaT
B5D I%)"#&#02&-#*)+3+(&"5)#,P#(%&(#-*&/+#&#02&-#56**)"(#-P#=#,#1E#3+#52"")5()-8#(%)#M)")*#56**)"(
/300#-)5*)&+)#94#,#1E=#F%)#52**)+'2"-3"<#5%&"<)#3"#M)")*#;20(&<)#5&"#9)#:26"-#:*21
∆@ . = ' Q ∆- G
= .S × ! , = ! .S#1T
F%6+#(%)#02&-#*)<60&(32"#3+
e
x
a)
∆@
V2&-#*)<60&(32" ≡ ??????????. = ! .S#1Ta1E
∆- P
B-D I%)"# &# 02&-# *)+3+(&"5)# 2:# . HΩ# 3+# 52"")5()-8# (%)# 02&-# 56**)"(# /300# 9)# &''*2A31&()04
`=^ Ta. HΩ#=#O=P#1E=#F%6+#(%)#5%&"<)#3"#M)")*#56**)"(#/300#9)#∆-G#=#−O=P#1E8#&"-#(%)#52**)+'2"-?
3"<#5%&"<)#3"#M)")*#;20(&<)#B26('6(#;20(&<)D#/300#(%6+#9)
∆@ . = ' Q ∆- G
e
x
e
a) x
= .S × ! O=P = ! `^#1T
F%3+#5&0560&(32"8#%2/);)*8#3+#&''*2A31&()8#9)5&6+)#3(#")<0)5(+#(%)#5%&"<)#3"#(%)#56**)"(#-=#E#12*)
&556*&()#)+(31&()#2:#∆@.#5&"#9)#29(&3")-#94#&"&04M3"<#(%)#53*563(#3"#L3<=#P=,UB9D=#F%)#*)+60(#2:#+65%
&"#&"&04+3+#3+#∆@.#=#−NS#1T=
B)D E"#,P#2:#S=Z#HΩ#/260-#-*&/#&#02&-#56**)"(#2:# `=^ ⁄ S=Z#=#,O=`#1E=#F%3+#3+#"2(#'2++390)8#9)5&6+)
(%)#56**)"(#-#+6''03)-#(%*26<%#,#3+#2"04#`=P#1E#B:2*#@ +#=#,S#TD=#F%)*):2*)8#(%)#M)")*#16+(#9)#56(#2::=
!:#(%3+#3+#3"-))-#(%)#5&+)8#(%)"#@.#3+#-)()*13")-#94#(%)#;20(&<)#-3;3-)*#:2*1)-#94#,P#&"-#,#BL3<=#P=,U&D8
e
x
!!!!!
+ ,P
?
@ . = @ ???????????????
, + ,P
S=Z
? = Z#T
= ,S ????????????????????
Text
S=Z +
S=Z
Y3"5)#(%3+#;20(&<)#3+#02/)*#(%&"#(%)#9*)&H-2/"#;20(&<)#2:#(%)#M)")*8#(%)#-32-)#3+#3"-))-#"2#02"<)*
2')*&(3"<#3"#(%)#9*)&H-2/"#*)<32"=
B: D L2*#(%)#M)")*#(2#9)#&(#(%)#)-<)#2:#(%)#9*)&H-2/"#*)<32"8#-G#=#-GH#=#S=.#1E#&"-#@G#!#@GH#!#`=N T=
E(#(%3+#'23"(#(%)#02/)+(#B/2*+(?5&+)D#56**)"(#+6''03)-#(%*26<%#,#3+#( U ! `=N ) ⁄ S=Z = P=`#1E8#&"-#(%6+
e
(%)#02&-#56**)"(#3+#P=`#−#S=.#=#P=P#1E=#F%)#52**)+'2"-3"<#;&06)#2:#,
P#3+
x
`=N
, P = ??????? ! ,=Z#HΩ
P=P
e
x
should give
diod 0.2 mA
even after
"drawn
current by
add RL"
e
x
= Vzo!!!
or 9- vzo - izk*rz ok
too (see prolem
e
set)
x
194 Chapter 4 Diodes
4.4.3 Temperature Effects
F%)#-)')"-)"5)#2:#(%)#M)")*#;20(&<)#@G#2"#()1')*&(6*)#3+#+')53:3)-#3"#()*1+#2:#3(+#,"=3"!(0
,+!"% *-"..'*'"1,%CD8#2*# ,"=*-#&+#3(# 3+#52112"04# H"2/"8#/%35%#3+# 6+6&004#)A'*)++)-#3"
1Ta°$=#F%)#;&06)#2:#F$#-)')"-+#2"#(%)#M)")*#;20(&<)8#&"-#:2*#&#<3;)"#-32-)#(%)#F$#;&*3)+
/3(%#(%)#2')*&(3"<#56**)"(=#o)")*#-32-)+#/%2+)#@G#&*)#02/)*#(%&"#&926(#Z#T#)A%393(#&#")<&?
(3;)#F$=#K"#(%)#2(%)*#%&"-8#M)")*+#/3(%#%3<%)*#;20(&<)+#)A%393(#&#'2+3(3;)#F$=#F%)#F$#2:#&
M)")*#-32-)#/3(%#&#@G#2:#&926(#Z#T#5&"#9)#1&-)#M)*2#94#2')*&(3"<#(%)#-32-)#&(#&#+')53:3)56**)"(=#E"2(%)*#52112"04#6+)-#()5%"3C6)#:2*#29(&3"3"<#&#*):)*)"5)#;20(&<)#/3(%#02/#()1?
')*&(6*)# 52)::353)"(# 3+# (2# 52"")5(# &# M)")*# -32-)# /3(%# &# '2+3(3;)# ()1')*&(6*)# 52)::353)"(# 2:
&926(# .# 1Ta°$# 3"# +)*3)+# /3(%# &# :2*/&*-?52"-65(3"<# -32-)=# Y3"5)# (%)# :2*/&*-?52"-65(3"<
-32-)#%&+#&#;20(&<)#-*2'#2:#!S=N#T#&"-#&#F$#2:#&926(#−.#1Ta°$8#(%)#+)*3)+#52193"&(32"
/300#'*2;3-)#&#;20(&<)#2:#B@G#+#S=ND#/3(%#&#F$#2:#&926(#M)*2=
EXERCISES
4.16# E#M)")*#-32-)#/%2+)#"213"&0#;20(&<)#3+#,S#T#&(#,S#1E#%&+#&"#3"5*)1)"(&0#*)+3+(&"5)#2:#ZS#Ω=#I%&(
;20(&<)#-2#426#)A')5(#3:#(%)#-32-)#56**)"(#3+#%&0;)-i#R2690)-i#I%&(#3+#(%)#;&06)#2:#@GS#3"#(%)#M)")*
12-)0i
Ans. U=NZ#T7#,S=Z#T7#U=Z#T
4.17# E#M)")*#-32-)#)A%393(+#&#52"+(&"(#;20(&<)#2:#Z=`#T#:2*#56**)"(+#<*)&()*#(%&"#:3;)#(31)+#(%)#H"))#56*?
*)"(=#-GH#3+#+')53:3)-#(2#9)#,#1E=#F%)#M)")*#3+#(2#9)#6+)-#3"#(%)#-)+3<"#2:#&#+%6"(#*)<60&(2*#:)-#:*21
&#,Z?T#+6''04=#F%)#02&-#56**)"(#;&*3)+#2;)*#(%)#*&"<)#2:#S#1E#(2#,Z#1E=#L3"-#&#+63(&90)#;&06)#:2*#(%)
*)+3+(2*#,=#I%&(#3+#(%)#1&A3161#'2/)*#-3++3'&(32"#2:#(%)#M)")*#-32-)i
Ans. PNS#Ω7#,,.#1I
4.18# E#+%6"(#*)<60&(2*#6(303M)+#&#M)")*#-32-)#/%2+)#;20(&<)#3+#Z=,#T#&(#&#56**)"(#2:#ZS#1E#&"-#/%2+)
3"5*)1)"(&0#*)+3+(&"5)#3+#N#Ω=#F%)#-32-)#3+#:)-#:*21#&#+6''04#2:#,Z?T#"213"&0#;20(&<)#(%*26<%#&#.SS?
Ω#*)+3+(2*=#I%&(#3+#(%)#26('6(#;20(&<)#&(#"2#02&-i#L3"-#(%)#03")#*)<60&(32"#&"-#(%)#02&-#*)<60&(32"=
Ans. Z=,#T7#OO=^#1TaT7#−N#1Ta1E
4.4.4 A Final Remark
F%26<%#+31'0)#&"-#6+):608#M)")*#-32-)+#%&;)#02+(#&#<*)&(#-)&0#2:#(%)3*#'2'60&*3(4#3"#*)5)"(
4)&*+=#F%)4#%&;)#9))"#;3*(6&004#*)'0&5)-#3"#;20(&<)?*)<60&(2*#-)+3<"#94#+')53&004#-)+3<")3"()<*&()-#53*563(+#B!$+D#(%&(#')*:2*1#(%)#;20(&<)#*)<60&(32"#:6"5(32"#165%#12*)#)::)5(3;)04
&"-#/3(%#<*)&()*#:0)A39303(4#(%&"#M)")*#-32-)+=
4.5 Rectifier Circuits
K")# 2:# (%)# 12+(# 31'2*(&"(# &''035&(32"+# 2:# -32-)+# 3+# 3"# (%)# -)+3<"# 2:# *)5(3:3)*# 53*563(+=# E
-32-)#*)5(3:3)*#:2*1+#&"#)++)"(3&0#9630-3"<#9025H#2:#(%)#-5#'2/)*#+6''03)+#*)C63*)-#(2#'2/)*
)0)5(*2"35#)C63'1)"(=#E#9025H#-3&<*&1#2:#+65%#&#'2/)*#+6''04#3+#+%2/"#3"#L3<=#P=.S=#E+
3"-35&()-8#(%)#'2/)*#+6''04#3+#:)-#:*21#(%)#,.S?T#B*1+D#`S?>M#&5#03")8#&"-#3(#-)03;)*+#&#-5
;20(&<)#@.#B6+6&004#3"#(%)#*&"<)#2:#Z#T#(2#.S#TD#(2#&"#)0)5(*2"35#53*563(#*)'*)+)"()-#94#(%)
4.5 Rectifier Circuits 195
t
Figure 4.20 _025H#-3&<*&1#2:#&#-5#'2/)*#+6''04=
<&)*#9025H=#F%)#-5#;20(&<)#@.#3+#*)C63*)-#(2#9)#&+#52"+(&"(#&+#'2++390)#3"#+'3()#2:#;&*3&(32"+
3"#(%)#&5#03")#;20(&<)#&"-#3"#(%)#56**)"(#-*&/"#94#(%)#02&-=
F%)#:3*+(#9025H#3"#&#-5#'2/)*#+6''04#3+#(%)#3-/"!%,!(1$.-!="!=#!(#52"+3+(+#2:#(/2#+)'&*&()
5230+#/26"-#&*26"-#&"#3*2"#52*)#(%&(#1&<")(35&004#526'0)+#(%)#(/2#/3"-3"<+=#F%)#3!'=(!A
/'1)'178#%&;3"<#R,#(6*"+8#3+#52"")5()-#(2#(%)#,.S?T#&5#+6''048#&"-#(%)#$"*-1)(!A%/'1)'178
%&;3"<# R.# (6*"+8# 3+# 52"")5()-# (2# (%)# 53*563(#2:# (%)# -5# '2/)*# +6''04=# F%6+# &"# &5# ;20(&<)# v5
2: ,.S ( R . ⁄ R , ) T#B*1+D#-);)02'+#9)(/))"#(%)#(/2#()*13"&0+#2:#(%)#+)52"-&*4#/3"-3"<=#_4
+)0)5(3"<#&"#&''*2'*3&()#(6*"+#*&(32# ( R , ⁄ R . ) #:2*#(%)#(*&"+:2*1)*8#(%)#-)+3<")*#5&"#+()'#(%)
03")#;20(&<)#-2/"#(2#(%)#;&06)#*)C63*)-#(2#43)0-#(%)#'&*(3560&*#-5#;20(&<)#26('6(#2:#(%)#+6''04=
L2*#3"+(&"5)8#&#+)52"-&*4#;20(&<)#2:#^?T#*1+#1&4#9)#&''*2'*3&()#:2*#&#-5#26('6(#2:#Z#T=#F%3+
5&"#9)#&5%3);)-#/3(%#&#,ZQ,#(6*"+#*&(32=
!"#&--3(32"#(2#'*2;3-3"<#(%)#&''*2'*3&()#+3"6+23-&0#&1'03(6-)#:2*#(%)#-5#'2/)*#+6''048
(%)#'2/)*#(*&"+:2*1)*#'*2;3-)+#)0)5(*35&0#3+20&(32"#9)(/))"#(%)#)0)5(*2"35#)C63'1)"(#&"-#(%)
'2/)*?03")#53*563(=#F%3+#3+20&(32"#13"313M)+#(%)#*3+H#2:#)0)5(*35#+%25H#(2#(%)#)C63'1)"(#6+)*=
F%)#-32-)#*)5(3:3)*#52";)*(+#(%)#3"'6(#+3"6+23-#v5#(2#&#6"3'20&*#26('6(8#/%35%#5&"#%&;)
(%)#'60+&(3"<#/&;):2*1#3"-35&()-#3"#L3<=#P=.S=#E0(%26<%#(%3+#/&;):2*1#%&+#&#"2"M)*2#&;)*?
&<)#2*#&#-5#521'2")"(8#3(+#'60+&(3"<#"&(6*)#1&H)+#3(#6"+63(&90)#&+#&#-5#+26*5)#:2*#)0)5(*2"35
53*563(+8#%)"5)#(%)#"))-#:2*#&#:30()*=#F%)#;&*3&(32"+#3"#(%)#1&<"3(6-)#2:#(%)#*)5(3:3)*#26('6(#&*)
52"+3-)*&904#*)-65)-#94#(%)#:30()*#9025H#3"#L3<=#P=.S=#!"#(%)#:2002/3"<#+)5(32"+#/)#+%&00#+(6-4
&#"619)*#2:#*)5(3:3)*#53*563(+#&"-#&#+31'0)#31'0)1)"(&(32"#2:#(%)#26('6(#:30()*=
F%)#26('6(#2:#(%)#*)5(3:3)*#:30()*8#(%26<%#165%#12*)#52"+(&"(#(%&"#/3(%26(#(%)#:30()*8
+(300#52"(&3"+#&#(31)?-)')"-)"(#521'2")"(8#H"2/"#&+#!'334"=#F2#*)-65)#(%)#*3''0)#&"-#(2
+(&9303M)#(%)#1&<"3(6-)#2:#(%)#-5#26('6(#;20(&<)#2:#(%)#+6''04#&<&3"+(#;&*3&(32"+#5&6+)94#5%&"<)+#3"#02&-#56**)"(8#&#;20(&<)#*)<60&(2*#3+#)1'024)-=#Y65%#&#*)<60&(2*#5&"#9)#31'0)?
1)"()-#6+3"<#(%)#M)")*#+%6"(#*)<60&(2*#52":3<6*&(32"#+(6-3)-#3"#Y)5(32"#P=P=#E0()*"&(3;)048
&"-#165%#12*)#52112"04#&(#'*)+)"(8#&"#3"()<*&()-?53*563(#*)<60&(2*#5&"#9)#6+)-=
4.5.1 The Half-Wave Rectifier
F%)#%&0:?/&;)#*)5(3:3)*#6(303M)+#&0()*"&()#%&0:?5450)+#2:#(%)#3"'6(#+3"6+23-=#L3<6*)#P=.,B&D
+%2/+# (%)# 53*563(# 2:# &# %&0:?/&;)# *)5(3:3)*=# F%3+# 53*563(# /&+# &"&04M)-# 3"# Y)5(32"# P=,# B+))
L3<=# P=OD# &++613"<# &"# 3-)&0# -32-)=# h+3"<# (%)# 12*)# *)&03+(35# 52"+(&"(?;20(&<)?-*2'# -32-)
12-)08#/)#29(&3"#
v.#\#S8
v5#c#@+
BP=.,&D
v.#\#v5#]#@+8
v5#!#@4
BP=.,9D
196 Chapter 4 Diodes
D
vS
"
!
vO
R
"
vO
!
Slope '1
(a)
0 VD
vS
(b)
v
VD
vS
Vs
vO
t
VD
(c )
Figure 4.21 5(6#>&0:?/&;)#*)5(3:3)*=#5&6#F*&"+:)*#5%&*&5()*3+(35#2:#(%)#*)5(3:3)*#53*563(=#5*6#!"'6(#&"-#26('6(
/&;):2*1+=
F%)#(*&"+:)*#5%&*&5()*3+(35#*)'*)+)"()-#94#(%)+)#)C6&(32"+#3+#+H)(5%)-#3"#L3<=#P=.,B9D8#/%)*)
@+ #=#S=N#T#2*#S=^#T=#L3<6*)#P=.,B5D#+%2/+#(%)#26('6(#;20(&<)#29(&3")-#/%)"#(%)#3"'6(#v5#3+#&
+3"6+23-=
!"#+)0)5(3"<#-32-)+#:2*#*)5(3:3)*#-)+3<"8#(/2#31'2*(&"(#'&*&1)()*+#16+(#9)#+')53:3)-Q#(%)
56**)"(?%&"-03"<#5&'&9303(4#*)C63*)-#2:#(%)#-32-)8#-)()*13")-#94#(%)#0&*<)+(#56**)"(#(%)#-32-)
3+#)A')5()-#(2#52"-65(8#&"-#(%)#3"(>%'1#"!$"%#-4,(7"#Bl!TD#(%&(#(%)#-32-)#16+(#9)#&90)#(2
/3(%+(&"-# /3(%26(# 9*)&H-2/"8# -)()*13")-# 94# (%)# 0&*<)+(# *);)*+)# ;20(&<)# (%&(# 3+# )A')5()(2 &'')&*#&5*2++#(%)#-32-)=#!"#(%)#*)5(3:3)*#53*563(#2:#L3<=#P=.,B&D8#/)#29+)*;)#(%&(#/%)"#v5#3+
")<&(3;)#(%)#-32-)#/300#9)#56(#2::#&"-#v.#/300#9)#M)*2=#!(#:2002/+#(%&(#(%)#l!T#3+#)C6&0#(2#(%)
')&H#2:#v5 8
l!T = @?
BP=..D
!(#3+#6+6&004#'*6-)"(8#%2/);)*8#(2#+)0)5(#&#-32-)#(%&(#%&+#&#*);)*+)#9*)&H-2/"#;20(&<)#&(#0)&+(
ZSj#<*)&()*#(%&"#(%)#)A')5()-#l!T=
4.5 Rectifier Circuits
_):2*)#0)&;3"<#(%)#%&0:?/&;)#*)5(3:3)*8#(%)#*)&-)*#+%260-#"2()#(/2#'23"(+=#L3*+(8#3(#3+#'2+?
+390)#(2#6+)#(%)#-32-)#)A'2")"(3&0#5%&*&5()*3+(35#(2#-)()*13")#(%)#)A&5(#(*&"+:)*#5%&*&5()*3+(35
2:# (%)# *)5(3:3)*# B+))# l*290)1# P=`ZD=# >2/);)*8# (%)# &126"(# 2:# /2*H# 3";20;)-# 3+# 6+6&004# (22
<*)&(#(2#9)#J6+(3:3)-#3"#'*&5(35)=#K:#526*+)8#+65%#&"#&"&04+3+#5&"#9)#)&+304#-2")#6+3"<#&#521?
'6()*#53*563(?&"&04+3+#'*2<*&1#+65%#&+#Yl!$@=#
Y)52"-8#/%)(%)*#/)#&"&04M)#(%)#53*563(#&556*&()04#2*#"2(8#3(#+%260-#9)#29;326+#(%&(#(%3+
53*563(# -2)+# "2(# :6"5(32"# '*2')*04# /%)"# (%)# 3"'6(# +3<"&0# 3+# +1&00=# L2*# 3"+(&"5)8# (%3+# 53*563(
5&""2(#9)#6+)-#(2#*)5(3:4#&"#3"'6(#+3"6+23-#2:#,SS?1T#&1'03(6-)=#L2*#+65%#&"#&''035&(32"#2")
*)+2*(+#(2#&#+2?5&00)-#'*)53+32"#*)5(3:3)*8#&#53*563(#6(303M3"<#-32-)+#3"#52"J6"5(32"#/3(%#2'
&1'+=#K")#+65%#53*563(#3+#'*)+)"()-#3"#Y)5(32"#P=Z=Z=
EXERCISE
4.19#L2*#(%)#%&0:?/&;)#*)5(3:3)*#53*563(#3"#L3<=#P=.,B&D8#+%2/#(%)#:2002/3"<Q#B&D#L2*#(%)#%&0:?5450)+#-6*3"<
/%35%#(%)#-32-)#52"-65(+8#52"-65(32"#9)<3"+#&(#&"#&"<0)#θ#=#+3"−, ( @ + ⁄ @ ? ) #&"-#()*13"&()+#&(#Bπ#−#θ D8
:2*# &# (2(&0# 52"-65(32"# &"<0)# 2:# Bπ# −# .θ D=# B9D# F%)# &;)*&<)# ;&06)# B-5# 521'2")"(D# 2:# v.# 3+
@ . # ! # ( , ⁄ π )@ ? ! @ + ⁄ .= #B5D#F%)#')&H#-32-)#56**)"(#3+#( @ ? ! @ + ) ⁄ , )=
L3"-#"61)*35&0#;&06)+#:2*#(%)+)#C6&"(3(3)+#:2*#(%)#5&+)#2:#,.?T#B*1+D#+3"6+23-&0#3"'6(8#@+ #!#S=N#T8
&"-#,#=#,SS#Ω=#E0+28#<3;)#(%)#;&06)#:2*#l!T=
Ans. B&D#θ#=#.=P°8#52"-65(32"#&"<0)#=#,NZ°7#B9D#Z=SZ#T7#B5D#,`O#1E7#,N#T
4.5.2 The Full-Wave Rectifier
F%)#:600?/&;)#*)5(3:3)*#6(303M)+#92(%#%&0;)+#2:#(%)#3"'6(#+3"6+23-=#F2#'*2;3-)#&#6"3'20&*#26(?
'6(8#3(#3";)*(+#(%)#")<&(3;)#%&0;)+#2:#(%)#+3")#/&;)=#K")#'2++390)#31'0)1)"(&(32"#3+#+%2/"#3"
L3<=#P=..B&D=#>)*)#(%)#(*&"+:2*1)*#+)52"-&*4#/3"-3"<#3+#*"1,"!0,(33")#(2#'*2;3-)#(/2#)C6&0
;20(&<)+# v5# &5*2++# (%)# (/2# %&0;)+# 2:# (%)# +)52"-&*4# /3"-3"<# /3(%# (%)# '20&*3(3)+# 3"-35&()-=
X2()#(%&(#/%)"#(%)#3"'6(#03")#;20(&<)#B:))-3"<#(%)#'*31&*4D#3+#'2+3(3;)8#92(%#2:#(%)#+3<"&0+
0&9)0)-#v5#/300#9)#'2+3(3;)=#!"#(%3+#5&+)#+,#/300#52"-65(#&"-#+.#/300#9)#*);)*+)#93&+)-=#F%)
56**)"(#(%*26<%#+,#/300#:02/#(%*26<%#,#&"-#9&5H#(2#(%)#5)"()*#(&'#2:#(%)#+)52"-&*4=#F%)#53*?
563(#(%)"#9)%&;)+#03H)#&#%&0:?/&;)#*)5(3:3)*8#&"-#(%)#26('6(#-6*3"<#(%)#'2+3(3;)#%&0:?5450)+
/%)"#+,#52"-65(+#/300#9)#3-)"(35&0#(2#(%&(#'*2-65)-#94#(%)#%&0:?/&;)#*)5(3:3)*=
X2/8#-6*3"<#(%)#")<&(3;)#%&0:?5450)#2:#(%)#&5#03")#;20(&<)8#92(%#2:#(%)#;20(&<)+#0&9)0)-#v5
/300#9)#")<&(3;)=#F%6+#+,#/300#9)#56(#2::#/%30)#+.#/300#52"-65(=#F%)#56**)"(#52"-65()-#94#+.
/300#:02/#(%*26<%#,#&"-#9&5H#(2#(%)#5)"()*#(&'=#!(#:2002/+#(%&(#-6*3"<#(%)#")<&(3;)#%&0:?5450)+
/%30)#+.#52"-65(+8#(%)#53*563(#9)%&;)+#&<&3"#&+#&#%&0:?/&;)#*)5(3:3)*=#F%)#31'2*(&"(#'23"(8
%2/);)*8#3+#(%&(#(%)#56**)"(#(%*26<%#,#&0/&4+#:02/+#3"#(%)#+&1)#-3*)5(32"8#&"-#(%6+#v.#/300
9)#6"3'20&*8#&+#3"-35&()-#3"#L3<=#P=..B5D=#F%)#26('6(#/&;):2*1#+%2/"#3+#29(&3")-#94#&++61?
3"<#(%&(#&#52"-65(3"<#-32-)#%&+#&#52"+(&"(#;20(&<)#-*2'#@+=#F%6+#(%)#(*&"+:)*#5%&*&5()*3+(35
2:#(%)#:600?/&;)#*)5(3:3)*#(&H)+#(%)#+%&')#+%2/"#3"#L3<=#P=..B9D=
F%)#:600?/&;)#*)5(3:3)*#29;326+04#'*2-65)+#&#12*)#e)")*<)(35f#/&;):2*1#(%&"#(%&(#'*2?
;3-)-#94#(%)#%&0:?/&;)#*)5(3:3)*=#!"#&012+(#&00#*)5(3:3)*#&''035&(32"+8#2")#2'(+#:2*#&#:600?/&;)
(4')#2:#+21)#H3"-=
197
198 Chapter 4 Diodes
D1
"
ac
line
voltage
!
"
vS
!
Center
tap
vO
R
"
vO
!
Slope !21
"
vS
!
Slope !1
2VD 0 VD
D2
vS
(b)
(a)
v
VD
vS
Vs
2vS
vO
t
(c)
Figure 4.22 L600?/&;)#*)5(3:3)*#6(303M3"<#&#(*&"+:2*1)*#/3(%#&#5)"()*?(&'')-#+)52"-&*4#/3"-3"<Q#
5(6 53*563(7#5&6#(*&"+:)*#5%&*&5()*3+(35#&++613"<#&#52"+(&"(?;20(&<)?-*2'#12-)0#:2*#(%)#-32-)+7#5*6#3"'6(#
&"- 26('6(#/&;):2*1+=
F2#:3"-#(%)#l!T#2:#(%)#-32-)+#3"#(%)#:600?/&;)#*)5(3:3)*#53*563(8#52"+3-)*#(%)#+3(6&(32"#-6*?
3"<#(%)#'2+3(3;)#%&0:?5450)+=#R32-)#+,#3+#52"-65(3"<8#&"-#+.#3+#56(#2::=#F%)#;20(&<)#&(#(%)#5&(%?
2-)# 2:# +.# 3+# v.8# &"-# (%&(# &(# 3(+# &"2-)# 3+# −v5=# F%6+# (%)# *);)*+)# ;20(&<)# &5*2++# +.# /300# 9)
Bv. + v5D8#/%35%#/300#*)&5%#3(+#1&A3161#/%)"#v.#3+#&(#3(+#')&H#;&06)#2:#B@?#−#@+D8#&"-#v5#3+#&(
3(+#')&H#;&06)#2:#@?7#(%6+8
l!T#=#.@?#−#@+
/%35%#3+#&''*2A31&()04#(/35)#(%&(#:2*#(%)#5&+)#2:#(%)#%&0:?/&;)#*)5(3:3)*=
EXERCISE
4.20# L2*#(%)#:600?/&;)#*)5(3:3)*#53*563(#3"#L3<=#P=..B&D8#+%2/#(%)#:2002/3"<Q#B&D#F%)#26('6(#3+#M)*2#:2*#&"#&"?
<0)#2:#.#+3"−,# ( @ + ⁄ @ ? ) #5)"()*)-#&*26"-#(%)#M)*2?5*2++3"<#'23"(+#2:#(%)#+3")?/&;)#3"'6(=#B9D#F%)
4.5 Rectifier Circuits
&;)*&<)#;&06)#B-5#521'2")"(D#2:#v.#3+# @ . ! # ( . ⁄ π )@ ? ! @ + = #B5D#F%)#')&H#56**)"(#(%*26<%#)&5%#-3?
2-)#3+# ( @ ? ! @ + ) ⁄ , =#L3"-#(%)#:*&5(32"#B')*5)"(&<)D#2:#)&5%#5450)#-6*3"<#/%35%#v.#>#S8#(%)#;&06)#2:
@.8#(%)#')&H#-32-)#56**)"(8#&"-#(%)#;&06)#2:#l!T8#&00#:2*#(%)#5&+)#3"#/%35%#v5#3+#&#,.?T#B*1+D#+3"6+23-8
@+#!#S=N#T8#&"-#,#=#,SS#Ω.
Ans. UN=Pj7#,S=,#T7#,`O#1E7#OO=.#T
4.5.3 The Bridge Rectifier
E"#&0()*"&(3;)#31'0)1)"(&(32"#2:#(%)#:600?/&;)#*)5(3:3)*#3+#+%2/"#3"#L3<=#P=.OB&D=#F%3+#53*?
563(8#H"2/"#&+#(%)#9*3-<)#*)5(3:3)*#9)5&6+)#2:#(%)#+3130&*3(4#2:#3(+#52":3<6*&(32"#(2#(%&(#2:#(%)
I%)&(+(2")#9*3-<)8#-2)+#"2(#*)C63*)#&#5)"()*?(&'')-#(*&"+:2*1)*8#&#-3+(3"5(#&-;&"(&<)#2;)*
(%)# :600?/&;)# *)5(3:3)*# 53*563(# 2:# L3<=# P=..=# F%)# 9*3-<)# *)5(3:3)*8# %2/);)*8# *)C63*)+# :26*
-32-)+# &+# 521'&*)-# (2# (/2# 3"# (%)# '*);326+# 53*563(=# F%3+# 3+# "2(# 165%# 2:# &# -3+&-;&"(&<)8
9)5&6+)#-32-)+#&*)#3")A')"+3;)#&"-#2")#5&"#964#&#-32-)#9*3-<)#3"#2")#'&5H&<)=
F%)# 9*3-<)# *)5(3:3)*# 53*563(# 2')*&()+# &+# :2002/+Q# R6*3"<# (%)# '2+3(3;)# %&0:?5450)+# 2:# (%)
3"'6(#;20(&<)8#v5#3+#'2+3(3;)8#&"-#(%6+#56**)"(#3+#52"-65()-#(%*26<%#-32-)#+,8#*)+3+(2*#,8#&"-32-)#+.=#m)&"/%30)8#-32-)+#+O#&"-#+P#/300#9)#*);)*+)#93&+)-=#K9+)*;)#(%&(#(%)*)#&*)#(/2
-32-)+#3"#+)*3)+#3"#(%)#52"-65(32"#'&(%8#&"-#(%6+#v.#/300#9)#02/)*#(%&"#v5#94#(/2#-32-)#-*2'+
B521'&*)-#(2#2")#-*2'#3"#(%)#53*563(#'*);326+04#-3+56++)-D=#F%3+#3+#+21)/%&(#2:#&#-3+&-;&"?
(&<)#2:#(%)#9*3-<)#*)5(3:3)*=
"
!
ac
line
voltage
"
D4
D1
!
vS
vO
"
R
!
D2
D3
(a)
v
2 VD
vS
Vs
!vS
vO
t
(b)
Figure 4.23 F%)#9*3-<)#*)5(3:3)*Q#5(6#53*563(7#5&6#3"'6(#&"-#26('6(#/&;):2*1+=
199
200 Chapter 4 Diodes
X)A(8#52"+3-)*#(%)#+3(6&(32"#-6*3"<#(%)#")<&(3;)#%&0:?5450)+#2:#(%)#3"'6(#;20(&<)=#F%)#+)5?
2"-&*4#;20(&<)#v5#/300#9)#")<&(3;)8#&"-#(%6+#−v5#/300#9)#'2+3(3;)8#:2*53"<#56**)"(#(%*26<%#+O8
,8#&"-#+P=#m)&"/%30)8#-32-)+#+,#&"-#+.#/300#9)#*);)*+)#93&+)-=#F%)#31'2*(&"(#'23"(#(2#"2()8
(%26<%8#3+#(%&(#-6*3"<#92(%#%&0:?5450)+8#56**)"(#:02/+#(%*26<%#,#3"#(%)#+&1)#-3*)5(32"#B:*21
*3<%(#(2#0):(D8#&"-#(%6+#v.#/300#&0/&4+#9)#'2+3(3;)8#&+#3"-35&()-#3"#L3<=#P=.OB9D=
F2#-)()*13")#(%)#')&H#3";)*+)#;20(&<)#Bl!TD#2:#)&5%#-32-)8#52"+3-)*#(%)#53*563(#-6*3"<
(%)# '2+3(3;)# %&0:?5450)+=# F%)# *);)*+)# ;20(&<)# &5*2++# +O# 5&"# 9)# -)()*13")-# :*21# (%)# 022'
:2*1)-#94#+O8#,8#&"-#+.#&+
v +O # ( *);)*+) ) = v . + v +. # ( :2*/&*- )
F%6+#(%)#1&A3161#;&06)#2:#v+O#2556*+#&(#(%)#')&H#2:#v.#&"-#3+#<3;)"#94
l!T = @ ? ! .@ + + @ + = @ ? ! @ +
K9+)*;)#(%&(#%)*)#(%)#l!T#3+#&926(#%&0:#(%)#;&06)#:2*#(%)#:600?/&;)#*)5(3:3)*#/3(%#&#5)"()*?
(&'')-#(*&"+:2*1)*=#F%3+#3+#&"2(%)*#&-;&"(&<)#2:#(%)#9*3-<)#*)5(3:3)*=
p)(#2")#12*)#&-;&"(&<)#2:#(%)#9*3-<)#*)5(3:3)*#53*563(#2;)*#(%&(#6(303M3"<#&#5)"()*?(&'')(*&"+:2*1)*#3+#(%&(#2"04#&926(#%&0:#&+#1&"4#(6*"+#&*)#*)C63*)-#:2*#(%)#+)52"-&*4#/3"-3"<#2:#(%)
(*&"+:2*1)*=#E"2(%)*#/&4#2:#022H3"<#&(#(%3+#'23"(#5&"#9)#29(&3")-#94#29+)*;3"<#(%&(#)&5%#%&0:#2:
(%)#+)52"-&*4#/3"-3"<#2:#(%)#5)"()*?(&'')-#(*&"+:2*1)*#3+#6(303M)-#:2*#2"04#%&0:#(%)#(31)=#F%)+)
&-;&"(&<)+#%&;)#1&-)#(%)#9*3-<)#*)5(3:3)*#(%)#12+(#'2'60&*#*)5(3:3)*#53*563(#52":3<6*&(32"=
EXERCISE
4.21#L2*#(%)#9*3-<)#*)5(3:3)*#53*563(#2:#L3<=#P=.OB&D8#6+)#(%)#52"+(&"(?;20(&<)?-*2'#-32-)#12-)0#(2#+%2/#(%&(#B&D
(%)# &;)*&<)# B2*# -5# 521'2")"(D# 2:# (%)# 26('6(# ;20(&<)# 3+# @ . # ! # ( . ⁄ π )@ ? ! .@ + # &"-# B9D# (%)# ')&H
-32-)#56**)"(#3+#( @ ? ! .@ + ) ⁄ , )=#L3"-#"61)*35&0#;&06)+#:2*#(%)#C6&"(3(3)+#3"#B&D#&"-#B9D#&"-#(%)#l!T
:2*#(%)#5&+)#3"#/%35%#v5#3+#&#,.?T#B*1+D#+3"6+23-8#@+#!#S=N#T8#&"-#,#=#,SS#Ω.
Ans. U=P#T7#,Z`#1E7#,`=O#T
4.5.4 The Rectifier with a Filter Capacitor—The Peak Rectifier
F%)#'60+&(3"<#"&(6*)#2:#(%)#26('6(#;20(&<)#'*2-65)-#94#(%)#*)5(3:3)*#53*563(+#-3+56++)-#&92;)
1&H)+#3(#6"+63(&90)#&+#&#-5#+6''04#:2*#)0)5(*2"35#53*563(+=#E#+31'0)#/&4#(2#*)-65)#(%)#;&*3&?
(32"#2:#(%)#26('6(#;20(&<)#3+#(2#'0&5)#&#5&'&53(2*#&5*2++#(%)#02&-#*)+3+(2*=#!(#/300#9)#+%2/"#(%&(
(%3+#.'4,"!%*(3(*',-!#+)*;)+#(2#*)-65)#+69+(&"(3&004#(%)#;&*3&(32"+#3"#(%)#*)5(3:3)*#26('6(#;20(&<)=
F2#+))#%2/#(%)#*)5(3:3)*#53*563(#/3(%#&#:30()*#5&'&53(2*#/2*H+8#52"+3-)*#:3*+(#(%)#+31'0)#53*?
563(#+%2/"#3"#L3<=#P=.P=#V)(#(%)#3"'6(#v-#9)#&#+3"6+23-#/3(%#&#')&H#;&06)#@#8#&"-#&++61)#(%)
-32-)#(2#9)#3-)&0=#E+#v-#<2)+#'2+3(3;)8#(%)#-32-)#52"-65(+#&"-#(%)#5&'&53(2*#3+#5%&*<)-#+2#(%&(
v.# =# v-=# F%3+# +3(6&(32"# 52"(3"6)+# 6"(30# v-# *)&5%)+# 3(+# ')&H# ;&06)# @#=# _)42"-# (%)# ')&H8# &+# v-)5*)&+)+#(%)#-32-)#9)521)+#*);)*+)#93&+)-#&"-#(%)#26('6(#;20(&<)#*)1&3"+#52"+(&"(#&(#(%)
;&06)#@#=#!"#:&5(8#(%)2*)(35&004#+')&H3"<8#(%)#5&'&53(2*#/300#*)(&3"#3(+#5%&*<)#&"-#%)"5)#3(+#;20(?
&<)#3"-):3"3()048#9)5&6+)#(%)*)#3+#"2#/&4#:2*#(%)#5&'&53(2*#(2#-3+5%&*<)=#F%6+#(%)#53*563(#'*2?
;3-)+#&#-5#;20(&<)#26('6(#)C6&0#(2#(%)#')&H#2:#(%)#3"'6(#+3")#/&;)=#F%3+#3+#&#;)*4#)"526*&<3"<
*)+60(#3"#;3)/#2:#26*#-)+3*)#(2#'*2-65)#&#-5#26('6(=
4.5 Rectifier Circuits 201
D
(a)
0
(b)
Figure 4.24 5(6# E# +31'0)# 53*563(# 6+)-# (2# 3006+(*&()# (%)# )::)5(# 2:# &# :30()*# 5&'&53(2*=# 5&6# !"'6(# &"-# 26('6(
/&;):2*1+#&++613"<#&"#3-)&0#-32-)=#X2()#(%&(#(%)#53*563(#'*2;3-)+#&#-5#;20(&<)#)C6&0#(2#(%)#')&H#2:#(%)#3"'6(
+3")#/&;)=#F%)#53*563(#3+#(%)*):2*)#H"2/"#&+#&##3)A0'3/4!%!3'#2*#&##3)A0*343/4&'=
X)A(8# /)# 52"+3-)*# (%)# 12*)# '*&5(35&0# +3(6&(32"# /%)*)# &# 02&-# *)+3+(&"5)# ,# 3+# 52"")5()&5*2++#(%)#5&'&53(2*#88#&+#-)'35()-#3"#L3<=#P=.ZB&D=#>2/);)*8#/)#/300#52"(3"6)#(2#&++61)
(%)#-32-)#(2#9)#3-)&0=#E+#9):2*)8#:2*#&#+3"6+23-&0#3"'6(8#(%)#5&'&53(2*#5%&*<)+#(2#(%)#')&H#2:
(%)#3"'6(#@#=#F%)"#(%)#-32-)#56(+#2::8#&"-#(%)#5&'&53(2*#-3+5%&*<)+#(%*26<%#(%)#02&-#*)+3+(&"5)
,=#F%)#5&'&53(2*#-3+5%&*<)#/300#52"(3"6)#:2*#&012+(#(%)#)"(3*)#5450)8#6"(30#(%)#(31)#&(#/%35%#v)A5))-+#(%)#5&'&53(2*#;20(&<)=#F%)"#(%)#-32-)#(6*"+#2"#&<&3"#&"-#5%&*<)+#(%)#5&'&53(2*#6'#(2
(%)#')&H#2:#v- 8#&"-#(%)#'*25)++#*)')&(+#3(+)0:=#K9+)*;)#(%&(#(2#H))'#(%)#26('6(#;20(&<)#:*21
-)5*)&+3"<#(22#165%#-6*3"<#5&'&53(2*#-3+5%&*<)8#2")#+)0)5(+#&#;&06)#:2*#8#+2#(%&(#(%)#(31)
52"+(&"(#8,#3+#165%#<*)&()*#(%&"#(%)#-3+5%&*<)#3"()*;&0=#
I)#&*)#"2/#*)&-4#(2#&"&04M)#(%)#53*563(#3"#-)(&30=#L3<6*)#P=.ZB9D#+%2/+#(%)#+()&-4?+(&()
3"'6(#&"-#26('6(#;20(&<)#/&;):2*1+#6"-)*#(%)#&++61'(32"#(%&(#8,#%#I8#/%)*)#I#3+#(%)#')*322:#(%)#3"'6(#+3"6+23-=#F%)#/&;):2*1+#2:#(%)#02&-#56**)"(
!P = v. ⁄ ,
BP=.OD
&"-#2:#(%)#-32-)#56**)"(#B/%)"#3(#3+#52"-65(3"<D
!+ = !8 + !P
*v
= 8 ???????- + ! P
*4
BP=.PD
BP=.ZD
202 Chapter 4 Diodes
iD
D
iC
iL
"
C
R
vO
vI "
!
!
(a)
T
vO
Vr
Vp
vI
vI
,t
t1
t2
t
Conduction
interval ,t
(b)
,t
iD derivative V0
which is vs
iL
(c)
t
Figure 4.25 T20(&<)# &"-# 56**)"(# /&;):2*1+# 3"# (%)# ')&H# *)5(3:3)*# 53*563(# /3(%# 8,# %# I=# F%)# -32-)# 3+
&++61)-#3-)&0=
&*)#+%2/"#3"#L3<=#P=.ZB5D=#F%)#:2002/3"<#29+)*;&(32"+#&*)#3"#2*-)*Q
1. F%)#-32-)#52"-65(+#:2*#&#9*3):#3"()*;&08#∆48#")&*#(%)#')&H#2:#(%)#3"'6(#+3"6+23-#&"-
+6''03)+# (%)# 5&'&53(2*# /3(%# 5%&*<)# )C6&0# (2# (%&(# 02+(# -6*3"<# (%)# 165%# 02"<)*# -3+?
5%&*<)#3"()*;&0=#F%)#0&(()*#3+#&''*2A31&()04#)C6&0#(2#(%)#')*32-#I=
2. E++613"<#&"#3-)&0#-32-)8#(%)#-32-)#52"-65(32"#9)<3"+#&(#(31)#4,8#&(#/%35%#(%)#3"'6(#v)C6&0+#(%)#)A'2")"(3&004#-)5&43"<#26('6(#v.=#$2"-65(32"#+(2'+#&(#4.#+%2*(04#&:()*#(%)
')&H#2:#v- 7#(%)#)A&5(#;&06)#2:#4.#5&"#9)#-)()*13")-#94#+)((3"<#!+#=#S#3"#@C=#BP=.ZD=
4.5 Rectifier Circuits 203
3. R6*3"<# (%)# -32-)?2::# 3"()*;&08# (%)# 5&'&53(2*# 8# -3+5%&*<)+# (%*26<%# ,8# &"-# (%6+# v.
-)5&4+# )A'2")"(3&004# /3(%# &# (31)# 52"+(&"(# 8,=# F%)# -3+5%&*<)# 3"()*;&0# 9)<3"+# J6+(
'&+(#(%)#')&H#2:#v-=#E(#(%)#)"-#2:#(%)#-3+5%&*<)#3"()*;&08#/%35%#0&+(+#:2*#&012+(#(%)
)"(3*)# ')*32-# I8# v.# =# @## −# @' 8# /%)*)# @'# 3+# (%)# ')&H?(2?')&H# *3''0)# ;20(&<)=# I%)"
8, %#I8#(%)#;&06)#2:#@'#3+#+1&00=
4. I%)"#@'#3+#+1&008#v.#3+#&012+(#52"+(&"(#&"-#)C6&0#(2#(%)#')&H#;&06)#2:#v-=#F%6+#(%)#-5
26('6(#;20(&<)#3+#&''*2A31&()04#)C6&0#(2#@#=#Y3130&*048#(%)#56**)"(#!P#3+#&012+(#52"?
+(&"(8#&"-#3(+#-5#521'2")"(#-P#3+#<3;)"#94
@#
- P = ?????
,
BP=.`D
!:#-)+3*)-8#&#12*)#&556*&()#)A'*)++32"#:2*#(%)#26('6(#-5#;20(&<)#5&"#9)#29(&3")-#94
(&H3"<#(%)#&;)*&<)#2:#(%)#)A(*)1)#;&06)+#2:#v.8
@ . = @ # ! ,??.? @ '
BP=.ND
I3(%#(%)+)#29+)*;&(32"+#3"#%&"-8#/)#"2/#-)*3;)#)A'*)++32"+#:2*#@'#&"-#:2*#(%)#&;)*&<)
&"-#')&H#;&06)+#2:#(%)#-32-)#56**)"(=#R6*3"<#(%)#-32-)?2::#3"()*;&08#v.#5&"#9)#)A'*)++)-#&+
v. = @# 3
! 4 ⁄ 8,
E(#(%)#)"-#2:#(%)#-3+5%&*<)#3"()*;&0#/)#%&;)
@ # ! @ ' # ! #@ # 3
! I ⁄ 8,
X2/8#+3"5)#8,#%#I8#/)#5&"#6+)#(%)#&''*2A31&(32"# 3
! I ⁄ 8,
! , ! I ⁄ 8, (2#29(&3"
I
@ ' ! @ # ????????
8,
BP=.^D
I)#29+)*;)#(%&(#(2#H))'#@'#+1&00#/)#16+(#+)0)5(#&#5&'&53(&"5)#8#+2#(%&(#8,#%#I=#F%)#!'334"
#-4,(7"#@'#3"#@C=#BP=.^D#5&"#9)#)A'*)++)-#3"#()*1+#2:#(%)#:*)C6)"54# % = , ⁄ I &+
@#
@ ' = ??????????
%8,
BP=.U&D
h+3"<#@C=#BP=.`D#/)#5&"#)A'*)++#@'#94#(%)#&0()*"&()#)A'*)++32"
@ ' = ?????P?
%8
BP=.U9D
X2()#(%&(#&"#&0()*"&(3;)#3"()*'*)(&(32"#2:#(%)#&''*2A31&(32"#1&-)#&92;)#3+#(%&(#(%)#5&'&53(2*
-3+5%&*<)+#94#1)&"+#2:#&#52"+(&"(#56**)"(# - P = @ # ⁄ ,=#F%3+#&''*2A31&(32"#3+#;&03-#&+#02"<
&+#@' ( @#=
E++613"<#(%&(#-32-)#52"-65(32"#5)&+)+#&012+(#&(#(%)#')&H#2:#v- 8#/)#5&"#-)()*13")#(%)
*-1)+*,'-1%'1,"!#(4#∆4#:*21
@ # 52+ ( ω ∆4 ) = @ # ! @ '
/%)*)# ω = . π % = . π ⁄ I 3+#(%)#&"<60&*#:*)C6)"54#2:#v- =#Y3"5)#Bω ∆4D#3+#&#+1&00#&"<0)8#/)
.
5&"#)1'024#(%)#&''*2A31&(32"# 52+ ( ω ∆4 ) ! , ! ,??.? ( ω ∆4 ) #(2#29(&3"
ω ∆4# ! .@ ' ⁄ @ #
I)#"2()#(%&(#/%)"#@'#(#@#8#(%)#52"-65(32"#&"<0)#ω ∆4#/300#9)#+1&008#&+#&++61)-=
BP=OSD
204 Chapter 4 Diodes
F2# -)()*13")# (%)# &;)*&<)# -32-)# 56**)"(# -6*3"<# 52"-65(32"8# !+&;8# /)# )C6&()# (%)# 5%&*<)
(%&(#(%)#-32-)#+6''03)+#(2#(%)#5&'&53(2*8
L +6''03)- = ! 8&; ∆4
/%)*)#:*21#@C=#BP=.PD8
! 8&; = ! +&; ! - P
(2#(%)#5%&*<)#(%&(#(%)#5&'&53(2*#02+)+#-6*3"<#(%)#-3+5%&*<)#3"()*;&08
L 02+( = 8@ '
(2#29(&3"8#6+3"<#@C+=#BP=OSD#&"-#BP=.U&D8
! +&; = - P ( , + π .@ # ⁄ @ ' )
BP=O,D
K9+)*;)#(%&(#/%)"#@'#(#@#8#(%)#&;)*&<)#-32-)#56**)"(#-6*3"<#52"-65(32"#3+#165%# <*)&()*
(%&"# (%)# -5# 02&-# 56**)"(=# F%3+# 3+# "2(# +6*'*3+3"<8# +3"5)# (%)# -32-)# 52"-65(+# :2*# &# ;)*4# +%2*(
3"()*;&0#&"-#16+(#*)'0)"3+%#(%)#5%&*<)#02+(#94#(%)#5&'&53(2*#-6*3"<#(%)#165%#02"<)*#3"()*;&0
3"#/%35%#3(#3+#-3+5%&*<)-#94#-P=
F%)#')&H#;&06)#2:#(%)#-32-)#56**)"(8#!+1&A8#5&"#9)#-)()*13")-#94#);&06&(3"<#(%)#)A'*)+?
+32"#3"#@C=#BP=.ZD#&(#(%)#2"+)(#2:#-32-)#52"-65(32"W(%&(#3+8#&(#4#=#4,#=#−∆4#B/%)*)#4#=#S#3+#&(#(%)
')&HD=#E++613"<#(%&(#!P#3+#&012+(#52"+(&"(#&(#(%)#;&06)#<3;)"#94#@C=#BP=.`D8#/)#29(&3"
! +1&A = - P ( , + . π .@ # ⁄ @ ' )
BP=O.D
L*21#@C+=#BP=O,D#&"-#BP=O.D8#/)#+))#(%&(#:2*#@'#(#@#8#!+1&A#!#.!+&;8#/%35%#52**)0&()+#/3(%#(%)
:&5(#(%&(#(%)#/&;):2*1#2:#!+#3+#&012+(#&#*3<%(?&"<0)#(*3&"<0)#B+))#L3<=#P=.Z5D=
Example 4.8
$2"+3-)*#&#')&H#*)5(3:3)*#:)-#94#&#`S?>M#+3"6+23-#%&;3"<#&#')&H#;&06)#@##=#,SS#T=#V)(#(%)#02&-#*)+3+?
(&"5)#,#=#,S#HΩ=#L3"-#(%)#;&06)#2:#(%)#5&'&53(&"5)#8#(%&(#/300#*)+60(#3"#&#')&H?(2?')&H#*3''0)#2:#.#T=
E0+28#5&0560&()#(%)#:*&5(32"#2:#(%)#5450)#-6*3"<#/%35%#(%)#-32-)#3+#52"-65(3"<#&"-#(%)#&;)*&<)#&"')&H#;&06)+#2:#(%)#-32-)#56**)"(=
Solution
L*21#@C=#BP=.U&D#/)#29(&3"#(%)#;&06)#2:#8#&+
@#
,SS
8 = ???????????? = ?????????????????????????????????????????O? = ^O=O#µL
@ ' %,
. × `S × ,S × ,S
F%)#52"-65(32"#&"<0)#ω#∆4#3+#:26"-#:*21#@C=#BP=OSD#&+
ω ∆4 =
. × . ⁄ ,SS = S=.#*&-
F%6+# (%)# -32-)# 52"-65(+# :2*# ( S=. ⁄ . π ) × ,SS = O=,^j 2:# (%)# 5450)=# F%)# &;)*&<)# -32-)# 56**)"(# 3+
29(&3")-#:*21#@C=#BP=O,D8#/%)*)# - P = ,SS ⁄ ,S = ,S#1E8 &+
! +&; = ,S ( , + π . × ,SS ⁄ . ) = O.P#1E
F%)#')&H#-32-)#56**)"(#3+#:26"-#6+3"<#@C=#BP=O.D8
! +1&A = ,S ( , + . π . × ,SS ⁄ . ) = `O^#1E
4.5 Rectifier Circuits 205
Figure 4.26 I&;):2*1+#3"#(%)#:600?/&;)#')&H#*)5(3:3)*=
F%)#53*563(#2:#L3<=#P=.ZB&D#3+#H"2/"#&+#&#%&0:?/&;)#3"(>%!"*,'.'"!=#F%)#:600?/&;)#*)5(3?
:3)*#53*563(+#2:#L3<+=#P=..B&D#&"-#P=.OB&D#5&"#9)#52";)*()-#(2#')&H#*)5(3:3)*+#94#3"506-3"<#&
5&'&53(2*# &5*2++# (%)# 02&-# *)+3+(2*=# E+# 3"# (%)# %&0:?/&;)# 5&+)8# (%)# 26('6(# -5# ;20(&<)# /300# 9)
&012+(#)C6&0#(2#(%)#')&H#;&06)#2:#(%)#3"'6(#+3")#/&;)#BL3<=#P=.`D=#F%)#*3''0)#:*)C6)"548#%2/?
);)*8#/300#9)#(/35)#(%&(#2:#(%)#3"'6(=#F%)#')&H?(2?')&H#*3''0)#;20(&<)8#:2*#(%3+#5&+)8#5&"#9)
-)*3;)-#6+3"<#&#'*25)-6*)#3-)"(35&0#(2#(%&(#&92;)#96(#/3(%#(%)#-3+5%&*<)#')*32-#I#*)'0&5)-#94
I ⁄ . 8#*)+60(3"<#3"
@#
@ ' = ?????????????
.%8,
BP=OOD
I%30)#(%)#-32-)#52"-65(32"#3"()*;&08#∆48#/300#+(300#9)#<3;)"#94#@C=#BP=OSD8#(%)#&;)*&<)#&"')&H#56**)"(+#3"#)&5%#2:#(%)#-32-)+#/300#9)#<3;)"#94
! +&; = - P ( , + π @ # ⁄ .@ ' )
BP=OPD
! +1&A = - P ( , + . π @ # ⁄ .@ ' )
BP=OZD
$21'&*3"<#(%)+)#)A'*)++32"+#/3(%#(%)#52**)+'2"-3"<#2")+#:2*#(%)#%&0:?/&;)#5&+)8#/)#"2()
(%&(#:2*#(%)#+&1)#;&06)+#2:#@#8#%8#,8#&"-#@'#B&"-#(%6+#(%)#+&1)#-PD8#/)#"))-#&#5&'&53(2*#%&0:#(%)
+3M)#2:#(%&(#*)C63*)-#3"#(%)#%&0:?/&;)#*)5(3:3)*=#E0+28#(%)#56**)"(#3"#)&5%#-32-)#3"#(%)#:600?
/&;)#*)5(3:3)*#3+#&''*2A31&()04#%&0:#(%&(#/%35%#:02/+#3"#(%)#-32-)#2:#(%)#%&0:?/&;)#53*563(=
F%)#&"&04+3+#&92;)#&++61)-#3-)&0#-32-)+=#F%)#&556*&54#2:#(%)#*)+60(+#5&"#9)#31'*2;)-#94
(&H3"<#(%)#-32-)#;20(&<)#-*2'#3"(2#&5526"(=#F%3+#5&"#9)#)&+304#-2")#94#*)'0&53"<#(%)#')&H ;20(&<)
@##(2#/%35%#(%)#5&'&53(2*#5%&*<)+#/3(%#B@##−#@+D#:2*#(%)#%&0:?/&;)#53*563(#&"-#(%)#:600?/&;)#53*?
563(#6+3"<#&#5)"()*?(&'')-#(*&"+:2*1)*#&"-#/3(%#B@##−#.@+D#:2*#(%)#9*3-<)?*)5(3:3)*#5&+)=
I)#52"506-)#(%3+#+)5(32"#94#"2(3"<#(%&(#')&H?*)5(3:3)*#53*563(+#:3"-#&''035&(32"#3"#+3<"&0?
'*25)++3"<#+4+()1+#/%)*)#3(#3+#*)C63*)-#(2#-)()5(#(%)#')&H#2:#&"#3"'6(#+3<"&0=#!"#+65%#&#5&+)8
(%)#53*563(#3+#*):)**)-#(2#&+#&#3"(>%)","*,-!=#E#'&*(3560&*04#'2'60&*#&''035&(32"#2:#(%)#')&H
-)()5(2*#3+#3"#(%)#-)+3<"#2:#&#-)12-60&(2*#:2*#&1'03(6-)?12-60&()-#BEmD#+3<"&0+=#I)#+%&00
"2(#-3+56++#(%3+#&''035&(32"#:6*(%)*#%)*)=#
EXERCISES
4.22# R)*3;)#(%)#)A'*)++32"+#3"#@C+=#BP=OOD8#BP=OPD8#&"-#BP=OZD=
4.23# $2"+3-)*#&#9*3-<)?*)5(3:3)*#53*563(#/3(%#&#:30()*#5&'&53(2*#8#'0&5)-#&5*2++#(%)#02&-#*)+3+(2*#,#:2*#(%)#5&+)
3"#/%35%#(%)#(*&"+:2*1)*#+)52"-&*4#-)03;)*+#&#+3"6+23-#2:#,.#T#B*1+D#%&;3"<#&#`S?>M#:*)C6)"54#&"-
206 Chapter 4 Diodes
&++613"<#@+#=#S=^#T &"-#&#02&-#*)+3+(&"5)#,#=#,SS#Ω=#L3"-#(%)#;&06)#2:#8#(%&(#*)+60(+#3"#&#*3''0)
;20(&<)#"2#0&*<)*#(%&"#,#T#')&H?(2?')&H=#I%&(#3+#(%)#-5#;20(&<)#&(#(%)#26('6(i#L3"-#(%)#02&-#56**)"(=
L3"-#(%)#-32-)+d#52"-65(32"#&"<0)=#l*2;3-)#(%)#&;)*&<)#&"-#')&H#-32-)#56**)"(+#I%&(#3+#(%)#')&H
*);)*+)#;20(&<)#&5*2++#)&5%#-32-)i#Y')53:4#(%)#-32-)#3"#()*1+#2:#3(+#')&H#56**)"(#&"-#3(+#l!T=
Ans. ,.^,#µL7#,Z=P#T#2*#B&#9)(()*#)+(31&()D#,P=U#T7#S=,Z#E7#S=O`#*&-#B.S=N°D7#,=PZ#E7#.=NP#E7
,`=. T=#F%6+#+)0)5(#&#-32-)#/3(%#O=Z?E#(2#P?E#')&H#56**)"(#&"-#&#.S?T#l!T#*&(3"<=
4.5.5 Precision Half-Wave Rectifier—The Superdiode 4
F%)#*)5(3:3)*#53*563(+#+(6-3)-#(%6+#:&*#+6::)*#:*21#%&;3"<#2")#2*#(/2#-32-)#-*2'+#3"#(%)#+3<"&0
'&(%+=#F%6+#(%)+)#53*563(+#/2*H#/)00#2"04#/%)"#(%)#+3<"&0#(2#9)#*)5(3:3)-#3+#165%#0&*<)*#(%&"
(%)#;20(&<)#-*2'#2:#&#52"-65(3"<#-32-)#BS=N#T#2*#+2D=#!"#+65%#&#5&+)8#(%)#-)(&30+#2:#(%)#-32-)
:2*/&*-#5%&*&5()*3+(35+#2*#(%)#)A&5(#;&06)#2:#(%)#-32-)#;20(&<)#-2#"2(#'0&4#&#'*213")"(#*20)
3"#-)()*13"3"<#53*563(#')*:2*1&"5)=#F%3+#3+#3"-))-#(%)#5&+)#3"#(%)#&''035&(32"#2:#*)5(3:3)*#53*?
563(+#3"#'2/)*?+6''04#-)+3<"=#F%)*)#&*)#2(%)*#&''035&(32"+8#%2/);)*8#/%)*)#(%)#+3<"&0#(2#9)
*)5(3:3)-#3+#+1&00#B)=<=8#2"#(%)#2*-)*#2:#,SS#1T#2*#+2D#&"-#(%6+#50)&*04#3"+6::353)"(#(2#(6*"#2"
&#-32-)=#E0+28#3"#3"+(*61)"(&(32"#&''035&(32"+8#(%)#"))-#&*3+)+#:2*#*)5(3:3)*#53*563(+#/3(%#;)*4
'*)53+)#&"-#'*)-35(&90)#(*&"+:)*#5%&*&5()*3+(35+=#L2*#(%)+)#&''035&(32"+8#&#50&++#2:#53*563(+#%&+
9))"#-);)02')-#6(303M3"<#2'#&1'+#B$%&'()*#.D#(2<)(%)*#/3(%#-32-)+#(2#'*2;3-)#'*)53+32"#*)5?
(3:35&(32"=#!"#(%)#:2002/3"<#-3+56++32"8#/)#+(6-4#2")#+65%#53*563(8#0)&;3"<#&#12*)#521'*)%)"?
+3;)#+(6-4#2:#2'#&1']-32-)#53*563(+#(2#$%&'()*#,N=
L3<6*)#P=.NB&D#+%2/+#&#'*)53+32"#%&0:?/&;)#*)5(3:3)*#53*563(#52"+3+(3"<#2:#&#-32-)#'0&5)3"#(%)#")<&(3;)?:))-9&5H#'&(%#2:#&"#2'#&1'8#/3(%#,#9)3"<#(%)#*)5(3:3)*#02&-#*)+3+(&"5)=#F%)#2'
&1'8#2:#526*+)8#"))-+#'2/)*#+6''03)+#:2*#3(+#2')*&(32"=#L2*#+31'0353(48#(%)+)#&*)#"2(#+%2/"#3"
(%)#53*563(#-3&<*&1=#F%)#53*563(#/2*H+#&+#:2002/+Q#!:#v-#<2)+#'2+3(3;)8#(%)#26('6(#;20(&<)#v6#2:
(%)#2'#&1'#/300#<2#'2+3(3;)#&"-#(%)#-32-)#/300#52"-65(8#(%6+#)+(&903+%3"<#&#502+)-#:))-9&5H
'&(%#9)(/))"#(%)#2'#&1'd+#26('6(#()*13"&0#&"-#(%)#")<&(3;)#3"'6(#()*13"&0=#F%3+#")<&(3;)?
:))-9&5H#'&(%#/300#5&6+)#&#;3*(6&0#+%2*(#53*563(#(2#&'')&*#9)(/))"#(%)#(/2#3"'6(#()*13"&0+#2:
(a)
(b)
Figure 4.27 F%)# e+6')*-32-)f# '*)53+32"# %&0:?/&;)# *)5(3:3)*# &"-# 3(+# &012+(?3-)&0# (*&"+:)*# 5%&*&5()*3+(35=
X2()#(%&(#/%)"#v - > S#&"-#(%)#-32-)#52"-65(+8#(%)#2'#&1'#+6''03)+#(%)#02&-#56**)"(8#&"-#(%)#+26*5)#3+#52";)?
"3)"(04#96::)*)-8#&"#&--)-#&-;&"(&<)=#X2(#+%2/"#&*)#(%)#2'?&1'#'2/)*#+6''03)+=
P
F%3+#+)5(32"#*)C63*)+#H"2/0)-<)#2:#2')*&(32"&0#&1'03:3)*+#B$%&'()*#.D=
Limiting and Clamping Circuits 207
(%)#2'#&1'=#F%6+#(%)#;20(&<)#&(#(%)#")<&(3;)#3"'6(#()*13"&08#/%35%#3+#&0+2#(%)#26('6(#;20(&<)
v. 8#/300#)C6&0#B(2#/3(%3"#&#:)/#13003;20(+D#(%&(#&(#(%)#'2+3(3;)#3"'6(#()*13"&08#/%35%#3+#(%)
3"'6(#;20(&<)#v- 8
v. = v-
v- ≥ S
X2()#(%&(#(%)#2::+)(#;20(&<)#B!S=N#TD#)A%393()-#3"#(%)#+31'0)#%&0:?/&;)#*)5(3:3)*#53*563(#2:
L3<=#P=.,#3+#"2#02"<)*#'*)+)"(=#L2*#(%)#2'?&1'#53*563(#(2#+(&*(#2')*&(32"8#v-#%&+#(2#)A5))-#2"04
&#")<03<3904#+1&00#;20(&<)#)C6&0#(2#(%)#-32-)#-*2'#-3;3-)-#94#(%)#2'#&1'd+#2')"?022'#<&3"=
!"#2(%)*#/2*-+8#(%)#+(*&3<%(?03")#(*&"+:)*#5%&*&5()*3+(35#v.]v-#&012+(#'&++)+#(%*26<%#(%)#2*3?
<3"=#F%3+#1&H)+#(%3+#53*563(#+63(&90)#:2*#&''035&(32"+#3";20;3"<#;)*4#+1&00#+3<"&0+=
$2"+3-)*#"2/#(%)#5&+)#/%)"#v-#<2)+#")<&(3;)=#F%)#2'#&1'd+#26('6(#;20(&<)#v6#/300#()"(2#:2002/#&"-#<2#")<&(3;)=#F%3+#/300#*);)*+)?93&+#(%)#-32-)8#&"-#"2#56**)"(#/300#:02/#(%*26<%
*)+3+(&"5)#,8#5&6+3"<#v.#(2#*)1&3"#)C6&0#(2#S#T=#F%6+8#:2*#v-#<#S8#v.#=#S=#Y3"5)#3"#(%3+#5&+)#(%)
-32-)#3+#2::8#(%)#2'#&1'#/300#9)#2')*&(3"<#3"#&"#2')"?022'#:&+%32"8#&"-#3(+#26('6(#/300#9)#&(#3(+
")<&(3;)#+&(6*&(32"#0);)0=
F%)# (*&"+:)*# 5%&*&5()*3+(35# 2:# (%3+# 53*563(# /300# 9)# (%&(# +%2/"# 3"# L3<=# P=.NB9D8# /%35%# 3+
&012+(#3-)"(35&0#(2#(%)#3-)&0#5%&*&5()*3+(35#2:#&#%&0:?/&;)#*)5(3:3)*=#F%)#"2"3-)&0#-32-)#5%&*&5?
()*3+(35+#%&;)#9))"#&012+(#521'0)()04#1&+H)-#94#'0&53"<#(%)#-32-)#3"#(%)#")<&(3;)?:))-9&5H
'&(%#2:#&"#2'#&1'=#F%3+#3+#&"2(%)*#-*&1&(35#&''035&(32"#2:#")<&(3;)#:))-9&5H8#&#+69J)5(#/)
/300#+(6-4#:2*1&004#3"#$%&'()*# ,S=#F%)#52193"&(32"#2:#-32-)#&"-#2'#&1'8#+%2/"#3"#(%)#-2(()92A#3"#L3<=#P=.NB&D8#3+#&''*2'*3&()04#*):)**)-#(2#&+#&#e+6')*-32-)=f#
EXERCISES
4.24# $2"+3-)*#(%)#-3"!(,'-1(4%!"*,'.'"!#2*#+6')*-32-)#53*563(#2:#L3<=#P=.NB&D8#/3(%#,#=#,#HΩ=#L2*#v-#=#,S 1T8
, T8#&"-#−,#T8#/%&(#&*)#(%)#;20(&<)+#(%&(#*)+60(#&(#(%)#*)5(3:3)*#26('6(#&"-#&(#(%)#26('6(#2:#(%)#2'#&1'i
E++61)#(%&(#(%)#2'#&1'#3+#3-)&0#&"-#(%&(#3(+#26('6(#+&(6*&()+#&(#±,.#T=#F%)#-32-)#%&+#&#S=N?T#-*2'#&(
,?1E#56**)"(=
Ans. ,S#1T8#S=ZU#T7#,#T8#,=N#T7#S#T8#−,.#T
4.25# !:#(%)#-32-)#3"#(%)#53*563(#2:#L3<=#P=.NB&D#3+#*);)*+)-8#:3"-#(%)#(*&"+:)*#5%&*&5()*3+(35#v.#&+#&#:6"5(32"#2:#v-=
Ans. v . = S%:2*%v - ≥ S7% v . = v - #:2*%v - ≤ S
4.6 Limiting and Clamping Circuits
!"#(%3+#+)5(32"8#/)#+%&00#'*)+)"(#&--3(32"&0#"2"03")&*#53*563(#&''035&(32"+#2:#-32-)+=
4.6.1 Limiter Circuits
L3<6*)# P=.^# +%2/+# (%)# <)")*&0# (*&"+:)*# 5%&*&5()*3+(35# 2:# &# 0313()*# 53*563(=# E+# 3"-35&()-8# :2*
3"'6(+#3"#&#5)*(&3"#*&"<)8# P − ⁄ H ≤ v - ≤ P + ⁄ H 8#(%)#0313()*#&5(+#&+#&#03")&*#53*563(8#'*2;3-3"<#&"
26('6(#'*2'2*(32"&0#(2#(%)#3"'6(8#v.#=#Hv-=#E0(%26<%#3"#<)")*&0#H#5&"#9)#<*)&()*#(%&"#,8#(%)#53*?
563(+#-3+56++)-#3"#(%3+#+)5(32"#%&;)#H#≤#,#&"-#&*)#H"2/"#&+#3($$'#"%4'=',"!$=#B@A&1'0)+#2:
&5(3;)#0313()*+#/300#9)#'*)+)"()-#3"#$%&'()*#,N=D#!:#v-#)A5))-+#(%)#6'')*#4:'3?:&<*# ( P + ⁄ H ) 8#(%)
26('6(#;20(&<)#3+#<!1!43*#2*#50&1')-#(2#(%)#6'')*#0313(3"<#0);)0#P+=#K"#(%)#2(%)*#%&"-8#3:#v-#3+
208 Chapter 4 Diodes
Figure 4.28 k)")*&0# (*&"+:)*# 5%&*&5()*3+(35
:2*#&#0313()*#53*563(=
Figure 4.29 E''043"<#&#+3")#/&;)#(2#&#0313()*#5&"#*)+60(#3"#503''3"<#2::#3(+#(/2#')&H+=
*)-65)-# 9)02/#(%)# 02/)*# 0313(3"<# (%*)+%20-# ( P − ⁄ H )8# (%)# 26('6(# ;20(&<)#v.# 3+# 0313()-#(2# (%)
02/)*#0313(3"<#0);)0# P − =
F%)# <)")*&0# (*&"+:)*# 5%&*&5()*3+(35# 2:# L3<=# P=.^# -)+5*39)+# &# )-+&4"% 4'=',"!W(%&(# 3+8# &
0313()*#(%&(#/2*H+#2"#92(%#(%)#'2+3(3;)#&"-#")<&(3;)#')&H+#2:#&"#3"'6(#/&;):2*1=#E'174"%4'=0
',"!$8#2:#526*+)8#)A3+(=#L3"&0048#"2()#(%&(#3:#&"#3"'6(#/&;):2*1#+65%#&+#(%&(#+%2/"#3"#L3<=#P=.U
3+#:)-#(2#&#-2690)#0313()*8#3(+#(/2#')&H+#/300#9)#/<!##3*0&%%=#V313()*+#(%)*):2*)#&*)#+21)(31)+
*):)**)-#(2#&+#*4'33"!$=
F%)#0313()*#/%2+)#5%&*&5()*3+(35+#&*)#-)'35()-#3"#L3<=#P=.^#3+#-)+5*39)-#&+#&#2(!)%4'=',"!=
E-.,%4'=','17#3+#5%&*&5()*3M)-#94#+122(%)*#(*&"+3(32"+#9)(/))"#(%)#03")&*#*)<32"#&"-#(%)#+&(?
6*&(32"#*)<32"+#&"-#&#+02')#<*)&()*#(%&"#M)*2#3"#(%)#+&(6*&(32"#*)<32"+8#&+#3006+(*&()-#3"#L3<=
P=OS=#R)')"-3"<#2"#(%)#&''035&(32"8#)3(%)*#%&*-#2*#+2:(#0313(3"<#1&4#9)#'*):)**)-=
V313()*+#:3"-#&''035&(32"#3"#&#;&*3)(4#2:#+3<"&0?'*25)++3"<#+4+()1+=#K")#2:#(%)3*#+31'0)+(
&''035&(32"+#3+#3"#0313(3"<#(%)#;20(&<)#9)(/))"#(%)#(/2#3"'6(#()*13"&0+#2:#&"#2'#&1'#(2#&#;&06)
02/)*#(%&"#(%)#9*)&H-2/"#;20(&<)#2:#(%)#(*&"+3+(2*+#(%&(#1&H)#6'#(%)#3"'6(#+(&<)#2:#(%)#2'?&1'
53*563(=#I)#/300#%&;)#12*)#(2#+&4#2"#(%3+#&"-#2(%)*#0313()*#&''035&(32"+#&(#0&()*#'23"(+#3"#(%3+#922H=
R32-)+# 5&"# 9)# 52193")-# /3(%# *)+3+(2*+# (2# '*2;3-)# +31'0)# *)&03M&(32"+# 2:# (%)# 0313()*
:6"5(32"=#E#"619)*#2:#)A&1'0)+#&*)#-)'35()-#3"#L3<=#P=O,=#!"#)&5%#'&*(#2:#(%)#:3<6*)#92(%#(%)
53*563(#&"-#3(+#(*&"+:)*#5%&*&5()*3+(35#&*)#<3;)"=#F%)#(*&"+:)*#5%&*&5()*3+(35+#&*)#29(&3")-#6+3"<
(%)# 52"+(&"(?;20(&<)?-*2'# B@+# =# S=N# TD# -32-)# 12-)0# 96(# &++613"<# &# +122(%# (*&"+3(32"
9)(/))"#(%)#03")&*#&"-#+&(6*&(32"#*)<32"+#2:#(%)#(*&"+:)*#5%&*&5()*3+(35=#
Limiting and Clamping Circuits 209
Figure 4.30 Y2:(#0313(3"<=
Figure 4.31 E#;&*3)(4#2:#9&+35#0313(3"<#53*563(+=
F%)#53*563(#3"#L3<=#P=O,B&D#3+#(%&(#2:#(%)#%&0:?/&;)#*)5(3:3)*#)A5)'(#(%&(#%)*)#(%)#26('6(#3+
(&H)"#&5*2++#(%)#-32-)=#L2*#v-#c#S=Z#T8#(%)#-32-)#3+#56(#2::8#"2#56**)"(#:02/+8#&"-#(%)#;20(&<)
-*2'#&5*2++#,#3+#M)*27#(%6+#v.#=#v- =#E+#v-#)A5))-+#S=Z#T8#(%)#-32-)#(6*"+#2"8#);)"(6&004#0313(3"<
210 Chapter 4 Diodes
v.# (2# 2")# -32-)# -*2'# BS=N# TD=# F%)# 53*563(# 2:# L3<=# P=O,B9D# 3+# +3130&*# (2# (%&(# 3"# L3<=# P=O,B&D
)A5)'(#(%&(#(%)#-32-)#3+#*);)*+)-=
R2690)#0313(3"<#5&"#9)#31'0)1)"()-#94#'0&53"<#(/2#-32-)+#2:#2''2+3()#'20&*3(4#3"#'&*&0?
0)08# &+# +%2/"# 3"# L3<=# P=O,B5D=# >)*)# (%)# 03")&*# *)<32"# 2:# (%)# 5%&*&5()*3+(35# 3+# 29(&3")-# :2*
! S=Z#T ≤ v - ≤ S=Z#T=#L2*#(%3+#*&"<)#2:#v-8#92(%#-32-)+#&*)#2::#&"-#v.#=#v- =#E+#v-#)A5))-+#S=Z#T8
+,#(6*"+#2"#&"-#);)"(6&004#0313(+#v.#(2#+ S=N#T=#Y3130&*048#&+#v-#<2)+#12*)#")<&(3;)#(%&"#]S=Z#T8
+.#(6*"+#2"#&"-#);)"(6&004#0313(+#v.#(2#]S=N#T=
F%)#(%*)+%20-+#&"-#+&(6*&(32"#0);)0+#2:#-32-)#0313()*+#5&"#9)#52"(*200)-#94#6+3"<#+(*3"<+
2:#-32-)+#&"-a2*#94#52"")5(3"<#&#-5#;20(&<)#3"#+)*3)+#/3(%#(%)#-32-)B+D=#F%)#0&(()*#3-)&#3+#3006+?
(*&()-#3"#L3<=#P=O,B-D=#L3"&0048#*&(%)*#(%&"#+(*3"<+#2:#-32-)+8#/)#1&4#6+)#(/2#M)")*#-32-)+#3"
+)*3)+8#&+#+%2/"#3"#L3<=#P=O,B)D=#!"#(%3+#53*563(8#0313(3"<#2556*+#3"#(%)#'2+3(3;)#-3*)5(32"#&(#&
;20(&<)#2:#@G .#+#S=N8#/%)*)#S=N#T#*)'*)+)"(+#(%)#;20(&<)#-*2'#&5*2++#M)")*#-32-)#G, /%)"
52"-65(3"<#3"#(%)#%&'()'*#-3*)5(32"=#L2*#")<&(3;)#3"'6(+8#G,#&5(+#&+#&#M)")*8#/%30)#G.#52"-65(+
3"#(%)#:2*/&*-#-3*)5(32"=#!(#+%260-#9)#1)"(32")-#(%&(#'&3*+#2:#M)")*#-32-)+#52"")5()-#3"#+)*3)+
&*)#&;&30&90)#5211)*53&004#:2*#&''035&(32"+#2:#(%3+#(4')#6"-)*#(%)#"&1)#)-+&4"0(1-)"%B"1"!=
m2*)# :0)A390)# 0313()*# 53*563(+# &*)# '2++390)# 3:# 2'# &1'+# &*)# 52193")-# /3(%# -32-)+# &"*)+3+(2*+=#@A&1'0)+#2:#+65%#53*563(+#&*)#-3+56++)-#3"#$%&'()*#,N=
EXERCISE
4.26# E++613"<#(%)#-32-)+#(2#9)#3-)&08#-)+5*39)#(%)#(*&"+:)*#5%&*&5()*3+(35#2:#(%)#53*563(#+%2/"#3"#L3<=#@P=.`=
"
!
Figure E4.26
Ans. v . = v #############:2*# ! Z ≤ v - ≤ +Z
v . = ??,.? v - ! .=Z
:2*# v - ≤ ! Z
v . = ??,.? v - + .=Z
:2*# v - ≥ +Z
4.6.2 The Clamped Capacitor or DC Restorer
!:#3"#(%)#9&+35#')&H?*)5(3:3)*#53*563(8#(%)#26('6(#3+#(&H)"#&5*2++#(%)#-32-)#*&(%)*#(%&"#&5*2++
(%)#5&'&53(2*8#&"#3"()*)+(3"<#53*563(#/3(%#31'2*(&"(#&''035&(32"+#*)+60(+=#F%)#53*563(8#5&00)-#&
-5#*)+(2*)*8#3+#+%2/"#3"#L3<=#P=O.#:)-#/3(%#&#+C6&*)#/&;)=#_)5&6+)#2:#(%)#'20&*3(4#3"#/%35%
(%)#-32-)#3+#52"")5()-8#(%)#5&'&53(2*#/300#5%&*<)#(2#&#;20(&<)#v8#/3(%#(%)#'20&*3(4#3"-35&()-#3"
L3<=#P=O.#&"-#)C6&0#(2#(%)#1&<"3(6-)#2:#(%)#12+(#")<&(3;)#')&H#2:#(%)#3"'6(#+3<"&0=#Y69+)?
C6)"(048#(%)#-32-)#(6*"+#2::#&"-#(%)#5&'&53(2*#*)(&3"+#3(+#;20(&<)#3"-):3"3()04=#!:8#:2*#3"+(&"5)8
(%)#3"'6(#+C6&*)#/&;)#%&+#(%)#&*93(*&*4#0);)0+#−`#T#&"-#+P#T8#(%)"#v8#/300#9)#)C6&0#(2#`#T=
X2/8#+3"5)#(%)#26('6(#;20(&<)#v.#3+#<3;)"#94#
v. = v- + v8
3(# :2002/+# (%&(# (%)# 26('6(# /&;):2*1# /300#9)# 3-)"(35&0# (2# (%&(# 2:# (%)# 3"'6(8# )A5)'(# (%&(# 3(# 3+
+%3:()-#6'/&*-#94#v8#;20(+=#!"#26*#)A&1'0)#(%)#26('6(#/300#(%6+#9)#&#+C6&*)#/&;)#/3(%#0);)0+
2:#S T#&"-#+,S#T=
Limiting and Clamping Circuits 211
! vC "
(a)
(b)
(c)
Figure 4.32 F%)#50&1')-#5&'&53(2*#2*#-5#*)+(2*)*#/3(%#&#+C6&*)?/&;)#3"'6(#&"-#"2#02&-=
E"2(%)*#/&4#2:#;3+6&03M3"<#(%)#2')*&(32"#2:#(%)#53*563(#3"#L3<=#P=O.#3+#(2#"2()#(%&(
9)5&6+)#(%)#-32-)#3+#52"")5()-#&5*2++#(%)#26('6(#/3(%#(%)#'20&*3(4#+%2/"8#3(#'*);)"(+#(%)
26('6(#;20(&<)#:*21#<23"<#9)02/#S#T#B94#52"-65(3"<#&"-#5%&*<3"<#6'#(%)#5&'&53(2*8#(%6+
5&6+3"<# (%)# 26('6(# (2# *3+)# (2# S# TD8# 96(# (%3+# 52"")5(32"# /300# "2(# 52"+(*&3"# (%)# '2+3(3;)
)A56*+32"# 2:# v.=# F%)# 26('6(# /&;):2*1# /300# (%)*):2*)# %&;)# 3(+# 02/)+(# ')&H# /<)1#3*# (2
S T8#/%35%#3+#/%4#(%)#53*563(#3+#5&00)-#&#*4(=3")%*(3(*',-!=#!(#+%260-#9)#29;326+#(%&(
*);)*+3"<# (%)# -32-)# '20&*3(4# /300# '*2;3-)# &"# 26('6(# /&;):2*1# /%2+)# %3<%)+(# ')&H# 3+
50&1')-#(2#S#T=#!"#)3(%)*#5&+)8#(%)#26('6(#/&;):2*1#/300#%&;)#&#:3"3()#&;)*&<)#;&06)#2*
-5#521'2")"(=#F%3+#-5#521'2")"(#3+#)"(3*)04#6"*)0&()-#(2#(%)#&;)*&<)#;&06)#2:#(%)#3"'6(
/&;):2*1=#E+#&"#&''035&(32"8#52"+3-)*#&#'60+)#+3<"&0#9)3"<#(*&"+13(()-#(%*26<%#&#5&'&5?
3(3;)04#526'0)-#2*#&5?526'0)-#+4+()1=#F%)#5&'&53(3;)#526'03"<#/300#5&6+)#(%)#'60+)#(*&3"
(2#02+)#/%&();)*#-5#521'2")"(#3(#2*3<3"&004#%&-=#L))-3"<#(%)#*)+60(3"<#'60+)#/&;):2*1
(2#&#50&1'3"<#53*563(#'*2;3-)+#3(#/3(%#&#/)00?-)()*13")-#-5#521'2")"(8#&#'*25)++#H"2/"
&+#)*%!"$,-!(,'-1=#F%3+#3+#/%4#(%)#53*563(#3+#&0+2#5&00)-#&#)*%!"$,-!"!=
[)+(2*3"<#-5#3+#6+):60#9)5&6+)#(%)#-5#521'2")"(#2*#&;)*&<)#;&06)#2:#&#'60+)#/&;):2*1#3+
&"#)::)5(3;)#1)&+6*)#2:#3(+#)+,A%*A*4"=Z#F%)#-6(4#5450)#2:#&#'60+)#/&;):2*1#5&"#9)#12-60&()B3"#&#'*25)++#5&00)-#3+4$"/'),2%=-)+4(,'-1D#&"-#1&-)#(2#5&**4#3":2*1&(32"=#!"#+65%#&#+4+()18
-)()5(32"#2*#-)12-60&(32"#5260-#9)#&5%3);)-#+31'04#94#:))-3"<#(%)#*)5)3;)-#'60+)#/&;):2*1
(2#&#-5#*)+(2*)*#&"-#(%)"#6+3"<#&#+31'0)#,8#02/?'&++#:30()*#(2#+)'&*&()#(%)#&;)*&<)#2:#(%)#26(?
'6(#/&;):2*1#:*21#(%)#+6')*31'2+)-#'60+)+=
I%)"# &# 02&-# *)+3+(&"5)# ,# 3+# 52"")5()-# &5*2++# (%)# -32-)# 3"# &# 50&1'3"<# 53*563(8# &+
+%2/"#3"#L3<=#P=OO8#(%)#+3(6&(32"#5%&"<)+#+3<"3:35&"(04=#I%30)#(%)#26('6(#3+#&92;)#<*26"-8
&#56**)"(#16+(#:02/#3"#,=#Y3"5)#&(#(%3+#(31)#(%)#-32-)#3+#2::8#(%3+#56**)"(#29;326+04#521)+
:*21#(%)#5&'&53(2*8#(%6+#5&6+3"<#(%)#5&'&53(2*#(2#-3+5%&*<)#&"-#(%)#26('6(#;20(&<)#(2#:&00=
F%3+#3+#+%2/"#3"#L3<=#P=OO#:2*#&#+C6&*)?/&;)#3"'6(=#R6*3"<#(%)#3"()*;&0#4S#(2#4,8#(%)#26('6(
;20(&<)#:&00+#)A'2")"(3&004#/3(%#(31)#52"+(&"(#8,=#E(#4,#(%)#3"'6(#-)5*)&+)+#94#@)#;20(+8
&"-#(%)#26('6(#&(()1'(+#(2#:2002/=#F%3+#5&6+)+#(%)#-32-)#(2#52"-65(#%)&;304#&"-#(2#C635H04
5%&*<)#(%)#5&'&53(2*=#E(#(%)#)"-#2:#(%)#3"()*;&0#4,#(2#4.8#(%)#26('6(#;20(&<)#/260-#"2*1&004
9)#&#:)/#()"(%+#2:#&#;20(#")<&(3;)#B)=<=8#−S=Z#TD=#F%)"8#&+#(%)#3"'6(#*3+)+#94#@)#;20(+#B&(#4.D8
(%)#26('6(#:2002/+8#&"-#(%)#5450)#*)')&(+#3(+)0:=#!"#(%)#+()&-4#+(&()#(%)#5%&*<)#02+(#94#(%)#5&'&5?
3(2*# -6*3"<# (%)# 3"()*;&0# 4S# (2# 4,# 3+# *)52;)*)-# -6*3"<# (%)# 3"()*;&0# 4,# (2# 4.=# F%3+# 5%&*<)
)C63039*361#)"&90)+#6+#(2#5&0560&()#(%)#&;)*&<)#-32-)#56**)"(#&+#/)00#&+#(%)#-)(&30+#2:#(%)
26('6(#/&;):2*1=
Z
F%)#-6(4#5450)#2:#&#'60+)#/&;):2*1#3+#(%)#'*2'2*(32"#2:#)&5%#5450)#2556'3)-#94#(%)#'60+)=#!"#2(%)*
/2*-+8#3(#3+#(%)#'60+)#/3-(%#)A'*)++)-#&+#&#:*&5(32"#2:#(%)#'60+)#')*32-=
212 Chapter 4 Diodes
(b)
(a)
(c)
Figure 4.33 F%)#50&1')-#5&'&53(2*#/3(%#&#02&-#*)+3+(&"5)#,=
4.6.3 The Voltage Doubler
L3<6*)#P=OPB&D#+%2/+#&#53*563(#521'2+)-#2:#(/2#+)5(32"+#3"#5&+5&-)Q#&#50&1')-#5&'&53(2*
:2*1)-# 94# 8,# &"-# +,8# &"-# &# ')&H# *)5(3:3)*# :2*1)-# 94# +.# &"-# 8.=# I%)"# )A53()-# 94# &
D
D
(a)
(b)
Figure 4.34 T20(&<)#-2690)*Q#5(6#53*563(7#5&6#/&;):2*1#2:#(%)#;20(&<)#&5*2++#+,=
4.7 Special Diode Types
!"#$!%"&'%(')*+,"-$&.'!"'-/.'0,)*+"#1'!.0-"%#'+2%3"&.!'-/.'3%,-)1.'4)3.(%2*'!/%4#5
)!!$*"#1'"&.),'&"%&.!5'"#'6"17'8798:;<7'=%-.'-/)-'4/",.'-/.'+%!"-"3.'+.)>!')2.'0,)*+.&
-%' ?' @5' -/.' #.1)-"3.' +.)>' 2.)0/.!' −A!"7' B#' 2.!+%#!.' -%' -/"!' 4)3.(%2*5' -/.' +.)>C
&.-.0-%2'!.0-"%#'+2%3"&.!')02%!!'0)+)0"-%2'#A')'#.1)-"3.'&0'3%,-)1.'%('*)1#"-$&.'A!"7
D.0)$!.'-/.'%$-+$-'3%,-)1.'"!'&%$;,.'-/.'"#+$-'+.)>5'-/.'0"20$"-'"!'>#%4#')!')'3%,-)1.
&%$;,.27'E/.'-.0/#"F$.'0)#';.'.G-.#&.&'-%'+2%3"&.'%$-+$-'&0'3%,-)1.!'-/)-')2.'/"1/.2
*$,-"+,.!'%('!"7
EXERCISE
4.27 B('-/.'&"%&.'"#'-/.'0"20$"-'%('6"17'879A'"!'2.3.2!.&5'4/)-'4",,'-/.'&0'0%*+%#.#-'%('v%';.0%*.U
Ans.!−!"#
4.7 Special Diode Types
B#'-/"!'!.0-"%#5'4.'&"!0$!!';2".(,H'!%*.'"*+%2-)#-'!+.0"),'-H+.!'%('&"%&.!7
4.7.1 The Schottky-Barrier Diode (SBD)
E/.'I0/%-->HC;)22".2'&"%&.':IDJ<'"!'(%2*.&';H';2"#1"#1'*.-),'"#-%'0%#-)0-'4"-/')'*%&C
.2)-.,H'&%+.&'$C-H+.'!.*"0%#&$0-%2'*)-.2"),7'E/.'2.!$,-"#1'*.-),K!.*"0%#&$0-%2'L$#0C
-"%#';./)3.!',">.')'&"%&.5'0%#&$0-"#1'0$22.#-'"#'%#.'&"2.0-"%#':(2%*'-/.'*.-),')#%&.'-%
-/.'!.*"0%#&$0-%2'0)-/%&.<')#&')0-"#1')!')#'%+.#'0"20$"-'"#'-/.'%-/.25')#&'"!'>#%4#')!
-/.' I0/%-->HC;)22".2' &"%&.' %2' !"*+,H' -/.' I0/%-->H' &"%&.7' B#' ()0-5' -/.' 0$22.#-K3%,-)1.
0/)2)0-.2"!-"0'%('-/.'IDJ'"!'2.*)2>);,H'!"*",)2'-%'-/)-'%(')'"$CL$#0-"%#'&"%&.5'4"-/'-4%
"*+%2-)#-'.G0.+-"%#!M
1. B#'-/.'IDJ5'0$22.#-'"!'0%#&$0-.&';H'*)L%2"-H'0)22".2!':.,.0-2%#!<7'E/$!'-/.'IDJ
&%.!' #%-' .G/";"-' -/.' *"#%2"-HC0)22".2' 0/)21.C!-%2)1.' .((.0-!' (%$#&' "#' (%24)2&C
;")!.&'"$'L$#0-"%#!7'N!')'2.!$,-5'I0/%-->H'&"%&.!'0)#';.'!4"-0/.&'(2%*'%#'-%'%((5
)#&'3"0.'3.2!)5'*$0/'()!-.2'-/)#'"!'+%!!";,.'4"-/'"$CL$#0-"%#'&"%&.!7
2. E/.'(%24)2&'3%,-)1.'&2%+'%(')'0%#&$0-"#1'IDJ'"!',%4.2'-/)#'-/)-'%(')'"$CL$#0C
-"%#' &"%&.7' 6%2' .G)*+,.5' )#' IDJ' *)&.' %(' !","0%#' .G/";"-!' )' (%24)2&' 3%,-)1.
&2%+'%('?79 @'-%'?7O'@5'0%*+)2.&'-%'-/.'?7P'@'-%'?7Q'@'(%$#&'"#'!","0%#'"$CL$#0C
-"%#' &"%&.!7' IDJ!' 0)#' ),!%' ;.' *)&.' %(' 1),,"$*' )2!.#"&.' :R)N!<' )#&5' "#' ()0-5
+,)H')#'"*+%2-)#-'2%,.'"#'-/.'&.!"1#'%('R)N!'0"20$"-!7P'R),,"$*C)2!.#"&.'IDJ!
.G/";"-'(%24)2&'3%,-)1.'&2%+!'%(');%$-'?7S'@7
N+)2-' (2%*' R)N!' 0"20$"-!5' I0/%-->H' &"%&.!' ("#&' )++,"0)-"%#' "#' -/.' &.!"1#' %(' )' !+.0"),
(%2*'%(';"+%,)2C-2)#!"!-%2',%1"0'0"20$"-!5'>#%4#')!'I0/%-->HCEET5'4/.2.'EET'!-)#&!'(%2
-2)#!"!-%2C-2)#!"!-%2',%1"07
D.(%2.',.)3"#1'-/.'!$;L.0-'%('I0/%-->HC;)22".2'&"%&.!5'"-'"!'"*+%2-)#-'-%'#%-.'-/)-'#%.3.2H'*.-),K!.*"0%#&$0-%2'0%#-)0-'"!')'&"%&.7'B#'()0-5'*.-),'"!'0%**%#,H'&.+%!"-.&'%#
P'
E/.'&"!0')00%*+)#H"#1'-/"!'-.G-'0%#-)"#'*)-.2"),'%#'R)N!'0"20$"-!7
213
214 Chapter 4 Diodes
(%)#+)1352"-65(2*#+6*:&5)#3"#2*-)*#(2#1&H)#()*13"&0+#:2*#(%)#+)1352"-65(2*#-);35)+#&"-#(2
52"")5(# -3::)*)"(# -);35)+# 3"# &"# 3"()<*&()-?53*563(# 5%3'=# Y65%# 1)(&0]+)1352"-65(2*# 52"(&5(+
&*)#H"2/"#&+#-2='*%*-1,(*,$#(2#-3+(3"<63+%#(%)1#:*21#(%)#*)5(3:43"<#52"(&5(+#(%&(#*)+60(#3"
Y_R+=#K%135#52"(&5(+#&*)#6+6&004#1&-)#94#-)'2+3(3"<#1)(&0#2"#;)*4#%)&;304#-2')-#B&"-#(%6+
02/?*)+3+(3;3(4D#+)1352"-65(2*#*)<32"+=#B[)5&00#(%&(#Y_R+#6+)#12-)*&()04#-2')-#1&()*3&0=D
4.7.2 Varactors
!"#$%&'()*#O#/)#0)&*")-#(%&(#*);)*+)?93&+)-##$#J6"5(32"+#)A%393(#&#5%&*<)?+(2*&<)#)::)5(#(%&(
3+#12-)0)-#/3(%#(%)#-)'0)(32"?0&4)*#2*#J6"5(32"#5&'&53(&"5)#8O=#E+#@C=#BO=PPD#3"-35&()+8#8O#3+
&#:6"5(32"#2:#(%)#*);)*+)?93&+#;20(&<)#@,=#F%3+#-)')"-)"5)#(6*"+#26(#(2#9)#6+):60#3"#&#"619)*
2:#&''035&(32"+8#+65%#&+#(%)#&6(21&(35#(6"3"<#2:#*&-32#*)5)3;)*+=#Y')53&0#-32-)+#&*)#(%)*):2*)
:&9*35&()-#(2#9)#6+)-#&+#;20(&<)?;&*3&90)#5&'&53(2*+#H"2/"#&+##(!(*,-!$=#F%)+)#-);35)+#&*)
2'(313M)-#(2#1&H)#(%)#5&'&53(&"5)#&#+(*2"<#:6"5(32"#2:#;20(&<)#94#&**&"<3"<#(%&(#(%)#<*&-3"<
52)::353)"(#1#3+#O#2*#P=
4.7.3 Photodiodes
!:#&#*);)*+)?93&+)-##$#J6"5(32"#3+#300613"&()-W(%&(#3+8#)A'2+)-#(2#3"53-)"(#03<%(W(%)#'%2?
(2"+#31'&5(3"<#(%)#J6"5(32"#5&6+)#52;&0)"(#92"-+#(2#9*)&H8#&"-#(%6+#)0)5(*2"]%20)#'&3*+#&*)
<)")*&()-#3"#(%)#-)'0)(32"#0&4)*=#F%)#)0)5(*35#:3)0-#3"#(%)#-)'0)(32"#*)<32"#(%)"#+/))'+#(%)
039)*&()-#)0)5(*2"+#(2#(%)#$#+3-)#&"-#(%)#%20)+#(2#(%)###+3-)8#<3;3"<#*3+)#(2#&#*);)*+)#56**)"(
&5*2++#(%)#J6"5(32"=#F%3+#56**)"(8#H"2/"#&+#'%2(256**)"(8#3+#'*2'2*(32"&0#(2#(%)#3"()"+3(4#2:
(%)#3"53-)"(#03<%(=#Y65%#&#-32-)8#5&00)-#&#'%2(2-32-)8#5&"#9)#6+)-#(2#52";)*(#03<%(#+3<"&0+#3"(2
)0)5(*35&0#+3<"&0+=
l%2(2-32-)+# &*)# 6+6&004# :&9*35&()-# 6+3"<# &# 521'26"-# +)1352"-65(2*N +65%# &+# <&00361
&*+)"3-)=#F%)#'%2(2-32-)#3+#&"#31'2*(&"(#521'2")"(#2:#&#<*2/3"<#:&1304#2:#53*563(+#H"2/"
&+#-3,-"4"*,!-1'*$#2*#32-,-1'*$=#E+#(%)#"&1)#31'03)+8#+65%#53*563(+#6(303M)#&"#2'(3161#521?
93"&(32"#2:#)0)5(*2"35+#&"-#2'(35+#:2*#+3<"&0#'*25)++3"<8#+(2*&<)8#&"-#(*&"+13++32"=#h+6&0048
)0)5(*2"35+# 3+# (%)# '*):)**)-# 1)&"+# :2*# +3<"&0# '*25)++3"<8# /%)*)&+# 2'(35+# 3+# 12+(# +63()-# :2*
(*&"+13++32"#&"-#+(2*&<)=#@A&1'0)+#3"506-)#:39)*?2'(35#(*&"+13++32"#2:#()0)'%2")#&"-#()0);3?
+32"#+3<"&0+#&"-#(%)#6+)#2:#2'(35&0#+(2*&<)#3"#$R?[Km#521'6()*#-3+H+=#K'(35&0#(*&"+13++32"
'*2;3-)+# ;)*4# /3-)# 9&"-/3-(%+# &"-# 02/# +3<"&0# &(()"6&(32"=# K'(35&0# +(2*&<)# &002/+# ;&+(
&126"(+#2:#-&(&#(2#9)#+(2*)-#*)03&904#3"#&#+1&00#+'&5)=
L3"&0048#/)#+%260-#"2()#(%&(#/3(%26(#*);)*+)#93&+8#(%)#300613"&()-#'%2(2-32-)#:6"5(32"+
&+#&#$-4(!%*"44=#h+6&004#:&9*35&()-#:*21#02/?52+(#+30352"8#&#+20&*#5)00#52";)*(+#03<%(#(2#)0)5(*3?
5&0#)")*<4=
4.7.4 Light-Emitting Diodes (LEDs)
F%)#03<%(?)13((3"<#-32-)#BV@RD#')*:2*1+#(%)#3";)*+)#2:#(%)#:6"5(32"#2:#(%)#'%2(2-32-)7#3(
52";)*(+#&#:2*/&*-#56**)"(#3"(2#03<%(=#F%)#*)&-)*#/300#*)5&00#:*21#$%&'()*#O#(%&(#3"#&#:2*/&*-?
93&+)-##$#J6"5(32"8#13"2*3(4#5&**3)*+#&*)#3"J)5()-#&5*2++#(%)#J6"5(32"#&"-#-3::6+)#3"(2#(%)##
N
I%)*)&+#&"#)0)1)"(&0#+)1352"-65(2*8#+65%#&+#+30352"8#6+)+#&"#)0)1)"(#:*21#52061"#!T#2:#(%)#')*32-35
(&90)8#&#521'26"-#+)1352"-65(2*#6+)+#&#52193"&(32"#2:#)0)1)"(+#:*21#52061"+#!!!#&"-#T#2*#!!#&"-#T!=
L2*#)A&1'0)8#k&E+#3+#:2*1)-#2:#<&00361#B52061"#!!!D#&"-#&*+)"35#B52061"#TD#&"-#3+#(%6+#H"2/"#&+#&
!!!?T#521'26"-=
4.7 Special Diode Types 215
&"-# $# *)<32"+=# F%)# -3::6+3"<# 13"2*3(4# 5&**3)*+# (%)"# *)52193")# /3(%# (%)# 1&J2*3(4# 5&**3)*+=
Y65%#*)52193"&(32"#5&"#9)#1&-)#(2#<3;)#*3+)#(2#03<%(#)13++32"=#F%3+#5&"#9)#-2")#94#:&9*35&(?
3"<#(%)##$#J6"5(32"#6+3"<#&#+)1352"-65(2*#2:#(%)#(4')#H"2/"#&+#-3*)5(?9&"-<&'#1&()*3&0+=
k&00361# &*+)"3-)# 9)02"<+# (2# (%3+# <*26'# &"-# 5&"# (%6+# 9)# 6+)-# (2# :&9*35&()# 03<%(?)13((3"<
-32-)+=
F%)#03<%(#)13(()-#94#&"#V@R#3+#'*2'2*(32"&0#(2#(%)#"619)*#2:#*)52193"&(32"+#(%&(#(&H)
'0&5)8#/%35%#3"#(6*"#3+#'*2'2*(32"&0#(2#(%)#:2*/&*-#56**)"(#3"#(%)#-32-)=
V@R+#&*)#;)*4#'2'60&*#-);35)+=#F%)4#:3"-#&''035&(32"#3"#(%)#-)+3<"#2:#"61)*26+#(4')+#2:
-3+'0&4+8#3"506-3"<#(%)#-3+'0&4+#2:#0&92*&(2*4#3"+(*61)"(+#+65%#&+#-3<3(&0#;20(1)()*+=#F%)4#5&"
9)#1&-)#(2#'*2-65)#03<%(#3"#&#;&*3)(4#2:#5202*+=#L6*(%)*12*)8#V@R+#5&"#9)#-)+3<")-#+2#&+#(2
'*2-65)#52%)*)"(#03<%(#/3(%#&#;)*4#"&**2/#9&"-/3-(%=#F%)#*)+60(3"<#-);35)#3+#&#4($"!%)'-)"=
V&+)*#-32-)+#:3"-#&''035&(32"#3"#2'(35&0#52116"35&(32"#+4+()1+#&"-#3"#$R#'0&4)*+8#&12"<
2(%)*#(%3"<+=
$2193"3"<#&"#V@R#/3(%#&#'%2(2-32-)#3"#(%)#+&1)#'&5H&<)#*)+60(+#3"#&#-);35)#H"2/"#&+
&"#-3,-'$-4(,-!=#F%)#V@R#52";)*(+#&"#)0)5(*35&0#+3<"&0#&''03)-#(2#(%)#2'(23+20&(2*#3"(2#03<%(8
/%35%#(%)#'%2(2-32-)#-)()5(+#&"-#52";)*(+#9&5H#(2#&"#)0)5(*35&0#+3<"&0#&(#(%)#26('6(#2:#(%)
2'(23+20&(2*=#h+)#2:#(%)#2'(23+20&(2*#'*2;3-)+#521'0)()#)0)5(*35&0#3+20&(32"#9)(/))"#(%)#)0)5?
(*35&0#53*563(#(%&(#3+#52"")5()-#(2#(%)#3+20&(2*d+#3"'6(#&"-#(%)#53*563(#(%&(#3+#52"")5()-#(2#3(+#26(?
'6(=# Y65%# 3+20&(32"# 5&"# 9)# 6+):60# 3"# *)-653"<# (%)# )::)5(# 2:# )0)5(*35&0# 3"()*:)*)"5)# 2"# +3<"&0
(*&"+13++32"#/3(%3"#&#+4+()18#&"-#(%6+#2'(23+20&(2*+#&*)#:*)C6)"(04#)1'024)-#3"#(%)#-)+3<"#2:
-3<3(&0#+4+()1+=#F%)4#5&"#&0+2#9)#6+)-#3"#(%)#-)+3<"#2:#1)-35&0#3"+(*61)"(+#(2#*)-65)#(%)#*3+H
2:#)0)5(*35&0#+%25H#(2#'&(3)"(+=
X2()#(%&(#(%)#2'(35&0#526'03"<#9)(/))"#&"#V@R#&"-#&#'%2(2-32-)#"))-#"2(#9)#&5521?
'03+%)-#3"+3-)#&#+1&00#'&5H&<)=#!"-))-8#3(#5&"#9)#31'0)1)"()-#2;)*#&#02"<#-3+(&"5)#6+3"<#&"
2'(35&0#:39)*8#&+#3+#-2")#3"#:39)*?2'(35#52116"35&(32"#03"H+=
Summary
!"#(%)#:2*/&*-#-3*)5(32"8#(%)#3-)&0#-32-)#52"-65(+#&"4
56**)"(#:2*5)-#94#(%)#)A()*"&0#53*563(#/%30)#-3+'0&43"<#&
M)*2#;20(&<)#-*2'=#F%)#3-)&0#-32-)#-2)+#"2(#52"-65(#3"
(%)#*);)*+)#-3*)5(32"7#&"4#&''03)-#;20(&<)#&'')&*+#&+#*)?
;)*+)#93&+#&5*2++#(%)#-32-)=
F%)#6"3-3*)5(32"&0?56**)"(?:02/#'*2')*(4# 1&H)+# (%)#-3?
2-)#6+):60#3"#(%)#-)+3<"#2:#*)5(3:3)*#53*563(+=
F%)# :2*/&*-# 52"-65(32"# 2:# '*&5(35&0# +30352"?J6"5(32"
-32-)+# 3+# &556*&()04# 5%&*&5()*3M)-# 94# (%)# *)0&(32"+%3'
v⁄@
! = -5 3 I =
E# +30352"# -32-)# 52"-65(+# &# ")<03<390)# 56**)"(# 6"(30# (%)
:2*/&*-# ;20(&<)# 3+# &(# 0)&+(# S=Z# T=# F%)"# (%)# 56**)"(# 3"?
5*)&+)+# *&'3-048# /3(%# (%)# ;20(&<)# -*2'# 3"5*)&+3"<# 94
`S 1T#:2*#);)*4#-)5&-)#2:#56**)"(#5%&"<)=
!"#(%)#*);)*+)#-3*)5(32"8#&#+30352"#-32-)#52"-65(+#&#56**)"(
2"#(%)#2*-)*#2:#,S−U#E=#F%3+#56**)"(#3+#165%#<*)&()*#(%&"#-5
&"-#3"5*)&+)+#/3(%#(%)#1&<"3(6-)#2:#*);)*+)#;20(&<)=
_)42"-#&#5)*(&3"#;&06)#2:#*);)*+)#;20(&<)#B(%&(#-)')"-+
2"#(%)#-32-)D8#9*)&H-2/"#2556*+8#&"-#56**)"(#3"5*)&+)+
*&'3-04#/3(%#&#+1&00#52**)+'2"-3"<#3"5*)&+)#3"#;20(&<)=
R32-)+#-)+3<")-#(2#2')*&()#3"#(%)#9*)&H-2/"#*)<32"#&*)
5&00)-#M)")*#-32-)+=#F%)4#&*)#)1'024)-#3"#(%)#-)+3<"#2:
;20(&<)# *)<60&(2*+# /%2+)# :6"5(32"# 3+# (2# '*2;3-)# &# 52"?
+(&"(#-5#;20(&<)#(%&(#;&*3)+#03((0)#/3(%#;&*3&(32"+#3"#'2/)*
+6''04#;20(&<)#&"-a2*#02&-#56**)"(=
!"#1&"4#&''035&(32"+8#&#52"-65(3"<#-32-)#3+#12-)0)-#&+
%&;3"<# &# 52"+(&"(# ;20(&<)# -*2'8# 6+6&004# &''*2A31&()04
S=N T=
E#-32-)#93&+)-#(2#2')*&()#&(#&#-5#56**)"(#-+#%&+#&#+1&00?
+3<"&0#*)+3+(&"5)# ' * = @ I ⁄ - + =
[)5(3:3)*+# 52";)*(# &5# ;20(&<)+# 3"(2# 6"3'20&*# ;20(&<)+=
>&0:?/&;)#*)5(3:3)*+#-2#(%3+#94#'&++3"<#(%)#;20(&<)#3"#%&0:
2:#)&5%#5450)#&"-#9025H3"<#(%)#2''2+3()?'20&*3(4#;20(&<)
3"# (%)# 2(%)*# %&0:# 2:# (%)# 5450)=# L600?/&;)# *)5(3:3)*+
216 Chapter 4 Diodes
&5521'03+%#(%)#(&+H#94#'&++3"<#(%)#;20(&<)#3"#%&0:#2:#)&5%
5450)#&"-#3";)*(3"<#(%)#;20(&<)#3"#(%)#2(%)*#%&0:?5450)=
'*);)"(#2")#2*#92(%#)A(*)13(3)+#2:#(%)#26('6(#/&;):2*1
:*21# <23"<# 9)42"-# '*)-)()*13")-# ;&06)+8# (%)# 0313(3"<
0);)0B+D=
F%)#9*3-<)?*)5(3:3)*#53*563(#3+#(%)#'*):)**)-#:600?/&;)#*)5?
(3:3)*#52":3<6*&(32"=
F%)#;&*3&(32"#2:#(%)#26('6(#/&;):2*1#2:#(%)#*)5(3:3)*#3+
*)-65)-#52"+3-)*&904#94#52"")5(3"<#&#5&'&53(2*#8#&5*2++
(%)#26('6(#02&-#*)+3+(&"5)#,=#F%)#*)+60(3"<#53*563(#3+#(%)
')&H#*)5(3:3)*=#F%)#26('6(#/&;):2*1#(%)"#52"+3+(+#2:#&#-5
;20(&<)#&012+(#)C6&0#(2#(%)#')&H#2:#(%)#3"'6(#+3")#/&;)8
@ # 8#2"#/%35%#3+#+6')*31'2+)-#&#*3''0)#521'2")"(#2:#:*)?
C6)"54# .%# B3"# (%)# :600# /&;)# 5&+)D# &"-# 2:# ')&H?(2?')&H
&1'03(6-)# @ ' " @ # ⁄ .%8,=# F2# *)-65)# (%3+# *3''0)# ;20(?
&<)#:6*(%)*#&#;20(&<)#*)<60&(2*#3+#)1'024)-=
E''043"<#&#(31)?;&*43"<#/&;):2*1#(2#&#53*563(#52"+3+(?
3"<#2:#&#5&'&53(2*#3"#+)*3)+#/3(%#&#-32-)#&"-#(&H3"<#(%)
26('6(# &5*2++# (%)# -32-)# '*2;3-)+# &# 50&1'3"<# :6"5(32"=
Y')53:35&0048#-)')"-3"<#2"#(%)#'20&*3(4#2:#(%)#-32-)#)3?
(%)*#(%)#'2+3(3;)#2*#")<&(3;)#')&H+#2:#(%)#+3<"&0#/300#9)
50&1')-#(2#(%)#;20(&<)#&(#(%)#2(%)*#()*13"&0#2:#(%)#-32-)
B6+6&004#<*26"-D=#!"#(%3+#/&4#(%)#26('6(#/&;):2*1#%&+#&
"2"# M)*2# &;)*&<)# 2*# -5# 521'2")"(# &"-# (%)# 53*563(# 3+
H"2/"#&+#&#-5#*)+(2*)*=
_4#5&+5&-3"<#&#50&1'3"<#53*563(#/3(%#&#')&H?*)5(3:3)*#53*?
563(8#&#;20(&<)#-2690)*#3+#*)&03M)-=
$2193"&(32"#2:#-32-)+8#*)+3+(2*+8#&"-#'2++3904#*):)*)"5)
;20(&<)+# 5&"# 9)# 6+)-# (2# -)+3<"# ;20(&<)# 0313()*+# (%&(
PROBLEMS
Computer Simulation Problems
52"")5()-# (2# (%)# ()*13"&0+# 2:# &"# 3-)&0# -32-)=# R)+5*39)
(/2 '2++390)#+3(6&(32"+#(%&(#*)+60(=#I%&(#&*)#(%)#-32-)#56**)"(
&"-#()*13"&0#;20(&<)#/%)"#B&D#(%)#52"")5(32"#3+ 9)(/))"#(%)
-32-)#5&(%2-)#&"-#(%)#'2+3(3;)#()*13"&0#2:#(%)#9&(()*4#&"-#B9D
(%)#&"2-)#&"-#(%)#'2+3(3;)#()*13"&0#&*)#52"")5()-i
l*290)1+#3-)"(3:3)-#94#(%3+#352"#&*)#3"()"-)-#(2#-)1?
2"+(*&()#(%)#;&06)#2:#6+3"<#Yl!$@#+3160&(32"#(2#;)*3:4#%&"&"&04+3+# &"-# -)+3<"8# &"-# (2# 3";)+(3<&()# 31'2*(&"(# 3++6)+
+65%# &+# &002/&90)# +3<"&0# +/3"<# &"-# "2"03")&*# -3+(2*(32"=
!"+(*65(32"+#(2#&++3+(#3"#+)((3"<#6'#lY'35)#&"-#m60(3+31#+31?
60&(32"+#:2*#&00#(%)#3"-35&()-#'*290)1+#5&"#9)#:26"-#3"#(%)
52**)+'2"-3"<# :30)+# 2"# (%)# -3+5=# X2()# (%&(# 3:# &# '&*(3560&*
'&*&1)()*#;&06)#3+#"2(#+')53:3)-#3"#(%)#'*290)1#+(&()1)"(8
426#&*)#(2#1&H)#&#*)&+2"&90)#&++61'(32"=
q#-3::3560(#'*290)17#qq#12*)#-3::3560(7#qqq#;)*4#5%&00)"<3"<
&"-a2*#(31)?52"+613"<7#RQ#-)+3<"#'*290)1=
4.2#L2*#(%)#53*563(+#+%2/"#3"#L3<=#lP=.#6+3"<#3-)&0#-32-)+8
:3"-#(%)#;&06)+#2:#(%)#;20(&<)+#&"-#56**)"(+#3"-35&()-=
4.3#L2*#(%)#53*563(+#+%2/"#3"#L3<=#lP=O#6+3"<#3-)&0#-32-)+8
:3"-#(%)#;&06)+#2:#(%)#0&9)0)-#;20(&<)+#&"-#56**)"(+
Section 4.1: The Ideal Diode
4.4#!"#)&5%#2:#(%)#3-)&0?-32-)#53*563(+#+%2/"#3"#L3<=#lP=P8
v-#3+#&#,?H>M8#,S?T#')&H#+3")#/&;)=#YH)(5%#(%)#/&;):2*1
*)+60(3"<# &(# v.=# I%&(# &*)# 3(+# '2+3(3;)# &"-# ")<&(3;)# ')&H
;&06)+i
4.1# E"# EE# :0&+%03<%(# 5)008# /%2+)# F%r;)"3"# )C63;&0)"(# 3+
& ;20(&<)# +26*5)# 2:# ,=Z# T# &"-# &# *)+3+(&"5)# 2:# , Ω8# 3+
4.5#F%)#53*563(#+%2/"#3"#L3<=#lP=Z#3+#&#12-)0#:2*#&#9&(()*4
5%&*<)*=#>)*)# v-#3+#&#,S?T#')&H#+3")#/&;)8#+,#&"-#+.#&*)
5
5
5
5
5
5
5
5
(a)
Figure P4.2
(b)
(c)
(d)
Problems 217
CHAPTER 4 P R O B L E M S
5
D
2
2
D
2
2
5
(a)
(b)
Figure P4.3
D1
vI
vO
vI
D1
D2
1 kV
vO
vI
D1
D2
vO
1 kV
1 kV
(a)
(c)
(b)
D3
vI
D1
vO
vI
1 kV
D2
D2
vO
vO
D1
Figure P4.4
vI
1 kV
1 kV
vO
1 kV
vO
D1
D1
D2
(h)
1 kV
(f )
(e)
1 kV
(g)
vO
D2
vI
vI
D1
1 kV
D1
(d)
vI
(i)
CHAPTER 4 P R O B L E M S
218 Chapter 4 Diodes
115 V
D3
A
I
1 mA
D1
vO
1 kV
vI
vO
1 kV
Y
B
D1
D4
X
A
I
B
D2
1 kV
D1
D2
vI
( j)
(a)
(b)
Figure P4.6
D 4.8&S#@#$3&H1'6%#-&I8T&>'1&3;#&%'B!/&B$3#&'>&G!B8&I8MN6O8
(k)
Figure P4.4 N()*+,-O
!"#$%&"!'"#()&!&!(&$&*+,-.&/011#23&('01/#)&$2"&"&!(&$&4,5&6$3,
3#178&9:#3/;&$2"&%$6#%&3;#&<$=#>'1-&'>&3;#&6$33#17&/011#23&#"8
?;$3& !(& !3(& @#$:& =$%0#A& ?;$3& !(& !3(& $=#1$B#& =$%0#A& C>& 3;#
@#$:&=$%0#&'>& v!&!(&1#"0/#"&67&D+E)&<;$3&"'&3;#&@#$:&$2"
$=#1$B#&=$%0#(&'>&#"&6#/'-#A
4.9&.((0-!2B&3;$3&3;#&"!'"#(&!2&3;#&/!1/0!3(&'>&G!B8&HI8U
$1#& !"#$%)& >!2"& 3;#& =$%0#(& '>& 3;#& %$6#%#"& ='%3$B#(& $2"
/011#23(8
13V
13V
I
iB
D
vI
D
D
D
vO
D1
D2
B
Figure P4.5
4.6& F;#& /!1/0!3(& (;'<2& !2& G!B8& HI8*& /$2& >02/3!'2& $(& %'B!/
B$3#(&>'1&!2@03&='%3$B#(&3;$3&$1#&#!3;#1&;!B;&'1&%'<8&J(!2B&KDL
3' "#2'3#& 3;#& ;!B;& =$%0#& $2"& K+L& 3'& "#2'3#& 3;#& %'<& =$%0#)
@1#@$1#&$&3$6%#&<!3;&>'01&/'%0-2(&!2/%0"!2B&$%%&@'((!6%#&!2@03
/'-6!2$3!'2(&$2"&3;#&1#(0%3!2B&=$%0#(&'>&$&$2"&%8&?;$3&%'B!/
>02/3!'2&!(&$&'>&&&$2"&"A&?;$3&%'B!/&>02/3!'2&!(&%&'>&&&$2"&"A
G'1&<;$3&=$%0#(&'>&&&$2"&"&"'&$&$2"&%&;$=#&3;#&($-#&=$%0#A
G'1&<;$3&=$%0#(&'>&&&$2"&"&"'&$&$2"&%&;$=#&'@@'(!3#&=$%0#(A
D 4.7&G'1&3;#&%'B!/&B$3#&'>&G!B8&I8MN$O)&$((0-#&!"#$%&"!'"#(
$2"& !2@03& ='%3$B#& %#=#%(& '>& +& 5& $2"& +M& 58& G!2"& $& (0!3$6%#
=$%0#& >'1& '& ('& 3;$3& 3;#& /011#23& 1#P0!1#"& >1'-& #$/;& '>& 3;#
!2@03&(!B2$%&('01/#(&"'#(&2'3&#Q/##"&+8R&-.8
23V
23V
(a)
(b)
Figure P4.9
4.10& .((0-!2B& 3;$3& 3;#& "!'"#(& !2& 3;#& /!1/0!3(& '>& G!B8
HI8D+& $1#& !"#$%)& 03!%!V#& F;W=#2!2X(& 3;#'1#-& 3'& (!-@%!>7
3;#& /!1/0!3(& $2"& 3;0(& >!2"& 3;#& =$%0#(& '>& 3;#& %$6#%#"& /01,
1#23(&$2"&='%3$B#(8
D 4.11& G'1& 3;#& 1#/3!>!#1& /!1/0!3& '>& G!B8& I84N$O)& %#3& 3;#& !2@03
(!2#&<$=#&;$=#&DR+,5&1-(&=$%0#&$2"&$((0-#&3;#&"!'"#&3'&6#
!"#$%8& 9#%#/3& $& (0!3$6%#& =$%0#& >'1& '& ('& 3;$3& 3;#& @#$:& "!'"#
/011#23&"'#(&2'3&#Q/##"&M+&-.8&?;$3&!(&3;#&B1#$3#(3&1#=#1(#
='%3$B#&3;$3&<!%%&$@@#$1&$/1'((&3;#&"!'"#A
Problems
"5 V
10 k*
(%)*)#1&4#9)#+);)*&0#2:#)&5%#(4')#2:#52"")5(32"8#&00#2"#2")
/3*)sD
10 k*
I
D
D
! V "
10 k*
(a)
10 k*
(b)
Figure P4.10
4.12# $2"+3-)*# (%)# *)5(3:3)*# 53*563(# 2:# L3<=# P=O# 3"# (%)# );)"(
(%&(# (%)# 3"'6(# +26*5)# v-# %&+# &# +26*5)# *)+3+(&"5)# ,?=# L2*# (%)
5&+)#,?#=#,#&"-#&++613"<#(%)#-32-)#(2#9)#3-)&08#+H)(5%#&"50)&*04#0&9)0#(%)#(*&"+:)*#5%&*&5()*3+(35#v.#;)*+6+#v-=
4.13#E#+411)(*35&0#+C6&*)#/&;)#2:#P?T#')&H?(2?')&H#&1'03?
(6-)#&"-#M)*2#&;)*&<)#3+#&''03)-#(2#&#53*563(#*)+)1903"<#(%&(#3"
L3<= P=OB&D#&"-#)1'0243"<#&#,SS?Ω#*)+3+(2*=#I%&(#3+#(%)#')&H
26('6(#;20(&<)#(%&(#*)+60(+i#I%&(#3+#(%)#&;)*&<)#26('6(#;20(&<)
(%&(#*)+60(+i#I%&(#3+#(%)#')&H#-32-)#56**)"(i#I%&(#3+#(%)#&;)*?
&<)# -32-)# 56**)"(i# I%&(# 3+# (%)# 1&A3161# *);)*+)# ;20(&<)
&5*2++#(%)#-32-)i
4.14 [)')&(# l*290)1# P=,O# :2*# (%)# +3(6&(32"# 3"# /%35%# (%)
&;)*&<)#;20(&<)#2:#(%)#+C6&*)#/&;)#3+#,#T8#/%30)#3(+#')&H?(2?
')&H#;&06)#*)1&3"+#&(#P#T=
Figure P4.16
Section 4.2: Terminal Characteristics
of Junction Diodes
4.17#$&0560&()#(%)#;&06)#2:#(%)#(%)*1&0#;20(&<)8#@I 8#&(#]PSt$8
St$8# uPSt$8#&"-# u,ZSt$=#E(#/%&(# ()1')*&(6*)# 3+#@I# )A&5(04
.Z#1Ti#
4.18#E(#/%&(#:2*/&*-#;20(&<)#-2)+#&#-32-)#52"-65(#&#56*?
*)"(#)C6&0#(2#,SSS-5i#!"#()*1+#2:#-5 8# /%&(#56**)"(# :02/+#3"
(%)#+&1)#-32-)#/%)"#3(+#:2*/&*-#;20(&<)#3+#S=N#Ti
4.19#E#-32-)#:2*#/%35%#(%)#:2*/&*-#;20(&<)#-*2'#3+#S=N#T#&(
,=S#1E#3+#2')*&()-#&(#S=Z#T=#I%&(#3+#(%)#;&06)#2:#(%)#56**)"(i
4.20#E#'&*(3560&*#-32-)#3+#:26"-#(2#52"-65(#S=Z#1E#/3(%#&
J6"5(32"#;20(&<)#2:#S=N#T=#I%&(#3+#3(+#+&(6*&(32"#56**)"(#-5i
I%&(#56**)"(#/300#:02/#3"#(%3+#-32-)#3:#(%)#J6"5(32"#;20(&<)#3+
*&3+)-#(2#S=N,#Ti#F2#S=^#Ti#!:#(%)#J6"5(32"#;20(&<)#3+#02/?
)*)-#(2#S=`U#Ti#F2#S=`#Ti#I%&(#5%&"<)#3"#J6"5(32"#;20(&<)
/300#3"5*)&+)#(%)#-32-)#56**)"(#94#&#:&5(2*#2:#,Si
D *4.15#R)+3<"#&#9&(()*4?5%&*<3"<#53*563(8#*)+)1903"<#(%&(
3"#L3<=#P=P#&"-#6+3"<#&"#3-)&0#-32-)8#3"#/%35%#56**)"(#:02/+
(2#(%)#,.?T#9&(()*4#.Sj#2:#(%)#(31)#/3(%#&"#&;)*&<)#;&06)#2:
,SS#1E=#I%&(#')&H?(2?')&H#+3")?/&;)#;20(&<)#3+#*)C63*)-i
I%&(# *)+3+(&"5)# 3+# *)C63*)-i# I%&(# ')&H# -32-)# 56**)"(
:02/+i#I%&(#')&H#*);)*+)#;20(&<)#-2)+#(%)#-32-)#)"-6*)i#!:
*)+3+(2*+#5&"#9)#+')53:3)-#(2#2"04#2")#+3<"3:35&"(#-3<3(8#&"(%)# ')&H?(2?')&H# ;20(&<)# 2"04# (2# (%)# ")&*)+(# ;20(8# /%&(
-)+3<"#/260-#426#5%22+)#(2#<6&*&"())#(%)#*)C63*)-#5%&*<3"<
56**)"(i#I%&(#:*&5(32"#2:#(%)#5450)#-2)+#-32-)#56**)"(#:02/i
I%&(#3+#(%)#&;)*&<)#-32-)#56**)"(i#I%&(#3+#(%)#')&H#-32-)
56**)"(i#I%&(#')&H#*);)*+)#;20(&<)#-2)+#(%)#-32-)#)"-6*)i
4.21# F%)# :2002/3"<# 1)&+6*)1)"(+# &*)# (&H)"# 2"# '&*(3560&*
J6"5(32"#-32-)+#:2*#/%35%#@#3+#(%)#()*13"&0#;20(&<)#&"-#-#3+
(%)#-32-)#56**)"(=#L2*#)&5%#-32-)8#)+(31&()#;&06)+#2:#-5#&"(%)#()*13"&0#;20(&<)#&(#,Sj#2:#(%)#1)&+6*)-#56**)"(=#
4.16#F%)#53*563(#2:#L3<=#lP=,`#5&"#9)#6+)-#3"#&#+3<"&003"<#+4+?
()1# 6+3"<# 2")# /3*)# '06+# &# 52112"# <*26"-# *)(6*"=# E(# &"4
121)"(8#(%)#3"'6(#%&+#2")#2:#(%*))#;&06)+Q#+O#T8#S#T8#−O#T=
I%&(# 3+# (%)#+(&(6+# 2:# (%)# 0&1'+# :2*# )&5%#3"'6(# ;&06)i# BX2()
(%&(#(%)#0&1'+#5&"#9)#025&()-#&'&*(#:*21#)&5%#2(%)*#&"-#(%&(
4.22#V3+()-#9)02/#&*)#(%)#*)+60(+#2:#1)&+6*)1)"(+#(&H)"#2"
+);)*&0# -3::)*)"(# J6"5(32"# -32-)+=# L2*# )&5%# -32-)8# (%)# -&(&
'*2;3-)-#&*)#(%)#-32-)#56**)"(#-#&"-#(%)#52**)+'2"-3"<#-32-)
;20(&<)#@=#!"#)&5%#5&+)8#)+(31&()#-5 8#&"-#(%)#-32-)#;20(&<)#&(
,S-#&"-#-a,S=
B&D @#=#S=NSS#T#&(#-#=#,=SS#E
B9D @#=#S=`ZS#T#&(#-#=#,=SS#1E
B5D @#=#S=`ZS#T#&(#-#=#,S#µE
B-D @#=#S=NSS#T#&(#-#=#,S#1E
CHAPTER 4 P R O B L E M S
"6 V
"6V
219
CHAPTER 4 P R O B L E M S
220 Chapter 4 Diodes
!"# $%&%'()*'+%%'(,
!-# $&%'()*'+%%'(,
!.# $%')*'/%%'(,
!0# $'()*'+%%'(,
!1# $%'µ)*'+%%'(,
4.23'231'.45.647'48'94:&';<&=>'674?4@1A'73511'401874."?'04B01A
3"C48:'!"'='$%−$D')&'9480'731'C"?61'BE'731'.655187'!'51F64510
7B'B-7"48'"8'B67G67'CB?7":1'#$'='=&<',&'HE'"'.655187'BE'$ ()
4A'05"I8'"I"J'E5B('731'B67G67'715(48"?'-J'"'?B"0*'I3"7'4A
731'.3"8:1'48'B67G67'CB?7":1K
4.26' 9B5' 731' .45.647' A3BI8' 48' 94:&' ;<&=D*' -B73' 04B01A' "51
401874."?&'9480'731'C"?61'BE'&'EB5'I34.3'#'='/%'(,&
I
10 mA
D2
D1
"
R
V
!
Figure P4.26
4.27' )' 04B01' E10' I473' "' .B8A7"87' .655187' !' P' $' ()' 3"A' "
CB?7":1' #' P' DQ%' (,' "7' =%°'S&' 9480' 731' 04B01' CB?7":1' "7
! =% °'S'"80'"7'W+%°'S&
Figure P4.23
4.24')'L68.74B8'04B01'4A'BG15"710'48'"'.45.647'48'I34.3'47'4A
A6GG?410'I473'"'.B8A7"87'.655187'!&'M3"7'4A'731'1EE1.7'B8'731
EB5I"50' CB?7":1' BE' 731' 04B01' 4E' "8' 401874."?' 04B01' 4A' .B8N
81.710'48'G"5"??1?K
4.25' H8' 731' .45.647' A3BI8' 48' 94:&' ;<&=O*' %$'3"A'$%'74(1A
731'L68.74B8'"51"'BE'%=&'M3"7'C"?61'BE'#'51A6?7AK'2B'B-7"48'"
C"?61'EB5'#'BE'O%'(,*'I3"7'.655187'!='4A'811010K'''''
I1
10 mA
D1
D2
I2
2 mA
Figure P4.25
4.28' H8' 731' .45.647' A3BI8' 48' 94:&' ;<&=/*' %$' 4A' "' ?"5:1N"51"*
34:3N.655187'04B01'I3BA1'51C15A1'?1"R":1'4A'34:3'"80'4801G18N
0187'BE'"GG?410'CB?7":1*'I34?1'%='4A'"'(6.3'A("??15*'?BIN.655187
04B01&' )7' "8' "(-4187' 71(G15"7651' BE' =%°S*' 51A4A7B5' &$' 4A
"0L6A710'7B'("R1'#&$'='#='='O=%'(,&'T6-A1F6187'(1"A651(187
4804."71A'73"7'&$'4A'O=%'RΩ&'M3"7'0B'JB6'1UG1.7'731'CB?7":1A
#&$'"80'#='7B'-1.B(1'"7'%°S'"80'"7'<%°SK
"10 V
R1
D1
"
V1
!
D2
"
V2
!
Figure P4.28
"
V
!
4.29'M318'"'$ON)'.655187'4A'"GG?410'7B'"'G"574.6?"5'04B01*
47 4A' EB680' 73"7' 731' L68.74B8' CB?7":1' 4((104"71?J' -1.B(1A
+%% (,&' VBI1C15*' "A' 731' GBI15' -148:' 04AA4G"710' 48' 731
04B01' 5"4A1A' 47A' 71(G15"7651*' 47' 4A' EB680' 73"7' 731' CB?7":1
Problems 221
*4.30#E#-)+3<")*#2:#&"#3"+(*61)"(#(%&(#16+(#2')*&()#2;)*
&# /3-)# +6''04?;20(&<)# *&"<)8# "2(3"<# (%&(# &# -32-)d+
J6"5(32"?;20(&<)# -*2'# 3+# *)0&(3;)04# 3"-)')"-)"(# 2:# J6"5?
(32"# 56**)"(8# 52"+3-)*+# (%)# 6+)# 2:# &# 0&*<)# -32-)# (2# )+(&9?
03+%# &# +1&00# *)0&(3;)04# 52"+(&"(# ;20(&<)=# E# '2/)*# -32-)8
:2*#/%35%#(%)#"213"&0#56**)"(#&(#S=^#T#3+#,S#E8#3+#&;&30?
&90)=#!:#(%)#56**)"(#+26*5)#:))-3"<#(%)#-32-)#5%&"<)+#3"#*%)
*&"<)#S=Z 1E# (2#,=Z 1E#&"-#3:8#3"#&--3(32"8#(%)#()1')*&?
(6*)# 5%&"<)+# 94# ±.Z°$8# /%&(# 3+# (%)# )A')5()-# *&"<)# 2:
-32-)#;20(&<)i
*4.31#E+#&"#&0()*"&(3;)#(2#(%)#3-)&#+6<<)+()-#3"#l*290)1
P=OS8#(%)#-)+3<")*#52"+3-)*+#&#+)52"-#&''*2&5%#(2#'*2-653"<
&# *)0&(3;)04# 52"+(&"(# +1&00# ;20(&<)# :*21# &# ;&*3&90)# 56**)"(
+6''04Q#!(#*)03)+#2"#(%)#&9303(4#(2#1&H)#C63()#&556*&()#52'3)+
2:#&"4#+1&00#56**)"(#(%&(#3+#&;&30&90)#B6+3"<#&#'*25)++#5&00)56**)"(#13**2*3"<D=#F%)#-)+3<")*#'*2'2+)+#(2#6+)#(%3+#3-)&#(2
+6''04#(/2#-32-)+#2:#-3::)*)"(#J6"5(32"#&*)&+#/3(%#(%)#+&1)
56**)"(# &"-# (2# 1)&+6*)# (%)3*# J6"5(32"?;20(&<)# -3::)*)"5)=
F/2#(4')+#2:#-32-)+#&*)#&;&30&90)7#:2*#&#:2*/&*-#;20(&<)#2:
NSS#1T8#2")#52"-65(+#S=,#1E8#/%30)#(%)#2(%)*#52"-65(+#,#E=
X2/8# :2*# 3-)"(35&0# 56**)"(+# 3"# (%)# *&"<)# 2:# S=Z# 1E# (2
,=Z 1E#+6''03)-#(2#)&5%8#/%&(#*&"<)#2:#-3::)*)"5)#;20(&<)+
*)+60(i#I%&(#3+#(%)#)::)5(#2:#&#()1')*&(6*)#5%&"<)#2:#±.Z°$
2"#(%3+#&**&"<)1)"(i
Section 4.3: Modeling the Diode Forward
Characteristic
*4.32#$2"+3-)*#(%)#<*&'%35&0#&"&04+3+#2:#(%)#-32-)#53*563(#2:
L3<=#P=,S#/3(%#@++#=#,#T8#,#=#,#HΩ8#&"-#&#-32-)#%&;3"<#-5#=
,S−,Z# E=# $&0560&()# &# +1&00# "619)*# 2:# '23"(+# 2"# (%)# -32-)
5%&*&5()*3+(35# 3"# (%)# ;353"3(4# 2:# /%)*)# 426# )A')5(# (%)# 02&03")#(2#3"()*+)5(#3(8#&"-#6+)#&#<*&'%35&0#'*25)++#(2#*):3")#426*
)+(31&()#2:#-32-)#56**)"(=#I%&(#;&06)#2:#-32-)#56**)"(#&";20(&<)# -2# 426# :3"-i# E"&04(35&0048# :3"-# (%)# ;20(&<)# 52**)?
+'2"-3"<#(2#426*#)+(31&()#2:#56**)"(=#_4#%2/#165%#-2)+#3(
-3::)*#:*21#(%)#<*&'%35&004#)+(31&()-#;&06)i
4.33%h+)#(%)#3()*&(3;)?&"&04+3+#'*25)-6*)#(2#-)()*13")#(%)
-32-)#56**)"(#&"-#;20(&<)#3"#(%)#53*563(#2:#L3<=#P=,S#:2*#@++#=
,#T8#,#=#,#HΩ8#&"-#&#-32-)#%&;3"<#-5#=#,S−,Z#E=
4.34%E#e,?1E#-32-)f#B3=)=8#2")#(%&(#%&+#v+#=#S=N#T#&(#!+#=
,# 1ED# 3+# 52"")5()-# 3"# +)*3)+# /3(%# &# .SS?Ω# *)+3+(2*# (2# &
,=S?T#+6''04=
B&D l*2;3-)#&#*26<%#)+(31&()#2:#(%)#-32-)#56**)"(#426#/260)A')5(=
B9D @+(31&()#(%)#-32-)#56**)"(#12*)#502+)04#6+3"<#3()*&(3;)
&"&04+3+=
D 4.35%E++613"<#(%)#&;&30&9303(4#2:#-32-)+#:2*#/%35%#v+#=
S=N#T#&(#!+#=#,#1E8#-)+3<"#&#53*563(#(%&(#6(303M)+#:26*#-32-)+
52"")5()-#3"#+)*3)+8#3"#+)*3)+#/3(%#&#*)+3+(2*#,#52"")5()-#(2#&
,S?T#'2/)*#+6''04=#F%)#;20(&<)#&5*2++#(%)#+(*3"<#2:#-32-)+
3+#(2#9)#O=S#T=
4.36% E# -32-)# 2')*&()+# 3"# &# +)*3)+# 53*563(# /3(%# ,# &"-# @=
E -)+3<")*8# 52"+3-)*3"<# 6+3"<# &# 52"+(&"(?;20(&<)# 12-)08# 3+
6"5)*(&3"# /%)(%)*# (2# 6+)# S=N# T# 2*# S=`# T# :2*# @+=# L2*# /%&(
;&06)#2:#@#3+#(%)#-3::)*)"5)#3"#(%)#5&0560&()-#;&06)+#2:#56*?
*)"(#2"04#,ji#L2*#@#=#.#T#&"-#,#= ,#HΩ8#/%&(#(/2#56**)"(+
/260-#*)+60(#:*21#(%)#6+)#2:#(%)#(/2#;&06)+#2:#@+i#I%&(#3+
(%)3*#')*5)"(&<)#-3::)*)"5)i
4.37%E#-)+3<")*#%&+#&#+6''04#2:#-32-)+#:2*#/%35%#&#56**)"(
2:#.#1E#:02/+#&(#S=N#T=#h+3"<#&#,?1E#56**)"(#+26*5)8#(%)
-)+3<")*#/3+%)+#(2#5*)&()#&#*):)*)"5)#;20(&<)#2:#,=.Z#T=#Y6<?
<)+(#&#52193"&(32"#2:#+)*3)+#&"-#'&*&00)0#-32-)+#(%&(#/300#-2
(%)#J29#&+#/)00#&+#'2++390)=#>2/#1&"4#-32-)+#&*)#"))-)-i
I%&(#;20(&<)#3+#&5(6&004#&5%3);)-i
4.38%Y20;)#(%)#'*290)1+#3"#@A&1'0)#P=.#6+3"<#(%)#52"+(&"(?
;20(&<)?-*2'#B@+#=#S=N#TD#-32-)#12-)0=#
4.39% L2*# (%)# 53*563(+# +%2/"# 3"# L3<=# lP=.8# 6+3"<# (%)
52"+(&"(?;20(&<)?-*2'# B@+# =# S=N# TD# -32-)# 12-)08# :3"-# (%)
;20(&<)+#&"-#56**)"(+#3"-35&()-=
4.40% L2*# (%)# 53*563(+# +%2/"# 3"# L3<=# lP=O8# 6+3"<# (%)
52"+(&"(?;20(&<)?-*2'# B@+# =# S=N# TD# -32-)# 12-)08# :3"-# (%)
;20(&<)+#&"-#56**)"(+#3"-35&()-=
4.41%L2*#(%)#53*563(+#3"#L3<=#lP=U8#6+3"<#(%)#52"+(&"(?;20(&<)?
-*2'#B@+#=#S=N#TD#-32-)#12-)08#:3"-#(%)#;&06)+#2:#(%)#0&9)0)56**)"(+#&"-#;20(&<)+=#
4.42%L2*#(%)#53*563(+#3"#L3<=#lP=,S8#6(303M)#F%r;)"3"d+#(%)2?
*)1#(2#+31'03:4#(%)#53*563(+#&"-#:3"-#(%)#;&06)+#2:#(%)#0&9)0)56**)"(+# &"-# ;20(&<)+=# E++61)# (%&(# 52"-65(3"<# -32-)+
5&" 9)# *)'*)+)"()-# 94# (%)# 52"+(&"(?;20(&<)?-*2'# 12-)0
B@+ = S=N#TD=
D 4.43%[)')&(#l*290)1#P=,,8#*)'*)+)"(3"<#(%)#-32-)#94#(%)
52"+(&"(?;20(&<)?-*2'#B@+#=#S=N#TD#12-)0=#>2/#-3::)*)"(#3+
(%)#*)+60(3"<#-)+3<"i
4.44% F%)# +1&00?+3<"&0# 12-)0# 3+# +&3-# (2# 9)# ;&03-# :2*# ;20(&<)
;&*3&(32"+#2:#&926(#Z#1T=#F2#/%&(#')*5)"(&<)#56**)"(#5%&"<)
-2)+#(%3+#52**)+'2"-i#B$2"+3-)*#92(%#'2+3(3;)#&"-#")<&(3;)
+3<"&0+=D#I%&(#3+#(%)#1&A3161#&002/&90)#;20(&<)#+3<"&0#B'2+3?
(3;)#2*#")<&(3;)D#3:#(%)#56**)"(#5%&"<)#3+#(2#9)#0313()-#(2 ,Sji
4.45%!"#&#'&*(3560&*#53*563(#&''035&(32"8#()"#e.S?1E#-32-)+f
B&#.S?1E#-32-)#3+#&#-32-)#(%&(#'*2;3-)+#&#S=N?T#-*2'#/%)"
(%)# 56**)"(# (%*26<%# 3(# 3+# .S# 1ED# 52"")5()-# 3"# '&*&00)0
CHAPTER 4 P R O B L E M S
-)5*)&+)+# &"-# );)"(6&004# *)&5%)+# `SS# 1T=# I%&(# 3+# (%)
&''&*)"(# *3+)# 3"# J6"5(32"# ()1')*&(6*)i# I%&(# 3+# (%)# '2/)*
-3++3'&()-#3"#(%)#-32-)#3"#3(+#:3"&0#+(&()i#I%&(#3+#(%)#()1')*?
&(6*)#*3+)#')*#/&((#2:#'2/)*#-3++3'&(32"i#BF%3+#3+#5&00)-#(%)
(%)*1&0#*)+3+(&"5)=D
CHAPTER 4 P R O B L E M S
222 Chapter 4 Diodes
!"#$%&#'%&'%'&!&%(')*$$#+&'!,'-./'0.'1!$'&2#'34!3#5')(!5#(6
7%&)2#38' 92%&' )*$$#+&' ,(!95' 4+' #%)2:' ;2%&' 45' &2#' )!$$#<
5"!+34+=' 57%((<54=+%(' $#545&%+)#' !,' #%)2' 34!3#' %+3' !,' &2#
)!7>4+%&4!+:'?!7"%$#'&245'94&2'&2#'4+)$#7#+&%('$#545&%+)#
!,' %' 54+=(#' 34!3#' )!+3*)&4+=' -./' 0.' @,' #%)2' !,' &2#' A-<70
34!3#5' 2%5' %' 5#$4#5' $#545&%+)#' !,' -.A' Ω' %55!)4%&#3' 94&2' &2#
94$#'>!+35'&!'&2#'B*+)&4!+8'92%&'45'&2#'#C*4D%(#+&'$#545&%+)#
!,'&2#'/-'"%$%((#(<)!++#)&#3'34!3#5:';2%&')!++#)&4!+'$#545<
&%+)#'9!*(3'%'54+=(#'34!3#'+##3'4+'!$3#$'&!'>#'&!&%((6'#C*4D<
%(#+&:' E!"#$%' F245' 45' 926' &2#' "%$%((#(' )!++#)&4!+' !,' $#%(
34!3#5')%+'!,&#+'>#'*5#3'&!'%3D%+&%=#.G
%+3'(A'%$#'(%$=#')!*"(4+=')%"%)4&!$5.'1!$'D#$6'57%(('4+"*&'54=<
+%(58'5!'&2%&'&2#'34!3#5')%+'>#'$#"$#5#+&#3>6'&2#4$'57%((<54=+%('
v
v/
v
v/
&2%&' <<<<"< " & 8'92#$#'&'45'4+''70.'14+3'' v " ⁄ v / ',!$'&'O'-'µ08
/ µ08'/-'µ08'/--'µ08'T--'µ08'J--'µ08'W--'µ08'WW-'µ08
%+3'/'70.
4.46!@+'&2#')4$)*4&'52!9+'4+'14=.'HI.IJ8'&'45'%'3)')*$$#+&'%+3
1 mA
v''45'%'54+*5!43%('54=+%(.'?%"%)4&!$5'(/'%+3'(A'%$#'D#$6'(%$=#K
&2#4$',*+)&4!+'45'&!')!*"(#'&2#'54=+%('&!'%+3',$!7'&2#'34!3#
>*&'>(!)L'&2#'3)')*$$#+&',$!7',(!94+='4+&!'&2#'54=+%('5!*$)#
!$'&2#'(!%3'E+!&'52!9+G.'M5#'&2#'34!3#'57%((<54=+%('7!3#('&!
52!9'&2%&'&2#'54=+%(')!7"!+#+&'!,'&2#'!*&"*&'D!(&%=#'45
- . + &) '
*
* +/ ! * +A
+A
$#545&%+)#5'*+/'%+3'*+A 8'52!9'&2%& <<<<"< " <<<<<<<<<<<<<<<<<<<
< '%+3'2#+)#
C2
vo
D1
C1
D2
vi
.
< '
v " = v ' <<<<<<<<<<<<<<<<<<<
@,' v''='/-'7N8',4+3' v"',!$'&'O'/'708'-./'708'%+3'/'µ0.'P#&
)' ='/'LΩ.'0&'92%&'D%(*#'!,'&'3!#5'v"'>#)!7#'!+#<2%(,'!, v':
Q!&#'&2%&'&245')4$)*4&',*+)&4!+5'%5'%'54=+%('%&&#+*%&!$'94&2'&2#
%&&#+*%&4!+',%)&!$')!+&$!((#3'>6'&2#'D%(*#'!,'&2#'3)')*$$#+&'&.
I
Figure P4.48
C1
*4.49 @+' &2#' )4$)*4&' 52!9+' 4+' 14=.' HI.IW8' 34!3#5' ,/
&2$!*=2',I'%$#'43#+&4)%('%+3'#%)2'#R24>4&5'%'D!(&%=#'3$!"'!,
-.S'N'%&'%'/<70')*$$#+&.
C2
"
vo
I
!
D3
D1
Figure P4.46
4.47'@+'&2#'%&&#+*%&!$')4$)*4&'!,'14=.'HI.IJ8'(#&')''='/-'LΩ.
F2#' 34!3#' 45' %' /<70' 3#D4)#K' &2%&' 458' 4&' #R24>4&5' %' D!(&%=#
3$!" !,'-.S'N'%&'%'3)')*$$#+&'!,'/'70.'1!$'57%(('4+"*&'54=<
+%(58' 92%&' D%(*#' !,' )*$$#+&' &' 45' +##3#3' ,!$' v " ⁄ v ' = ' -.T-:
-./-:' -.-/:' -.--/:' @+' #%)2' )%5#8' 92%&' 45' &2#' (%$=#5&' 4+"*&
54=+%('&2%&')%+'>#'*5#3'924(#'#+5*$4+='&2%&'&2#'54=+%(')!7<
"!+#+&'!,'&2#'34!3#')*$$#+&'45'(474&#3'&!'±/-U'!,'4&5'3)')*$<
$#+&:';2%&'!*&"*&'54=+%(5')!$$#5"!+3:
4.48 @+'&2#')%"%)4&!$<)!*"(#3'%&&#+*%&!$')4$)*4&'52!9+'4+'14=.
HI.IV8'&'45'%'3)')*$$#+&'&2%&'D%$4#5',$!7'-'70'&!'/'708'%+3'(/
vo
vi
"
!
D2
D4
I
Figure P4.49
10 k#
Problems
**4.50 !"# l*290)1# P=PU# /)# 3";)+(3<&()-# (%)# 2')*&(32"# 2:
(%)#53*563(#3"#L3<=#lP=PU#:2*#+1&00#3"'6(#+3<"&0+=#!"#(%3+#'*29?
0)1# /)# /3+%# (2# :3"-# (%)# ;20(&<)# (*&"+:)*# 5%&*&5()*3+(35
BTF$D# v . #;)*+6+#v - #:2*# ! ,.#T ≤ v - ≤ ,.#T #:2*#(%)#5&+)#-#\
,#1E#&"-#)&5%#2:#(%)#-32-)+#)A%393(+#&#;20(&<)#-*2'#2:#S=N#T
&(#&#56**)"(#2:#,#1E=#F2/&*-#(%3+#)"-8#6+)#(%)#-32-)#)A'2?
")"(3&0#5%&*&5()*3+(35#(2#52"+(*65(#&#(&90)#(%&(#<3;)+#(%)#;&0?
6)+#2:Q#(%)#56**)"(# ! . #3"#(%)#,S?H Ω #*)+3+(2*8#(%)#56**)"(#3"
)&5%#2:#(%)#:26*#-32-)+8#(%)#;20(&<)#-*2'#&5*2++#)&5%#2:#(%)
:26*# -32-)+8# &"-# (%)# 3"'6(# ;20(&<)# v -8# :2*# v . " S8# u,# T8
u. T8#uZ#T8#uU#T8#uU=U#T8#uU=UU#T8#u,S=Z#T8#u,,#T8#&"u,. T=#h+)#(%)+)#-&(&8#/3(%#)A(*&'20&(32"#(2#")<&(3;)#;&06)+
2:# v -# &"-# v .8# (2# +H)(5%# (%)# *)C63*)-# TF$=# E0+2# +H)(5%# (%)
TF$#(%&(#*)+60(+#3:#-#3+#*)-65)-#(2#S=Z#1E=
*4.51 !"#(%)#53*563(#+%2/"#3"#L3<=#lP=Z,8#-#3+#&#-5#56*?
*)"(#&"-# v!#3+#&#+3"6+23-&0#+3<"&0#/3(%#+1&00#&1'03(6-)#B0)++
(%&"#,S 1TD#&"-#&#:*)C6)"54#2:#,SS#H>M=#[)'*)+)"(3"<#(%)
-32-)#94#3(+#+1&00?+3<"&0#*)+3+(&"5)#'* 8#/%35%#3+#&#:6"5(32"#2:
-8# +H)(5%# (%)# 53*563(# :2*# -)()*13"3"<# (%)# +3"6+23-&0# 26('6(
;20(&<)#@&8#&"-#(%6+#:3"-#(%)#'%&+)#+%3:(#9)(/))"#@!#&"-#@&=
L3"-#(%)#;&06)#2:#-#(%&(#/300#'*2;3-)#&#'%&+)#+%3:(#2:#−PZ°8
&"-#:3"-#(%)#*&"<)#2:#'%&+)#+%3:(#&5%3);)-#&+#-#3+#;&*3)-#2;)*
(%)#*&"<)#2:#S=,#(31)+#(2#,S#(31)+#(%3+#;&06)=#
*4.52 $2"+3-)*# (%)# ;20(&<)?*)<60&(2*# 53*563(# +%2/"# 3"
L3<= lP=Z.=# F%)# ;&06)# 2:# ,# 3+# +)0)5()-# (2# 29(&3"# &"# 26('6(
;20(&<)#@.#B&5*2++#(%)#-32-)D#2:#S=N#T=#
B&D h+)#(%)#-32-)#+1&00?+3<"&0#12-)0#(2#+%2/#(%&(#(%)#5%&"<)
3"#26('6(#;20(&<)#52**)+'2"-3"<#(2#&#5%&"<)#2:#,#T#3"#@ +#3+
@I
∆@.
??????????
? = ???????????????????????????????
?
+#
+
∆@
@ + @ I ! S=N
F%3+#C6&"(3(4#3+#H"2/"#&+#(%)#03")#*)<60&(32"#&"-#3+#6+6&004
)A'*)++)-#3"#1TaT=
B9D k)")*&03M)#(%)#)A'*)++32"#&92;)#:2*#(%)#5&+)#2:#1#-32-)+
52"")5()-# 3"# +)*3)+# &"-# (%)# ;&06)# 2:# ,0 &-J6+()-# +2# (%&(# (%)
;20(&<)#&5*2++#)&5%#-32-)#3+#S=N#T#B&"-#@. = S=N1#TDN
B5D $&0560&()#(%)#;&06)#2:#03")#*)<60&(32"#:2*#(%)#5&+)#@ +#=
,S T#B"213"&004D#&"-#B3D#1#=#,#&"-#B33D#1#\#O=
V"
R
"
VO
!
Figure P4.52
*4.53 $2"+3-)*# (%)# ;20(&<)?*)<60&(2*# 53*563(# +%2/"# 3"
L3< lP=Z.#6"-)*#(%)#52"-3(32"#(%&(#&#02&-#56**)"(#-P#3+#-*&/"
:*21#(%)#26('6(#()*13"&0=
B&D !:# (%)# ;&06)# 2:# -P# 3+# +6::353)"(04# +1&00# (%&(# (%)# 52**)?
+'2"-3"<# 5%&"<)# 3"# *)<60&(2*# 26('6(# ;20(&<)# ∆@.0 3+# +1&00
)"26<%#(2#J6+(3:4#6+3"<#(%)#-32-)#+1&00?+3<"&0#12-)08#+%2/
(%&(
∆@ .
?????????? = ! ( ' * #vv#, )
-P
I
vo
vi "
!
Figure P4.51
C
10 nF
F%3+#C6&"(3(4#3+#H"2/"#&+#(%)#02&-#*)<60&(32"#&"-#3+#6+6&004
)A'*)++)-#3"#1Ta1E=
B9D !:#(%)#;&06)#2:#,#3+#+)0)5()-#+65%#(%&(#&(#"2#02&-#(%)#;20(?
&<)# &5*2++# (%)# -32-)# 3+# S=N# T# &"-# (%)# -32-)# 56**)"(# 3+# -+8
+%2/#(%&(#(%)#)A'*)++32"#-)*3;)-#3"#B&D#9)521)+
+
∆@
@
#@ − S=N
??????????. = ! ?????I? ?????????????????????????????????
#
+
-P
- + @ − S=N + @
I
Y)0)5(#(%)#02/)+(#'2++390)#;&06)#:2*#-+#(%&(#*)+60(+#3"#&#02&*)<60&(32"#≤ Z#1Ta1E=#!:#@ +#3+#"213"&004#,S#T8#/%&(#;&06)
CHAPTER 4 P R O B L E M S
B&D L2*#+1&00#3"'6(#+3<"&0+#B)=<=8#,S#1T#')&HD8#:3"-#;&06)+
2:#(%)#+1&00?+3<"&0#(*&"+13++32"# v & ⁄ v ! #:2*#;&*326+#;&06)+#2:
- Q#S µE8#,#µE8#,S#µE8#,SS#µE8#,#1E8#&"-#,S#1E=
B9D L2*# &# :2*/&*-?52"-65(3"<# -32-)8# /%&(# 3+# (%)# 0&*<)+(
+3<"&0?;20(&<)#1&<"3(6-)#(%&(#3(#5&"#+6''2*(#/%30)#(%)#52**)?
+'2"-3"<#+3<"&0#56**)"(#3+#0313()-#(2#,Sj#2:#(%)#-5#93&+#56*?
*)"(=#X2/8#:2*#(%)#53*563(#3"#L3<=#lP=PU8#:2*#,S?1T#')&H#3"'6(8
/%&(# 3+# (%)# +1&00)+(# ;&06)# 2:# -# :2*# /%35%# (%)# -32-)# 56**)"(+
*)1&3"#/3(%3"#±,Sj#2:#(%)3*#-5#;&06)i
B5D L2*#-#\#,#1E8#/%&(#3+#(%)#0&*<)+(#'2++390)#26('6(#+3<"&0
:2*#/%35%#(%)#-32-)#56**)"(+#-);3&()#94#&(#12+(#,Sj#2:#(%)3*
-5# ;&06)+i# I%&(# 3+# (%)# 52**)+'2"-3"<# ')&H#3"'6(i# I%&(# 3+
(%)#(2(&0#56**)"(#3"#)&5%#-32-)i
223
CHAPTER 4 P R O B L E M S
224 Chapter 4 Diodes
!"#!#$%#&'()$&'*+#,-%!.#%/'0$"1#23'#*$!*'#&'()$&'*#$4#2'&5%#!"
$2%#"# 6
708 9'4'&:-$;'#23'#'</&'%%$!4#*'&$='*#$4#7>8#"!&#23'#0:%'#!"
$ *$!*'%#0!44'02'*#$4#%'&$'%#:4*#!#:*?)%2'*#2!#!>2:$4#%&#=
@6A$#B#:2#4!#-!:*6
*4.54 C'%$D4#:#*$!*'#=!-2:D'#&'D)-:2!&#2!#%)//-1#E6F#B#2!#:
EF@GΩ#-!:*6#H%'#2I!#*$!*'%#%/'0$"$'*#2!#3:='#:#@6AGB#*&!/#:2
:#0)&&'42#!"#E@#5,6#J3'#*$!*'%#:&'#2!#>'#0!44'02'*#2!#:#+FGB
%)//-1#23&!)D3#:#&'%$%2!&#!6#K/'0$"1#23'#=:-)'#"!&#!6#L3:2#$%
23'# *$!*'# 0)&&'42# I$23# 23'# -!:*# 0!44'02'*+# L3:2# $%# 23'
$40&':%'#&'%)-2$4D#$4#23'#!)2/)2#=!-2:D'#I3'4#23'#-!:*#$%#*$%G
0!44'02'*+# L3:2# 03:4D'# &'%)-2%# $"# 23'# -!:*# &'%$%2:40'# $%
&'*)0'*#2!#E@@#Ω+#J!#AF#Ω+#J!#F@#Ω+#7'()*M#H%'#23'#%5:--G
%$D4:-#*$!*'#5!*'-#2!#0:-0)-:2'#:--#03:4D'%#$4#!)/)2#=!-2:D'68
*4.55 ,#=!-2:D'#&'D)-:2!&#0!4%$%2$4D#!"#2I!#*$!*'%#$4#%'&$'%
"'*#I$23#:#0!4%2:42G0)&&'42#%!)&0'#$%#)%'*#:%#:#&'/-:0'5'42
"!&# :# %$4D-'# 0:&>!4G;$40# 0'--# 7>:22'&18# !"# 4!5$4:-# =!-2:D'
E6F B6#J3'#&'D)-:2!&#-!:*#0)&&'42#=:&$'%#"&!5#N#5,#2!#A#5,6
O!4%2:42G0)&&'42#%)//-$'%#!"#F#5,.#E@#5,.#:4*#EF 5,#:&'
:=:$-:>-'6#L3$03#I!)-*#1!)#03!!%'.#:4*#I31+#L3:2#03:4D'
$4#!)2/)2#=!-2:D'#I!)-*#&'%)-2#I3'4#23'#-!:*#0)&&'42#=:&$'%
!='&#$2%#")--#&:4D'+
**4.56 ,#/:&2$0)-:&#*'%$D4#!"#:#=!-2:D'#&'D)-:2!&#$%#%3!I4
$4 P$D6# QR6FS6# C$!*'%# +E# :4*# +N# :&'# E@G5,# )4$2%T# 23:2# $%.
':03 3:%#:#=!-2:D'#*&!/#!"#@6A#B#:2#:#0)&&'42#!"#E@#5,6#H%'
23'#*$!*'#'</!4'42$:-#5!*'-#:4*#$2'&:2$='#:4:-1%$%#2!#:4%I'&
23'#"!--!I$4D#()'%2$!4%M
7:8 L3:2#$%#23'#&'D)-:2!&#!)2/)2#=!-2:D'#%&#I$23#23'#EF@GΩ
-!:*#0!44'02'*+
7>8 P$4*#%&#I$23#4!#-!:*6
708 L$23#23'#-!:*#0!44'02'*.#2!#I3:2#=:-)'#0:4#23'#FGB#%)/G
/-1#>'#-!I'&'*#I3$-'#5:$42:$4$4D#23'#-!:*'*#!)2/)2#=!-2:D'
I$23$4#@6E#B#!"#$2%#4!5$4:-#=:-)'+
7*8 L3:2#*!'%#23'#-!:*'*#!)2/)2#=!-2:D'#>'0!5'#I3'4#23'
FGB#%)//-1#$%#&:$%'*#>1#23'#%:5'#:5!)42#:%#23'#*&!/#"!)4*
$4 708+
"5 V
180 !
"
D1
VO
D2
#
Figure P4.56
150 !
7'8 P!&# 23'# &:4D'# !"# 03:4D'%# '</-!&'*# $4# 708# :4*# 7*8.# >1
I3:2# /'&0'42:D'# *!'%# 23'# !)2/)2# =!-2:D'# 03:4D'# "!&# ':03
/'&0'42:D'#03:4D'#!"#%)//-1#=!-2:D'#$4#23'#I!&%2#0:%'+
Section 4.4: Operation in the Reverse
Breakdown Region—Zener Diodes
4.57 Q:&2$:-#%/'0$"$0:2$!4%#!"#:#0!--'02$!4#!"#;'4'&#*$!*'%#:&'
/&!=$*'*#>'-!I6#P!&#':03.#$*'42$"1#23'#5$%%$4D#/:&:5'2'&.#:4*
'%2$5:2'#$2%#=:-)'6#U!2'#"&!5#P$D6#R6EA#23:2# %,- ! %,@ 6
7:8 %,#=#E@6@#B.#%,-.=#V6S#B.#:4*#",/#=#F@#5,
7>8 ",/#=#E@#5,.#%,#=#V6E#B.#:4*#0;#=#W@#Ω
708 01#=#N#Ω.#%,#=#S6X#B.#:4*#%,-#=#S6S#B
7*8 %,#=#EX#B.#",/#=#F#5,.#:4*#%,-#=#EA6S#B
7'8 ",/#=#N@@#5,.#%,#=#A6F#B.#:4*.01#=#E6F#Ω
,%%)5$4D# 23:2# 23'# /!I'&# &:2$4D# !"# :# >&':Y*!I4# *$!*'# $%
'%2:>-$%3'*# :2# :>!)2# 2I$0'# 23'# %/'0$"$'*# ;'4'&# 0)&&'42# 7",/8.
I3:2# $%# 23'# /!I'&# &:2$4D# !"# ':03# !"# 23'# *$!*'%# *'%0&$>'*
:>!='+
D 4.58 ,# *'%$D4'&# &'()$&'%# :# %3)42# &'D)-:2!&# !"# ://&!<$G
5:2'-1#N@#B6#JI!#Y$4*%#!"#;'4'&#*$!*'%#:&'#:=:$-:>-'M#S6XGB
*'=$0'%# I$23# 01# !"# E@# Ω# :4*# F6EGB# *'=$0'%# I$23# 01# !"# W@# Ω6
P!& 23'#2I!#5:?!&#03!$0'%#/!%%$>-'.#"$4*#23'#-!:*#&'D)-:2$!46#Z4
23$%#0:-0)-:2$!4#4'D-'02#23'#'""'02#!"#23'#&'D)-:2!&#&'%$%2:40'#!6
4.59 ,# %3)42# &'D)-:2!&# )2$-$;$4D# :# ;'4'&# *$!*'# I$23# :4
$40&'5'42:-#&'%$%2:40'#!"#F#Ω#$%#"'*#23&!)D3#:4#XNGΩ#&'%$%G
2!&6#Z"#23'#&:I#%)//-1#03:4D'%#>1#E6@#B.#I3:2#$%#23'#0!&&'G
%/!4*$4D#03:4D'#$4#23'#&'D)-:2'*#!)2/)2#=!-2:D'+#
4.60 ,#V6EGB#;'4'&#*$!*'#'<3$>$2%#$2%#4!5$4:-#=!-2:D'#:2#:
2'%2#0)&&'42#!"#NX#5,6#,2#23$%#0)&&'42#23'#$40&'5'42:-#&'%$%G
2:40'#$%#%/'0$"$'*#:%#F Ω6#P$4*#%,@#!"#23'#;'4'&#5!*'-6#P$4*
23'#;'4'&#=!-2:D'#:2#:#0)&&'42#!"#E@#5,#:4*#:2#E@@#5,6
D 4.61 C'%$D4#:#A6FGB#;'4'&#&'D)-:2!&#0$&0)$2#)%$4D#:#A6FGB
;'4'&# %/'0$"$'*# :2# EN# 5,6# J3'# ;'4'&# 3:%# :4# $40&'5'42:&'%$%2:40'#01#[#W@#Ω#:4*#:#Y4''#0)&&'42#!"#@6F#5,6#J3'#&'D)G
-:2!&# !/'&:2'%# "&!5# :# E@GB# %)//-1# :4*# 3:%# :# E6NGYΩ# -!:*6
L3:2#$%#23'#=:-)'#!"#!#1!)#3:='#03!%'4+#L3:2#$%#23'#&'D)-:G
2!&# !)2/)2# =!-2:D'# I3'4# 23'# %)//-1# $%# E@\# 3$D3+# Z%# E@\
-!I+# L3:2# $%# 23'# !)2/)2# =!-2:D'# I3'4# >!23# 23'# %)//-1# $%
E@\# 3$D3# :4*# 23'# -!:*# $%# &'5!='*+# L3:2# $%# 23'# %5:--'%2
/!%%$>-'#-!:*#&'%$%2!&#23:2#0:4#>'#)%'*#I3$-'#23'#;'4'&#!/'&G
:2'%# :2# :# 0)&&'42# 4!# -!I'&# 23:4# 23'# Y4''# 0)&&'42# I3$-'# 23'
%)//-1#$%#E@\#-!I+#L3:2#$%#23'#-!:*#=!-2:D'#$4#23$%#0:%'+
*D 4.62 Q&!=$*'# 2I!# *'%$D4%# !"# %3)42# &'D)-:2!&%# )2$-$;$4D
23'#EUFNWF#;'4'&#*$!*'.#I3$03#$%#%/'0$"$'*#:%#"!--!I%M#%,#=
S6X#B#:4*#01#=#F#Ω#"!&#",#=#N@#5,T#:2#",#=#@6NF#5,#74':&'&#23'
Y4''8.# 01# =# AF@# Ω6# P!&# >!23# *'%$D4%.# 23'# %)//-1# =!-2:D'# $%
4!5$4:--1# V# B# :4*# =:&$'%# >1# ±E# B6# P!&# 23'# "$&%2# *'%$D4.
:%%)5'#23:2#23'#:=:$-:>$-$21#!"#%)//-1#0)&&'42#$%#4!2#:#/&!>-'5.
Problems 225
4.66 h+3"<#(%)#)A'2")"(3&0#-32-)#5%&*&5()*3+(358#+%2/#(%&(
:2*#v5#&"-#v.#92(%#<*)&()*#(%&"#M)*28#(%)#53*563(#2:#L3<=#P=.,B&D
%&+#(%)#(*&"+:)*#5%&*&5()*3+(35#
D *4.63 E#M)")*#+%6"(#*)<60&(2*#)1'024+#&#U=,?T#M)")*#-32-)
:2*#/%35%#@G#=#U=,#T#&(#-G#=#U#1E8#/3(%#'Q#=#OS#Ω#&"-#-GH#=#S=O
1E=#F%)#&;&30&90)#+6''04#;20(&<)#2:#,Z#T#5&"#;&*4#&+#165%#&+
±,Sj=#L2*#(%3+#-32-)8#/%&(#3+#(%)#;&06)#2:#@GSi#L2*#&#"213"&0
02&-# *)+3+(&"5)# ,P# 2:# ,# HΩ# &"-# &# "213"&0# M)")*# 56**)"(# 2:# ,S
1E8# /%&(# 56**)"(# 16+(# :02/# 3"# (%)# +6''04# *)+3+(2*# ,i# L2*# (%)
"213"&0# ;&06)# 2:# +6''04# ;20(&<)8# +)0)5(# &# ;&06)# :2*# *)+3+(2*# ,8
+')53:3)-#(2#2")#+3<"3:35&"(#-3<3(8#(2#'*2;3-)#&(#0)&+(#(%&(#56**)"(=
I%&(#"213"&0#26('6(#;20(&<)#*)+60(+i#L2*#&#±,Sj#5%&"<)#3"#(%)
+6''04#;20(&<)8#/%&(#;&*3&(32"#3"#26('6(#;20(&<)#*)+60(+i#!:#(%)
02&-# 56**)"(# 3+# *)-65)-# 94# ZSj8# /%&(# 3"5*)&+)# 3"# @.# *)+60(+i
I%&(#3+#(%)#+1&00)+(#;&06)#2:#02&-#*)+3+(&"5)#(%&(#5&"#9)#(20)*&()/%30)# 1&3"(&3"3"<# *)<60&(32"# /%)"# (%)# +6''04# ;20(&<)# 3+# 02/i
I%&(#3+#(%)#02/)+(#'2++390)#26('6(#;20(&<)#(%&(#*)+60(+i#$&0560&()
;&06)+#:2*#(%)#03")#*)<60&(32"#&"-#:2*#(%)#02&-#*)<60&(32"#:2*#(%3+
53*563(#6+3"<#(%)#"61)*35&0#*)+60(+#29(&3")-#3"#(%3+#'*290)1=
/%)*)# v5#&"-# v.#&*)#3"#;20(+#&"-#,#3+#3"#H302%1+=#X2()#(%&(
(%3+# *)0&(32"+%3'# 5&"# 9)# 6+)-# (2# 29(&3"# (%)# ;20(&<)# (*&"+:)*
5%&*&5()*3+(35# v.#;+# v5#94#:3"-3"<# v5#52**)+'2"-3"<#(2#;&*3?
26+#;&06)+#2:#v. =
D *4.64 !(#3+#*)C63*)-#(2#-)+3<"#&#M)")*#+%6"(#*)<60&(2*#(2
'*2;3-)# &# *)<60&()-# ;20(&<)# 2:# &926(# ,S# T=# F%)# &;&30&90)
,S?T8#,?I#M)")*#2:#(4')#,XPNPS#3+#+')53:3)-#(2#%&;)#&#,S?T
-*2'#&(#&#()+(#56**)"(#2:#.Z#1E=#E(#(%3+#56**)"(8#3(+#'Q#3+#N#Ω=
F%)#*&/#+6''048#@5 8#&;&30&90)#%&+#&#"213"&0#;&06)#2:#.S#T
96(#5&"#;&*4#94#&+#165%#&+#±.Zj=#F%)#*)<60&(2*#3+#*)C63*)(2# +6''04# &# 02&-# 56**)"(# 2:# S 1E# (2# .S# 1E=# R)+3<"# :2*# &
13"3161#M)")*#56**)"(#2:#Z#1E=
B&D L3"-#@GS=
B9D $&0560&()#(%)#*)C63*)-#;&06)#2:#,=
B5D L3"-# (%)# 03")# *)<60&(32"=# I%&(# 3+# (%)# 5%&"<)# 3"# @.# )A?
'*)++)-#&+#&#')*5)"(&<)8#52**)+'2"-3"<#(2#(%)#±.Zj#5%&"<)
3"#@5i
B-D L3"-# (%)# 02&-# *)<60&(32"=# _4# /%&(# ')*5)"(&<)# -2)+# @.
5%&"<)#:*21#(%)#"2?02&-#(2#(%)#:600?02&-#52"-3(32"i
B)D I%&(# 3+# (%)# 1&A3161# 56**)"(# (%&(# (%)# M)")*# 3"# 426*
-)+3<"#3+#*)C63*)-#(2#52"-65(i#I%&(#3+#(%)#M)")*#'2/)*#-3+?
+3'&(32"#6"-)*#(%3+#52"-3(32"i
Section 4.5: Rectifier Circuits
4.65 $2"+3-)*#(%)#%&0:?/&;)#*)5(3:3)*#53*563(#2:#L3<=#P=.,B&D
/3(%#(%)#-32-)#*);)*+)-=#V)(#v5#9)#&#+3"6+23-#/3(%#,.?T#')&H
&1'03(6-)8# &"-# 0)(# ,# =# ,=Z# HΩ=# h+)# (%)# 52"+(&"(?;20(&<)?
-*2'#-32-)#12-)0#/3(%#@+#=#S=N#T=
B&D YH)(5%#(%)#(*&"+:)*#5%&*&5()*3+(35=
B9D YH)(5%#(%)#/&;):2*1#2:#v.=
B5D L3"-#(%)#&;)*&<)#;&06)#2:#v.=
B-D L3"-#(%)#')&H#56**)"(#3"#(%)#-32-)=
B)D L3"-#(%)#l!T#2:#(%)#-32-)=
v . = v 5 ! v + # ( &( ! + = ,#1E ) ! @ I #0"# ( v . ⁄ , )
4.67 $2"+3-)*# &# %&0:?/&;)# *)5(3:3)*# 53*563(# /3(%# &
(*3&"<60&*?/&;)# 3"'6(# 2:# Z?T# ')&H?(2?')&H# &1'03(6-)# &"M)*2#&;)*&<)8#&"-#/3(%#,0=#,#HΩ=#E++61)#(%&(#(%)#-32-)#5&"
9)#*)'*)+)"()-#94#(%)#52"+(&"(?;20(&<)?-*2'#12-)0#/3(%#@+ =
S=N T=#L3"-#(%)#&;)*&<)#;&06)#2:#v. =
4.68 E#%&0:?/&;)#*)5(3:3)*#53*563(#/3(%#&#,?HΩ#02&-#2')*?
&()+#:*21#&#,.S?T#B*1+D#`S?>M#%26+)%20-#+6''04#(%*26<%
&# ,S?(2?,# +()'?-2/"# (*&"+:2*1)*=# !(# 6+)+# &# +30352"# -32-)
(%&(#5&"#9)#12-)0)-#(2#%&;)#&#S=N?T#-*2'#:2*#&"4#56**)"(=
I%&(#3+#(%)#')&H#;20(&<)#2:#(%)#*)5(3:3)-#26('6(i#L2*#/%&(
:*&5(32"#2:#(%)#5450)#-2)+#(%)#-32-)#52"-65(i#I%&(#3+#(%)
&;)*&<)#26('6(#;20(&<)i#I%&(#3+#(%)#&;)*&<)#56**)"(#3"#(%)
02&-i
4.69 E#:600?/&;)#*)5(3:3)*#53*563(#/3(%#&#,?HΩ#02&-#2')*&()+
:*21#&#,.S?T#B*1+D#`S?>M#%26+)%20-#+6''04#(%*26<%#&#Z?(2?
,#(*&"+:2*1)*#%&;3"<#&#5)"()*?(&'')-#+)52"-&*4#/3"-3"<=#!(
6+)+#(/2#+30352"#-32-)+#(%&(#5&"#9)#12-)0)-#(2#%&;)#&#S=N?T
-*2'#:2*#&00#56**)"(+=#I%&(#3+#(%)#')&H#;20(&<)#2:#(%)#*)5(3?
:3)-# 26('6(i# L2*# /%&(# :*&5(32"# 2:# &# 5450)# -2)+# )&5%# -32-)
52"-65(i# I%&(# 3+# (%)# &;)*&<)# 26('6(# ;20(&<)i# I%&(# 3+# (%)
&;)*&<)#56**)"(#3"#(%)#02&-i
4.70 E#:600?/&;)#9*3-<)#*)5(3:3)*#53*563(#/3(%#&#,?HΩ#02&2')*&()+# :*21# &# ,.S?T# B*1+D# `S?>M# %26+)%20-# +6''04
(%*26<%# &# ,S?(2?,# +()'?-2/"# (*&"+:2*1)*# %&;3"<# &# +3"<0)
+)52"-&*4#/3"-3"<=#!(#6+)+#:26*#-32-)+8#)&5%#2:#/%35%#5&"
9)#12-)0)-#(2#%&;)#&#S=N?T#-*2'#:2*#&"4#56**)"(=#I%&(#3+
(%)#')&H#;&06)#2:#(%)#*)5(3:3)-#;20(&<)#&5*2++#(%)#02&-i#L2*
/%&(#:*&5(32"#2:#&#5450)#-2)+#)&5%#-32-)#52"-65(i#I%&(#3+
(%)# &;)*&<)# ;20(&<)# &5*2++# (%)# 02&-i# I%&(# 3+# (%)# &;)*&<)
56**)"(#(%*26<%#(%)#02&-i
4.71 !(#3+#*)C63*)-#(2#-)+3<"#&#:600?/&;)#*)5(3:3)*#53*563(#6+3"<
(%)#53*563(#2:#L3<=#P=..#(2#'*2;3-)#&"#&;)*&<)#26('6(#;20(&<)#2:Q
B&D ,S#T
B9D ,SS#T
!"#)&5%#5&+)#:3"-#(%)#*)C63*)-#(6*"+#*&(32#2:#(%)#(*&"+:2*1)*=
E++61)#(%&(#&#52"-65(3"<#-32-)#%&+#&#;20(&<)#-*2'#2:#S=N#T=
F%)#&5#03")#;20(&<)#3+#,.S#T#*1+=
CHAPTER 4 P R O B L E M S
&"-#(%6+#2')*&()#(%)#-32-)#&(#.S#1E=#L2*#(%)#+)52"-#-)+3<"8
&++61)# (%&(# (%)# 56**)"(# :*21# (%)# *&/# +6''04# 3+# 0313()-8# &"(%)*):2*)#426#&*)#:2*5)-#(2#2')*&()#(%)#-32-)#&(#S=.Z#1E=#L2*
(%)#'6*'2+)#2:#(%)+)#3"3(3&0#-)+3<"+8#&++61)#"2#02&-=#L2*#)&5%
-)+3<"#:3"-#(%)#;&06)#2:#,#&"-#(%)#03")#*)<60&(32"=
CHAPTER 4 P R O B L E M S
226 Chapter 4 Diodes
D
D
D
D
Figure P4.74
4.72 !"#"$%&'()*+",&-./0&1)(&%2"&*(345"&("6%313"(&63(673%&)1
835.&-.9:.
D 4.73 ;)<=34"(&%2"&17++>?$@"&("6%313"(&3<&835.&-.99&?2"<
%2"&%($<=1)(,"(&%7(<=&($%3)&3=&=762&%2$%&%2"&@)+%$5"&$6()==&%2"
"<%3("& ="6)<4$(A& ?3<43<5& 3=& 9-& B& (,=.& C1& %2"& 3<#7%& $6& +3<"
@)+%$5"&D09E&B&(,=F&1+76%7$%"=&*A&$=&,762&$=&±0EGH&13<4&%2"
("I73("4& 'CB& )1& %2"& 43)4"=.& D!",",*"(& %)& 7="& $& 1$6%)(& )1
=$1"%A&3<&A)7(&4"=35<.F
4.74 J2"& 63(673%& 3<& 835.& '-./-& 3,#+","<%=& $& 6),#+","<>
%$(A>)7%#7%&("6%313"(.&KL"%62&$<4&6+"$(+A&+$*"+&%2"&?$@"1)(,=
)1&v $+ &$<4&v $− .&M==7,"&$&E./>B&4()#&$6()==&"$62&6)<476%3<5
43)4".&C1&%2"&,$5<3%74"&)1&%2"&$@"($5"&)1&"$62&)7%#7%&3=&%)&*"
0N&BH&13<4&%2"&("I73("4&$,#+3%74"&)1&%2"&=3<"&?$@"&$6()==&%2"
"<%3("&="6)<4$(A&?3<43<5.&O2$%&3=&%2"&'CB&)1&"$62&43)4"P
4.75 M75,"<%&%2"&("6%313"(&63(673%&)1&'()*+",&-.QR&?3%2&$
6$#$63%)(&62)="<&%)&#()@34"&$&#"$L>%)>#"$L&(3##+"&@)+%$5"&)1
D3F&0EG&)1&%2"&#"$L&)7%#7%&$<4&D33F&0G&)1&%2"&#"$L&)7%#7%.&C<
"$62&6$="S
D$F O2$%&$@"($5"&)7%#7%&@)+%$5"&("=7+%=P
D*F O2$%&1($6%3)<&)1&%2"&6A6+"&4)"=&%2"&43)4"&6)<476%P
D6F O2$%&3=&%2"&$@"($5"&43)4"&67(("<%P
D4F O2$%&3=&%2"&#"$L&43)4"&67(("<%P
4.76 !"#"$%&'()*+",&-./N&1)(&%2"&("6%313"(&3<&'()*+",&-.QT.
4.77 !"#"$%&'()*+",&-./N&1)(&%2"&("6%313"(&3<&'()*+",&-./E.
D *4.78 C%&3=&("I73("4&%)&7="&$&#"$L&("6%313"(&%)&4"=35<&$&46
#)?"(&=7##+A&%2$%&#()@34"=&$<&$@"($5"&46&)7%#7%&@)+%$5"&)1
0N&B&)<&?2362&$&,$U3,7,&)1&±0>B&(3##+"&3=&$++)?"4.&J2"
("6%313"(&1""4=&$&+)$4&)1&0NE&Ω.&J2"&("6%313"(&3=&1"4&1(),&%2"
+3<"&@)+%$5"&D09E&B&(,=H&QE&VWF&%2()752&$&%($<=1)(,"(.&J2"
43)4"=& $@$3+$*+"& 2$@"& E./>B& 4()#& ?2"<& 6)<476%3<5.& C1& %2"
4"=35<"(&)#%=&1)(&%2"&2$+1>?$@"&63(673%S
D$F K#"631A& %2"& (,=& @)+%$5"& %2$%& ,7=%& $##"$(& $6()==& %2"
%($<=1)(,"(&="6)<4$(A.
D*F 83<4&%2"&("I73("4&@$+7"&)1&%2"&13+%"(&6$#$63%)(.
D6F 83<4& %2"& ,$U3,7,& ("@"(="& @)+%$5"& %2$%& ?3++& $##"$(
$6()==&%2"&43)4"H&$<4&=#"631A&%2"&'CB&($%3<5&)1&%2"&43)4".
D4F ;$+67+$%"&%2"&$@"($5"&67(("<%&%2()752&%2"&43)4"&47(3<5
6)<476%3)<.
D"F ;$+67+$%"&%2"&#"$L&43)4"&67(("<%.
D *4.79 !"#"$%& '()*+",& -./R& 1)(& %2"& 6$="& 3<& ?2362& %2"
4"=35<"(&)#%=&1)(&$&17++>?$@"&63(673%&7%3+3W3<5&$&6"<%"(>%$##"4
%($<=1)(,"(.
D *4.80 !"#"$%& '()*+",& -./R& 1)(& %2"& 6$="& 3<& ?2362& %2"
4"=35<"(&)#%=&1)(&$&17++>?$@"&*(345"&("6%313"(&63(673%.
D *4.81 ;)<=34"(&$&2$+1>?$@"&#"$L&("6%313"(&1"4&?3%2&$&@)+%>
$5"& v!& 2$@3<5& $& %(3$<57+$(& ?$@"1)(,& ?3%2& 9E>B& #"$L>%)>
#"$L& $,#+3%74"H& W"()& $@"($5"H& $<4& 0>LVW& 1("I7"<6A.
M==7,"& %2$%& %2"& 43)4"& 2$=& $& E./>B& 4()#& ?2"<& 6)<476%3<5.
X"%&%2"&+)$4&("=3=%$<6"&"&=&0EE&Ω&$<4&%2"&13+%"(&6$#$63%)(&#&=
0EE&µ8.&83<4&%2"&$@"($5"&46&)7%#7%&@)+%$5"H&%2"&%3,"&3<%"(@$+
47(3<5&?2362&%2"&43)4"&6)<476%=H&%2"&$@"($5"&43)4"&67(("<%
47(3<5&6)<476%3)<H&$<4&%2"&,$U3,7,&43)4"&67(("<%.
D *4.82 ;)<=34"(&%2"&63(673%&3<&835.&'-./-&?3%2&%?)&"I7$+
13+%"(&6$#$63%)(=&#+$6"4&$6()==&%2"&+)$4&("=3=%)(=&".&M==7,"
%2$%& %2"& 43)4"=& $@$3+$*+"& "U23*3%& $& E./>B& 4()#& ?2"<& 6)<>
476%3<5.& Y"=35<& %2"& 63(673%& %)& #()@34"& ± 0N>B& 46& )7%#7%
@)+%$5"=& ?3%2& $& #"$L>%)>#"$L& (3##+"& <)& 5("$%"(& %2$<& 0& B.
Z$62& =7##+A& =2)7+4& *"& 6$#$*+"& )1& #()@343<5& 9EE& ,M& 46
67(("<%&%)&3%=&+)$4&("=3=%)(&".&;),#+"%"+A&=#"631A&%2"&6$#$6>
3%)(=H&43)4"=&$<4&%2"&%($<=1)(,"(.
4.83 J2"&)#&$,#&3<&%2"&#("63=3)<&("6%313"(&63(673%&)1&835.&'-.R:
3=&34"$+&?3%2&)7%#7%&=$%7($%3)<&+"@"+=&)1&±09&B.&M==7,"&%2$%
?2"<&6)<476%3<5&%2"&43)4"&"U23*3%=&$&6)<=%$<%&@)+%$5"&4()#
)1&E./&B.&83<4&v−H&v$H&$<4&v%&1)(S
D$F v&&=&+0&B
D*F v&&=&+9&B
D6F v&&=&−0&B
D4F v&&=&−9&B
Problems
vI
D
"
!
v!
"2 V
vI
vO
vA
(a)
RL
R
vO
1 k*
"2 V
R
vI
Figure P4.83
4.84 F%)#2'#&1'#3"#(%)#53*563(#2:#L3<=#lP=^P#3+#3-)&0#/3(%
26('6(#+&(6*&(32"#0);)0+#2:##±,.#T=#F%)#-32-)+#)A%393(#&#52"?
+(&"(#S=N?T#-*2'#/%)"#52"-65(3"<=#L3"-#v−8#v68#&"-#v.#:2*Q
B&D v-#=#+,#T
B9D v-#=#+.#T
B5D v-#=#−,#T
B-D v-#=#−.#T
(b)
vI
1 k*
(c)
D1
vI
v!
vO
!2 V
R
R
vO
1 k*
!
D2
"
vA
vI
1 k*
vO
vO
!2 V
Figure P4.84
(d)
Figure P4.85
Section 4.6: Limiting and Clamping
Circuits
4.85#YH)(5%#(%)#(*&"+:)*#5%&*&5()*3+(35# v.#;)*+6+# v-#:2*#(%)
0313()*#53*563(+#+%2/"#3"#L3<=#lP=^Z=#E00#-32-)+#9)<3"#52"?
-65(3"<#&(#&#:2*/&*-#;20(&<)#-*2'#2:#S=Z#T#&"-#%&;)#;20(&<)
-*2'+#2:#S=N#T#/%)"#52"-65(3"<#&#56**)"(#!+#-#,#1E=
4.86 F%)#53*563(+#3"#L3<=#lP=^ZB&D#&"-#B-D#&*)#52"")5()-#&+
:2002/+Q#F%)#(/2#3"'6(#()*13"&0+#&*)#(3)-#(2<)(%)*8#&"-#(%)
(/2# 26('6(# ()*13"&0+# &*)# (3)-# (2<)(%)*=# YH)(5%# (%)# (*&"+:)*
5%&*&5()*3+(35#2:#(%)#53*563(#*)+60(3"<8#&++613"<#(%&(#(%)#56(?
3"#;20(&<)#2:#(%)#-32-)+#3+#S=Z#T#&"-#(%)3*#;20(&<)#-*2'#/%)"
52"-65(3"<#&#56**)"(#!+#-#,#1E#3+#S=N#T=
4.87 [)')&(# l*290)1# P=^`# :2*# (%)# (/2# 53*563(+# 3"# L3<=
lP=^ZB&D#&"-#B9D#52"")5()-#(2<)(%)*#&+#:2002/+Q#F%)#(/2#3"'6(
()*13"&0+#&*)#(3)-#(2<)(%)*8#&"-#(%)#(/2#26('6(#()*13"&0+#&*)
(3)-#(2<)(%)*=
4.88 YH)(5%#&"-#50)&*04#0&9)0#(%)#(*&"+:)*#5%&*&5()*3+(35#2:
(%)#53*563(#3"#L3<=#lP=^^#:2*#−.S#T# .# v-# .#+.S#T=#E++61)
(%&(#(%)#-32-)+#5&"#9)#*)'*)+)"()-#94#(%)#52"+(&"(?;20(&<)?
CHAPTER 4 P R O B L E M S
E0+28#:3"-#(%)#&;)*&<)#26('6(#;20(&<)#29(&3")-#/%)"# v-#3+#&
+411)(*35&0# +C6&*)# /&;)# 2:# ,?H>M# :*)C6)"548# O?T# &1'03?
(6-)8#&"-#M)*2#&;)*&<)=
227
228 Chapter 4 Diodes
CHAPTER 4 P R O B L E M S
$"#7*!'%3%?3(*;"3+'!%2M'+?,%#>%+,'%7#(+38'2%3+%#4+$4+2%V%36!
H%7'"242% v).%@#"%3%CF0%$'3MD%G--FW5%2*642#*!%3$$(*'!%3+%1D
2M'+?,%+,'%2*863(2%3+%6#!'2%V 36!%H.
D
D
A
D
D
5 k"
B
D2
D3
D1
D4
C
1 k"
Figure P4.88
!"#$% &#!'(% )*+,% !" % =% -./% 0.% 1(2#% 3224&'% +,3+% +,'% 5'6'"
7#(+38'%*2%9.:%0%36!%+,3+%#$%*2%6'8(*8*;(<%2&3((.
*4.89 =(#+% +,'% +"362>'"% ?,3"3?+'"*2+*?% #>% +,'% ?*"?4*+% *6
@*8. =A.9B% ;<% '73(43+*68% v%% ?#""'2$#6!*68% +#% v&% =% -.C% 0D
-.E 0D%-./%0D%-.9%0D%-%0D%−-.C%0D%−-.E%0D%−-./%0D%36!%−-.9 0.
1224&'%+,3+%+,'%!*#!'2%,37'%-./F0%!"#$2%3+%GF&1%?4""'6+2.
H,3"3?+'"*5'%+,'%?*"?4*+%32%3%,3"!%#"%2#>+%(*&*+'".%I,3+%*2%+,'
73(4'%#>%'J%K2+*&3+'%( +%36!%( −.
Figure P4.92
**4.93 XM'+?,%36!%(3;'(%+,'%7#(+38'%+"362>'"%?,3"3?+'"*2+*?
v&*7'"242%v%*#>%+,' ?*"?4*+%2,#)6%*6%@*8.%=A.BQ%#7'"%3%±G-F0
"368'%#>%*6$4+%2*863(2.%1((%!*#!'2%3"'%GF&1%46*+2%O*.'.D%'3?,
'U,*;*+2% 3% -./F0% !"#$% 3+% 3% ?4""'6+% #>% G% &1P.% I,3+% 3"'% +,'
2(#$'2%#>%+,'%?,3"3?+'"*2+*?%3+%+,'%'U+"'&'%±G-F0%('7'(2J%
#1 V
1 k"
vI
3 k"
D1
vO
D2
Figure P4.89
4.90 L'2*86%(*&*+'"%?*"?4*+2%42*68%#6(<%!*#!'2%36!%G-FMΩ
"'2*2+#"2%+#%$"#7*!'%36%#4+$4+%2*863(%(*&*+'!%+#%+,'%"368'N
O3P −-./%0%36!%3;#7'
O;P −:.G%0%36!%3;#7'
O?P ±G.A%0
1 k"
D3
$2 V
Figure P4.93
1224&'%+,3+%'3?,%!*#!'%,32%3%-./F0%!"#$%),'6%?#6!4?+*68.
4.91 L'2*86% 3% +)#F2*!'!% (*&*+*68% ?*"?4*+% 42*68% 3% "'2*2+#"D
+)#%!*#!'2D%36!%+)#%$#)'"%24$$(*'2%+#%>''!%3%GFMΩ%(#3!%)*+,
6#&*63(%(*&*+*68%('7'(2%#>%±Q%0.%R2'%!*#!'2%&#!'('!%;<%3
?#62+36+% -./% 0.% S6% +,'% 6#6(*&*+*68%"'8*#6D% +,'% 7#(+38'%83*6
2,#4(!%;'%3+%('32+%-.BC%0T0.
*4.92 S6%+,'%?*"?4*+%2,#)6%*6%@*8.%=A.B:D%+,'%!*#!'2%'U,*;*+
3%-./F0%!"#$%3+%-.G%&1.%@#"%*6$4+2%#7'"%+,'%"368'%#>%±C%0D
4.94 1%?(3&$'!%?3$3?*+#"%42*68%36%*!'3(%!*#!'%)*+,%?3+,#!'
8"#46!'!%*2%24$$(*'!%)*+,%3%2*6'%)37'%#>%G-F0%"&2.%I,3+%*2
+,'%37'"38'%O!?P%73(4'%#>%+,'%"'24(+*68%#4+$4+J
*4.95 @#"%+,'%?*"?4*+2%*6%@*8.%=A.BCD%'3?,%4+*(*5*68%36%*!'3(
!*#!'% O#"% !*#!'2PD% 2M'+?,% +,'% #4+$4+% >#"% +,'% *6$4+% 2,#)6.
Y3;'(% +,'% &#2+% $#2*+*7'% 36!% &#2+% 6'83+*7'% #4+$4+% ('7'(2.
1224&'%+,%!%-.
Problems 229
CHAPTER 4 P R O B L E M S
(a)
(e)
Figure P4.95
(b)
(c)
(d)
(f)
(g)
(h)
CHAPTER 5
MOS Field-Effect
Transistors (MOSFETs)
Introduction
5.1
5.6 Basic MOSFET Amplifier
Configurations 291
231
Device Structure and Physical
Operation 232
5.2 Current—Voltage Characteristics
5.3 MOSFET Circuits at DC
258
5.4 Applying the MOSFET in Amplifier
Design 268
5.5 Small-Signal Operation and
Models 276
247
5.7 Biasing in MOS Amplifier Circuits
306
5.8 Discrete-Circuit MOS Amplifiers
314
5.9 The Body Effect and Other Topics
Summary
328
Problems
329
323
IN THIS CHAPTER YOU WILL LEARN
1. The physical structure of the MOS transistor and how it works.
2. How the voltage between two terminals of the transistor controls the
current that flows through the third terminal, and the equations that describe these current–voltage characteristics.
3. How to analyze and design circuits that contain MOS transistors, resistors, and dc sources.
4. How the transistor can be used to make an amplifier, and how it can be
used as a switch in digital circuits.
5. How to obtain linear amplification from the fundamentally nonlinear
MOS transistor.
6. The three basic ways for connecting a MOSFET to construct amplifiers
with different properties.
7. Practical circuits for MOS–transistor amplifiers that can be constructed using discrete components.
Introduction
!"#$%&' ()*+$,+' )-,' .*%/)$0%' +$0+,1' 2-$/-' $(' )-,' 30()' 4"($/' )205),63$%"7' (,3$/0%+*/)06
+,#$/,1' 2,' %02' )*6%' 0*6' ")),%)$0%' )0' )-6,,5),63$%"7' (,3$/0%+*/)06' +,#$/,(8' 9-6,,5),63$%"7
+,#$/,('"6,':"6'306,'*(,:*7')-"%')205),63$%"7'0%,('4,/"*(,')-,;'/"%'4,'*(,+'$%'"'3*7)$)*+,
0:'"<<7$/")$0%(1'6"%&$%&' :603' ($&%"7'"3<7$:$/")$0%')0'+$&$)"7' 70&$/'"%+'3,306;8' 9-,'4"($/
<6$%/$<7,' $%#07#,+' $(' )-,' *(,' 0:' )-,' #07)"&,' 4,)2,,%' )20' ),63$%"7(' )0' /0%)607' )-,' /*66,%)
:702$%&'$%')-,')-$6+'),63$%"78'=%')-$('2";'"')-6,,5),63$%"7'+,#$/,'/"%'4,'*(,+')0'6,"7$>,'"
/0%)6077,+'(0*6/,1'2-$/-'"('2,'-"#,'7,"6%,+'$%'?-"<),6'@'$(')-,'4"($(':06'"3<7$:$,6'+,($&%8
A7(01'$%')-,',B)6,3,1')-,'/0%)607'($&%"7'/"%'4,'*(,+')0'/"*(,')-,'/*66,%)'$%')-,')-$6+'),63$%"7
)0'/-"%&,':603'>,60')0'"'7"6&,'#"7*,1')-*('"7702$%&')-,'+,#$/,')0'"/)'"('"'(2$)/-8'A('2,'(-"77
(,,'$%'?-"<),6'@C1')-,'(2$)/-'$(')-,'4"($(':06')-,'6,"7$>")$0%'0:')-,'70&$/'$%#,6),61')-,'4"($/
,7,3,%)'0:'+$&$)"7'/$6/*$)(8
9-,6,' "6,' )20' 3".06' );<,(' 0:' )-6,,5),63$%"7' (,3$/0%+*/)06' +,#$/,(D' )-,' 3,)"750B$+,5
(,3$/0%+*/)06' :$,7+5,::,/)' )6"%($()06' EFGHIJ9K1' 2-$/-' $(' ()*+$,+' $%' )-$(' /-"<),61' "%+' )-,
231
232 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
4$<07"6'.*%/)$0%')6"%($()06'ELM9K1'2-$/-'2,'(-"77'()*+;'$%'?-"<),6'N8'A7)-0*&-',"/-'0:')-,')20
)6"%($()06');<,('0::,6('*%$O*,':,")*6,('"%+'"6,"('0:'"<<7$/")$0%1')-,'FGHIJ9'-"('4,/03,'4;
:"6')-,'30()'2$+,7;'*(,+',7,/)60%$/'+,#$/,1',(<,/$"77;'$%')-,'+,($&%'0:'$%),&6"),+'/$6/*$)('E=?(K1
2-$/-'"6,',%)$6,'/$6/*$)(':"46$/"),+'0%'"'($%&7,'($7$/0%'/-$<8
?03<"6,+')0'LM9(1'FGHIJ9('/"%'4,'3"+,'O*$),'(3"77'E$8,81'6,O*$6$%&'"'(3"77'"6,"'0%
)-,'($7$/0%'=?'/-$<K1'"%+')-,$6'3"%*:"/)*6$%&'<60/,(('$('6,7")$#,7;'($3<7,'E(,,'A<<,%+$B'AK8
A7(01' )-,$6' 0<,6")$0%' 6,O*$6,(' /03<"6")$#,7;' 7$))7,' <02,68' I*6)-,6306,1' /$6/*$)' +,($&%,6(
-"#,':0*%+'$%&,%$0*('2";(')0'$3<7,3,%)'+$&$)"7'"%+'"%"70&':*%/)$0%('*)$7$>$%&'FGHIJ9(
"730()',B/7*($#,7;'E$8,81'2$)-'#,6;':,2'06'%0'6,($()06(K8'A77'0:')-,(,'<60<,6)$,('-"#,'3"+,'$)
<0(($47,')0 <"/P'7"6&,'%*34,6('0:'FGHIJ9('E"('3"%;'"('Q'4$77$0%RK'0%'"'($%&7,'=?'/-$<')0
$3<7,3,%)' #,6;' (0<-$()$/"),+1' #,6;57"6&,5(/"7,5$%),&6"),+' ESTH=K' +$&$)"7' /$6/*$)(' (*/-' "(
)-0(,':06'3,306;'"%+'3$/60<60/,((06(8'A%"70&'/$6/*$)('(*/-'"('"3<7$:$,6('"%+':$7),6('/"%
"7(0'4,'$3<7,3,%),+'$%'FGH'),/-%070&;1'"74,$)'$%'(3"77,61'7,((5+,%(,'/-$<(8'A7(01'40)-'"%"5
70&'"%+'+$&$)"7':*%/)$0%('"6,'$%/6,"($%&7;'4,$%&'$3<7,3,%),+'0%')-,'("3,'=?'/-$<1'$%'2-")'$(
P%02%'"('3$B,+5($&%"7'+,($&%8
9-,'04.,/)$#,'0:')-$('/-"<),6'$(')0'+,#,70<'$%')-,'6,"+,6'"'-$&-'+,&6,,'0:':"3$7$"6$);'2$))-,'FGHIJ9D' $)(' <-;($/"7' ()6*/)*6,'"%+'0<,6")$0%1' ),63$%"7' /-"6"/),6$()$/(1' /$6/*$)' 30+,7(1
"%+'4"($/'/$6/*$)'"<<7$/")$0%(8'A7)-0*&-'+$(/6,),'FGH')6"%($()06(',B$()1'"%+')-,'3"),6$"7'()*+5
$,+'$%')-$('/-"<),6'2$77',%"47,')-,'6,"+,6')0'+,($&%'+$(/6,),'FGH'/$6/*$)(1'0*6'()*+;'0:')-,
FGHIJ9'$('()60%&7;'$%:7*,%/,+'4;')-,':"/)')-")'30()'0:'$)('"<<7$/")$0%('"6,'$%'$%),&6"),+5/$65
/*$)'+,($&%8'9-,'+,($&%'0:'=?'"%"70&'"%+'+$&$)"7'FGH'/$6/*$)('0//*<$,('"'7"6&,'<60<06)$0%'0:
)-,'6,3"$%+,6'0:')-$('400P8
5.1 Device Structure and Physical Operation
9-,',%-"%/,3,%)5);<,'FGHIJ9'$(')-,'30()'2$+,7;'*(,+':$,7+5,::,/)')6"%($()068'JB/,<)':06
)-,'7"()'(,/)$0%1')-$('/-"<),6'$('+,#0),+')0')-,'()*+;'0:')-,',%-"%/,3,%)5);<,'FGHIJ98'U,
4,&$%'$%')-$('(,/)$0%'4;'7,"6%$%&'"40*)'$)('()6*/)*6,'"%+'<-;($/"7'0<,6")$0%8'9-$('2$77'7,"+')0
)-,'/*66,%)V#07)"&,'/-"6"/),6$()$/('0:')-,'+,#$/,1'()*+$,+'$%')-,'%,B)'(,/)$0%8
5.1.1 Device Structure
I$&*6,'W8@1'(-02(')-,'<-;($/"7'()6*/)*6,'0:')-,'!5/-"%%,7',%-"%/,3,%)5);<,'FGHIJ98'9-,
3,"%$%&'0:')-,'%"3,('X,%-"%/,3,%)Y'"%+'X!5/-"%%,7Y'2$77'4,/03,'"<<"6,%)'(-06)7;8'9-,
)6"%($()06'$(':"46$/"),+'0%'"'"5);<,'(*4()6"),1'2-$/-'$('"'($%&7,5/6;()"7'($7$/0%'2":,6')-")'<605
#$+,('<-;($/"7'(*<<06)':06')-,'+,#$/,'E"%+':06')-,',%)$6,'/$6/*$)'$%')-,'/"(,'0:'"%'$%),&6"),+
/$6/*$)K8'920'-,"#$7;'+0<,+'!5);<,'6,&$0%(1'$%+$/"),+'$%')-,':$&*6,'"(')-,'!+'!"#$%&@'"%+')-,
!+''$()*'6,&$0%(1'"6,'/6,"),+'$%')-,'(*4()6"),8'A')-$%'7";,6'0:'($7$/0%'+$0B$+,'EH$GQK'0:')-$/P5
%,(('#$%'E);<$/"77;'@')0'@Z'%3K1Q'2-$/-'$('"%',B/,77,%)',7,/)6$/"7'$%(*7")061'$('&602%'0%')-,'(*65
:"/,' 0:' )-,' (*4()6"),1' /0#,6$%&' )-,' "6,"' 4,)2,,%' )-,' (0*6/,' "%+' +6"$%' 6,&$0%(8' F,)"7' $(
+,<0($),+'0%')0<'0:')-,'0B$+,'7";,6')0':063')-,+,(-&+&.&%-$"'&'0:')-,'+,#$/,8'F,)"7'/0%)"/)(
"6,'"7(0'3"+,')0')-,'(0*6/,'6,&$0%1')-,'+6"$%'6,&$0%1'"%+')-,'(*4()6"),1'"7(0'P%02%'"(')-,
9-,'%0)")$0%'!+'$%+$/"),('-,"#$7;'+0<,+'!5);<,'($7$/0%8'?0%#,6(,7;1'!−'$('*(,+')0'+,%0),'7$&-)7;'+0<,+
!5);<,'($7$/0%8'H$3$7"6'%0)")$0%'"<<7$,(':06'"5);<,'($7$/0%8
Q
A'%"%03,),6'E%3K'$('@Z−['3'06'Z8ZZ@'µ38'A'3$/603,),6'Eµ3K1'06'3$/60%1'$('@Z−N'38'H03,)$3,(')-,
0B$+,')-$/P%,(('$(',B<6,((,+'$%'"%&()603(8'A%'"%&()603'E\K'$('@Z−@'%31'06'@Z−@Z'38
@
5.1 Device Structure and Physical Operation
S
Metal
G
W
D
Oxide (SiO2 )
Source
region
n!
L
p-type substrate
(Body)
n!
Channel
region
B
Drain region
(a)
Source (S)
Gate (G)
Oxide (SiO2)
(thickness " tox)
n!
Drain (D)
Metal
Channel
region
n!
L
p-type substrate
(Body)
Body
(B)
(b)
Figure 5.1 _-;($/"7'()6*/)*6,'0:')-,',%-"%/,3,%)5);<,'`FGH')6"%($()06D'1(2'<,6(<,/)$#,'#$,2a'1/2'/60(('(,/5
)$0%8'9;<$/"77;'&'= Z8ZC'µ3')0'@'µ31'''='Z8@'µ3')0'@ZZ'µ31'"%+')-,')-$/P%,(('0:')-,'0B$+,'7";,6'E#$%K'$('$%')-,
6"%&,'0:''@')0'@Z'%38
/"'08C'9-*(':0*6'),63$%"7('"6,'460*&-)'0*)D')-,'&"),'),63$%"7'E]K1')-,'(0*6/,'),63$%"7'EHK1
)-,'+6"$%'),63$%"7'E^K1'"%+')-,'(*4()6"),'06'40+;'),63$%"7'ELK8
A)')-$('<0$%)'$)'(-0*7+'4,'/7,"6')-")')-,' %"3,'0:')-,'+,#$/,'E3,)"750B$+,5(,3$/0%+*/)06
IJ9K'$('+,6$#,+':603'$)('<-;($/"7'()6*/)*6,8'9-,'%"3,1'-02,#,61'-"('4,/03,'"'&,%,6"7'0%,'"%+
C
=%'I$&8'W8@1')-,'/0%)"/)')0')-,'40+;'$('(-02%'0%')-,'40))03'0:')-,'+,#$/,8'9-$('2$77'<60#,'-,7<:*7'$%
H,/)$0%'W8['$%',B<7"$%$%&'"'<-,%03,%0%'P%02%'"(')-,'X40+;',::,/)8Y'=)'$('$3<06)"%)')0'%0),1'-02,#,61
)-")'$%'"/)*"7'=?(1'/0%)"/)')0')-,'40+;'$('3"+,'")'"'70/")$0%'0%')-,')0<'0:')-,'+,#$/,8
233
234 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
$('*(,+'"7(0':06'IJ9(')-")'+0'%0)'*(,'3,)"7':06')-,'&"),',7,/)60+,8'=%':"/)1'30()'30+,6%'FGH5
IJ9('"6,':"46$/"),+'*($%&'"'<60/,(('P%02%'"('($7$/0%5&"),'),/-%070&;1'$%'2-$/-'"'/,6)"$%');<,'0:
($7$/0%1'/"77,+'<07;($7$/0%1'$('*(,+')0':063')-,'&"),',7,/)60+,'E(,,'A<<,%+$B'AK8'G*6'+,(/6$<)$0%
0:'FGHIJ9'0<,6")$0%'"%+'/-"6"/),6$()$/('"<<7$,('$66,(<,/)$#,'0:')-,');<,'0:'&"),',7,/)60+,8
A%0)-,6'%"3,':06')-,'FGHIJ9'$(')-,')*!#.(-&'3,(-&+456'06'784568'9-$('%"3,'"7(0
"6$(,(':603')-,'<-;($/"7'()6*/)*6,'0:')-,'+,#$/,1',3<-"($>$%&')-,':"/)')-")')-,'&"),',7,/)60+,'$(
,7,/)6$/"77;' $%(*7"),+' :603' )-,' +,#$/,' 40+;' E4;' )-,' 0B$+,' 7";,6K8' =)' $(' )-$(' $%(*7")$0%' )-")
/"*(,(')-,'/*66,%)'$%')-,'&"),'),63$%"7')0'4,',B)6,3,7;'(3"77'E0:')-,'06+,6'0:'@Z−@W'AK8
G4(,6#,')-")')-,'(*4()6"),':063('"!'.*%/)$0%('2$)-')-,'(0*6/,'"%+'+6"$%'6,&$0%(8'=%'%063"7
0<,6")$0%')-,(,'"!'.*%/)$0%('"6,'P,<)'6,#,6(,54$"(,+'")'"77')$3,(8'H$%/,1'"('2,'(-"77'(,,'(-06)7;1
)-,'+6"$%'2$77'"72";('4,'") "'<0($)$#,'#07)"&,'6,7")$#,')0')-,'(0*6/,1')-,')20'"!'.*%/)$0%('/"%'4,
,::,/)$#,7;'/*)'0::'4;'($3<7;'/0%%,/)$%&')-,'(*4()6"),'),63$%"7')0')-,'(0*6/,'),63$%"78'U,'(-"77
"((*3,')-$(')0'4, )-,'/"(,'$%')-,':07702$%&'+,(/6$<)$0%'0:'FGHIJ9'0<,6")$0%8'9-*(1'-,6,1')-,
(*4()6"),'2$77'4,'/0%($+,6,+'"('-"#$%&'%0',::,/)'0%'+,#$/,'0<,6")$0%1'"%+')-,'FGHIJ9'2$77'4,
)6,"),+'"('"')-6,,5),63$%"7'+,#$/,1'2$)-')-,'),63$%"7('4,$%&')-,'&"),'E]K1')-,'(0*6/,'EHK1'"%+')-,
+6"$%'E^K8'=)'2$77'4,'(-02%')-")'"'#07)"&,'"<<7$,+')0')-,'&"),'/0%)607('/*66,%)':702'4,)2,,%
(0*6/,'"%+'+6"$%8'9-$('/*66,%)'2$77':702'$%')-,'70%&$)*+$%"7'+$6,/)$0%':603'+6"$%')0'(0*6/,'$%')-,
6,&$0%' 7"4,7,+' X/-"%%,7' 6,&$0%8Y' `0),' )-")' )-$(' 6,&$0%' -"(' "' 7,%&)-' &' "%+' "' 2$+)-' '1' )20
$3<06)"%)'<"6"3,),6('0:')-,'FGHIJ98'9;<$/"77;1'&'$('$%')-,'6"%&,'0:'Z8ZC'µ3')0'@'µ31'"%+''
$('$%')-,'6"%&,'0:'Z8@'µ3')0'@ZZ'µ38'I$%"77;1'%0),')-")')-,'FGHIJ9'$('"'(;33,)6$/"7'+,#$/,a
)-*('$)('(0*6/,'"%+'+6"$%'/"%'4,'$%),6/-"%&,+'2$)-'%0'/-"%&,'$%'+,#$/,'/-"6"/),6$()$/(8
5.1.2 Operation with Zero Gate Voltage
U$)-'>,60'#07)"&,'"<<7$,+')0')-,'&"),1')20'4"/P5)054"/P'+$0+,(',B$()'$%'(,6$,('4,)2,,%'+6"$%
"%+'(0*6/,8'G%,'+$0+,'$(':063,+'4;')-,'"!'.*%/)$0%'4,)2,,%')-,'!+'+6"$%'6,&$0%'"%+')-,'"5
);<,'(*4()6"),1'"%+')-,'0)-,6'+$0+,'$(':063,+'4;')-,'"!'.*%/)$0%'4,)2,,%')-,'"5);<,'(*4()6"),
"%+')-,'!+'(0*6/,'6,&$0%8'9-,(,'4"/P5)054"/P'+$0+,('<6,#,%)'/*66,%)'/0%+*/)$0%':603'+6"$%
)0'(0*6/,'2-,%'"'#07)"&,'v()'$('"<<7$,+8'=%':"/)1')-,'<")-'4,)2,,%'+6"$%'"%+'(0*6/,'-"('"'#,6;
-$&-'6,($()"%/,'E0:')-,'06+,6'0:'@Z@Q'ΩK8
5.1.3 Creating a Channel for Current Flow
?0%($+,6'%,B)')-,'($)*")$0%'+,<$/),+'$%'I$&8'W8Q8'!,6,'2,'-"#,'&60*%+,+')-,'(0*6/,'"%+')-,
+6"$%'"%+'"<<7$,+'"'<0($)$#,'#07)"&,')0')-,'&"),8'H$%/,')-,'(0*6/,'$('&60*%+,+1')-,'&"),'#07)"&,
"<<,"6('$%',::,/)'4,)2,,%'&"),'"%+'(0*6/,'"%+')-*('$('+,%0),+'v*)8'9-,'<0($)$#,'#07)"&,'0%')-,
&"),'/"*(,(1'$%')-,':$6()'$%()"%/,1')-,':6,,'-07,('E2-$/-'"6,'<0($)$#,7;'/-"6&,+K')0'4,'6,<,77,+
:603')-,'6,&$0%'0:')-,'(*4()6"),'*%+,6')-,'&"),'E)-,'/-"%%,7'6,&$0%K8'9-,(,'-07,('"6,'<*(-,+
+02%2"6+'$%)0')-,'(*4()6"),1'7,"#$%&'4,-$%+'"'/"66$,65+,<7,)$0%'6,&$0%8'9-,'+,<7,)$0%'6,&$0%'$(
<0<*7"),+'4;')-,'40*%+'%,&")$#,'/-"6&,'"((0/$"),+'2$)-')-,'"//,<)06'")03(8'9-,(,'/-"6&,('"6,
X*%/0#,6,+Y'4,/"*(,')-,'%,*)6"7$>$%&'-07,('-"#,'4,,%'<*(-,+'+02%2"6+'$%)0')-,'(*4()6"),8
A('2,771')-,'<0($)$#,'&"),'#07)"&,'"))6"/)(',7,/)60%(':603')-,'!+'(0*6/,'"%+'+6"$%'6,&$0%(
E2-,6,')-,;'"6,'$%'"4*%+"%/,K'$%)0')-,'/-"%%,7'6,&$0%8'U-,%'"'(*::$/$,%)'%*34,6'0:',7,/)60%(
"//*3*7"),'%,"6')-,'(*6:"/,'0:')-,'(*4()6"),'*%+,6')-,'&"),1'"%'!'6,&$0%'$('$%',::,/)'/6,"),+1
/0%%,/)$%&')-,'(0*6/,'"%+'+6"$%'6,&$0%(1'"('$%+$/"),+'$%'I$&8'W8Q8'`02'$:'"'#07)"&,'$('"<<7$,+
4,)2,,%'+6"$%'"%+'(0*6/,1'/*66,%)':702(')-60*&-')-$('$%+*/,+'!'6,&$0%1'/"66$,+'4;')-,'304$7,
,7,/)60%(8'9-,'+!,-./,0!'6,&$0%')-*(':063('"'%9(**&.':06'/*66,%)':702':603'+6"$%')0'(0*6/,
"%+'+102"#340.233/,01$8'?066,(<0%+$%&7;1')-,'FGHIJ9'0:'I$&8'W8Q'$('/"77,+'"%'!3%9(**&.
:;<456' 061' "7),6%")$#,7;1' "%' =:;<+ -$(*!)!-"$8' `0),' )-")' "%' !5/-"%%,7' FGHIJ9' $(
5.1 Device Structure and Physical Operation
Gate electrode
!
vGS
#
G
S
Oxide (SiO2 )
n!
Induced
n-type
channel
D
n!
L
p-type substrate
Depletion region
B
Figure 5.2 9-,' ,%-"%/,3,%)5);<,' `FGH' )6"%($()06' 2$)-' "' <0($)$#,' #07)"&,' "<<7$,+' )0' )-,' &"),8' A%
! /-"%%,7'$('$%+*/,+'")')-,')0<'0:')-,'(*4()6"),'4,%,")-')-,'&"),8
:063,+'$%'"'"5);<,'(*4()6"),D'9-,'/-"%%,7'$('/6,"),+'4;'+!5/6#+!7')-,'(*4()6"),'(*6:"/,':603'"
);<,')0'!');<,8'!,%/,')-,'$%+*/,+'/-"%%,7'$('"7(0'/"77,+'"%')*>&$!)"*+.(0&$8
9-,'#"7*,'0:' v *) '")'2-$/-'"'(*::$/$,%)'%*34,6'0:'304$7,',7,/)60%('"//*3*7"),'$%')-,
/-"%%,7'6,&$0%')0':063'"'/0%+*/)$%&'/-"%%,7'$('/"77,+')-,'-9$&!9".'+>".-(,&'"%+'$('+,%0),+
8# 8b' G4#$0*(7;1' 8#' :06' "%' !5/-"%%,7' IJ9' $(' <0($)$#,8' 9-,' #"7*,' 0:' 8#' $(' /0%)6077,+' +*6$%&
+,#$/,':"46$/")$0%'"%+');<$/"77;'7$,('$%')-,'6"%&,'0:'Z8C'S')0'@8Z'S8
9-,'&"),'"%+')-,'/-"%%,7'6,&$0%'0:')-,'FGHIJ9':063'"'<"6"77,75<7"),'/"<"/$)061'2$))-,'0B$+,'7";,6'"/)$%&'"(')-,'/"<"/$)06'+$,7,/)6$/8'9-,'<0($)$#,'&"),'#07)"&,'/"*(,('<0($)$#,
/-"6&,')0'"//*3*7"),'0%')-,')0<'<7"),'0:')-,'/"<"/$)06'E)-,'&"),',7,/)60+,K8'9-,'/066,(<0%+5
$%&'%,&")$#,'/-"6&,'0%')-,'40))03'<7"),'$(':063,+'4;')-,',7,/)60%('$%')-,'$%+*/,+'/-"%%,78
A%' ,7,/)6$/' :$,7+' )-*(' +,#,70<(' $%' )-,' #,6)$/"7' +$6,/)$0%8' =)' $(' )-$(' :$,7+' )-")' /0%)607(' )-,
"30*%)' 0:' /-"6&,' $%' )-,' /-"%%,71' "%+' )-*(' $)' +,),63$%,(' )-,' /-"%%,7' /0%+*/)$#$);' "%+1' $%
)*6%1')-,'/*66,%)')-")'2$77':702')-60*&-')-,'/-"%%,7'2-,%'"'#07)"&,'v()'$('"<<7$,+8'9-$('$('')-,
06$&$%'0:')-,'%"3,'X:$,7+5,::,/)')6"%($()06Y'EIJ9K8
9-,'#07)"&,'"/60((')-$('<"6"77,75<7"),'/"<"/$)061')-")'$(1')-,'#07)"&,'"/60((')-,'0B$+,1'3*()
,B/,,+' 8 #' :06' "' /-"%%,7' )0' :0638' U-,%' v () & Z1'"(' $%' I$&8' W8Q1' )-,' #07)"&,' ")' ,#,6;' <0$%)
"70%&' )-,' /-"%%,7' $(' >,601' "%+' )-,' #07)"&,' "/60((' )-,' 0B$+,' E$8,81' 4,)2,,%' )-,' &"),' "%+' )-,
<0$%)('"70%&')-,'/-"%%,7K'$('*%$:063'"%+',O*"7')0' v *) 8'9-,',B/,(('0:' v *) '0#,6'8 #'$('),63,+')-,
&??&%-)>&+>".-(,&'06')-,'">&$'$)>&+>".-(,&'"%+'$(')-,'O*"%)$);')-")'+,),63$%,(')-,'/-"6&,'$%
)-,'/-"%%,78'=%')-$('400P1'2,'(-"77'+,%0),' ( v *) ' 8 # ) '4;' v :8 1
v *) ' 8 # ≡ v :8
!"#$%
U,'/"%',B<6,((')-,'3"&%$)*+,'0:')-,',7,/)60%'/-"6&,'$%')-,'/-"%%,7'4;'
; & < $% ( '& ) v :8
EW8QK
b
H03,'),B)('*(,'89')0'+,%0),')-,')-6,(-07+'#07)"&,8'U,'*(,'8#')0'"#0$+'/0%:*($0%'2$)-')-,')-,63"7
#07)"&,'89 8
235
236 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
2-,6,' < $% 1'/"77,+')-,'"@)'&+%(A(%)-(*%&1'$(')-,'/"<"/$)"%/,'0:')-,'<"6"77,75<7"),'/"<"/$)06
<,6'*%$)'&"),'"6,"'E$%'*%$)('0:'Ic3QK1'''$(')-,'2$+)-'0:')-,'/-"%%,71'"%+'&'$(')-,'7,%&)-'0:')-,
/-"%%,78'9-,'0B$+,'/"<"/$)"%/,'< $%'$('&$#,%'4;
ε $%
< $% & 5555555
5
# $%
EW8CK
2-,6,' ε $% '$(')-,'<,63$))$#$);'0:')-,'($7$/0%'+$0B$+,1
ε $% & C8[ε Z & C8[ × d8dWb × @Z
' @Q
& C8bW × @Z
' @@
'Ic3
9-,'0B$+,')-$/P%,((' # $%'$('+,),63$%,+'4;')-,'<60/,(('),/-%070&;'*(,+')0':"46$/"),')-,'FGH5
IJ98'A('"%',B"3<7,1':06'"'<60/,(('2$)-' # $% & b '%31
' @@
'C
C8bW × @Z
< $% & 5555555555555555555555555555
5 & d8N × @Z 'Ic3Q
'[
b × @Z
=)'$('3*/-'306,'/0%#,%$,%)')0',B<6,((' < $%'<,6'3$/60%'(O*"6,+8'I06'0*6',B"3<7,1')-$(';$,7+(
' @W
d8N':Icµ3Q1'2-,6,':I'+,%0),(':,3)0:"6"+'E@Z IK8'I06'"'FGHIJ9':"46$/"),+'$%')-$('),/-5
%070&;'2$)-'"'/-"%%,7'7,%&)-'&'e'Z8@d'µ3'"%+'"'/-"%%,7'2$+)-'''e'Z8fQ'µ31')-,')0)"7'/"<"/5
$)"%/,'4,)2,,%'&"),'"%+'/-"%%,7'$('
< & < $% '& & d8N × Z8@d × Z8fQ & @8@':I
I$%"77;1'%0),':603'JO8'EW8QK')-")'"(' v :8 '$('$%/6,"(,+1')-,'3"&%$)*+,'0:')-,'/-"%%,7'/-"6&,
$%/6,"(,('<60<06)$0%"),7;8'H03,)$3,(')-$('$('+,<$/),+'"('"%'$%/6,"(,'$%')-,'+,<)-'0:')-,'/-"%5
%,7a')-")'$(1')-,'7"6&,6')-,'0#,6+6$#,'#07)"&,1')-,'+,,<,6')-,'/-"%%,78
5.1.4 Applying a Small vDS
!"#$%&'$%+*/,+'"'/-"%%,71'2,'%02'"<<7;'"'<0($)$#,'#07)"&,'v()'4,)2,,%'+6"$%'"%+'(0*6/,1'"(
(-02%'$%'I$&8'W8C8'U,':$6()'/0%($+,6')-,'/"(,'2-,6,'v()'$('(3"77'E$8,81'WZ'3S'06'(0K8'9-,'#07)"&,
v()'/"*(,('"'/*66,%)'+(')0':702')-60*&-')-,'$%+*/,+'!'/-"%%,78'?*66,%)'$('/"66$,+'4;':6,,',7,/5
)60%(')6"#,7$%&':603'(0*6/,')0'+6"$%'E-,%/,')-,'%"3,('(0*6/,'"%+'+6"$%K8'L;'/0%#,%)$0%1')-,
+$6,/)$0%'0:'/*66,%)':702'$('0<<0($),')0')-")'0:')-,':702'0:'%,&")$#,'/-"6&,8'9-*(')-,'/*66,%)
$%')-,'/-"%%,71'+( 1'2$77'4,':603'+6"$%')0'(0*6/,1'"('$%+$/"),+'$%'I$&8'W8C8'
U,'%02'2$(-')0'/"7/*7"),')-,'#"7*,'0:'+ (8'902"6+')-")',%+1'2,':$6()'%0),')-")'4,/"*(,'v ()'$(
(3"771'2,'/"%'/0%)$%*,')0'"((*3,')-")')-,'#07)"&,'4,)2,,%')-,'&"),'"%+'#"6$0*('<0$%)('"70%&')-,
/-"%%,7'6,3"$%('"<<60B$3"),7;'/0%()"%)'"%+',O*"7')0')-,'#"7*,'")')-,'(0*6/,',%+1' v *)8'9-*(1')-,
,::,/)$#,'#07)"&,'4,)2,,%')-,'&"),'"%+')-,'#"6$0*('<0$%)('"70%&')-,'/-"%%,7'6,3"$%(',O*"7')0
v :8 1'"%+')-,'/-"%%,7'/-"6&,';'$('()$77'&$#,%'4;'JO8'EW8QK8'G:'<"6)$/*7"6'$%),6,()'$%'/"7/*7")$%&')-,
/*66,%)'+ ('$(')-,'/-"6&,'<,6'*%$)'/-"%%,7'7,%&)-1'2-$/-'/"%'4,':0*%+':603'JO8'EW8QK'"('
;
' 5555555555555555555555555555555555555555555555555555 & < $% ' v :8
*%$)'/-"%%,7'7,%&)-
EW8bK
9-,'#07)"&,' v ()',()"47$(-,('"%',7,/)6$/':$,7+'='"/60((')-,'7,%&)-'0:')-,'/-"%%,71
v
()
= & 5555555
5
&
EW8WK
9-$(',7,/)6$/':$,7+'$%')*6%'/"*(,(')-,'/-"%%,7',7,/)60%(')0'+6$:)')02"6+')-,'+6"$%'2$)-'"'#,70/5
$);'&$#,%'4;'
v
()
5
J7,/)60%'+6$:)'#,70/$);'e'µ!' = 'e'µ!' 5555555
&
EW8NK
5.1 Device Structure and Physical Operation
n+
iD
n+
Figure 5.3 A%'`FGH')6"%($()06'2$)-'v*)'>'8#'"%+'2$)-'"'(3"77'v()'"<<7$,+8'9-,'+,#$/,'"/)('"('"'6,($()"%/,
2-0(,'#"7*,'$('+,),63$%,+'4;'v*)8'H<,/$:$/"77;1')-,'/-"%%,7'/0%+*/)"%/,'$('<60<06)$0%"7')0'v*)'−'8#1'"%+')-*('+(
$('<60<06)$0%"7')0'Ev*)'−'8#Kv()8'`0),')-")')-,'+,<7,)$0%'6,&$0%'$('%0)'(-02%'E:06'($3<7$/$);K8
2-,6,' µ!'$(')-,'304$7$);'0:')-,',7,/)60%('")')-,'(*6:"/,'0:')-,'/-"%%,78'=)'$('"'<-;($/"7'<"6"3,),6
2-0(,'#"7*,'+,<,%+('0%')-,':"46$/")$0%'<60/,(('),/-%070&;8'9-,'#"7*,'0:'+ ('/"%'%02'4,':0*%+'4;
3*7)$<7;$%&')-,'/-"6&,'<,6'*%$)'/-"%%,7'7,%&)-'EJO8'W8bK'4;')-,',7,/)60%'+6$:)'#,70/$);'EJO8'W8NK1'
'
+ ( & ( µ ! < $% ) 55555 v :8 v ()
&
EW8fK
9-*(1':06'(3"77' v () 1')-,'/-"%%,7'4,-"#,('"('"'7$%,"6'6,($()"%/,'2-0(,'#"7*,'$('/0%)6077,+'4;
)-,'0#,6+6$#,'#07)"&,' v :8 1'2-$/-'$%')*6%'$('+,),63$%,+'4;' v *) D
'
+ ( & ( µ ! < $% ) 55555 ( v *) ' 8 # ) v ()
&
EW8dK
9-,'/0%+*/)"%/,' 7 () '0:')-,'/-"%%,7'/"%'4,':0*%+':603'JO8'EW8fK'06'EW8dK'"(
'
7 () & ( µ ! < $% ) 55555 v :8
&
EW8[K
'
7 () & ( µ ! < $% ) 55555 ( v *) ' 8 # )
&
EW8@ZK
06
G4(,6#,')-")')-,'/0%+*/)"%/,'$('+,),63$%,+'4;')-,'<60+*/)'0:')-6,,':"/)06(D' ( µ ! < $% )1'E'c&K1
"%+' v :8 'E06',O*$#"7,%)7;1' v *) ' 8 # K8'90'&"$%'$%($&-)'$%)0'FGHIJ9'0<,6")$0%1'2,'/0%($+,6
,"/-'0:')-,')-6,,':"/)06('$%')*6%8
9-,':$6()':"/)061' ( µ ! < $% )1'$('+,),63$%,+'4;')-,'<60/,(('),/-%070&;'*(,+')0':"46$/"),')-,
FGHIJ98' =)' $(' )-,' <60+*/)' 0:' )-,' ,7,/)60%' 304$7$);1' µ! 1'"%+')-,' 0B$+,' /"<"/$)"%/,1' < $%8' =)
3"P,('<-;($/"7'(,%(,':06')-,'/-"%%,7'/0%+*/)"%/,')0'4,'<60<06)$0%"7')0',"/-'0:' µ!' "%+' < $%
237
238 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
E2-;gK' "%+' -,%/,' )0' )-,$6' <60+*/)1' 2-$/-' $(' ),63,+' )-,' A$"%&!!+ -$(*!%"*'#%-(*%&
A($(B&-&$W'"%+'&$#,%')-,'(;3407' > !′ '2-,6,')-,'(*4(/6$<)'!'+,%0),('!'/-"%%,71'
> !′ & µ ! < $%
EW8@@K
=)'/"%'4,'(-02%')-")'2$)-'µ!'-"#$%&')-,'+$3,%($0%('0:'3,),6('(O*"6,+'<,6'#07)5(,/0%+'E3QcSh(K
"%+' < $%'-"#$%&')-,'+$3,%($0%('0:':"6"+('<,6'3,),6'(O*"6,+'EIc3QK1')-,'+$3,%($0%('0:' > !′ '"6,
"3<,6,('<,6'#07)'(O*"6,+'EAcSQK8'
9-,'(,/0%+':"/)06'$%')-,',B<6,(($0%':06')-,'/0%+*/)"%/,' 7 () '$%'JO(8'EW8[K'"%+'EW8@ZK'$(
)-,')6"%($()06'(!A&%-+$(-)"'E'c&K8'9-")')-,'/-"%%,7'/0%+*/)"%/,'$('<60<06)$0%"7')0')-,'/-"%%,7
2$+)-' '' "%+' $%#,6(,7;' <60<06)$0%"7' )0' )-,' /-"%%,7' 7,%&)-' &' (-0*7+' 3"P,' <,6:,/)' <-;($/"7
(,%(,8'9-,'E'c&K'6")$0'$('04#$0*(7;'"'+$3,%($0%7,(('O*"%)$);')-")'$('+,),63$%,+'4;')-,'+,#$/,
+,($&%,68'=%+,,+1')-,'#"7*,('0:'''"%+'&0/"%'4,'(,7,/),+'4;')-,'+,#$/,'+,($&%,6')0'&$#,')-,
+,#$/,' )-,' +' v' /-"6"/),6$()$/(' +,($6,+8' I06' "' &$#,%' :"46$/")$0%' <60/,((1' -02,#,61' )-,6,' $(' "
3$%$3*3'/-"%%,7'7,%&)-1'&3$%8'=%':"/)1')-,'3$%$3*3'/-"%%,7'7,%&)-')-")'$('<0(($47,'2$)-'"
&$#,%':"46$/")$0%'<60/,(('$('*(,+')0'/-"6"/),6$>,')-,'<60/,(('"%+'$('4,$%&'/0%)$%*"77;'6,+*/,+
"('),/-%070&;'"+#"%/,(8'I06'$%()"%/,1'$%'QZZ[')-,'()"),50:5)-,5"6)'$%'/033,6/$"77;'"#"$7"47,
FGH'),/-%070&;'2"('"'bW5%3'<60/,((1'3,"%$%&')-")':06')-$('<60/,((')-,'3$%$3*3'/-"%%,7
7,%&)-'<0(($47,'2"('bW'%38'I$%"77;1'2,'(-0*7+'%0),')-")')-,'0B$+,')-$/P%,((' # $% '(/"7,('+02%
2$)-'&3$%8'9-*(1':06'"'Z8@C5µ3'),/-%070&;1' # $% '$('Q8f'%31'4*)':06')-,'30+,6%'bW5%3'),/-%075
0&;' # $%'$('"40*)'@8b'%38'
9-,'<60+*/)'0:')-,'<60/,((')6"%(/0%+*/)"%/,'<"6"3,),6' > ′! '"%+')-,')6"%($()06'"(<,/)'6")$0
E'c&K'$(')-,':;<456+-$(*!%"*'#%-(*%&+A($(B&-&$' > !1
> ! & > ′!'E'c&K
EW8@Q"K
> ! & ( µ ! < $% ) 'E'c&K''
EW8@Q4K
06
9-,'FGHIJ9'<"6"3,),6' > ! '-"(')-,'+$3,%($0%('0:'AcSQ8
9-,')-$6+'),63'$%')-,',B<6,(($0%'0:')-,'/-"%%,7'/0%+*/)"%/,' 7 () '$(')-,'0#,6+6$#,'#07)"&,
v :8 8'9-$('$('-"6+7;'(*6<6$($%&'($%/,' v :8 '+$6,/)7;'+,),63$%,(')-,'3"&%$)*+,'0:',7,/)60%'/-"6&,
$%' )-,' /-"%%,78' A(' 2$77' 4,' (,,%1' v :8 ' $(' "' #,6;' $3<06)"%)' /$6/*$)5+,($&%' <"6"3,),68' =%' )-$(
400P1'2,'2$77'*(,' v :8 '"%+' v *) ' 8 # '$%),6/-"%&,"47;8
U,'/0%/7*+,')-$('(*4(,/)$0%'4;'%0)$%&')-")'2$)-' v ()'P,<)'(3"771')-,'FGHIJ9'4,-"#,('"(
"'7$%,"6'6,($()"%/,'6 ()'2-0(,'#"7*,'$('/0%)6077,+'4;')-,'&"),'#07)"&,' v *) 1
@5
6 () & 5555555
7 ()
@
6 () & 555555555555555555555555555555555555555555555
( µ ! < $% ) ( ' ⁄ & ) v :8
EW8@C"K
@
6 () & 555555555555555555555555555555555555555555555555555555555555
5
( µ ! < $% ) ( ' ⁄ & ) ( v *) ' 8 # )
EW8@C4K
9-,'0<,6")$0%'0:')-,'FGHIJ9'"('"'#07)"&,5/0%)6077,+'6,($()"%/,'$(':*6)-,6'$77*()6"),+'$%
I$&8' W8b1' 2-$/-' $(' "' (P,)/-' 0:' + ( ' #,6(*(' v ()' :06' #"6$0*(' #"7*,(' 0:' v *)8' G4(,6#,' )-")' )-,
9-$('%"3,'"6$(,(':603')-,':"/)')-")'( µ ! < $% )'+,),63$%,(')-,')6"%(/0%+*/)"%/,'0:')-,'FGHIJ91'"('2$77
4,'(,,%'(-06)7;8
W
5.1 Device Structure and Physical Operation
iD
Slope ! gDS = kn VOV
vGS " Vt + VOV3
vGS " Vt + VOV2
vGS
vGS " Vt + VOV1
vGS $ Vt
0
vDS
Figure 5.4 9-,'+(Vv()'/-"6"/),6$()$/('0:')-,'FGHIJ9'$%'I$&8'W8C'2-,%')-,'#07)"&,'"<<7$,+'4,)2,,%'+6"$%
"%+'(0*6/,1'v() 1'$('P,<)'(3"778'9-,'+,#$/,'0<,6"),('"('"'7$%,"6'6,($()"%/,'2-0(,'#"7*,'$('/0%)6077,+'4;'v*)8
6,($()"%/,'$('$%:$%$),':06' v *) ≤ 8 # '"%+'+,/6,"(,('"(' v *)'$('$%/6,"(,+'"40#,'8 # 8'=)'$('$%),6,()5
$%&')0'%0),')-")'"7)-0*&-' v *)'$('*(,+'"(')-,'<"6"3,),6':06')-,'(,)'0:'&6"<-('$%'I$&8'W8b1')-,
&6"<-('$%':"/)'+,<,%+'0%7;'0%' v :8 'E"%+1'0:'/0*6(,1' > !K8
9-,'+,(/6$<)$0%'"40#,'$%+$/"),(')-")':06')-,'FGHIJ9')0'/0%+*/)1'"'/-"%%,7'-"(')0'4,
$%+*/,+8'9-,%1'$%/6,"($%&' v *)'"40#,')-,')-6,(-07+'#07)"&,'8#',%-"%/,(')-,'/-"%%,71'-,%/,')-,
%"3,('&*9(*%&B&*-3B"'&+"A&$(-)"*'"%+'&*9(*%&B&*-3-0A&+:;<4568'I$%"77;1'2, %0),
)-")')-,'/*66,%)')-")'7,"#,(')-,'(0*6/,'),63$%"7'E+)K'$(',O*"7')0')-,'/*66,%)')-")',%),6(')-,'+6"$%
),63$%"7'E+(K1'"%+')-,'&"),'/*66,%)'+*'='Z8
EXERCISE
5.1
A'Z8@d5µ3':"46$/")$0%'<60/,(('$('(<,/$:$,+')0'-"#,' # $% & b '%31'µ!'e'bWZ'/3QcS • (1'"%+'8 # & Z8W'S8
I$%+')-,'#"7*,'0:')-,'<60/,((')6"%(/0%+*/)"%/,'<"6"3,),6' > ′! 8'I06'"'FGHIJ9'2$)-'3$%$3*3'7,%&):"46$/"),+'$%')-$('<60/,((1':$%+')-,'6,O*$6,+'#"7*,'0:'''(0')-")')-,'+,#$/,',B-$4$)('"'/-"%%,7'6,($()"%/,
6 ()'0:'@'PΩ'")' v *) & @S8
Ans. Cdd'µAcSQa'Z8[C'µ3
5.1.5 Operation as vDS Is Increased
U,'%,B)'/0%($+,6')-,'($)*")$0%'"('v () '$('$%/6,"(,+8'I06')-$('<*6<0(,1'7,)' v *) '4,'-,7+'/0%()"%)'")'"
#"7*,'&6,"),6')-"%'8 # a')-")'$(1'7,)')-,'FGHIJ9'4,'0<,6"),+'")'"'/0%()"%)'0#,6+6$#,'#07)"&,' 8 :8 8
i,:,6')0'I$&8'W8W1'"%+'%0),')-")' v () '"<<,"6('"('"'#07)"&,'+60<'"/60((')-,'7,%&)-'0:')-,'/-"%%,78
9-")'$(1'"('2,')6"#,7'"70%&')-,'/-"%%,7':603'(0*6/,')0'+6"$%1')-,'#07)"&,'E3,"(*6,+'6,7")$#,')0')-,
(0*6/,K'$%/6,"(,(':603'>,60')0' v () 8'9-*(')-,'#07)"&,'4,)2,,%')-,'&"),'"%+'<0$%)('"70%&')-,'/-"%5
%,7'+,/6,"(,(':603' v *) & 8 # ( 8 :8 '")')-,'(0*6/,',%+')0' v *( & v *) ' v () & 8 # ( 8 :8 ' v () '")
)-,'+6"$%',%+8'H$%/,')-,'/-"%%,7'+,<)-'+,<,%+('0%')-$('#07)"&,1'"%+'(<,/$:$/"77;'0%')-,'"30*%)
4;'2-$/-')-$('#07)"&,',B/,,+('8 # 1'2,':$%+')-")')-,'/-"%%,7'$('%0'70%&,6'0:'*%$:063'+,<)-a'6")-,61
)-,'/-"%%,7'2$77')"P,')-,')"<,6,+'(-"<,'(-02%'$%'I$&8'W8W1''4,$%&'+,,<,()'")')-,'(0*6/,',%+'E2-,6,
)-,'+,<)-'$('<60<06)$0%"7')0' 8 :8 K'"%+'(-"7702,()'")')-,'+6"$%',%+N'E2-,6,')-,'+,<)-'$('<60<065
)$0%"7')0'8 :8 ' v () K8'9-$('<0$%)'$(':*6)-,6'$77*()6"),+'$%'I$&8'W8N8
N
I06'($3<7$/$);1'2,'+0'%0)'(-02'$%'I$&8'W8W')-,'+,<7,)$0%'6,&$0%8'_-;($/"77;'(<,"P$%&1'$)'$(')-,'2$+,%$%&
0:')-,'+,<7,)$0%'6,&$0%'"('"'6,(*7)'0:')-,'$%/6,"(,+' v () ')-")'3"P,(')-,'/-"%%,7'(-"7702,6'%,"6')-,'+6"$%8
239
240 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
n!
n!
Figure 5.5 G<,6")$0%' 0:' )-,' ,%-"%/,3,%)' `FGH' )6"%($()06' "(' v () ' $(' $%/6,"(,+8' 9-,' $%+*/,+' /-"%%,7
"/O*$6,('"')"<,6,+'(-"<,1'"%+'$)('6,($()"%/,'$%/6,"(,('"(' v () '$('$%/6,"(,+8'!,6,1' v *) '$('P,<)'/0%()"%)'")'"
#"7*, j'8# a' v *) & 8 # ' ( 8 :8 8
Voltage
VGS
Vt
vGD
(VOV # 21 vDS)
VOV
Source 0
% VOV
vDS
Voltage drop
along the channel
L
2
Average = 21 vDS
L Drain
x
(a)
%(VOV # vDS)
Channel
Drain
Source
(b)
Figure 5.6 E(K'I06'"'FGHIJ9'2$)-'v*) e 8# k 8:8 1'"<<7$/")$0%'0:'v()'/"*(,(')-,'#07)"&,'+60<'"70%&')-,
/-"%%,7')0'#"6;'7$%,"67;1'2$)-'"%'"#,6"&,'#"7*,'0:' @55Q5v() '")')-,'3$+<0$%)8'H$%/,'v*('j'8#1')-,'/-"%%,7'()$77',B$()(
")')-,'+6"$%',%+8'E/K'9-,'/-"%%,7'(-"<,'/066,(<0%+$%&')0')-,'($)*")$0%'$%'E"K8'U-$7,')-,'+,<)-'0:')-,'/-"%%,7
")')-,'(0*6/,',%+'$('()$77'<60<06)$0%"7')0'8:8 1')-")'")')-,'+6"$%',%+'$('<60<06")$0%"7')0'E8:8 V v()K8
5.1 Device Structure and Physical Operation
iD
Triode
(vDS ! VOV)
Curve bends because
the channel resistance
increases with vDS
Saturation
(vDS & VOV)
Current saturates because the
channel is pinched off at the
drain end, and vDS no longer
affects the channel.
Almost a straight line
with slope proportional
to VOV
vGS = Vt + VOV
0
VDS sat " VOV
vDS
Figure 5.7 9-,'+6"$%'/*66,%)'+('#,6(*(')-,'+6"$%5)05(0*6/,'#07)"&,'v()':06'"%',%-"%/,3,%)5);<,'`FGH
)6"%($()06'0<,6"),+'2$)-'v*)'='8#'k'8:8 8
A(' v () '$('$%/6,"(,+1')-,'/-"%%,7'4,/03,('306,')"<,6,+'"%+'$)('6,($()"%/,'$%/6,"(,('/065
6,(<0%+$%&7;8'9-*(1')-,' + ( ' v ()'/*6#,'+0,('%0)'/0%)$%*,'"('"'()6"$&-)'7$%,'4*)'4,%+('"('(-02%
$%'I$&8'W8f8'9-,',O*")$0%'+,(/6$4$%&')-$('<06)$0%'0:')-,'+ ( ' v () '/*6#,'/"%'4,',"($7;'+,6$#,+'4;
*)$7$>$%&')-,'$%:063")$0%'$%'I$&8'W8N8'H<,/$:$/"77;1'%0),')-")')-,'/-"6&,'$%')-,')"<,6,+'/-"%%,7'$(
<60<06)$0%"7')0')-,'/-"%%,7'/60((5(,/)$0%"7'"6,"'(-02%'$%'I$&8'W8NE4K8'9-$('"6,"'$%')*6%'/"%'4,
,"($7;'(,,%'"('<60<06)$0%"7')0' 5@Q [ 8 :8 ( ( 8 :8 ' v () ) ] '06' ( 8 :8 ' 5@Q v () ) 8'9-*(1')-,'6,7")$0%(-$<
4,)2,,%'+ ('"%+'v ()'/"%'4,':0*%+'4;'6,<7"/$%&'8 :8 '$%'JO8'EW8fK'4;' ( 8 :8 ' 5@Q v () ) 1''
'
@
+ ( & > ′! 55555 8 :8 ' 555 v () v ()
& Q
EW8@bK
9-$(' 6,7")$0%(-$<' +,(/6$4,(' )-,' (,3$<"6"407$/' <06)$0%' 0:' )-,' + ( ' v ()' /*6#,' $%' I$&8' W8f8' =)
"<<7$,(')0')-,',%)$6,'(,&3,%)'+02%')0' v () & Z8'H<,/$:$/"77;1'%0),')-")'"(' v () '$('6,+*/,+1'2,
/"%'%,&7,/)' 5@Q v () '6,7")$#,')0'8 :8 '$%')-,':"/)06'$%'<"6,%)-,(,(1'"%+')-,',B<6,(($0%'6,+*/,(')0
)-")'$%'JO8'EW8fK8'9-,'7")),6'0:'/0*6(,'$('"%'"<<60B$3")$0%'"%+'"<<7$,('0%7;':06'(3"77' v ()
E$8,81'%,"6')-,'06$&$%K8
9-,6,'$('"%0)-,6'*(,:*7'$%),6<6,)")$0%'0:')-,',B<6,(($0%'$%'JO8'EW8@bK8'I603'I$&8'W8NE"K'2,
(,,')-")')-,'"#,6"&,'#07)"&,'"70%&')-,'/-"%%,7'$(' 5@Q v ()8'9-*(1')-,'"#,6"&,'#07)"&,')-")'&$#,(
6$(,')0'/-"%%,7'/-"6&,'"%+'-,%/,')0'+ ('$('%0'70%&,6'8 :8 '4*)' ( 8 :8 ' 5@Q v () )1'2-$/-'$('$%+,,+')-,
:"/)06')-")'"<<,"6('$%'JO8'EW8@bK8'I$%"77;1'2,'%0),')-")'JO8'EW8@bK'$(':6,O*,%)7;'26$)),%'$%')-,
"7),6%"),':063'
'
@ Q
+ ( & > ′! 55555 8 :8 v () ' ' ' 555 v ()
& Q
EW8@WK
I*6)-,6306,1':06'"%'"64$)6"6;'#"7*,'0:'8 :8 1'2,'/"%'6,<7"/,'8 :8 '4;'( v *) ' 8 # )'"%+'6,26$),'JO8
EW8@WK'"('
'
@ Q
+ ( & > ′! 55555 ( v *) ' 8 # ) v () ' ' ' 555 v ()
&
Q
EW8@NK
241
242 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.1.6 Operation for vDS'VOV
9-,'"40#,'+,(/6$<)$0%'0:'0<,6")$0%'"((*3,+')-")',#,%')-0*&-')-,'/-"%%,7'4,/"3,')"<,6,+1'$)'()$77
-"+'"':$%$),'E%0%>,60K'+,<)-'")')-,'+6"$%',%+8'9-$('$%')*6%'$('"/-$,#,+'4;'P,,<$%&' v () '(*::$/$,%)7;
(3"77')-")')-,'#07)"&,'4,)2,,%')-,'&"),'"%+')-,'+6"$%1'v *(1',B/,,+('8 # 8'9-$('$('$%+,,+')-,'($)*")$0%
(-02%' $%' I$&8' W8NE"K8' `0),' )-")' :06' )-$(' ($)*")$0%' )0' 04)"$%1' v () ' 3*()' %0)' ,B/,,+' 8 :8 1' :06' "(
v () & 8 :8 1' v *( & 8 # 1'"%+')-,'/-"%%,7'+,<)-'")')-,'+6"$%',%+'6,+*/,(')0'>,608
I$&*6,' W8d' (-02(' v () ' 6,"/-$%&' 8 :8 ' "%+' v *(' /066,(<0%+$%&7;' 6,"/-$%&' 8 # 8' 9-,' >,60
+,<)-'0:')-,'/-"%%,7'")')-,'+6"$%',%+'&$#,('6$(,')0')-,'),63'%9(**&.+A)*%93"??8'=%/6,"($%&' v ()
4,;0%+')-$('#"7*,'E$8,81' v () > 8 :8 K'-"('%0',::,/)'0%')-,'/-"%%,7'(-"<,'"%+'/-"6&,1'"%+')-,
/*66,%)')-60*&-')-,'/-"%%,7'6,3"$%('/0%()"%)'")')-,'#"7*,'6,"/-,+':06' v () & 8 :8 8'9-,'+6"$%
/*66,%)')-*('!(-#$(-&!'")')-,'#"7*,':0*%+'4;'(*4()$)*)$%&' v () & 8 :8 '$%'JO8'EW8@bK1
+( &
@
555 > ′! '
55555 8 Q
Q & :8
EW8@fK
9-,'FGHIJ9'$(')-,%'("$+')0'-"#,',%),6,+')-,'!(-#$(-)"*+$&,)"*'E061',O*$#"7,%)7;1')-,'(")*5
6")$0%'30+,'0:'0<,6")$0%K8'9-,'#07)"&,' v ()'")'2-$/-'(")*6")$0%'0//*6('$('+,%0),+'8 ()(")1
EW8@dK
8 ()(") & 8 :8 & 8 *) ' 8 #
=)'(-0*7+'4,'%0),+')-")'/-"%%,7'<$%/-50::'+0,('!$#'3,"%'/-"%%,7'470/P"&,D'?*66,%)'/0%)$%5
*,(')0':702')-60*&-')-,'<$%/-,+50::'/-"%%,71'"%+')-,',7,/)60%(')-")'6,"/-')-,'+6"$%',%+'0:')-,
Voltage
VGS
vGD = Vt
Vt
1
2 VOV
VOV
Source 0
Source
L
2
Voltage drop
along the channel
(a)
Channel
Average = 12 VOV
vDS = VOV
L Drain
x
Drain
(b)
Figure 5.8 G<,6")$0%'0:'FGHIJ9'2$)-'v*) e 8# k 8:8 1'"('v()'$('$%/6,"(,+')0'8:8 8'A)')-,'+6"$%',%+1'v*(
+,/6,"(,(')0'8#'"%+')-,'/-"%%,7'+,<)-'")')-,'+6"$%',%+'6,+*/,(')0'>,60'E<$%/-'0::K8'A)')-$('<0$%)1')-,'FGHIJ9
,%),6(' )-,' (")*6")$0%' 30+,' 0:' 0<,6")$0%8' I*6)-,6' $%/6,"($%&' v()' E4,;0%+' 8Dsat' e' 8:8K' -"(' %0' ,::,/)' 0%' )-,
/-"%%,7'(-"<,'"%+'+('6,3"$%('/0%()"%)8
5.1 Device Structure and Physical Operation
/-"%%,7'"6,'"//,7,6"),+')-60*&-')-,'+,<7,)$0%'6,&$0%')-")',B$()(')-,6,'E%0)'(-02%'$%'I$&8'W8WK
"%+' $%)0' )-,' +6"$%' ),63$%"78' A%;' $%/6,"(,' $%' v () ' "40#,' 8 ()(")' "<<,"6(' "(' "' #07)"&,' +60<
"/60((')-,'+,<7,)$0%'6,&$0%8'9-*(1'40)-')-,'/*66,%)')-60*&-')-,'/-"%%,7'"%+')-,'#07)"&,'+60<
"/60(('$)'6,3"$%'/0%()"%)'$%'(")*6")$0%8'
9-,'(")*6")$0%'<06)$0%'0:')-,' + ( ' v () '/*6#,'$(1'"(',B<,/),+1'"'-06$>0%)"7'()6"$&-)'7$%,1'"(
$%+$/"),+'$%'I$&8'W8f8'A7(0'$%+$/"),+'$%'I$&8'W8f'$(')-,'%"3,'0:')-,'6,&$0%'0:'0<,6")$0%'04)"$%,+
2$)-' "' /0%)$%*0*(' E%0%5<$%/-,+50::K' /-"%%,71' )-,' -$)"'&+ $&,)"*8' 9-$(' %"3,' $(' "' /"66;0#,6
:603')-,'+";('0:'#"/**35)*4,'+,#$/,(1'2-0(,'0<,6")$0%'"'IJ9'6,(,347,(8
I$%"77;1'2,'%0),')-")')-,' + ( ' v () '6,7")$0%(-$<'$%'(")*6")$0%'/"%'4,'&,%,6"7$>,+'4;'6,<7"/5
$%&')-,'/0%()"%)'0#,6+6$#,'#07)"&,'8 :8 '4;'"'#"6$"47,'0%,1' v :8 D
@
' Q
+ ( & 555 > ′! 55555 v :8
Q &
EW8@[K
A7(01' v :8 '/"%'4,'6,<7"/,+'4;' ( v *) ' 8 # ) ')0'04)"$%')-,'"7),6%"),',B<6,(($0%':06'(")*6")$0%5
30+,' + (1
@
'
Q
EW8QZK
+ ( & 555 > ′! 55555 ( v *) ' 8 # )
Q
&
Example 5.1
?0%($+,6'"'<60/,(('),/-%070&;':06'2-$/-'&3$%'='Z8b'µ31'#$%'='d'%31'µ!'='bWZ'/3QcS⋅ (1'"%+'8#'='Z8f'S8
E"K I$%+'<$%'"%+' > !′ 8
E4K I06'"'FGHIJ9'2$)-' ' ⁄ & = d'µ3 ⁄ Z8d' µ31'/"7/*7"),')-,'#"7*,('0:'8:8 1'8*) 1'"%+'8()3$%'%,,+,+')0
0<,6"),')-,')6"%($()06'$%')-,'(")*6")$0%'6,&$0%'2$)-'"'+/'/*66,%)'?('='@ZZ'µA8
E/K I06')-,'+,#$/,'$%'E4K1':$%+')-,'#"7*,('0:'8:80"%+'8*)'6,O*$6,+')0'/"*(,')-,'+,#$/,')0'0<,6"),'"('"'@ZZZ5(
6,($()06':06'#,6;'(3"77'v() 8
Solution
ε $%
× @Z
5 = C8bW
5555555555555555555555555555
5 = b8CQ × @Z 'C Ic3 Q
< $% = 555555
'[
# $%
d × @Z
Q
= b8CQ':Icµ3
' @@
E"K
Q
Q
> !′ = µ ! < $% = bWZ ( /3 cS⋅( ) × b8CQ ( :Icµ3 )
d
Q
= bWZ × @Z ( µ3 cS⋅( ) × b8CQ × @Z
'N
= @[b × @Z ( IcS⋅( )
= @[b'µAcS
Q
E4K I06'0<,6")$0%'$%')-,'(")*6")$0%'6,&$0%1
@ '
Q
+ ( = 555 > !′ 55555 v :8
Q &
9-*(1
@
d Q
@ZZ = 555 × @[b × 5555555 8 :8
Q
Z8d
2-$/-'6,(*7)('$%
8 :8 = Z8CQ'S
' @W
Q
( Icµ3 )
243
244 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.1 continued
9-*(1
8 *) = 8 # ' ( '8 :8 ' & @8ZQ 'S
"%+
8 ()3$% = 8 :8 ' = Z8CQ'S
E/K I06')-,'FGHIJ9'$%')-,')6$0+,'6,&$0%'2$)-'v()'#,6;'(3"771
@
6 () & 5555555555555555555555
'
>′ ! 55555 8 :8
&
9-*(
@
5
@ZZZ = 555555555555555555555555555555555555555555555555555555
'N
@[b × @Z × '@Z × 8 :8
2-$/-';$,7+(
8 :8 = Z8WQ'S
9-*(1
8 *) = @8QQ'S
EXERCISES
5.2' I06'"'Z8d5µ3'<60/,(('),/-%070&;':06'2-$/-'#$%'='@W'%3'"%+'µ!'='WWZ'/3QcS⋅ (1'':$%+'<$%1' > !′ 1'"%+')-,
0#,6+6$#,'#07)"&,'8 :8 '6,O*$6,+')0'0<,6"),'"')6"%($()06'-"#$%&' ' ⁄ & = QZ '$%'(")*6")$0%'2$)-'?('='Z8Q
3A8'U-")'$(')-,'3$%$3*3'#"7*,'0:'8()'%,,+,+g
Q
Ans. Q8C':Icµ3Qa @Qf0µAcS a Z8bZ'Sa'Z8bZ'S
D5.3 A'/$6/*$)'+,($&%,6'$%),%+$%&')0'0<,6"),'"'FGHIJ9'$%'(")*6")$0%'$('/0%($+,6$%&')-,',::,/)'0:'/-"%&5
$%&')-,'+,#$/,'+$3,%($0%('"%+'0<,6")$%&'#07)"&,('0%')-,'+6"$%'/*66,%)'? ( 8'H<,/$:$/"77;1'4;'2-")':"/5
)06'+0,(' ? ( '/-"%&,'$%',"/-'0:')-,':07702$%&'/"(,(g
E"K'9-,'/-"%%,7'7,%&)-'$('+0*47,+8
E4K'9-,'/-"%%,7'2$+)-'$('+0*47,+8
E/K'9-,'0#,6+6$#,'#07)"&,'$('+0*47,+8
E+K'9-,'+6"$%5)05(0*6/,'#07)"&,'$('+0*47,+8
E,K'?-"%&,('E"K1'E4K1'E/K1'"%+'E+K'"6,'3"+,'($3*7)"%,0*(7;8
U-$/-'0:')-,(,'/"(,('3$&-)'/"*(,')-,'FGHIJ9')0'7,"#,')-,'(")*6")$0%'6,&$0%g
Ans. Z8Wa'Qa'ba'%0'/-"%&,a'ba'/"(,'E/K'$:' v () '$('(3"77,6')-"%'Q'8 :8
5.1.7 The p-Channel MOSFET
I$&*6,'W8[E"K'(-02('"'/60((5(,/)$0%"7'#$,2'0:'"'"5/-"%%,7',%-"%/,3,%)5);<,'FGHIJ98'9-,
()6*/)*6,'$('($3$7"6')0')-")'0:')-,'`FGH'+,#$/,',B/,<)')-")'-,6,')-,'(*4()6"),'$('!');<,'"%+
)-,'(0*6/,'"%+')-,'+6"$%'6,&$0%('"6,'"k');<,a')-")'$(1'"77'(,3$/0%+*/)06'6,&$0%('"6,'6,#,6(,+'$%
<07"6$);'6,7")$#,')0')-,$6'/0*%),6<"6)('$%')-,'`FGH'/"(,8'9-,'_FGH'"%+'`FGH')6"%($()06
"6,'("$+')0'4,'.$@"3/@/!#264'+,#$/,(8
90'$%+*/,'"'/-"%%,7':06'/*66,%)':702'4,)2,,%'(0*6/,'"%+'+6"$%1'"'%,&")$#,'#07)"&,'$('"<<7$,+
)0')-,'&"),1')-")'$(1'4,)2,,%'&"),'"%+'(0*6/,1'"('$%+$/"),+'$%'I$&8'W8[E4K8'L;'$%/6,"($%&')-,'3"&%$5
5.1 Device Structure and Physical Operation
S
G
D
p+
p+
n-type substrate
B
(a)
!
vGS
S
#
G
iG = 0
iD
iD
p+
iD
D
!
vDS
#
p+
induced p channel
n-type substrate
B
Figure 5.9 E(K'_-;($/"7'()6*/)*6,'0:')-,'_FGH')6"%($()068'`0),')-")'$)'$('($3$7"6')0')-,'`FGH')6"%($()06'(-02%'
$%'I$&8'W8@E4K',B/,<)')-")'"77'(,3$/0%+*/)06'6,&$0%('"6,'6,#,6(,+'$%'<07"6$);8'E/K'A'%,&")$#,'#07)"&,'v*)'0:'3"&%$)*+,'
&6,"),6')-"%''l8#"l'$%+*/,('"'"'/-"%%,71'"%+'"'%,&")$#,'v()'/"*(,('"'/*66,%)'+(')0':702':603'(0*6/,')0'+6"$%8
)*+,'0:')-,'%,&")$#,' v *) '4,;0%+')-,'3"&%$)*+,'0:')-,')-6,(-07+'#07)"&,'8 #"1'2-$/-'4;'/0%#,%)$0%
$('%,&")$#,1'"'"'/-"%%,7'$(',()"47$(-,+'"('(-02%'$%'I$&8'W8[E4K8'9-$('/0%+$)$0%'/"%'4,'+,(/6$4,+'"(
v *) ≤ 8 #"
061')0'"#0$+'+,"7$%&'2$)-'%,&")$#,'($&%(1'
v *) ≥ 8 #"
`021')0'/"*(,'"'/*66,%)'+ ( ')0':702'$%')-,'"'/-"%%,71'"'%,&")$#,'#07)"&,' v () '$('"<<7$,+')0')-,
+6"$%8'9-,'/*66,%)' + ( '$('/"66$,+'4;'-07,('"%+':702(')-60*&-')-,'/-"%%,7':603'(0*6/,')0'+6"$%8
A('2,'-"#,'+0%,':06')-,'`FGH')6"%($()061'2,'+,:$%,')-,'<60/,((')6"%(/0%+*/)"%/,'<"6"3,5
),6':06')-,'_FGH'+,#$/,'"('
>′" & µ " < $%
245
246 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
2-,6,'µ"'$(')-,'304$7$);'0:')-,'-07,('$%')-,'$%+*/,+'"'/-"%%,78'9;<$/"77;1 µ"'e'Z8QW'µ!')0'Z8W
µ!0 "%+' $(' <60/,((' ),/-%070&;' +,<,%+,%)8' 9-,' )6"%($()06' )6"%(/0%+*/)"%/,' <"6"3,),6' > "' $(
04)"$%,+'4;'3*7)$<7;$%&'>′"'4;')-,'"(<,/)'6")$0''c&1'
> " & >′" ( ' ⁄ & )
9-,'6,3"$%+,6'0:')-,'+,(/6$<)$0%'0:')-,'<-;($/"7'0<,6")$0%'0:')-,'"5/-"%%,7'FGHIJ9
:07702(')-")':06')-,'`FGH'+,#$/,1',B/,<)'0:'/0*6(,':06')-,'($&%'6,#,6("7('0:'"77'#07)"&,(8'U,
2$77'<6,(,%)')-,'/03<7,),'/*66,%)V#07)"&,'/-"6"/),6$()$/('0:'40)-'`FGH'"%+'_FGH')6"%($(5
)06('$%')-,'%,B)'(,/)$0%8
_FGH'),/-%070&;'06$&$%"77;'+03$%"),+'FGH'$%),&6"),+5/$6/*$)'3"%*:"/)*6$%&1'"%+
)-,'06$&$%"7'3$/60<60/,((06('*)$7$>,+'_FGH')6"%($()06(8'A(')-,'),/-%070&$/"7'+$::$/*7)$,(
0:':"46$/")$%&'`FGH')6"%($()06('2,6,'(07#,+1'`FGH'/03<7,),7;'(*<<7"%),+'_FGH8'9-,
3"$%'6,"(0%':06')-$('/-"%&,'$(')-")',7,/)60%'304$7$);'µ!0$('-$&-,6'4;'"':"/)06'0:'Q')0'b')-"%
)-,' -07,' 304$7$);' µ" 1' 6,(*7)$%&' $%' `FGH' )6"%($()06(' -"#$%&' &6,"),6' &"$%(' "%+' (<,,+(' 0:
0<,6")$0%')-"%'_FGH'+,#$/,(8'H*4(,O*,%)7;1'"'),/-%070&;'2"('+,#,70<,+')-")'<,63$)(')-,
:"46$/")$0%'0:'40)-'`FGH'"%+'_FGH')6"%($()06('0%')-,'("3,'/-$<8'A<<60<6$"),7;'/"77,+
%"BA.&B&*-($0+:;<1'06'C:;<1')-$('),/-%070&;'$('/*66,%)7;')-,'+03$%"%)',7,/)60%$/(
),/-%070&;8
5.1.8 Complementary MOS or CMOS
A(')-,'%"3,'$3<7$,(1'/03<7,3,%)"6;'FGH'),/-%070&;',3<70;('FGH')6"%($()06('0:'40)<07"6$)$,(8' A7)-0*&-' ?FGH' /$6/*$)(' "6,' (03,2-")' 306,' +$::$/*7)' )0' :"46$/"),' )-"%
`FGH1')-,'"#"$7"4$7$);'0:'/03<7,3,%)"6;'+,#$/,('3"P,('<0(($47,'3"%;'<02,6:*7'/$6/*$)'/0%5
:$&*6")$0%(8'=%+,,+1'")')-,'<6,(,%)')$3,'?FGH'$(')-,'30()'2$+,7;'*(,+'0:'"77')-,'=?'),/-5
%070&$,(8' 9-$(' ()"),3,%)' "<<7$,(' )0' 40)-' "%"70&' "%+' +$&$)"7' /$6/*$)(8' ?FGH' ),/-%070&;
-"('#$6)*"77;'6,<7"/,+'+,($&%('4"(,+'0%'`FGH')6"%($()06('"70%,8'I*6)-,6306,1'4;'QZZ[
?FGH'),/-%070&;'-"+')"P,%'0#,6' 3"%;'"<<7$/")$0%(')-")'.*()'"':,2';,"6(',"67$,6'2,6,
<0(($47,' 0%7;' 2$)-' 4$<07"6' +,#$/,(8' 9-60*&-0*)' )-$(' 400P1' 2,' 2$77' ()*+;' 3"%;' ?FGH
/$6/*$)'),/-%$O*,(8
I$&*6,' W8@Z' (-02(' "' /60((' (,/)$0%' 0:' "' ?FGH' /-$<' $77*()6")$%&' -02' )-,' _FGH' "%+
`FGH' )6"%($()06(' "6,' :"46$/"),+8' G4(,6#,' )-")' 2-$7,' )-,' `FGH' )6"%($()06' $(' $3<7,3,%),+
+$6,/)7;' $%' )-,' "5);<,' (*4()6"),1' )-,' _FGH' )6"%($()06' $(' :"46$/"),+' $%' "' (<,/$"77;' /6,"),+' !
6,&$0%1'P%02%'"('"%'!'D&..8'9-,')20'+,#$/,('"6,'$(07"),+':603',"/-'0)-,6'4;'"')-$/P'6,&$0%'0:
0B$+,')-")':*%/)$0%('"('"%'$%(*7")068'`0)'(-02%'0%')-,'+$"&6"3'"6,')-,'/0%%,/)$0%('3"+,')0
)-,'"5);<,'40+;'"%+')0')-,'!'2,778'9-,'7")),6'/0%%,/)$0%'(,6#,('"(')-,'40+;'),63$%"7':06')-,
_FGH')6"%($()068
5.1.9 Operating the MOS Transistor in the Subthreshold Region
9-,'"40#,'+,(/6$<)$0%'0:')-,'!5/-"%%,7'FGHIJ9'0<,6")$0%'$3<7$,(')-")':06'v*)'<'8# 1'%0'/*65
6,%)':702('"%+')-,'+,#$/,'$('/*)'0::8'9-$('$('%0)',%)$6,7;')6*,1':06'$)'-"('4,,%':0*%+')-")':06
#"7*,('0:'v*)'(3"77,6')-"%'4*)'/70(,')0'8# 1'"'(3"77'+6"$%'/*66,%)':702(8'=%')-$('!#/-9$&!9".'
$&,)"*'0:'0<,6")$0%1')-,'+6"$%'/*66,%)'$(',B<0%,%)$"77;'6,7"),+')0'v*) 1'3*/-'7$P,')-,'+< VvA=
6,7")$0%(-$<'0:'"'LM91'"('2$77'4,'(-02%'$%')-,'%,B)'/-"<),68
A7)-0*&-'$%'30()'"<<7$/")$0%(')-,'FGH')6"%($()06'$('0<,6"),+'2$)-' v*)'>'8# 1')-,6,'"6,
(<,/$"71'4*)'"'&602$%&'%*34,6'0:1'"<<7$/")$0%(')-")'3"P,'*(,'0:'(*4)-6,(-07+'0<,6")$0%8'=%
?-"<),6'@C1'2,'2$77'46$,:7;'/0%($+,6'(*4)-6,(-07+'0<,6")$0%8
5.2 Current–Voltage Characteristics
NMOS
S
SiO2
PMOS
D
G
Gate
oxide
D
G
S
Polysilicon
Thick SiO2 (isolation)
n!
n!
SiO2
p!
p!
n well
p-type body
Figure 5.10 ?60((5(,/)$0%'0:'"'?FGH'$%),&6"),+'/$6/*$)8'`0),')-")')-,'_FGH')6"%($()06'$(':063,+'$%'"
(,<"6"),'!5);<,'6,&$0%1'P%02%'"('"%'!'2,778'A%0)-,6'"66"%&,3,%)'$('"7(0'<0(($47,'$%'2-$/-'"%'!5);<,'40+;'$(
*(,+'"%+')-,'!'+,#$/,'$(':063,+'$%'"'"'2,778'`0)'(-02%'"6,')-,'/0%%,/)$0%('3"+,')0')-,'"5);<,'40+;'"%+')0
)-,'!'2,77a')-,'7")),6':*%/)$0%('"(')-,'40+;'),63$%"7':06')-,'"5/-"%%,7'+,#$/,8
5.2 Current–Voltage Characteristics
L*$7+$%&'0%')-,'<-;($/"7':0*%+")$0%',()"47$(-,+'$%')-,'<6,#$0*('(,/)$0%':06')-,'0<,6")$0%'0:
)-,' ,%-"%/,3,%)' FGH' )6"%($()061' $%' )-$(' (,/)$0%' 2,' <6,(,%)' $)(' /03<7,),' /*66,%)V#07)"&,
/-"6"/),6$()$/(8'9-,(,'/-"6"/),6$()$/('/"%'4,'3,"(*6,+'")'+/'06'")'702':6,O*,%/$,('"%+')-*(
"6,'/"77,+'()")$/'/-"6"/),6$()$/(8'9-,'+;%"3$/',::,/)(')-")'7$3$)')-,'0<,6")$0%'0:')-,'FGHIJ9
")'-$&-':6,O*,%/$,('"%+'-$&-'(2$)/-$%&'(<,,+('2$77'4,'+$(/*((,+'$%'?-"<),6'[8
5.2.1 Circuit Symbol
I$&*6,' W8@@E"K' (-02(' )-,' /$6/*$)' (;3407' :06' )-,' !5/-"%%,7' ,%-"%/,3,%)5);<,' FGHIJ98
G4(,6#,')-")')-,'(<"/$%&'4,)2,,%')-,')20'#,6)$/"7'7$%,(')-")'6,<6,(,%)')-,'&"),'"%+')-,'/-"%5
%,7'$%+$/"),(')-,':"/)')-")')-,'&"),',7,/)60+,'$('$%(*7"),+':603')-,'40+;'0:')-,'+,#$/,8'9-,
<07"6$);'0:')-,'"5);<,'(*4()6"),'E40+;K'"%+')-,'!'/-"%%,7'$('$%+$/"),+'4;')-,'"6602-,"+'0%')-,
D
D
B
G
B
G
G
S
S
(a)
D
(b)
S
(c)
Figure 5.11 1(2'?$6/*$)'(;3407':06')-,'!5/-"%%,7',%-"%/,3,%)5);<,'FGHIJ98'1/2'F0+$:$,+'/$6/*$)'(;35
407'2$)-'"%'"6602-,"+'0%')-,'(0*6/,'),63$%"7')0'+$()$%&*$(-'$)':603')-,'+6"$%'"%+')0'$%+$/"),'+,#$/,'<07"6$);
E$8,81'!'/-"%%,7K8'1%2'H$3<7$:$,+'/$6/*$)'(;3407')0'4,'*(,+'2-,%')-,'(0*6/,'$('/0%%,/),+')0')-,'40+;'06'2-,%
)-,',::,/)'0:')-,'40+;'0%'+,#$/,'0<,6")$0%'$('*%$3<06)"%)8
247
248 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
7$%,'6,<6,(,%)$%&')-,'40+;'ELK8'9-$('"6602-,"+'"7(0'$%+$/"),(')-,'<07"6$);'0:')-,')6"%($()061
%"3,7;1')-")'$)'$('"%'!5/-"%%,7'+,#$/,8
A7)-0*&-')-,'FGHIJ9'$('"'(;33,)6$/"7'+,#$/,1'$)'$('0:),%'*(,:*7'$%'/$6/*$)'+,($&%')0'+,(5
$&%"),'0%,'),63$%"7'"(')-,'(0*6/,'"%+')-,'0)-,6'"(')-,'+6"$%'E2$)-0*)'-"#$%&')0'26$),'H'"%+'^
4,($+,' )-,' ),63$%"7(K8' 9-$(' 04.,/)$#,' $(' "/-$,#,+' $%' )-,' 30+$:$,+' /$6/*$)' (;3407' (-02%' $%
I$&8 W8@@E4K8'!,6,'"%'"6602-,"+'$('<7"/,+'0%')-,'(0*6/,'),63$%"71')-*('+$()$%&*$(-$%&'$)':603
)-,' +6"$%' ),63$%"78' 9-,' "6602-,"+' <0$%)(' $%' )-,' %063"7' +$6,/)$0%' 0:' /*66,%)' :702' "%+' )-*(
$%+$/"),(' )-,' <07"6$);' 0:' )-,' +,#$/,' E$8,81' !' /-"%%,7K8' G4(,6#,' )-")' $%' )-,' 30+$:$,+' (;34071
)-,6,' $(' %0' %,,+' )0' (-02' )-,' "6602-,"+' 0%' )-,' 40+;' 7$%,8' A7)-0*&-' )-,' /$6/*$)' (;3407' 0:
I$&8 W8@@E4K'/7,"67;'+$()$%&*$(-,(')-,'(0*6/,':603')-,'+6"$%1'$%'<6"/)$/,'$)'$(')-,'<07"6$);'0:')-,
#07)"&,' $3<6,((,+' "/60((' )-,' +,#$/,' )-")' +,),63$%,(' (0*6/,' "%+' +6"$%a' #B/0 ,62+!0 +10 23C241
"$1+#+5/06/32#+5/0#$0#B/01$-6./0+!02!0!D.B2!!/30E=98
=%'"<<7$/")$0%('2-,6,')-,'(0*6/,'$('/0%%,/),+')0')-,'40+;'0:')-,'+,#$/,1'"':*6)-,6'($3<7$:$/"5
)$0%'0:')-,'/$6/*$)'(;3407'$('<0(($47,1'"('$%+$/"),+'$%'I$&8'W8@@E/K8'9-$('(;3407'$('"7(0'*(,+'$%'"<<7$5
/")$0%('2-,%')-,',::,/)'0:')-,'40+;'0%'/$6/*$)'0<,6")$0%'$('%0)'$3<06)"%)1'"('2$77'4,'(,,%'7"),68
5.2.2 The iD–vDS Characteristics
9"47,'W8@'<60#$+,('"'/03<$7")$0%'0:')-,'/0%+$)$0%('"%+')-,':063*7"(':06')-,'0<,6")$0%'0:')-,
`FGH')6"%($()06'$%',"/-'0:')-,')-6,,'<0(($47,'6,&$0%(D')-,'/*)0::'6,&$0%1')-,')6$0+,'6,&$0%1
"%+')-,'(")*6")$0%'6,&$0%8'9-,':$6()')20'"6,'*(,:*7'$:')-,'FGHIJ9'$(')0'4,'*)$7$>,+'"('"'(2$)/-8
G%')-,'0)-,6'-"%+1'$:')-,'FGHIJ9'$(')0'4,'*(,+')0'+,($&%'"%'"3<7$:$,61'$)'3*()'4,'0<,6"),+'$%
)-,'(")*6")$0%'6,&$0%8'9-,'6")$0%"7,':06')-,(,'/-0$/,('2$77'4,'"++6,((,+'$%'H,/)$0%'W8b8
A)')-,')0<'0:'9"47,'W8@'2,'(-02'"'/$6/*$)'/0%($()$%&'0:'"%'`FGH')6"%($()06'"%+')20'+/
(*<<7$,('<60#$+$%&' v *) '"%+' v () 8'9-$('/0%/,<)*"7'/$6/*$)'/"%'4,'*(,+')0'3,"(*6,')-,'+(V v ()
/-"6"/),6$()$/' /*6#,(' 0:' )-,' `FGH' )6"%($()068' J"/-' /*6#,' $(' 3,"(*6,+' 4;' (,))$%&' v *) ' )0' "
+,($6,+'/0%()"%)'#"7*,1'#"6;$%&' v () 1'"%+'3,"(*6$%&')-,'/066,(<0%+$%&' + ( 8'920'0:')-,(,'/-"65
"/),6$()$/'/*6#,('"6,'(-02%'$%')-,'"//03<"%;$%&'+$"&6"3D'0%,':06' v *) < 8 #! '"%+')-,'0)-,6':06
v *) & 8 #! ( v :8 8 'E`0),')-")'2,'%02'*(,' 8 #!')0'+,%0),')-,')-6,(-07+'#07)"&,'0:')-,'`FGH
)6"%($()061')0'+$()$%&*$(-'$)':603')-")'0:')-,'_FGH')6"%($()061'+,%0),+' 8 #"8K
A('9"47,'W8@'(-02(1')-,'40*%+"6;'4,)2,,%')-,')6$0+,'6,&$0%'"%+')-,'(")*6")$0%'6,&$0%'$(
+,),63$%,+' 4;' 2-,)-,6' v () ' $(' 7,(('06' &6,"),6')-"%' )-,'0#,6+6$#,' #07)"&,' v :8 ' ")' 2-$/-' )-,
)6"%($()06'$('0<,6")$%&8'A%',O*$#"7,%)'2";')0'/-,/P':06')-,'6,&$0%'0:'0<,6")$0%'$(')0',B"3$%,
)-,'6,7")$#,'#"7*,('0:')-,'+6"$%'"%+'&"),'#07)"&,(8'90'0<,6"),'$%')-,')6$0+,'6,&$0%1')-,'&"),'#07)5
"&,'3*()',B/,,+')-,'+6"$%'#07)"&,'4;'")'7,"()'8 #!'#07)(1'2-$/-',%(*6,(')-")')-,'/-"%%,7'6,3"$%(
/0%)$%*0*('E%0)'<$%/-,+'0::K8'G%')-,'0)-,6'-"%+1')0'0<,6"),'$%'(")*6")$0%1')-,'/-"%%,7'3*()'4,
<$%/-,+'0::'")')-,'+6"$%',%+a'<$%/-50::'$('"/-$,#,+'-,6,'4;'P,,<$%&' v ( '-$&-,6')-"%' v * ' 8 #! 1
)-")'$(1'%0)'"7702$%&' v ( ')0':"77'4,702' v *'4;'306,')-"%'8 #! '#07)(8'9-,'&6"<-$/"7'/0%()6*/)$0%'0:
I$&8'W8@Q'(-0*7+'(,6#,')0'6,3$%+')-,'6,"+,6'0:')-,(,'/0%+$)$0%(8
A'(,)'0:' + ( ' v () +/-"6"/),6$()$/(':06')-,'`FGH')6"%($()06'$('(-02%'$%'I$&8'W8@C8'G4(,6#,
)-")',"/-'&6"<-'$('04)"$%,+'4;'(,))$%&' v *) '"40#,' 8 #!'4;'"'(<,/$:$/'#"7*,'0:'0#,6+6$#,'#07)"&,1
+,%0),+'8 :8@1'8 :8Q1'8 :8C1'"%+'8 :8b8'9-$('$%')*6%'$(')-,'#"7*,'0:' v () '")'2-$/-')-,'/066,(<0%+$%&
&6"<-'(")*6"),(1'"%+')-,'#"7*,'0:')-,'6,(*7)$%&'(")*6")$0%'/*66,%)'$('+$6,/)7;'+,),63$%,+'4;')-,
Q
Q
#"7*,'0:' v :81'%"3,7;1' 5@Q >′!8 :8@1' 5@Q >′!8 :8Q1'8 8 8'9-,'6,"+,6'$('"+#$(,+')0'/033$)')0'3,306;'40))-,'()6*/)*6,'0:')-,(,'&6"<-('"%+')-,'/006+$%"),('0:')-,'(")*6")$0%'<0$%)(8
I$%"77;1'04(,6#,')-")')-,'40*%+"6;'4,)2,,%')-,')6$0+,'"%+')-,'(")*6")$0%'6,&$0%(1')-")'$(1
)-,'70/*('0:')-,'(")*6")$0%'<0$%)(1'$('"'<"6"407$/'/*6#,'+,(/6$4,+'4;
@
' Q
+ ( & 555 >′! 55555 v ()
Q &
5.2 Current–Voltage Characteristics
Table 5.1 Regions of Operation of the Enhancement NMOS Transistor
iD
+
vGD
−
+
iD
Saturation
vDS ≥ vOV
( ) v 2OV
vDS
+
Triode
vDS < vOV
1 ) W
k
2 n L
vGS = Vtn + vOV
vGS
−
−
Cut-off
vGS < Vtn
Slope =
gDS = r1
DS
0
v
= kn) ( W
L ) OV
vOV
vDS
v *) < 8 #! D'%0'/-"%%,7a')6"%($()06'$%'/*)50::a' + ( & Z
v *) & 8 #! ( v :8 D'"'/-"%%,7'$('$%+*/,+a')6"%($()06'0<,6"),('$%')-,')6$0+,'6,&$0%'06')-,'(")*6")$0%'6,&$0%'+,<,%+5
$%&'0%'2-,)-,6')-,'/-"%%,7'$('/0%)$%*0*('06'<$%/-,+50::'")')-,'+6"$%',%+a
96+$,/0F/7+$!
)2#-62#+$!0F/7+$!
?0%)$%*0*('/-"%%,71'04)"$%,+'4;D
_$%/-,+50::'/-"%%,71'04)"$%,+'4;D
v *( > 8 #!
v *( * 8 #!
06',O*$#"7,%)7;D
06',O*$#"7,%)7;D
v () < v :8
v () ' v :8
9-,%1
9-,%
'
@ Q
+ ( & > !′ 55555 ( v *) ' 8 #! ) v () ' 555 v ()
&
Q
06',O*$#"7,%)7;1
Q
@
'
+ ( & 555 > !′ 55555 ( v *) ' 8 #! )
Q &
06',O*$#"7,%)7;1
'
@
+ ( & > !′ 55555 v :8 ' 555 v () v ()
& Q
@
' Q
+ ( & 555 > !′ 55555 v :8
Q &
Overdrive
voltage
VOV
Figure 5.12 9-,'6,7")$#,'7,#,7('0:')-,'),63$%"7'#07)"&,('0:')-,',%-"%/,3,%)'`FGH')6"%($()06':06'0<,6"5
)$0%'$%')-,')6$0+,'6,&$0%'"%+'$%')-,'(")*6")$0%'6,&$0%8
249
250 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
iD
1 ) W
k ( ) VO2V4
2 n L
vDS $ vOV
Triode
region
vDS " vOV
Saturation region
vGS = V t + VOV4
vDS = vOV
2
iD = 12 kn ( WL ) vDS
1 ) W
k ( ) VO2V3
2 n L
vGS = Vt + VOV3
1 ) W
k ( ) VO2V2
2 n L
vGS = V t + VOV2
1 ) W
k ( ) VO2V1
2 n L
vGS = V t + VOV1
0 VOV1 VOV2 VOV3 VOV4
vGS $ Vt (Cutoff)
vDS
Figure 5.13 9-,'+(V v () '/-"6"/),6$()$/(':06'"%',%-"%/,3,%)5);<,'`FGH')6"%($()068
5.2.3 The iD– vGS Characteristic
U-,%')-,'FGHIJ9'$('*(,+')0'+,($&%'"%'"3<7$:$,61'$)'$('0<,6"),+'$%')-,'(")*6")$0%'6,&$0%8'A(
I$&8'W8@C'$%+$/"),(1'$%'(")*6")$0%')-,'+6"$%'/*66,%)'$('/0%()"%)'+,),63$%,+'4;' v *) 'E06' v :8 K
"%+' $(' $%+,<,%+,%)' 0:' v () 8 ' 9-")' $(1' )-,' FGHIJ9' 0<,6"),(' "(' "' /0%()"%)5/*66,%)' (0*6/,
2-,6,')-,'#"7*,'0:')-,'/*66,%)'$('+,),63$%,+'4;' v *) 8 '=%',::,/)1')-,%1')-,'FGHIJ9'0<,6"),(
"('"'#07)"&,5/0%)6077,+'/*66,%)'(0*6/,'2$)-')-,'/0%)607'6,7")$0%(-$<'+,(/6$4,+'4;
@
'
Q
+ ( & 555 >′! 55555 ( v *) ' 8 #! )
Q &
EW8Q@K
@
' Q
+ ( & 555 >′! 55555 v :8
Q &
EW8QQK
06'$%'),63('0:' v :8 1
9-$('$(')-,'6,7")$0%(-$<')-")'*%+,67$,(')-,'"<<7$/")$0%'0:')-,'FGHIJ9'"('"%'"3<7$:$,68'9-")'$)
$('%0%7$%,"6'(-0*7+'4,'0:'/0%/,6%')0')-0(,'$%),6,(),+'$%'+,($&%$%&'7$%,"6'"3<7$:$,6(8'`,#,65
)-,7,((1'7"),6'$%')-$('/-"<),61'2,'2$77'(,,'-02'0%,'/"%'04)"$%'7$%,"6'"3<7$:$/")$0%':603')-$(
%0%7$%,"6'/0%)607'06')6"%(:,6'/-"6"/),6$()$/8
I$&*6,'W8@b'(-02(')-,'+(V v *) +/-"6"/),6$()$/'0:'"%'`FGH')6"%($()06'0<,6")$%&'$%'(")*6"5
)$0%8'`0),')-")'$:'2,'"6,'$%),6,(),+'$%'"'<70)'0:' + ( '#,6(*(' v :8 1'2,'($3<7;'(-$:)')-,'06$&$%')0')-,
<0$%)'v *) & 8 #! 8
9-,'#$,2'0:')-,'FGHIJ9'$%')-,'(")*6")$0%'6,&$0%'"('"'#07)"&,5/0%)6077,+'/*66,%)'(0*6/,
$('$77*()6"),+'4;')-,',O*$#"7,%)5/$6/*$)'6,<6,(,%)")$0%'(-02%'$%'I$&8'W8@W8'I06'6,"(0%(')-")'2$77
4,/03,'"<<"6,%)'(-06)7;1')-,'/$6/*$)'$%'I$&8'W8@W'$('P%02%'"('"'.($,&3!),*(.+&E#)>(.&*-+%)$3
%#)-8'`0),')-")')-,'/*66,%)'(0*6/,'$('$+,"71'2$)-'"%'$%:$%$),'0*)<*)'6,($()"%/,'6,<6,(,%)$%&')-,
$%+,<,%+,%/,1' $%' (")*6")$0%1' 0:' + (' :603' v () 8 ' 9-$(1' 0:' /0*6(,1' -"(' 4,,%' "((*3,+' $%' )-,
$+,"7$>,+'30+,7'0:'+,#$/,'0<,6")$0%'*)$7$>,+')-*(':"68'U,'"6,'"40*)')0'6,/)$:;'"%'$3<06)"%)
(-06)/03$%&'0:')-$('30+,78'I$6()1'-02,#,61'2,'<6,(,%)'"%',B"3<7,8
5.2 Current–Voltage Characteristics
iD
vDS " vGS – Vtn
0
Vtn
vGS
0
vOV
Figure 5.14 9-,'+(Vv*)'/-"6"/),6$()$/'0:'"%'`FGH')6"%($()06'0<,6")$%&'$%')-,'(")*6")$0%'6,&$0%8'9-,'+(Vv:8
/-"6"/),6$()$/'/"%'4,'04)"$%,+'4;'($3<7;'6,57"4,77$%&')-,'-06$>0%)"7'"B$(a')-")'$(1'(-$:)$%&')-,'06$&$%')0')-,
<0$%)'v*) 'e'8#!8
'
RD
+
Y
+
k)
X
tn
+
Z
RG
RS
#5 V
tn
tn
Figure 5.15 T"6&,5($&%"7' ,O*$#"7,%)5/$6/*$)' 30+,7
0:'"%'!5/-"%%,7' FGHIJ9'0<,6")$%&' $%')-,' (")*6")$0%
Example 5.2
?0%($+,6'"%'`FGH')6"%($()06':"46$/"),+'$%'"'Z8@d5µ3'<60/,(('2$)-'&'e'Z8@d'µ3'"%+'''e'Q'µ38'9-,'<605
/,(('),/-%070&;'$('(<,/$:$,+')0'-"#,' < $% & d8N':Icµ3Q1'µ!'e'bWZ'/3Qc S ⋅ (1'"%+'8 #! & Z8W'S8
E"K'I$%+'8 *) '"%+' 8 () ')-")'6,(*7)'$%')-,'FGHIJ9'0<,6")$%&'")')-,',+&,'0:'(")*6")$0%'2$)-' ? ( & @ZZ 'µA8
E4K'=:'8 *)'$('P,<)'/0%()"%)1':$%+'8 ()')-")'6,(*7)('$%' ? ( & WZ 'µA8
E/K' 90' $%#,()$&"),' )-,' *(,' 0:' )-,' FGHIJ9' "(' "' 7$%,"6' "3<7$:$,61' 7,)' $)' 4,' 0<,6")$%&' $%' (")*6")$0%' 2$)8 () & Z8C'S8'I$%+')-,'/-"%&,'$%'+ ('6,(*7)$%&':603'v *) '/-"%&$%&':603'Z8f'S'4;' kZ8Z@ S'"%+'4;' ' Z8Z@'S8
251
252 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Solution
I$6()'2,'+,),63$%,')-,'<60/,((')6"%(/0%+*/)"%/,'<"6"3,),6' >′!
>′! & µ ! < $%
'b
& bWZ × @Z × d8N × @Z
' @W
@Q
× @Z 'AcSQ
e'Cdf'µAcSQ
"%+')-,')6"%($()06')6"%(/0%+*/)"%/,'<"6"3,),6' > ! 1'
'
> ! & >′! 55555
&
Q
& Cdf 5555555555 & b8C '3AcSQ
Z8@d
E"K'U$)-')-,')6"%($()06'0<,6")$%&'$%'(")*6")$0%1'
@
Q
? ( & 555 > ! 8 :8
Q
9-*(1
@
C
Q
@ZZ & 555 × b8C × @Z × 8 :8
Q
2-$/-'6,(*7)('$%
8 :8 & Z8QQ 'S
9-*(1
8 *) & 8 #! ( 8 :8 & Z8W ( Z8QQ & Z8fQ'S
"%+'($%/,'0<,6")$0%'$('")')-,',+&,'0:'(")*6")$0%1
8 () & 8 :8 & Z8QQ 'S
E4K'U$)-' 8 *) 'P,<)'/0%()"%)'")'Z8fQ'S'"%+' ? ( '6,+*/,+':603')-,'#"7*,'04)"$%,+'")')-,',+&,'0:'(")*6")$0%1
)-,'FGHIJ9'2$77'%02'4,'0<,6")$%&'$%')-,')6$0+,'6,&$0%1')-*(
@ Q
? ( & > ! 8 :8 8 () ' 555 8 ()
Q
@ Q
C
WZ & b8C × @Z Z8QQ8 () ' 555 8 ()
Q
2-$/-'/"%'4,'6,"66"%&,+')0')-,':063
Q
8 () ' Z8bb8 () ( Z8ZQC & Z
9-$('O*"+6")$/',O*")$0%'-"(')20'(07*)$0%(
8 () & Z8ZN S "%+
8 () & Z8C[ 'S
9-,'(,/0%+'"%(2,6'$('&6,"),6')-"%'8 :8'"%+')-*('$('<-;($/"77;'3,"%$%&7,((1'($%/,'2,'P%02')-")')-,')6"%($(5
)06'$('0<,6")$%&'$%')-,')6$0+,'6,&$0%8'9-*('2,'-"#,
8 () & Z8ZN 'S
5.2 Current–Voltage Characteristics
Example 5.2 continued
E/K'I06' v *) & Z8f'S1'8 :8 & Z8Q'S1'"%+'($%/,'8 () & Z8C'S1')-,')6"%($()06'$('0<,6")$%&'$%'(")*6")$0%'"%+'
@
Q
? ( & 555 > ! 8 :8
Q
@
& 555 × bCZZ × Z8Zb
Q
'e'dN'µA
`02':06' v *) & Z8f@Z'S1' v :8 & Z8Q@ 'S'"%+'
@
Q
+ ( & 555 × bCZZ × Z8Q@ & [b8d 'µA
Q
"%+':06' v *) & Z8N[Z'S1'v :8 & Z8@['S1'"%+'
@
Q
+ ( & 555 × bCZZ × Z8@[ & ff8N 'µA
Q
9-*(1'2$)-' ∆8 *) & kZ8Z@'S1' ∆+ ( & d8d 'µAa'"%+':06' ∆8 *) & ' Z8Z@'S1'∆+ ( & ' d8b'µA8
U,'/0%/7*+,')-")')-,')20'/-"%&,('"6,'"730()',O*"71'"%'$%+$/")$0%'0:'"730()57$%,"6'0<,6")$0%'2-,%')-,
/-"%&,('$%'v *)'"6,'P,<)'(3"778'9-$('$('.*()'"'<6,#$,2'0:')-,'X(3"775($&%"7'0<,6")$0%Y'0:')-,'FGHIJ9'()*+5
$,+'$%'H,/)$0%('W8b'"%+'W8W8
EXERCISES
5.4 A%'`FGH')6"%($()06'$('0<,6")$%&'")')-,',+&,'0:'(")*6")$0%'2$)-'"%'0#,6+6$#,'#07)"&,'8 :8 '"%+'"'+6"$%
/*66,%)' ? ( 8 '=:' 8 :8 '$('+0*47,+1'"%+'2,'3*()'3"$%)"$%'0<,6")$0%'")')-,',+&,'0:'(")*6")$0%1'2-")'(-0*7+
8 () '4,'/-"%&,+')0g'U-")'#"7*,'0:'+6"$%'/*66,%)'6,(*7)(g
Ans. Q' 8 :8 a'b'? (
5.5 A%'!5/-"%%,7'FGHIJ9'0<,6")$%&'2$)-'8 :8 & Z8W'S',B-$4$)('"'7$%,"6'6,($()"%/,' 6 () 'e'@'PΩ'2-,%
v () '$('#,6;'(3"778'U-")'$(')-,'#"7*,'0:')-,'+,#$/,')6"%(/0%+*/)"%/,'<"6"3,),6'>!g'U-")'$(')-,'#"7*,
0:')-,'/*66,%)' ? ( '04)"$%,+'2-,%' v () '$('$%/6,"(,+')0'Z8W'Sg'"%+')0'@'Sg
Ans. Q'3AcSQa'Z8QW'3Aa'Z8QW'3A
5.2.4 Finite Output Resistance in Saturation
JO*")$0%'EW8Q@K'"%+')-,'/066,(<0%+$%&'7"6&,5($&%"7',O*$#"7,%)'/$6/*$)'$%'I$&8'W8@W1'"('2,77'"(
)-,'&6"<-('$%'I$&8'W8@C1'$%+$/"),')-")'$%'(")*6")$0%1'+('$('$%+,<,%+,%)'0:' v()8'9-*(1'"'/-"%&,
∆v()'$%')-,'+6"$%5)05(0*6/,'#07)"&,'/"*(,('"'>,60'/-"%&,'$%'+(1'2-$/-'$3<7$,(')-")')-,'$%/6,5
3,%)"7'6,($()"%/,'700P$%&'$%)0')-,'+6"$%'0:'"'(")*6"),+'FGHIJ9'$('$%:$%$),8'9-$(1'-02,#,61
$('"%'$+,"7$>")$0%'4"(,+'0%')-,'<6,3$(,')-")'0%/,')-,'/-"%%,7'$('<$%/-,+'0::'")')-,'+6"$%',%+1
:*6)-,6'$%/6,"(,('$%' v()'-"#,'%0',::,/)'0%')-,'/-"%%,7m('(-"<,8'L*)1'$%'<6"/)$/,1'$%/6,"($%&' v()
4,;0%+' v:8'+0,('"::,/)')-,'/-"%%,7'(03,2-")8'H<,/$:$/"77;1'"(' v()'$('$%/6,"(,+1')-,'/-"%%,7
<$%/-50::'<0$%)'$('30#,+'(7$&-)7;'"2";':603')-,'+6"$%1')02"6+')-,'(0*6/,8'9-$('$('$77*()6"),+
$%'I$&8'W8@N1':603'2-$/-'2,'%0),')-")')-,'#07)"&,'"/60((')-,'/-"%%,7'6,3"$%('/0%()"%)'")'v:8 1
"%+')-,'"++$)$0%"7'#07)"&,'"<<7$,+')0')-,'+6"$%'"<<,"6('"('"'#07)"&,'+60<'"/60((')-,'%"6602
+,<7,)$0%'6,&$0%'4,)2,,%')-,',%+'0:')-,'/-"%%,7'"%+')-,'+6"$%'6,&$0%8'9-$('#07)"&,'"//,7,65
"),(')-,',7,/)60%(')-")'6,"/-')-,'+6"$%',%+'0:')-,'/-"%%,7'"%+'(2,,<(')-,3'"/60((')-,'+,<7,5
)$0%'6,&$0%'$%)0')-,'+6"$%8'`0),1'-02,#,61')-")'E2$)-'+,<7,)$0%57";,6'2$+,%$%&K')-,'/-"%%,7
253
254 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Source
Drain
Channel
#
vOV
!
L # !L
# ! vDS # vOV
!L
L
Figure 5.16 =%/6,"($%&'v()'4,;0%+'v()(")0/"*(,(')-,'/-"%%,7'<$%/-50::'<0$%)')0'30#,'(7$&-)7;'"2";':603')-,'
+6"$%1')-*('6,+*/$%&')-,',::,/)$#,'/-"%%,7'7,%&)-'E4;'∆&K8
7,%&)-' $(' $%' ,::,/)' 6,+*/,+1' :603' &' )0' & ' ∆& 1' "' <-,%03,%0%' P%02%' "(' %9(**&.3.&*,-9
B"'#.(-)"*8' `021' ($%/,' +(' $(' $%#,6(,7;' <60<06)$0%"7' )0' )-,' /-"%%,7' 7,%&)-' EJO8' W8Q@K1' +(
$%/6,"(,('2$)-'v()8'
9-$(' ,::,/)' /"%' 4,' "//0*%),+' :06' $%' )-,' ,B<6,(($0%' :06' + ( ' 4;' $%/7*+$%&' "' :"/)06
@ ( λ ( v () ' v :8 )'061':06'($3<7$/$);1' ( @ ( λ v () )1
@
'
Q
+ ( & 555 > ′! 55555 ( v *) ' 8 #! ) ( @ ( λ v () )
Q &
EW8QCK
'@
!,6,' λ '$('"'+,#$/,'<"6"3,),6'-"#$%&')-,'*%$)('0:'6,/$<60/"7'#07)('( S )8'9-,'#"7*,'0:' λ '+,<,%+(
40)-'0%')-,'<60/,(('),/-%070&;'*(,+')0':"46$/"),')-,'+,#$/,'"%+'0%')-,'/-"%%,7'7,%&)-'&')-")')-,
/$6/*$)'+,($&%,6'(,7,/)(8'H<,/$:$/"77;1')-,'#"7*,'0:' λ '$('3*/-'7"6&,6':06'%,2,6'(*43$/60%'),/-%075
0&$,(' )-"%' :06' 07+,6' ),/-%070&$,(8' 9-$(' 3"P,(' $%)*$)$#,' (,%(,D' `,2,6' ),/-%070&$,(' -"#,' #,6;
(-06)' /-"%%,7(1' "%+' "6,' )-*(' 3*/-' &6,")7;' $3<"/),+' 4;' )-,' /-"%%,757,%&)-' 30+*7")$0%' ,::,/)8
A7(01':06'"'&$#,%'<60/,(('),/-%070&;1'λ '$('$%#,6(,7;'<60<06)$0%"7')0'&8'
A');<$/"7'(,)'0:'+(Vv()'/-"6"/),6$()$/('(-02$%&')-,',::,/)'0:'/-"%%,757,%&)-'30+*7")$0%'$(
+$(<7";,+'$%'I$&8'W8@f8'9-,'04(,6#,+'7$%,"6'+,<,%+,%/,'0:'+('0%'v()'$%')-,'(")*6")$0%'6,&$0%'$(
6,<6,(,%),+'$%'JO8'EW8QCK'4;')-,':"/)06'E@'+' λ v()K8'I603'I$&8'W8@f'2,'04(,6#,')-")'2-,%')-,
()6"$&-)57$%,' +(Vv()' /-"6"/),6$()$/(' "6,' ,B)6"<07"),+1' )-,;' $%),6/,<)' )-,' v()' "B$(' ")' )-,' <0$%)1
v() = −8G1' 2-,6,' 8G' $(' "' <0($)$#,' #07)"&,8' JO*")$0%' EW8QCK1' -02,#,61' $%+$/"),(' )-")' +(' =' Z
") v () = ' @ ⁄ λ 8 '=)':07702(')-")'
@
8 G = 555 ''
λ
"%+')-*('8G'$('"'+,#$/,'<"6"3,),6'2$)-')-,'+$3,%($0%('0:'S8'I06'"'&$#,%'<60/,((1'8G'$('<605
<06)$0%"7')0')-,'/-"%%,7'7,%&)-'&')-")')-,'+,($&%,6'(,7,/)(':06'"'FGHIJ98'U,'/"%'$(07"),')-,
+,<,%+,%/,'0:'8G'0%'&'4;',B<6,(($%&'$)'"(
8 G = 8 G′ &
2-,6,' 8 G′' $(' ,%)$6,7;' <60/,((5),/-%070&;' +,<,%+,%)' 2$)-' )-,' +$3,%($0%(' 0:' #07)(' <,6' 3$/60%8
9;<$/"77;1'8 G′ ':"77('$%')-,'6"%&,'0:'W'Scµ3')0'WZ'Scµ38'9-,'#07)"&,'8G'$('*(*"77;'6,:,66,+')0'"(')-,
J"67;'#07)"&,1'":),6'M8'F8'J"67;1'2-0'+$(/0#,6,+'"'($3$7"6'<-,%03,%0%':06')-,'LM9'E?-"<),6'NK8'''
JO*")$0%' EW8QCK' $%+$/"),(' )-")' 2-,%' /-"%%,757,%&)-' 30+*7")$0%' $(' )"P,%' $%)0' "//0*%)1
)-, (")*6")$0%' #"7*,(' 0:' +(' +,<,%+' 0%' v()8' 9-*(1' :06' "' &$#,%' v*)1' "' /-"%&,' ∆ v()' ;$,7+(' "
/066,(<0%+$%&'/-"%&,'∆+('$%')-,'+6"$%'/*66,%)'+(8'=)':07702(')-")')-,'0*)<*)'6,($()"%/,'0:')-, /*66,%)
(0*6/,'6,<6,(,%)$%&'+('$%'(")*6")$0%'$('%0'70%&,6'$%:$%$),8'^,:$%$%&')-,'0*)<*)'6,($()"%/,'6$'"(f'
f
=%')-$('400P'2,'*(,'6$')0'+,%0),')-,'0*)<*)'6,($()"%/,'$%'(")*6")$0%1'"%+'6()')0'+,%0),')-,'+6"$%5)05(0*6/,
6,($()"%/,'$%')-,')6$0+,'6,&$0%1':06'(3"77'v()8
5.2 Current–Voltage Characteristics
iD
Triode
Saturation
VOV
1
Slope "
ro
0
#VA " #1/ ,
vDS
Figure 5.17 J::,/)'0:'v()'0%'+('$%')-,'(")*6")$0%'6,&$0%8'9-,'FGHIJ9'<"6"3,),6'8G'+,<,%+('0%')-,'<605
/,(('),/-%070&;'"%+1':06'"'&$#,%'<60/,((1'$('<60<06)$0%"7')0')-,'/-"%%,7'7,%&)-'&8
!
vGS
)
tn
#
Figure 5.18 T"6&,5($&%"7',O*$#"7,%)'/$6/*$)'30+,7'0:')-,'!5/-"%%,7'FGHIJ9'$%'(")*6")$0%1'$%/06<06")$%&
)-,' 0*)<*)' 6,($()"%/,' 6$8' 9-,' 0*)<*)' 6,($()"%/,' 30+,7(' )-,' 7$%,"6' +,<,%+,%/,' 0:' +(' 0%' v()' "%+' $(' &$#,%' 4;
JO8 EW8QCK8'
∂ + ( '@
5
6 $ ≡ 5555555555
EW8QbK
∂ v () v*) /0%()"%)
"%+'*($%&'JO8'EW8QCK'6,(*7)('$%
> !′ '
5 55555 ( 8 ' 8 #! ) Q
6 $ = λ 55555
Q & *)
'@
EW8QWK
2-$/-'/"%'4,'26$)),%'"(
@
6 $ = 55555555
λ ?(
EW8QNK
8
6 $ = 55555G5
?(
EW8QfK
061',O*$#"7,%)7;1
2-,6,'?('$(')-,'+6"$%'/*66,%)'C+#B$-#'/-"%%,757,%&)-'30+*7")$0%')"P,%'$%)0'"//0*%)a')-")'$(1
@ 0'
Q
? ( = 555 > !′ 555555 '( 8 *) ' 8 #! )
Q &
EW8Qf′K
255
256 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
9-*(' )-,' 0*)<*)' 6,($()"%/,' $(' $%#,6(,7;' <60<06)$0%"7' )0' )-,' +6"$%' /*66,%)8' I$%"77;1' 2,
(-02'$%'I$&8'W8@d')-,'7"6&,5($&%"71',O*$#"7,%)5/$6/*$)'30+,7'$%/06<06")$%&'6$H
EXERCISE
5.6' A%'`FGH')6"%($()06'$(':"46$/"),+'$%'"'Z8b5µ3'<60/,(('-"#$%&'µ!<$%'='QZZ'µAcSQ'"%+'8′G = WZ'Scµ3
0:'/-"%%,7'7,%&)-8'=:'&0='Z8d'µ3'"%+'''= 16 µ31':$%+'8G'"%+'λ8'I$%+')-,'#"7*,'0:'?(')-")'6,(*7)('2-,%
)-,'+,#$/,'$('0<,6"),+'2$)-'"%'0#,6+6$#,'#07)"&,'8:8'='Z8W'S'"%+'8()'='@'S8'A7(01':$%+')-,'#"7*,'0:'6$
")')-$('0<,6")$%&'<0$%)8'=:'8()'$('$%/6,"(,+'4;'Q'S1'2-")'$(')-,'/066,(<0%+$%&'/-"%&,'$%'?(g
Ans. bZ'Sa'Z8ZQW'S−@a'Z8W@'3Aa'dZ'PΩa'Z8ZQW'3A
5.2.5 Characteristics of the p-Channel MOSFET
9-,'/$6/*$)'(;3407':06')-,'"5/-"%%,7',%-"%/,3,%)5);<,'FGHIJ9'$('(-02%'$%'I$&8'W8@[E"K8
I$&*6,'W8@[E4K'(-02('"'30+$:$,+'/$6/*$)'(;3407'$%'2-$/-'"%'"6602-,"+'<0$%)$%&'$%')-,'%065
3"7' +$6,/)$0%' 0:' /*66,%)' :702' $(' $%/7*+,+' 0%' )-,' (0*6/,' ),63$%"78' I06' )-,' /"(,' 2-,6,' )-,
(0*6/,'$('/0%%,/),+')0')-,'(*4()6"),1')-,'($3<7$:$,+'(;3407'0:'I$&8'W8@[E/K'$('*(*"77;'*(,+8'
S
G
S
B
G
B
D
(a)
D
(b)
(c)
Figure 5.19 1(2'?$6/*$)'(;3407':06')-,'"5/-"%%,7',%-"%/,3,%)5);<,'FGHIJ98'1/2'F0+$:$,+'(;3407'2$)"%'"6602-,"+'0%')-,'(0*6/,'7,"+8'1%2'H$3<7$:$,+'/$6/*$)'(;3407':06')-,'/"(,'2-,6,')-,'(0*6/,'$('/0%%,/),+
)0')-,'40+;8
9-,' 6,&$0%(' 0:' 0<,6")$0%' 0:' )-,' _FGH' )6"%($()06' "%+' )-,' /066,(<0%+$%&' /0%+$)$0%(
"%+',B<6,(($0%':06' + ( '"6,'(-02%'$%'9"47,'W8Q8'G4(,6#,')-")')-,',O*")$0%('"6,'26$)),%'$%'"
2";')-")',3<-"($>,('<-;($/"7'$%)*$)$0%'"%+'"#0$+(')-,'/0%:*($0%'0:'%,&")$#,'($&%(8'9-*(
2-$7,' 8 #"'$('4;'/0%#,%)$0%'%,&")$#,1'2,'*(,' 8 #" 1'"%+')-,'#07)"&,(' v )* '"%+' v )( '"6,'<0($5
)$#,8'A7(01'$%'"77'0:'0*6'/$6/*$)'+$"&6"3('2,'2$77'"72";('+6"20"5/-"%%,7'+,#$/,('2$)-')-,$6
(0*6/,(' 0%' )0<' (0' )-")' /*66,%)' :702(' :603' )0<' )0' 40))038' I$%"77;1' 2,' %0),' )-")' _FGH
+,#$/,(' "7(0' (*::,6' :603' )-,' /-"%%,757,%&)-' 30+*7")$0%' ,::,/)8' 9-$(' /"%' 4,' )"P,%' $%)0
"//0*%)' 4;' $%/7*+$%&' "' :"/)06' ( @ ( λ v )( ) ' $%' )-,' (")*6")$0%56,&$0%' ,B<6,(($0%' :06' + (' "(
:07702(
@ '
Q
EW8QdK
+ ( & 555 > "′ 55555 ( v )* ' 8 #" ) ( @ ( λ v )( )
Q &
257
06',O*$#"7,%)7;
v )( @ '
Q
+ ( & 555 > "′ 55555 ( v )* ' 8 #" ) @ ( 55555555
5
Q
&
8G
EW8Q[K
2-,6,' λ ' "%+' 8 G' E)-,' J"67;' #07)"&,' :06' )-,' _FGH' )6"%($()06K' "6,' 4;' /0%#,%)$0%' %,&")$#,
O*"%)$)$,(1'-,%/,'2,'*(,' λ '"%+' 8 G 8
I$%"77;1'2,'(-0*7+'%0),')-")':06'"'&$#,%'?FGH':"46$/")$0%'<60/,(('λ !'"%+' λ " '"6,'&,%,65
"77;'%0)',O*"71'"%+'($3$7"67;':06'8 G!'"%+' 8 G" 8
90'6,/"<1')0')*6%'"'_FGH')6"%($()06'0%1')-,'&"),'#07)"&,'-"(')0'4,'3"+,'702,6')-"%')-")
0:')-,'(0*6/,'4;'")'7,"()' 8 #" 8'90'0<,6"),'$%')-,')6$0+,'6,&$0%1')-,'+6"$%'#07)"&,'-"(')0',B/,,+
)-")'0:')-,'&"),'4;'")'7,"()' 8 #" a'0)-,62$(,1')-,'_FGH'0<,6"),('$%'(")*6")$0%8'I$%"77;1'I$&8'W8QZ
<60#$+,('"'<$/)06$"7'6,<6,(,%)")$0%'0:')-,(,'0<,6")$%&'/0%+$)$0%(8'
Table 5.2 Regions of Operation of the Enhancement PMOS Transistor
+
−
iD
+
vSG
vDG
( ) v 2OV
+
iD
Saturation
vSD ≥ |vOV|
1 ) W
k
2 p L
vSD
−
Triode
vSD < |vOV|
vSG = |Vtp| + |vOV|
Cut-off
vSG < |Vtp|
−
Slope =
gDS = r1 0
|v OV|
DS
|v |
= k p) ( W
L ) OV
v SD
v )* < 8 #" D'%0'/-"%%,7a')6"%($()06'$%'/*)50::a' + ( & Z
v )* & 8 #" ( v :8 D'"'/-"%%,7'$('$%+*/,+a')6"%($()06'0<,6"),('$%')-,')6$0+,'6,&$0%'06'$%')-,'(")*6")$0%'6,&$0%
+,<,%+$%&'0%'2-,)-,6')-,'/-"%%,7'$('/0%)$%*0*('06'<$%/-,+50::'")')-,'+6"$%',%+a
96+$,/0F/7+$!
?0%)$%*0*('/-"%%,71'04)"$%,+'4;D
)2#-62#+$!0F/7+$!
_$%/-,+50::'/-"%%,71'04)"$%,+'4;D
v (* > 8 #"
06',O*$#"7,%)7;D
v (* * 8 #"
06',O*$#"7,%)7;
v )( < v :8
9-,%1
v )( ' v :8
9-,%
'
@ Q
+ ( & > "′ 55555 ( v )* ' 8 #" ) v )( ' 555 v )(
&
Q
06',O*$#"7,%)7;
'
@
+ ( & > "′ 55555 v :8 ' 555 v )( v )(
& Q
Q
@
'
+ ( & 555 > "′ 55555 ( v )* ' 8 #" )
Q
&
06',O*$#"7,%)7;
@
'
+ ( & 555 > "′ 55555 v Q:8
Q &
258 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Voltage
S
Threshold
Vtp
G
Overdrive
voltage
Triode VOV
Vtp
Saturation
D
Figure 5.20 9-,'6,7")$#,'7,#,7('0:')-,'),63$%"7'
#07)"&,('0:')-,',%-"%/,3,%)5);<,'_FGH')6"%($(5
)06':06'0<,6")$0%'$%')-,')6$0+,'6,&$0%'"%+'$%')-,'
(")*6")$0%'6,&$0%8
EXERCISE
Q
5.7' 9-,'_FGH')6"%($()06'(-02%'$%'I$&8'JW8f'-"(' 8 #" = ' @'S1'>′" = NZ'µAc S 1 "%+' ' ⁄ & = @Z8
E"K'I$%+')-,'6"%&,'0:'8*':06'2-$/-')-,')6"%($()06'/0%+*/)(8'
E4K'=%'),63('0:08*1':$%+')-,'6"%&,'0:'8(':06'2-$/-')-,')6"%($()06'0<,6"),('$%')-,')6$0+,'6,&$0%8'
E/K'=%'),63('0:'8*1':$%+')-,'6"%&,'0:'8(':06'2-$/-')-,')6"%($()06'0<,6"),('$%'(")*6")$0%8'
E+K'`,&7,/)$%&'/-"%%,757,%&)-'30+*7")$0%'E$8,81'"((*3$%&'λ'='ZK1':$%+')-,'#"7*,('0: 8:8 '"%+'8*'
"%+')-,'/066,(<0%+$%&'6"%&,'0:'8(')0'0<,6"),')-,')6"%($()06'$%')-,'(")*6")$0%'30+,'2$)-'?( ='fW'µA8'
E,K'=:'λ'='−Z8ZQ'S−@1':$%+')-,'#"7*,'0:'6$'/066,(<0%+$%&')0')-,'0#,6+6$#,'#07)"&,'+,),63$%,+'$% E+K8''
E:K'I06'λ'='−Z8ZQ'S−@'"%+':06')-,'#"7*,'0:'8:8'+,),63$%,+'$%'E+K1':$%+'?('")'8(0= +C'S'"%+'")'8('='Z Sa
-,%/,1'/"7/*7"),')-,'#"7*,'0:')-,'"<<"6,%)'0*)<*)'6,($()"%/,'$%'(")*6")$0%8'?03<"6,')0')-,'#"7*,':0*%+
$% E,K8
!5 V
VG
ID
VD
Figure E5.7
Ans. E"K'8 * ≤ '+b'Sa'E4K'8 ( ≥ 8 * + @a'E/K'8 ( ≤ 8 * + @a'E+K'Z8W'S1'C8W'S1' ≤ b8W'Sa'E,K'Z8Nf'FΩa
E:K fd'µA1'dQ8W'µA1'Z8Nf'FΩ'E("3,K
5.3 MOSFET Circuits at DC
!"#$%&'()*+$,+')-,'/*66,%)V#07)"&,'/-"6"/),6$()$/('0:'FGHIJ9(1'2,'%02'/0%($+,6'/$6/*$)(
$%'2-$/-'0%7;'+/'#07)"&,('"%+'/*66,%)('"6,'0:'/0%/,6%8'H<,/$:$/"77;1'2,'(-"77'<6,(,%)'"'(,6$,(
0:'+,($&%'"%+'"%"7;($(',B"3<7,('0:'FGHIJ9'/$6/*$)('")'+/8'9-,'04.,/)$#,'$(')0'$%()$77'$%')-,
6,"+,6'"':"3$7$"6$);'2$)-')-,'+,#$/,'"%+')-,'"4$7$);')0'<,6:063'FGHIJ9'/$6/*$)'"%"7;($('40)6"<$+7;'"%+',::,/)$#,7;8
=%')-,':07702$%&',B"3<7,(1')0'P,,<'3")),6('($3<7,'"%+')-*(':0/*('")),%)$0%'0%')-,',((,%/,
0:'FGHIJ9'/$6/*$)'0<,6")$0%1'2,'2$77'&,%,6"77;'%,&7,/)'/-"%%,757,%&)-'30+*7")$0%a')-")'$(1
2,'2$77'"((*3,'λ'='Z8'U,'2$77':$%+'$)'/0%#,%$,%)')0'206P'$%'),63('0:')-,'0#,6+6$#,'#07)"&,a
8:8 '='8*) − 8#!':06'`FGH'"%+' 8 :8 & 8 )* ' 8 #" ':06'_FGH8
5.3 MOSFET Circuits at DC
Example 5.3
^,($&%')-,'/$6/*$)'0:'I$&8'W8Q@1')-")'$(1'+,),63$%,')-,'#"7*,('0:' F ('"%+' F )1''(0')-")')-,')6"%($()06'0<,6"),(
")'?('='Z8b'3A'"%+'8('='+Z8W'S8'9-,'`FGH')6"%($()06'-"('8#'='Z8f'S1'µ!<$%'='@ZZ'µAcSQ1'&'='@'µ31'"%+
''='CQ'µ38'`,&7,/)')-,'/-"%%,757,%&)-'30+*7")$0%',::,/)'E$8,81'"((*3,')-")'λ'='ZK8'
VDD " !2.5 V
VSS " #2.5 V
Figure 5.21 ?$6/*$)':06'JB"3<7,'W8C8
Solution
90',()"47$(-'"'+/'#07)"&,'0:'+Z8W'S'")')-,'+6"$%1'2,'3*()'(,7,/)'F('"(':07702(D
8 (( ' 8 (
5
F ( = 5555555555555555555555
?(
Q8W ' Z8W
= 555555555555555555555 = W'PΩ
Z8b
90'+,),63$%,')-,'#"7*,'6,O*$6,+':06' F ) 1'2,'%,,+')0'P%02')-,'#07)"&,'")')-,'(0*6/,1'2-$/-'/"%'4,',"($7;
:0*%+'$:'2,'P%02'8 *)8'9-$('$%')*6%'/"%'4,'+,),63$%,+':603'8 :8 8'902"6+')-")',%+1'2,'%0),')-")'($%/,'8('=
Z8W'S'$('&6,"),6')-"%'8* 1')-,'`FGH')6"%($()06'$('0<,6")$%&'$%')-,'(")*6")$0%'6,&$0%1'"%+'2,'/"%'*(,')-,'(")5
*6")$0%56,&$0%',B<6,(($0%'0:'+(')0'+,),63$%,')-,'6,O*$6,+'#"7*,'0:'8:8 1
@
' Q
? ( = 555 µ ! < $% 55555 8 :8
Q
&
9-,%'(*4()$)*)$%&'?('='Z8b'3A'='bZZ'µA1'µ!<$%'='@ZZ'µAcSQ1'"%+ ' ⁄ & = CQ ⁄ @ '&$#,(
2-$/-'6,(*7)('$%'
9-*(1
@
CQ Q
bZZ = 555 × @ZZ × 555555 8 :8
Q
@
8 :8 = Z8W'S
8 *) = 8 # + 8 :8 = Z8f + Z8W = @8Q'S
i,:,66$%&')0'I$&8'W8Q@1'2,'%0),')-")')-,'&"),'$('")'&60*%+'<0),%)$"78'9-*(1')-,'(0*6/,'3*()'4,'")'−@8Q'S1'"%+')-,
6,O*$6,+'#"7*,'0:'F)'/"%'4,'+,),63$%,+':603
8 ) ' 8 ))
5
F ) = 5555555555555555555
?(
−@8Q' ' ' ( ' Q8W )
= 5555555555555555555555555555555555 = C8QW'PΩ
Z8b
259
260 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
EXERCISE
D5.8 i,+,($&%'')-, '/$6/*$)'0:'I$&8'W8Q@':06')-,':07702$%&'/"(,D08(('=' −8))' ='Q8W'S1'8#'='@'S1'µ!<$%'='NZ
µAcSQ1'' ' ⁄ & = @QZ'µ3 ⁄ C 'µ31 ?('='Z8C'3A1'"%+'8('='+Z8b'S8
Ans. F('='f'PΩ; F)0= C8C'PΩ
Example 5.4
I$&*6,'W8QQ'(-02('"%'`FGH')6"%($()06'2$)-'$)('+6"$%'"%+'&"),'),63$%"7('/0%%,/),+')0&,)-,68'I$%+')-,' + ' v
6,7")$0%(-$<' 0:' )-,' 6,(*7)$%&' )205),63$%"7' +,#$/,' $%' ),63(' 0:' )-,' FGHIJ9' <"6"3,),6(' > ! & >′! ( ' ⁄ & )
"%+'8 #! 8'`,&7,/)'/-"%%,757,%&)-'30+*7")$0%'E$8,81'λ ' & ZK 8'`0),')-")')-$(')205),63$%"7'+,#$/,'$('P%02%'"('"
')"'&3%"**&%-&'+-$(*!)!-"$8
i
!
v
#
Figure 5.22
Solution
H$%/,'v ( & v *'$3<7$,('0<,6")$0%'$%')-,'(")*6")$0%'30+,1'
@ '
Q
+ ( & 555 >′! 55555 ( v *) ' 8 #! )
Q &
`021'+ & + ( '"%+' v & v *) 1')-*('
@ '
Q
+ & 555 >′! 55555 ( v ' 8 #! )
Q &
'
i,<7"/$%&' >′! 55555 '4;'> ! '6,(*7)('$%'
&
@
Q
+ & 555 > ! ( v ' 8 #! )
Q
5.3 MOSFET Circuits at DC
EXERCISES
D5.9 I06')-,'/$6/*$)'$%'I$&8'JW8[1':$%+')-,'#"7*,'0:'F')-")'6,(*7)('$%' 8 ( & Z8d'S8''9-,'FGHIJ9'-"(
Z8fQ'µ3
8 #! & Z8W'S1' µ ! < $% & Z8b '3AcSQ1'' ⁄ & & 555555555555555555555 1'"%+'λ & Z8
Z8@d'µ3
Ans. @C8['PΩ
!1.8 V
R
VD
Q1
Figure E5.9
D5.10 I$&*6,'JW8@Z1'(-02('"'/$6/*$)'04)"$%,+'4;'"*&3,%)$%&')-,'/$6/*$)'0:'I$&8'JW8['/0%($+,6,+'$%'JB,65
/$(,'W8['2$)-'"')6"%($()06'; Q'$+,%)$/"7')0'; @'"%+'"'6,($()"%/,' F Q8'I$%+')-,'#"7*,'0:' F Q')-")'6,(*7)('$%
; Q'0<,6")$%&'")')-,',+&,'0:')-,'(")*6")$0%'6,&$0%8'n(,';0*6'(07*)$0%')0'JB,6/$(,'W8[8
Ans. QZ8d'PΩ
VDD!1.8 V
R2
R
Q2
Q1
Figure E5.10
Example 5.5
^,($&%')-,'/$6/*$)'$%'I$&8'W8QC')0',()"47$(-'"'+6"$%'#07)"&,'0:'Z8@'S8'U-")'$(')-,',::,/)$#,'6,($()"%/,'4,)2,,%
Q
+6"$%'"%+'(0*6/,'")')-$('0<,6")$%&'<0$%)g'T,)'8 #! = @'S'"%+' > !′ ( ' ⁄ & ) = @'3AcS 8
VDD " !5 V
ID
RD
VD " !0.1 V
Figure 5.23 ?$6/*$)':06'JB"3<7,'W8W8
261
262 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.5 continued
Solution
H$%/,')-,'+6"$%'#07)"&,'$('702,6')-"%')-,'&"),'#07)"&,'4;'b8['S'"%+'8 #! = @'S1')-,'FGHIJ9'$('0<,6")$%&
$%')-,')6$0+,'6,&$0%8'9-*(')-,'/*66,%)'?('$('&$#,%'4;
@ Q
'
? ( = > !′ 55555 ( 8 *) ' 8 #! )8 () ' 555 8 ()
Q
&
@
? ( = @ × ( W ' @ ) × Z8@ ' 555 × Z8Z@
Q
= Z8C[W'3A
9-,'6,O*$6,+'#"7*,':06'F('/"%'4,':0*%+'"(':07702(D
8 (( ' 8 (
5
F ( = 5555555555555555555555
?(
W ' Z8@
= 5555555555555555 = @Q8b'PΩ
Z8C[W
=%'"'<6"/)$/"7'+$(/6,),5/$6/*$)'+,($&%'<6047,31'0%,'(,7,/)(')-,'/70(,()'()"%+"6+'#"7*,'"#"$7"47,':061'(";1'Wo
6,($()06(p$%')-$('/"(,1'@Q'PΩa'(,,'A<<,%+$B']8'H$%/,')-,')6"%($()06'$('0<,6")$%&'$%')-,')6$0+,'6,&$0%'2$)-'"
(3"77'8()1')-,',::,/)$#,'+6"$%5)05(0*6/,'6,($()"%/,'/"%'4,'+,),63$%,+'"(':07702(D
8 ()
5
6 () = 55555555
?(
Z8@
= 5555555555555 = QWC'Ω
Z8C[W
EXERCISE
5.11' =:'$%')-,'/$6/*$)'0:'JB"3<7,'W8W')-,'#"7*,'0:'F('$('+0*47,+1':$%+'"<<60B$3"),'#"7*,(':06'?('"%+'8(8
Ans. Z8Q'3Aa'Z8ZW'S
5.3 MOSFET Circuits at DC
Example 5.6
A%"7;>,')-,'/$6/*$)'(-02%'$%'I$&8'W8QbE"K')0'+,),63$%,')-,'#07)"&,('")'"77'%0+,('"%+')-,'/*66,%)(')-60*&"77' 46"%/-,(8' T,)'8 #! = @'S' "%+' > !′ ( ' ⁄ & ) = @'3AcS Q 8' `,&7,/)' )-,' /-"%%,757,%&)-' 30+*7")$0%' ,::,/)
E$8,81'"((*3,' λ = ZK8
VDD " !10 V
!10 V
0.5 µA
ID
RD " 6 k( 10 M(
RG1 " 10 M(
6 k(
0
10 # 6 ID
!5 V
6 ID
RG2 " 10 M(
RS " 6 k(
10 M(
6 k(
ID
(a)
(b)
Figure 5.24 1(2'?$6/*$)':06'JB"3<7,'W8N8'1/2'9-,'/$6/*$)'2$)-'(03,'0:')-,'"%"7;($('+,)"$7('(-02%8
Solution
H$%/,')-,'&"),'/*66,%)'$('>,601')-,'#07)"&,'")')-,'&"),'$('($3<7;'+,),63$%,+'4;')-,'#07)"&,'+$#$+,6':063,+
4;')-,')20'@Z5FΩ'6,($()06(1
F *Q
@Z
5 = @Z × 555555555555555555 = +W'S
8 * = 8 (( 55555555555555555555555
@Z + @Z
F *Q + F *@
U$)-')-$('<0($)$#,'#07)"&,'")')-,'&"),1')-,'`FGH')6"%($()06'2$77'4,')*6%,+'0%8'U,'+0'%0)'P%021'-02,#,61
2-,)-,6')-,')6"%($()06'2$77'4,'0<,6")$%&'$%')-,'(")*6")$0%'6,&$0%'06'$%')-,')6$0+,'6,&$0%8'U,'(-"77'"((*3,
(")*6")$0%56,&$0%'0<,6")$0%1'(07#,')-,'<6047,31'"%+')-,%'/-,/P')-,'#"7$+$);'0:'0*6'"((*3<)$0%8'G4#$0*(7;1
$:' 0*6' "((*3<)$0%' )*6%(' 0*)' %0)' )0' 4,' #"7$+1' 2,' 2$77' -"#,' )0' (07#,' )-,' <6047,3' "&"$%' :06' )6$0+,56,&$0%
0<,6")$0%8
i,:,6' )0' I$&8' W8QbE4K8' H$%/,' )-,' #07)"&,' ")' )-,' &"),' $(' W' S' "%+' )-,' #07)"&,' ")' )-,' (0*6/,' $(
? ( ' ( 3A ) × N' ( PΩ ) = N? ( 1 '2,'-"#,
8 *) = W ' N? (
9-*(1'?('$('&$#,%'4;
@ '
Q
? ( = 555 > !′ 55555 ( 8 *) ' 8 #! )
Q &
@
Q
= 555 × @ × ( W ' N? ( ' @ )
Q
2-$/-'6,(*7)('$%')-,':07702$%&'O*"+6")$/',O*")$0%'$%'?(D
Q
@d? ( ' QW? ( + d = Z
263
264 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.6 continued
9-$(',O*")$0%';$,7+(')20'#"7*,(':06'?(D'Z8d['3A'"%+'Z8W'3A8'9-,':$6()'#"7*,'6,(*7)('$%'"'(0*6/,'#07)"&,'0:
N × Z8d[ = W8Cb S1 '2-$/-'$('&6,"),6')-"%')-,'&"),'#07)"&,'"%+'+0,('%0)'3"P,'<-;($/"7'(,%(,'"('$)'20*7+
$3<7;')-")')-,'`FGH')6"%($()06'$('/*)'0::8'9-*(1
? ( = Z8W'3A
8 ) = Z8W × N = +C'S
8 *) = W ' C = Q'S
8 ( = @Z ' N × Z8W = +f'S
H$%/,' 8 ( > 8 * ' 8 #! 1 ')-,')6"%($()06'$('0<,6")$%&'$%'(")*6")$0%1'"('$%$)$"77;'"((*3,+8
EXERCISES
5.12' I06')-,'/$6/*$)'0:'I$&8'W8Qb1'2-")'$(')-,'7"6&,()'#"7*,')-")'F('/"%'-"#,'2-$7,')-,')6"%($()06'6,3"$%(
$%')-,'(")*6")$0%'30+,g
Ans. @Q'PΩ
D5.13' i,+,($&%')-,'/$6/*$)'0:'I$&8'W8Qb':06')-,':07702$%&'6,O*$6,3,%)(D' 8 (( = +W'S1 ? ( = Z8CQ'3A1
8) = @8N S1'8('='C8b'S1'2$)-'"'@5µA'/*66,%)')-60*&-')-,'#07)"&,'+$#$+,6'F*@1'F*Q8'A((*3,')-,'("3,
FGHIJ9'"('$%'JB"3<7,'W8N8
Ans. F*@'='@8N'FΩa'F*Q'='C8b'FΩ1'F)'='F('='W'PΩ
Example 5.7
^,($&%' )-,' /$6/*$)' 0:' I$&8' W8QW' (0' )-")' )-,' )6"%($()06' 0<,6"),(' $%' (")*6")$0%' 2$)-' ? ( = Z8W'3A ' "%+
8 ( = +C'S8 T,)' )-,' ,%-"%/,3,%)5);<,' _FGH' )6"%($()06' -"#,' 8 #" = ' @'S ' "%+' > "′ ( ' ⁄ & ) = ' @ 3AcSQ8
A((*3,'λ'='Z8'U-")'$(')-,'7"6&,()'#"7*,')-")'F('/"%'-"#,'2-$7,'3"$%)"$%$%&'(")*6")$0%56,&$0%'0<,6")$0%g
VDD " !5 V
RG1
VD " !3 V
RG2
RD
ID " 0.5 mA
Figure 5.25 ?$6/*$)':06'JB"3<7,'W8f8
5.3 MOSFET Circuits at DC
Solution
H$%/,')-,'FGHIJ9'$(')0'4,'$%'(")*6")$0%1'2,'/"%'26$),
@ '
Q
? ( & 555 > "′ 55555 8:8
Q &
Q
H*4()$)*)$%&'?('='Z8W'3A'"%+' > "′' ⁄ & = @'3AcS 1'2,'04)"$%
8 :8 = @'S
"%+
8 )* & 8 #" ( 8 :8 & @ ( @ & Q'S
H$%/,')-,'(0*6/,'$('")'+W'S1')-,'&"),'#07)"&,'3*()'4,'(,)')0'+C'S8'9-$('/"%'4,'"/-$,#,+'4;')-, "<<60<6$"),
(,7,/)$0%'0:')-,'#"7*,('0:'F*@'"%+'F*Q8'A'<0(($47,'(,7,/)$0%'$('F*@'='Q'FΩ'"%+'F*Q'='C'FΩ8
9-,'#"7*,'0:'F('/"%'4,':0*%+':603
8
C
F ( = 555555( = 5555555 = N'PΩ
?(
Z8W
H")*6")$0%530+,'0<,6")$0%'2$77'4,'3"$%)"$%,+'*<')0')-,'<0$%)')-")'8(',B/,,+('8*'4;' 8 #" a )-")'$(1'*%)$7
8 ( 3"B = C + @ = b'S
9-$('#"7*,'0:'+6"$%'#07)"&,'$('04)"$%,+'2$)-'F('&$#,%'4;
b
F ( = 5555555 = d'PΩ
Z8W
EXERCISE
D5.14 'I06')-,'/$6/*$)'$%'I$&8'JW8@b1':$%+')-,'#"7*,'0:'F')-")'6,(*7)('$%')-,'_FGH')6"%($()06'0<,6")$%&'2$)"%'0#,6+6$#,'#07)"&,' 8 :8 & Z8N'S8'9-,')-6,(-07+'#07)"&,'$(' 8 #" & ' Z8b'S1')-,'<60/,((')6"%(/0%5
+*/)"%/,'<"6"3,),6'> " ′ & Z8@'3AcSQ1'"%+''c&'e'@Z'µ3cZ8@d'µ38
Ans. dZZ'Ω
"1.8 V
R
Figure E5.14
265
266 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.8
9-,' `FGH' "%+' _FGH' )6"%($()06(' $%' )-,' /$6/*$)' 0:' I$&8' W8QNE"K' "6,' 3")/-,+1' 2$)- > !′ ( ' ! ⁄ & ! ) =
Q
> "′( ' " ⁄ & " ) = @'3AcS '"%+' 8 #! = ' 8 #" = @'S8 'A((*3$%&' λ = Z ':06'40)-'+,#$/,(1':$%+')-,'+6"$%'/*65
6,%)('+(I'"%+'+(J1'"('2,77'"(')-,'#07)"&,'v: 1':06' v ? = Z'S1 +Q8W'S1'"%+' ' Q8W'S8
!2.5 V
!2.5 V
QP
QP
iDP
vI
vO
iDN
QN
IDP
vO
0V
IDN
QN
10 k(
#2.5 V
#2.5 V
(a)
(b)
10 k(
!2.5 V
QP
!2.5 V
IDN
QN
IDP
vO #2.5 V
vO
IDN
IDP
10 k(
10 k(
#2.5 V
(c)
(d)
Figure 5.26 ?$6/*$)(':06'JB"3<7,'W8d8
Solution
I$&*6,'W8QNE4K'(-02(')-,'/$6/*$)':06')-,'/"(,' v ? = Z'S8'U,'%0),')-")'($%/,';I'"%+';J'"6,'<,6:,/)7;'3")/-,+
"%+' "6,' 0<,6")$%&' ")' ,O*"7' #"7*,(' 0:' 8 *) EQ8W' SK1' )-,' /$6/*$)' $(' (;33,)6$/"71' 2-$/-' +$/)"),(' )-")
v : = Z'S8 9-*('40)-';I'"%+';J'"6,'0<,6")$%&'2$)-' 8 (* = Z "%+1'-,%/,1'$%'(")*6")$0%8'9-,'+6"$%'/*65
6,%)('/"%'%02'4,':0*%+':603
Q
? (J = ? (I = 55@Q5 × @ × ( Q8W ' @ ) = @8@QW'3A
5.3 MOSFET Circuits at DC
267
`,B)1'2,'/0%($+,6')-,'/$6/*$)'2$)-' v ? = +Q8W'S8 '96"%($()06';J'2$77'-"#,'"'8)*'0:'>,60'"%+')-*('2$77'4,'/*)
0::1'6,+*/$%&')-,'/$6/*$)')0')-")'(-02%'$%'I$&8'W8QNE/K8'U,'%0),')-")' v:'2$77'4,'%,&")$#,1'"%+')-*('v*('2$77
4,'&6,"),6')-"%' 8 #! 1 '/"*($%&';I')0'0<,6"),'$%')-,')6$0+,'6,&$0%8'I06'($3<7$/$);'2,'(-"77'"((*3,')-")' v()'$(
(3"77'"%+')-*('*(,
?(I0"' > !′ ( ' ! ⁄ & ! ) ( 8 *) ' 8 #! ) 8 ()
= @ [ Q8W ' ( ' Q8W ) ' @ ] [ v : ' ( ' Q8W ) ]
I603')-,'/$6/*$)'+$"&6"3'(-02%'$%'I$&8'W8QNE/K1'2,'/"%'"7(0'26$),
Z ' v:
5
? (I ( 3A ) = 5555555555555555555
@Z ( PΩ )
9-,(,')20',O*")$0%('/"%'4,'(07#,+'($3*7)"%,0*(7;')0';$,7+
? (I = Z8Qbb'3A
v : = ' Q8bb'S
`0),')-")' 8 () = −Q8bb ' ( ' Q8W ) = Z8ZN'S1 2-$/-'$('(3"77'"('"((*3,+8
I$%"77;1')-,'($)*")$0%':06')-,'/"(,'v ? = ' Q8W'S'qI$&8'W8QNE+Kr'2$77'4,')-,',B"/)'/03<7,3,%)'0:')-,'/"(,
v ? = +Q8W'SD' 96"%($()06' ;I' 2$77' 4,' 0::8' 9-*(' ? (I = Z1' ;J' 2$77' 4,' 0<,6")$%&' $%' )-,' )6$0+,' 6,&$0%' 2$)? (J = Q8bb'3A'"%+' v : = +Q8bb'S8
EXERCISE
5.15' 9-,' `FGH' "%+' _FGH' )6"%($()06(' $%' )-,' /$6/*$)' 0:' I$&8' JW8@W' "6,' 3")/-,+' 2$)-' > !′ ( ' ! ⁄ & ! ) =
Q
> "′ ( ' " ⁄ & " ) = @'3AcS '"%+'8 #! = ' 8 #" = @'S8'A((*3$%&' λ = Z':06'40)-'+,#$/,(1':$%+')-,'+6"$%
/*66,%)('+(I'"%+'+(J'"%+')-,'#07)"&,'v:':06'v ? = Z'S1'+Q8W'S1'"%+'−Q8W'S8
Ans. v? '='Z'SD'Z'3A1'Z'3A1'Z'Sa'v? '='+Q8W'SD'Z8@Zb'3A1'Z'3A1'@8Zb'Sa'v? '='−Q8W'SD'Z'3A1'Z8@Zb'3A1
−@8Zb'S
!2.5 V
QN
vI
iDN
vO
iDP
QP
#2.5 V
10 k(
Figure E5.15
268 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.4 Applying the MOSFET in Amplifier Design
U,'%02'4,&$%'0*6'()*+;'0:')-,'*)$7$>")$0%'0:')-,'FGHIJ9'$%')-,'+,($&%'0:'"3<7$:$,6(8'9-,
4"($(':06')-$('$3<06)"%)'"<<7$/")$0%'$(')-")'2-,%'0<,6"),+'$%'(")*6")$0%1')-,'FGHIJ9':*%/5
)$0%('"('#07)"&,5/0%)6077,+'/*66,%)'(0*6/,D'9-,'&"),5)05(0*6/,'#07)"&,' v *)'/0%)607(')-,'+6"$%
/*66,%)' + (8' A7)-0*&-' )-,' /0%)607' 6,7")$0%(-$<' $(' %0%7$%,"6' E(O*"6,' 7"2K1' 2,' 2$77' (-06)7;
+,#$(,'"'3,)-0+':06'04)"$%$%&'"730()57$%,"6'"3<7$:$/")$0%':603')-$(':*%+"3,%)"77;'%0%7$%,"6
+,#$/,8
5.4.1 Obtaining a Voltage Amplifier
=%')-,'$%)60+*/)$0%')0'"3<7$:$,6'/$6/*$)('$%'H,/)$0%'@8W1'2,'7,"6%,+')-")'"'#07)"&,5/0%)6077,+
/*66,%)'(0*6/,'/"%'(,6#,'"('"')6"%(/0%+*/)"%/,'"3<7$:$,6a')-")'$(1'"%'"3<7$:$,6'2-0(,'$%<*)
($&%"7'$('"'#07)"&,'"%+'2-0(,'0*)<*)'($&%"7'$('"'/*66,%)8'F06,'/0330%7;1'-02,#,61'0%,'$(
$%),6,(),+'$%'#07)"&,'"3<7$:$,6(8'A'($3<7,'2";')0'/0%#,6)'"')6"%(/0%+*/)"%/,'"3<7$:$,6')0'"
#07)"&,'"3<7$:$,6'$(')0'<"((')-,'0*)<*)'/*66,%)')-60*&-'"'6,($()06'"%+')"P,')-,'#07)"&,'"/60((
)-,'6,($()06'"(')-,'0*)<*)8'^0$%&')-$(':06'"'FGHIJ9'6,(*7)('$%')-,'($3<7,'"3<7$:$,6'/$6/*$)
(-02%'$%'I$&8'W8QfE"K8'!,6,' v *)'$(')-,'$%<*)'#07)"&,1' F ( 'EP%02%'"('"'."('+$&!)!-(*%&K'/0%5
#,6)(')-,'+6"$%'/*66,%)' + (')0'"'#07)"&,'E + ( F ( K1'"%+'8 (( '$(')-,'(*<<7;'#07)"&,')-")'<02,6('*<
)-,'"3<7$:$,6'"%+1')0&,)-,6'2$)-' F ( 1',()"47$(-,('0<,6")$0%'$%')-,'(")*6")$0%'6,&$0%1'"('2$77'4,
(-02%'(-06)7;8
=%')-,'"3<7$:$,6'/$6/*$)'0:'I$&8'W8QfE"K')-,'0*)<*)'#07)"&,'$(')"P,%'4,)2,,%')-,'+6"$%'"%+
&60*%+1'6")-,6')-"%'($3<7;'"/60((' F ( 8'9-$('$('+0%,'4,/"*(,'0:')-,'%,,+')0'3"$%)"$%'"'&60*%+
6,:,6,%/,')-60*&-0*)')-,'/$6/*$)8'9-,'0*)<*)'#07)"&,'v () '$('&$#,%'4;
v () & 8 (( ' + ( F (
EW8CZK
9-*('$)'$('"%'$%#,6),+'#,6($0%'E%0),')-,'3$%*('($&%K'0:' + ( F (')-")'$('(-$:),+'4;')-,'/0%()"%)
#"7*,'0:')-,'(*<<7;'#07)"&,'8 ((8
5.4.2 The Voltage Transfer Characteristic (VTC)
A'#,6;'*(,:*7')007')-")';$,7+('&6,")'$%($&-)'$%)0')-,'0<,6")$0%'0:'"%'"3<7$:$,6'/$6/*$)'$('$)(
#07)"&,')6"%(:,6'/-"6"/),6$()$/'ES9?K8'9-$('$('($3<7;'"'<70)'E06'"'/7,"67;'7"4,7,+'(P,)/-K'0:
)-,'0*)<*)'#07)"&,'#,6(*(')-,'$%<*)'#07)"&,8'I06')-,'FGH'"3<7$:$,6'$%'I$&8'W8QfE"K1')-$('$(')-,
<70)'0:' v ()'#,6(*(' v *)'(-02%'$%'I$&8'W8QfE4K8
G4(,6#,' )-")' :06' v *) < 8 # 1' )-,' )6"%($()06' $(' /*)' 0::1' + ( & Z' "%+1' :603' JO8' EW8CZK1
v () & 8 ((8'A(' v *) ',B/,,+('8 # 1')-,')6"%($()06')*6%('0%'"%+' v ()'+,/6,"(,(8'!02,#,61'($%/,'$%$5
)$"77;' v ()'$('()$77'-$&-1')-,'FGHIJ9'2$77'4,'0<,6")$%&'$%'(")*6")$0%8'9-$('/0%)$%*,('"(' v *)'$(
$%/6,"(,+'*%)$7')-,'#"7*,'0:' v *)'$('6,"/-,+')-")'6,(*7)('$%' v ()'4,/03$%&'702,6')-"%' v *)'4;'8 #
#07)('E<0$%)'L'0%')-,'S9?'$%'I$&8'W8Qf4K8'I06' v *)'&6,"),6')-"%')-")'")'<0$%)'L1')-,')6"%($()06
0<,6"),('$%')-,')6$0+,'6,&$0%'"%+' v ()'+,/6,"(,('306,'(7027;8
9-,'S9?'$%'I$&8'W8QfE4K'$%+$/"),(')-")')-,'(,&3,%)'0:'&6,"),()'(70<,'E"%+'-,%/,'<0),%5
)$"77;')-,'7"6&,()'"3<7$:$,6'&"$%K'$(')-")'7"4,7,+'AL1'2-$/-'/066,(<0%+(')0'0<,6")$0%'$%')-,'(")5
*6")$0%'6,&$0%8'A%',B<6,(($0%':06')-,'(,&3,%)'AL'/"%'4,'04)"$%,+'4;'(*4()$)*)$%&':06'+('$%
JO8'EW8CZK'4;'$)('(")*6")$0%56,&$0%'#"7*,
@
Q
+ ( & 555 > ! ( v *) ' 8 # )
Q
EW8C@K
5.4 Applying the MOSFET in Amplifier Design
vDS Cut- Saturation
Triode
off
A
VDD
VDD
iD
RD
+
vO = vDS
vGS !
#
–
B
VDS#B
"VGS#B–Vt
C
0
VGS#B
Vt
VDD
vGS
(b)
(a)
Figure 5.27 '1(2'H$3<7,'FGHIJ9'"3<7$:$,6'2$)-'$%<*)'v*)'"%+'0*)<*)'v()8'1/2'9-,'#07)"&,')6"%(:,6'/-"65
"/),6$()$/'ES9?K'0:')-,'"3<7$:$,6'$%'1(28'9-,')-6,,'(,&3,%)('0:')-,'S9?'/066,(<0%+')0')-,')-6,,'6,&$0%('0:
0<,6")$0%'0:')-,'FGHIJ98
2-,6,'2,'-"#,':06'($3<7$/$);'%,&7,/),+'/-"%%,757,%&)-'30+*7")$0%8'9-,'6,(*7)'$(
@
Q
v () & 8 (( ' 555 > ! F ( ( v *) ' 8 # )
Q
EW8CQK
9-$('$('04#$0*(7;'"'%0%7$%,"6'6,7")$0%(-$<8'`,#,6)-,7,((1'7$%,"6'E06'"730()57$%,"6K'"3<7$:$/"5
)$0%' /"%' 4,' 04)"$%,+' 4;' *($%&' )-,' ),/-%$O*,' 0:' 4$"($%&' )-,' FGHIJ98' L,:06,' /0%($+,6$%&
4$"($%&1'-02,#,61'$)'$('*(,:*7')0'+,),63$%,')-,'/006+$%"),('0:'<0$%)'L1'2-$/-'$('")')-,'40*%+5
"6;' 4,)2,,%' )-,' (")*6")$0%' "%+' )-,' )6$0+,' 6,&$0%(' 0:' 0<,6")$0%8' 9-,(,' /"%' 4,' 04)"$%,+' 4;
(*4()$)*)$%&'$%'JO8'EW8CQK1' v *) & 8 *) '"%+' v () & 8 () & 8 *) ' 8 # 8'9-,'6,(*7)'$(
L
L
L
Q> ! F ( 8 (( ( @ ' @
8 *) & 8 # ( 55555555555555555555555555555555555555555555555
5
L
>! F(
EW8CCK
EXERCISE
5.16
?0%($+,6')-,'"3<7$:$,6'0:'I$&8'W8QfE"K'2$)-' 8 (( & @8d 'S1' F ( & @f8W 'P Ω1'"%+'2$)-'"'FGHIJ9
(<,/$:$,+')0'-"#,' 8 # & Z8b 'S1' > ! & b'3AcSQ1'"%+'λ & Z8'^,),63$%,')-,'/006+$%"),('0:')-,',%+
<0$%)(' 0:' )-,' (")*6")$0%56,&$0%' (,&3,%)' 0:' )-,' S9?8' A7(01' +,),63$%,' 8 () ' "((*3$%&
?
8 *) & 8 (( 8
?
Ans. AD'Z8b'S1'@8d'Sa'LD'Z8N@C'S1'Z8Q@C'Sa' 8 ()
?
& @d '3S
5.4.3 Biasing the MOSFET to Obtain Linear Amplification
L$"($%&',%"47,('*(')0'04)"$%'"730()57$%,"6'"3<7$:$/")$0%':603')-,'FGHIJ98'9-,'),/-%$O*,
$('$77*()6"),+'$%'I$&8'W8QdE"K8'A'+/'#07)"&,' 8 *) '$('(,7,/),+')0'04)"$%'0<,6")$0%'")'"'<0$%)'s'0%
)-,'(,&3,%)'AL'0:')-,'S9?8'!02')0'(,7,/)'"%'"<<60<6$"),'70/")$0%':06')-,'4$"('<0$%)'s'2$77
4,' +$(/*((,+' (-06)7;8' I06' )-,' )$3,' 4,$%&1' 04(,6#,' )-")' )-,' /006+$%"),(' 0:' s' "6,' )-,' +/
269
270 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
vDS
VDD
A
VDD
ID
RD
+
VDS
+
VGS
Q
VDS
–
–
B
C
(a)
0
Vt
VGS
VDD
vGS
(b)
Figure 5.28 L$"($%&')-,'FGHIJ9'"3<7$:$,6'")'"'<0$%)'s'70/"),+'0%')-,'(,&3,%)'AL'0:')-,'S9?8
#07)"&,('8*)'"%+'8()1'2-$/-'"6,'6,7"),+'4;
@
Q
8 () & 8 (( ' 555 > ! F ( ( 8 *) ' 8 # )
Q
EW8CbK
_0$%)'s'$('P%02%'"(')-,'/)(!+A")*-'06')-,''%+"A&$(-)*,+A")*-8'A7(01'($%/,'")'s'%0'($&%"7'/035
<0%,%)'$('<6,(,%)1'$)'$('"7(0'P%02%'"(')-,'E#)&!%&*-+A")*-'E2-$/-'$(')-,'06$&$%'0:')-,'(;3407'sK8
`,B)1')-,'($&%"7')0'4,'"3<7$:$,+1' v 711'"':*%/)$0%'0:')$3,' # 1'$('(*<,6$3<0(,+'0%')-,'4$"(
#07)"&,'8 *)1'"('(-02%'$%'I$&8'W8Q[E"K8'9-*(')-,')0)"7'$%()"%)"%,0*('#"7*,'0:' v *)'4,/03,(
v *) ( # ) & 8 *) ( v 71 ( # )
'
9-,'6,(*7)$%&' v () ( # )'/"%'4,'04)"$%,+'4;'(*4()$)*)$%&':06' v *) ( # )'$%)0'JO8'EW8CQK8']6"<-$/"77;1
2,'/"%'*(,')-,'S9?')0'04)"$%' v () ( # )'<0$%)54;5<0$%)1'"('$77*()6"),+'$%'I$&8'W8Q[E4K8'!,6,'2,
(-02')-,'/"(,'0:' v 71'4,$%&'"')6$"%&*7"6'2"#,'0:'X(3"77Y'"3<7$)*+,8'H<,/$:$/"77;1')-,'"3<7$5
)*+,'0:' v 71'$('(3"77',%0*&-')0'6,()6$/)')-,',B/*6($0%'0:')-,'$%()"%)"%,0*('0<,6")$%&'<0$%)')0'"
(-06)1'"730()57$%,"6'(,&3,%)'0:')-,'S9?'"60*%+')-,'4$"('<0$%)'s8'9-,'(-06),6')-,'(,&3,%)1
)-,'&6,"),6')-,'7$%,"6$);'"/-$,#,+1'"%+')-,'/70(,6')0'"%'$+,"7')6$"%&*7"6'2"#,')-,'($&%"7'/035
<0%,%)'")')-,'0*)<*)1' v ,11'2$77'4,8'9-$('$(')-,',((,%/,'0:'04)"$%$%&'7$%,"6'"3<7$:$/")$0%':603
)-,'%0%7$%,"6'FGHIJ98'
5.4.4 The Small-Signal Voltage Gain
=:')-,'$%<*)'($&%"7' v 71 '$('P,<)'(3"771')-,'/066,(<0%+$%&'($&%"7'")')-,'0*)<*)' v ,1 '2$77'4,'%,"67;
<60<06)$0%"7')0' v 71 '2$)-')-,'/0%()"%)'0:'<60<06)$0%"7$);'4,$%&')-,'(70<,'0:')-,'"730()57$%,"6
(,&3,%)'0:')-,'S9?'"60*%+'s8'9-$('$(')-,'#07)"&,'&"$%'0:')-,'"3<7$:$,61'"%+'$)('#"7*,'/"%'4,
+,),63$%,+'4;',#"7*")$%&')-,'(70<,'0:')-,')"%&,%)')0')-,'S9?'")')-,'4$"('<0$%)'s1
, v ()
5
EW8CWK
G v ≡ 5555555555
, v *)
v
'
&
8
*)
*)
n)$7$>$%&'JO8'EW8CQK'2,'04)"$%
G v & ' > ! ( 8 *) ' 8 # )F (
EW8CNK
2-$/-'/"%'4,',B<6,((,+'$%'),63('0:')-,'0#,6+6$#,'#07)"&,'")')-,'4$"('<0$%)'8 :8 '"(
G v & ' > ! 8 :8 F (
EW8CfK
5.4 Applying the MOSFET in Amplifier Design
VDD
iD
RD
vDS
vgs
VGS
!
#
!
vGS
#
(a)
vDS
VDD
A
Slope at Q 5 voltage gain
vds
VDS
Q
Time
B
C
Vt
VGS
VDD
vGS
vgs
Time
(b)
Figure 5.29 9-,'FGHIJ9'"3<7$:$,6'2$)-'"'(3"77')$3,5#"6;$%&'($&%"7'v71E#K'(*<,6$3<0(,+'0%')-,'+/'4$"('#07)"&,'8*)8
9-,'FGHIJ9'0<,6"),('0%'"'(-06)'"730()57$%,"6'(,&3,%)'0:')-,'S9?'"60*%+')-,'4$"('<0$%)'s'"%+'<60#$+,('"%'0*)<*)'#07)5
"&,'v,1'e'Gv'v71 H
271
272 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
U,'3"P,')-,':07702$%&'04(,6#")$0%('0%')-$(',B<6,(($0%':06')-,'#07)"&,'&"$%8
1. 9-,'&"$%'$('%,&")$#,1'2-$/-'($&%$:$,(')-")')-,'"3<7$:$,6'$('$%#,6)$%&a')-")'$(1')-,6,'$('"
@dZ ° <-"(,'(-$:)'4,)2,,%')-,'$%<*)'"%+')-,'0*)<*)8'9-$('$%#,6($0%'$('04#$0*('$%'I$&8
W8Q[E4K'"%+'(-0*7+'-"#,'4,,%'"%)$/$<"),+':603'JO8'EW8CQK8'
2. 9-,' &"$%' $(' <60<06)$0%"7' )0' )-,' 70"+' 6,($()"%/,' F ( 1' )0' )-,' )6"%($()06' )6"%(/0%+*/5
)"%/,' <"6"3,),6' > ! 1' "%+' )0' )-,' 0#,6+6$#,' #07)"&,' 8 :8 8' 9-$(' "77' 3"P,(' $%)*$)$#,
(,%(,8
A%0)-,6' ($3<7,' "%+' $%($&-):*7' ,B<6,(($0%' :06' )-,' #07)"&,' &"$%' G v ' /"%' 4,' +,6$#,+' 4;
6,/"77$%&')-")')-,'+/'/*66,%)'$%')-,'+6"$%'")')-,'4$"('<0$%)'$('6,7"),+')0'8:8 '4;
@
Q
? ( & 555 > ! 8 :8
Q
9-$(',O*")$0%'/"%'4,'/034$%,+'2$)-'JO8'EW8CfK')0';$,7+'
?( F(
G v & ' 555555555555555
5
8 :8 ⁄ Q
EW8CdK
9-")'$(1')-,'&"$%'$('($3<7;')-,'6")$0'0:')-,'+/'#07)"&,'+60<'"/60((')-,'70"+'6,($()"%/,' F ( ')0
8 :8 ⁄ Q8' 9-$(' 6,7")$0%(-$<' "7702(' 0%,' )0' :$%+' "%' "4(07*),' *<<,6' 7$3$)' 0%' )-,' 3"&%$)*+,' 0:
#07)"&,'&"$%'"/-$,#"47,':603')-$('"3<7$:$,6'/$6/*$)8'H$3<7;'%0),')-")' ? ( F ( '/"%'"<<60"/-'4*)
%,#,6',B/,,+')-,'<02,65(*<<7;'#07)"&,'8 ((a')-*(1
8 ((
G v3"B & 555555555555555
5
8 :8 ⁄ Q
I06'30+,6%'?FGH'),/-%070&$,('8 :8 '$('*(*"77;'%0'702,6')-"%'"40*)'Z8Q'S1'2$)-')-,'6,(*7)
)-")')-,'3"B$3*3'"/-$,#"47,'&"$%'$('"40*)'@Z' 8 (( 8'9-*(':06'"'Z8@C5µ3'?FGH'),/-%070&;
)-")'*)$7$>,(' 8 (( & @8C'S1')-,'"<<60B$3"),'#"7*,'0:' G 3"B '$('@C'ScS8'=%'"/)*"7'/$6/*$)(1'-025
,#,61')-,'3"B$3*3'&"$%'"/-$,#"47,'$('702,6')-"%')-$('"4(07*),'3"B$3*38
Example 5.9
?0%($+,6' )-,' "3<7$:$,6' /$6/*$)' (-02%' $%' I$&8' W8Q[E"K8' 9-,' )6"%($()06' $(' (<,/$:$,+' )0' -"#,' 8 # & Z8b' S1
> !′ & Z8b '3AcSQ1''c&'e'@Z1'"%+' λ & Z 8'A7(01'7,)' 8 (( & @8d 'S1' F ( & @f8W 'P Ω 1'"%+'8 *) & Z8N'S8
E"K'I06' v 71 & Z 'E"%+'-,%/,' v ,1 & Z K1':$%+'8 :8 1' ? (1'8 () 1'"%+' G v8
E4K' U-")' $(' )-,' 3"B$3*3' (;33,)6$/"7' ($&%"7' (2$%&' "7702,+' ")' )-,' +6"$%g' !,%/,' :$%+' )-,' 3"B$3*3
"7702"47,'"3<7$)*+,'0:'"'($%*(0$+"7' v 718
Solution
E"K'U$)-'8 *) & Z8N 'S1' 8 :8 & Z8N ' Z8b & Z8Q'S8'
9-*(1'
@
Q
? ( & 555 × Z8b × @Z × Z8Q & Z8Zd '3A
Q
8 () & 8 (( ' F ( ? (
& @8d ' @f8W × Z8Zd & Z8b 'S
5.4 Applying the MOSFET in Amplifier Design
273
H$%/,' 8 ()'$('&6,"),6')-"%' 8 :8 1')-,')6"%($()06'$('$%+,,+'0<,6")$%&'$%'(")*6")$0%8'9-,'#07)"&,'&"$%'/"%'4,
:0*%+':603'JO8'EW8CfK1
G v & ' > ! 8 :8 F (
& ' Z8b × @Z × Z8Q × @f8W
& ' @b 'ScS
A%'$+,%)$/"7'6,(*7)'/"%'4,':0*%+'*($%&'JO8'EW8CdK8
E4K'H$%/,' 8 :8 & Z8Q 'S'"%+' 8 () & Z8b 'S1'2,'(,,')-")')-,'3"B$3*3'"7702"47,'%,&")$#,'($&%"7'(2$%&'")
)-,'+6"$%'$('Z8Q'S8'=%')-,'<0($)$#,'+$6,/)$0%1'"'(2$%&'0:' kZ8Q 'S'20*7+'%0)'/"*(,')-,')6"%($()06')0'/*)'0::'"%+
)-*('$('"7702,+8'9-*(')-,'3"B$3*3'(;33,)6$/"7'($&%"7'(2$%&'"7702"47,'")')-,'+6"$%'$(' ± Z8Q 'S8'9-,'/066,5
(<0%+$%&'"3<7$)*+,'0:' v 71 '/"%'4,':0*%+':603
vt ,1
S5 & @b8Q'3S
vt 71 & 55555555
& Z8Q
555555555555
@b
Gv
H$%/,' vt 71 - 8 :8 1')-,'0<,6")$0%'2$77'4,'6,"(0%"47;'7$%,"6'E306,'0%')-$('$%'7"),6'(,/)$0%(K8
]6,"),6' $%($&-)' $%)0' )-,' $((*,' 0:' "7702"47,' ($&%"7' (2$%&' /"%' 4,' 04)"$%,+' 4;' ,B"3$%$%&' )-,' ($&%"7
2"#,:063('(-02%'$%'I$&8'W8CZ8'`0),')-")':06')-,'FGHIJ9')0'6,3"$%'$%'(")*6")$0%'")')-,'%,&")$#,'<,"P'0:
v ,1 1'2,'3*()',%(*6,')-")
v ()3$% ≥ v *)3"B ' 8 #
)-")'$(1
Z8b ' G v vt 71 ≥ Z8N ( vt 71 ' Z8b
2-$/-'6,(*7)('$%
Z8Q
vt 71 ≤ 555555555555555555 & @C8C'3S
Gv ( @
9-$('$('"'306,'<6,/$(,'6,(*7)')-"%')-,'0%,'04)"$%,+',"67$,68
vGS)
vgs
vGSmax = VGS ! vˆgs
VGS
Vt
t
0
vDS
vds
VDS
vDSmin = VDS # vˆds
0
t
Figure 5.30 H$&%"7'2"#,:063('")'&"),'"%+
+6"$%':06')-,'"3<7$:$,6'$%'JB"3<7,'W8[8'`0),
)-")' )0' ,%(*6,' 0<,6")$0%' $%' )-,' (")*6")$0%
6,&$0%'")'"77')$3,(1'v()3$% & v*)3"B V 8# 8
274 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
EXERCISE
5.17 I06')-,'"3<7$:$,6'/$6/*$)'()*+$,+'$%'JB"3<7,'W8[1'<60#$+,')20'"7),6%")$#,'+,($&%(1',"/-'<60#$+$%&'"
#07)"&,'&"$%'0:'@Z'4;'E"K'/-"%&$%&' F ( '2-$7,'P,,<$%&' 8 :8 '/0%()"%)1'"%+'E4K'/-"%&$%&' 8 :8 '2-$7,
P,,<$%&' F ( '/0%()"%)8'I06',"/-'+,($&%1'(<,/$:;' 8 *) 1' ? ( 1' F ( 1'"%+'8 () 8
Ans. E"K'Z8N'S1'Z8Zd'3A1'@Q8W'PΩ1'Z8d'Sa'E4K'Z8Wb'S1'Z8Zb'3A1'@f8W'P Ω 1'@8@'S
5.4.5 Determining the VTC by Graphical Analysis
I$&*6,' W8C@' (-02(' "' &6"<-$/"7' 3,)-0+' :06' +,),63$%$%&' )-,' S9?' 0:' )-,' "3<7$:$,6' 0:' I$&8
W8Q[E"K8'A7)-0*&-'&6"<-$/"7'"%"7;($('0:')6"%($()06'/$6/*$)('$('6"6,7;',3<70;,+'$%'<6"/)$/,1'$)'$(
*(,:*7' :06' *(' ")' )-$(' ()"&,' :06' &"$%$%&' &6,"),6' $%($&-)' $%)0' /$6/*$)' 0<,6")$0%1' ,(<,/$"77;' $%
"%(2,6$%&')-,'O*,()$0%'0:'2-,6,')0'70/"),')-,'4$"('<0$%)'s8
9-,'&6"<-$/"7'"%"7;($('$('4"(,+'0%')-,'04(,6#")$0%')-")':06',"/-'#"7*,'0:' v *) 1')-,'/$6/*$)
2$77'4,'0<,6")$%&'")')-,'<0$%)'0:'$%),6(,/)$0%'0:')-,'+ ( ' v ()'&6"<-'/066,(<0%+$%&')0')-,'<"6)$/5
*7"6'#"7*,'0:' v *) '"%+')-,'()6"$&-)'7$%,'6,<6,(,%)$%&'JO8'EW8CZK1'2-$/-'/"%'4,'6,26$)),%'$%')-,
:063
8 (( @
EW8C[K
+ ( & 555555555
5 ' 555555 v
F ( F ( ()
iD
vGS " VDD
Triode
Saturation
vGS " ...
vGS " VGS#
C
B
B
vGS " ...
Q
ID
vGS " VGS
Load-line
slope " #1.RD
0 VDS# VDS# " VGS# # Vt
C
B
B
VDS
A
VDD
vGS " …
vDS
Figure 5.31 ]6"<-$/"7' /0%()6*/)$0%' )0' +,),63$%,' )-,' #07)"&,' )6"%(:,6' /-"6"/),6$()$/' 0:' )-,' "3<7$:$,6' $%
I$&8 W8Q[E"K8
5.4 Applying the MOSFET in Amplifier Design
VDD
0
VDD
RD
RD
vDS = VDD
vDS = VDS #
C
rDS
vGS ≤ Vt
vGS = VDD
(a)
(b)
Figure 5.32 G<,6")$0%' 0:' )-,' FGHIJ9' $%
I$&*6,' W8Q[E"K' "(' "' (2$)/-D' 1(2' G<,%1' /066,5
(<0%+$%&' )0' <0$%)' A' $%' I$&*6,' W8C@a' 1/2
?70(,+1' /066,(<0%+$%&' )0' <0$%)' ?' $%' I$&*6,
W8C@8'9-,'/70(*6,'6,($()"%/,'$('"<<60B$3"),7;
,O*"7')0'6()'4,/"*(,'8()'$('*(*"77;'#,6;'(3"778
9-,'()6"$&-)'7$%,'6,<6,(,%)$%&')-$('6,7")$0%(-$<'$('(*<,6$3<0(,+'0%')-,' + ( ' v () '/-"6"/),6$()$/(
$%'I$&8'W8C@8'=)'$%),6(,/)(')-,'-06$>0%)"7'"B$('")' v () & 8 (( '"%+'-"('"'(70<,'0:' ' @ ⁄ F ( 8 'H$%/,')-$(
()6"$&-)'7$%,'6,<6,(,%)('$%',::,/)')-,'70"+'6,($()"%/,' F ( 1'$)'$('/"77,+')-,'."('+.)*&8'9-,'S9?'$(
)-,%'+,),63$%,+'<0$%)'4;'<0$%)8'`0),')-")'2,'-"#,'7"4,7,+':0*6'$3<06)"%)'<0$%)(D'<0$%)'A'")
2-$/-' v *) & 8 # 1' <0$%)' s' ")' 2-$/-' )-,' FGHIJ9' /"%' 4,' 4$"(,+' :06' "3<7$:$,6' 0<,6")$0%
E v *) & 8 *) '"%+' v () & 8 () K1'<0$%)'L'")'2-$/-')-,'FGHIJ9'7,"#,('(")*6")$0%'"%+',%),6(')-,
)6$0+,'6,&$0%1'"%+'<0$%)'?1'2-$/-'$('+,,<'$%)0')-,')6$0+,'6,&$0%'"%+':06'2-$/-' v *) & 8 (( 8'=:
)-,'FGHIJ9'$(')0'4,'*(,+'"('"'(2$)/-1')-,%'0<,6")$%&'<0$%)('A'"%+'?'"6,'"<<7$/"47,D'A)'A')-,
)6"%($()06'$('0::'E0<,%'(2$)/-K1'"%+'")'?')-,')6"%($()06'0<,6"),('"('"'7025#"7*,+'6,($()"%/,' 6 ()
"%+' -"(' "' (3"77' #07)"&,' +60<' E/70(,+' (2$)/-K8' 9-,' $%/6,3,%)"7' 6,($()"%/,' ")' <0$%)' ?' $(' "7(0
P%02%'"(')-,'%."!#$&+$&!)!-(*%&8'9-,'0<,6")$0%'0:')-,'FGHIJ9'"('"'(2$)/-'$('$77*()6"),+'$%
I$&8' W8CQ8'A'+,)"$7,+'()*+;' 0:' )-,' "<<7$/")$0%' 0:' )-,' FGHIJ9' "(' "' (2$)/-' $(' *%+,6)"P,%' $%
?-"<),6'@C'+,"7$%&'2$)-'?FGH'+$&$)"7'70&$/'/$6/*$)(8
5.4.6 Locating the Bias Point Q
9-,'4$"('<0$%)'s'$('+,),63$%,+'4;')-,'#"7*,'0:'8 *) '"%+')-")'0:')-,'70"+'6,($()"%/,' F ( 8'920
$3<06)"%)' /0%($+,6")$0%(' $%' +,/$+$%&' 0%' )-,' 70/")$0%' 0:' s' "6,' )-,' 6,O*$6,+' &"$%' "%+' )-,
"7702"47,'($&%"7'(2$%&'")')-,'0*)<*)8'90'$77*()6"),1'/0%($+,6')-,'S9?'(-02%'$%'I$&8'W8Q[E4K8
!,6,')-,'#"7*,'0:' F ( '$(':$B,+'"%+')-,'0%7;'#"6$"47,'6,3"$%$%&'$(')-,'#"7*,'0:'8 *) 8'H$%/,')-,
(70<,'$%/6,"(,('"('2,'30#,'/70(,6')0'<0$%)'L1'2,'04)"$%'-$&-,6'&"$%'4;'70/")$%&'s'"('/70(,')0
L'"('<0(($47,8'!02,#,61')-,'/70(,6's'$(')0')-,'40*%+"6;'<0$%)'L1')-,'(3"77,6')-,'"7702"47,
3"&%$)*+,' 0:' %,&")$#,' ($&%"7' (2$%&8' 9-*(1' "(' 0:),%' -"<<,%(' $%' ,%&$%,,6$%&' +,($&%1' 2,
,%/0*%),6'"'($)*")$0%'6,O*$6$%&'"')6"+,50::8
=%'+,/$+$%&'0%'"'#"7*,':06' F ( 1'$)'$('*(,:*7')0'6,:,6')0')-,' + ( ' v () '<7"%,8'I$&*6,'W8CC'(-02(
)20'70"+'7$%,('6,(*7)$%&'$%')20',B)6,3,'4$"('<0$%)(D'_0$%)' s @'$(')00'/70(,')0'8 (( 1'6,(*7)$%&'$%'"
(,#,6,'/0%()6"$%)'0%')-,'<0($)$#,'($&%"7'(2$%&'0:' v ,1 8 'JB/,,+$%&')-,'"7702"47,'<0($)$#,'3"B$5
3*3'6,(*7)('$%')-,'<0($)$#,'<,"P('0:')-,'($&%"7'4,$%&'/7$<<,+'0::1'($%/,')-,'FGHIJ9'2$77')*6%
0::':06')-,'<"6)'0:',"/-'/;/7,'%,"6')-,'<0($)$#,'<,"P8'U,'(<,"P'0:')-$('($)*")$0%'4;'(";$%&')-")
)-,'/$6/*$)'+0,('%0)'-"#,'(*::$/$,%)'X-,"+60038Y'H$3$7"67;1'<0$%)' s Q '$(')00'/70(,')0')-,'40*%+5
"6;' 0:' )-,' )6$0+,' 6,&$0%1' )-*(' (,#,6,7;' 7$3$)$%&' )-,' "7702"47,' %,&")$#,' ($&%"7' (2$%&' 0:' v ,1 8
JB/,,+$%&')-$('7$3$)'20*7+'6,(*7)'$%')-,')6"%($()06',%),6$%&')-,')6$0+,'6,&$0%':06'<"6)'0:',"//;/7,'%,"6')-,'%,&")$#,'<,"P(1'6,(*7)$%&'$%'"'+$()06),+'0*)<*)'($&%"78'=%')-$('($)*")$0%'2,'(";
)-")')-,'/$6/*$)'+0,('%0)'-"#,'(*::$/$,%)'X7,&60038Y'U,'2$77'-"#,'306,')0'(";'0%'4$"('+,($&%
$%')-,'H,/)$0%'W8f8'''
275
276 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
iD
vGS " ...
Q1
Q2
0
VDD
vDS
Figure 5.33 920'70"+'7$%,('"%+'/066,(<0%+$%&'4$"('<0$%)(8'L$"('<0$%)'s@'+0,('%0)'7,"#,'(*::$/$,%)'6003
:06'<0($)$#,'($&%"7'(2$%&'")')-,'+6"$%'E)00'/70(,')0'8((K8'L$"('<0$%)'sQ'$(')00'/70(,')0')-,'40*%+"6;'0:')-,')6$5
0+,'6,&$0%'"%+'3$&-)'%0)'"7702':06'(*::$/$,%)'%,&")$#,'($&%"7'(2$%&8
5.5 Small-Signal Operation and Models
=%'0*6'()*+;'0:')-,'0<,6")$0%'0:')-,'FGHIJ9'"3<7$:$,6'$%'H,/)$0%'W8b'2,'7,"6%,+')-")'7$%,"6
"3<7$:$/")$0%'/"%'4,'04)"$%,+'4;'4$"($%&')-,'FGHIJ9')0 0<,6"),'$%')-,'(")*6")$0%'6,&$0%
"%+'4;'P,,<$%&')-,'$%<*)'($&%"7'(3"778'=%')-$('(,/)$0%1'2,',B<706,')-,'(3"775($&%"7'0<,6")$0%
$%' (03,' +,)"$78' I06' )-$(' <*6<0(,' 2,' *)$7$>,' )-,' /0%/,<)*"7' "3<7$:$,6' /$6/*$)' (-02%' $%
I$&8 W8Cb8'!,6,')-,'FGH')6"%($()06'$('4$"(,+'4;'"<<7;$%&'"'+/'#07)"&,d'8*)1'"%+')-,'$%<*)'($&5
%"7')0'4,'"3<7$:$,+1' v71 1'$('(*<,6$3<0(,+'0%')-,'+/'4$"('#07)"&,'8*) 8'9-,'0*)<*)'#07)"&,'$(
)"P,%'")')-,'+6"$%8'
5.5.1 The DC Bias Point
9-,'+/'4$"('/*66,%)'?('/"%'4,':0*%+'4;'(,))$%&')-,'($&%"7'v71')0'>,60a')-*(1'
@
@
Q
Q
? ( = 555 > !' ( 8 *) ' 8 # ) = 555 > ! 8 :8
Q
Q
EW8bZK
2-,6,' 2,' -"#,' %,&7,/),+' /-"%%,757,%&)-'30+*7")$0%'E$8,81' 2,'-"#,'"((*3,+' λ'=' ZK8'!,6,
8 :8 & 8 *) ' 8 # '$(')-,'0#,6+6$#,'#07)"&,'")'2-$/-')-,'FGHIJ9'$('4$"(,+')0'0<,6"),8'9-,'+/
d
_6"/)$/"7'4$"($%&'"66"%&3,%)('2$77'4,'()*+$,+'$%'H,/)$0%'W8f8
5.5 Small-Signal Operation and Models
VDD
iD
RD
vDS
vgs
VGS
!
#
!
vGS
Figure 5.34 ?0%/,<)*"7' /$6/*$)' *)$7$>,+' )0' ()*+;' )-,' 0<,6")$0%' 0:
)-,'FGHIJ9'"('"'(3"775($&%"7'"3<7$:$,68
#
#07)"&,'")')-,'+6"$%1'8() 1'2$77'4,
8 () = 8 (( ' F ( ? (
EW8b@K
90',%(*6,'(")*6")$0%56,&$0%'0<,6")$0%1'2,'3*()'-"#,
8 () > 8 :8
I*6)-,6306,1'($%/,')-,')0)"7'#07)"&,'")')-,'+6"$%'2$77'-"#,'"'($&%"7'/03<0%,%)'(*<,6$3<0(,+
0%'8() 1'8()'-"(')0'4,'(*::$/$,%)7;'&6,"),6')-"%' ( 8 :8 )')0'"7702':06')-,'6,O*$6,+'($&%"7'(2$%&8
5.5.2 The Signal Current in the Drain Terminal
`,B)1'/0%($+,6')-,'($)*")$0%'2$)-')-,'$%<*)'($&%"7'v71'"<<7$,+8'9-,')0)"7'$%()"%)"%,0*('&"),5)05
(0*6/,'#07)"&,'2$77'4,
v *) = 8 *) + v 71
EW8bQK
6,(*7)$%&'$%'"')0)"7'$%()"%)"%,0*('+6"$%'/*66,%)'+(1
@
Q
+ ( = 555 > !' ( 8 *) + v 71 ' 8 # )
Q
@
@
Q
= 555 > !' ( 8 *) ' 8 # ) + > !' ( 8 *) ' 8 # ) v 71 + 555 > ! ' v Q71
Q
Q
EW8bCK
9-,':$6()'),63'0%')-,'6$&-)5-"%+'($+,'0:'JO8'EW8bCK'/"%'4,'6,/0&%$>,+'"(')-,'+/'4$"('/*66,%)'?('EJO8
W8bZK8'9-,'(,/0%+'),63'6,<6,(,%)('"'/*66,%)'/03<0%,%)')-")'$('+$6,/)7;'<60<06)$0%"7')0')-,'$%<*)
($&%"7'v718'9-,')-$6+'),63'$('"'/*66,%)'/03<0%,%)')-")'$('<60<06)$0%"7')0')-,'(O*"6,'0:')-,'$%<*)'($&5
%"78'9-$('7"()'/03<0%,%)'$('*%+,($6"47,'4,/"*(,'$)'6,<6,(,%)('!$!3+!/260,+1#$6#+$!8'90'6,+*/,')-,
%0%7$%,"6'+$()06)$0%'$%)60+*/,+'4;')-,'FGHIJ91')-,'$%<*)'($&%"7'(-0*7+'4,'P,<)'(3"77'(0')-")
@ Q
555 > !' v 71 - > !' ( 8 *) ' 8 # ) v 71
Q
277
278 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
6,(*7)$%&'$%
v 71 '-'Q ( 8 *) ' 8 # )
EW8bbK
v 71 '-'Q8 :8
EW8bWK
061',O*$#"7,%)7;1
=:')-$('!B(..3!),*(.+%"*')-)"*'$('(")$(:$,+1'2,'3";'%,&7,/)')-,'7"()'),63'$%'JO8'EW8bCK'"%+
,B<6,(('+('"(
h
EW8bNK
+ ( ' " '? ( + + ,
2-,6,
+ , = > ! ( 8 *) ' 8 # ) v 71
9-,'<"6"3,),6')-")'6,7"),('+,'"%+'v71'$(')-,'FGHIJ9'-$(*!%"*'#%-(*%&'7@1
+
7 @ ≡ 55555,5 = > ! ( 8 *) ' 8 # )
v 71
EW8bfK
06'$%'),63('0:')-,'0#,6+6$#,'#07)"&,'8:8 1
7 @ = > !8 :8
EW8bdK
I$&*6,'W8CW'<6,(,%)('"'&6"<-$/"7'$%),6<6,)")$0%'0:')-,'(3"775($&%"7'0<,6")$0%'0:')-,'FGHIJ9
"3<7$:$,68'`0),')-")'7@'$(',O*"7')0')-,'(70<,'0:')-,'+( − v*)'/-"6"/),6$()$/'")')-,'4$"('<0$%)1
∂ +(
5
7 @ ≡ 5555555555
∂ v *) v*) = 8*)
Q
VGS
0
VOV
Figure 5.35 H3"775($&%"7'0<,6")$0%'0:')-,'FGHIJ9'"3<7$:$,68
EW8b[K
5.5 Small-Signal Operation and Models
9-$('$(')-,':063"7'+,:$%$)$0%'0:'7@ 1'2-$/-'/"%'4,'(-02%')0';$,7+')-,',B<6,(($0%('&$#,%'$%
JO(8'EW8bfK'"%+'EW8bdK8
5.5.3 The Voltage Gain
i,)*6%$%&')0')-,'/$6/*$)'0:'I$&8'W8Cb1'2,'/"%',B<6,((')-,')0)"7'$%()"%)"%,0*('+6"$%'#07)"&,'v()
"(':07702(D
v () = 8 (( ' F ( + (
n%+,6')-,'(3"775($&%"7'/0%+$)$0%1'2,'-"#,
v () = 8 (( ' F ( ( ? ( + + , )
2-$/-'/"%'4,'6,26$)),%'"(
v () = 8 () ' F ( + ,
9-*(')-,'($&%"7'/03<0%,%)'0:')-,'+6"$%'#07)"&,'$('
v ,1 = ' + , F ( = ' 7 @ v 71 F (
EW8WZK
2-$/-'$%+$/"),(')-")')-,'#07)"&,'&"$%'$('&$#,%'4;
v
,1
5 = '7@ F(
G v ≡ 55555
v 71
EW8W@K
9-,'3$%*('($&%'$%'JO8'EW8W@K'$%+$/"),(')-")')-,'0*)<*)'($&%"7'v,1'$('@dZ° 0*)'0:'<-"(,'2$)6,(<,/)')0')-,'$%<*)'($&%"7' v718'9-$('$('$77*()6"),+'$%'I$&8'W8CN1'2-$/-'(-02(' v*)'"%+' v()8'9-,
$%<*)'($&%"7'$('"((*3,+')0'-"#,'"')6$"%&*7"6'2"#,:063'2$)-'"%'"3<7$)*+,'3*/-'(3"77,6')-"%
QE8*)'V'8#K1')-,'(3"775($&%"7'/0%+$)$0%'$%'JO8'EW8bbK1')0',%(*6,'7$%,"6'0<,6")$0%8'I06'0<,6")$0%
$%')-,'(")*6")$0%'6,&$0%'")'"77')$3,(1')-,'3$%$3*3'#"7*,'0:'v()'(-0*7+'%0)':"77'4,702')-,'/066,5
(<0%+$%&'#"7*,'0:'v*)'4;'306,')-"%'8#8'A7(01')-,'3"B$3*3'#"7*,'0:'v()'(-0*7+'4,'(3"77,6')-"%
8((a'0)-,62$(,')-,'IJ9'2$77',%),6')-,'/*)0::'6,&$0%'"%+')-,'<,"P('0:')-,'0*)<*)'($&%"7'2"#,5
:063'2$77'4,'/7$<<,+'0::8
I$%"77;1'2,'%0),')-")'4;'(*4()$)*)$%&':06'7@':603'JO8'EW8bdK')-,'#07)"&,'&"$%',B<6,(($0%'$%
JO8'EW8W@K'4,/03,('$+,%)$/"7')0')-")'+,6$#,+'$%'H,/)$0%'W8bp%"3,7;1'JO8'EW8CfK8
5.5.4 Separating the DC Analysis and the Signal Analysis
I603')-,'<6,/,+$%&'"%"7;($(1'2,'(,,')-")'*%+,6')-,'(3"775($&%"7'"<<60B$3")$0%1'($&%"7'O*"%5
)$)$,('"6,'(*<,6$3<0(,+'0%'+/'O*"%)$)$,(8'I06'$%()"%/,1')-,')0)"7'+6"$%'/*66,%)'+(',O*"7(')-,'+/
/*66,%)' ?(' <7*(' )-,' ($&%"7' /*66,%)' +, 1' )-,' )0)"7' +6"$%' #07)"&,' v()' =' 8()' +' v,11' "%+' (0' 0%8' =)
:07702(')-")')-,'"%"7;($('"%+'+,($&%'/"%'4,'&6,")7;'($3<7$:$,+'4;'(,<"6")$%&'+/'06'4$"('/"7/*5
7")$0%(' :603' (3"775($&%"7' /"7/*7")$0%(8' 9-")' $(1' 0%/,' "' ()"47,' +/' 0<,6")$%&' <0$%)' -"(' 4,,%
,()"47$(-,+'"%+'"77'+/'O*"%)$)$,('/"7/*7"),+1'2,'3";')-,%'<,6:063'($&%"7'"%"7;($('$&%06$%&'+/
O*"%)$)$,(8
279
280 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
vGS
V
VGS
V - 2 (V # V )
GS
t
2
vGS
0
t
vDS
vDSmax $ VDD
(gm RD ) V
VDS
vDS min " vGS max # Vt
0
t
Figure 5.36 90)"7'$%()"%)"%,0*('#07)"&,('v*)'"%+'v()':06')-,'/$6/*$)'$%'I$&8'W8Cb8
5.5.5 Small-Signal Equivalent-Circuit Models
I603' "' ($&%"7' <0$%)' 0:' #$,21' )-,' IJ9' 4,-"#,(' "(' "' #07)"&,5/0%)6077,+' /*66,%)' (0*6/,8' =)
"//,<)('"'($&%"7'v71'4,)2,,%'&"),'"%+'(0*6/,'"%+'<60#$+,('"'/*66,%)'7@v71'")')-,'+6"$%'),63$%"78
9-,' $%<*)' 6,($()"%/,' 0:' )-$(' /0%)6077,+' (0*6/,' $(' #,6;' -$&-p$+,"77;1' $%:$%$),8' 9-,' 0*)<*)
6,($()"%/,p)-")'$(1')-,'6,($()"%/,'700P$%&'$%)0')-,'+6"$%p"7(0'$('-$&-1'"%+'2,'-"#,'"((*3,+
$)')0'4,'$%:$%$),')-*(':"68'_*))$%&'"77'0:')-$(')0&,)-,61'2,'"66$#,'")')-,'/$6/*$)'$%'I$&8'W8CfE"K1
2-$/-' 6,<6,(,%)(' )-,' (3"775($&%"7' 0<,6")$0%' 0:' )-,' FGHIJ9' "%+' $(' )-*(' "' !B(..3!),*(.
B"'&.'06'"'!B(..3!),*(.+&E#)>(.&*-+%)$%#)-8
=%' )-,' "%"7;($(' 0:' "' FGHIJ9' "3<7$:$,6' /$6/*$)1' )-,' )6"%($()06' /"%' 4,' 6,<7"/,+' 4;' )-,
,O*$#"7,%)'/$6/*$)'30+,7'(-02%'$%'I$&8'W8CfE"K8'9-,'6,()'0:')-,'/$6/*$)'6,3"$%('*%/-"%&,+
,B/,<)')-")'+,/230.$!1#2!#0,.05$3#27/01$-6./1026/06/"32./,0K401B$6#0.+6.-+#18'9-$('$('"'6,(*7)
0:')-,':"/)')-")')-,'#07)"&,'"/60(('"%'$+,"7'/0%()"%)'+/'#07)"&,'(0*6/,'+0,('%0)'/-"%&,1'"%+
)-*(')-,6,'2$77'"72";('4,'"'>,60'#07)"&,'($&%"7'"/60(('"'/0%()"%)'+/'#07)"&,'(0*6/,8'A'+*"7
()"),3,%)'"<<7$,(':06'/0%()"%)'+/'/*66,%)'(0*6/,(a'%"3,7;1')-,'($&%"7'/*66,%)'0:'"%'$+,"7'/0%5
()"%)'+/'/*66,%)'(0*6/,'2$77'"72";('4,'>,601'"%+')-*('2!0+,/230.$!1#2!#0,.0.-66/!#01$-6./0.2!
K/06/"32./,0K402!0$"/!0.+6.-+#'$%')-,'(3"775($&%"7',O*$#"7,%)'/$6/*$)'0:')-,'"3<7$:$,68'9-,
5.5 Small-Signal Operation and Models
G
D
!
vgs
G
D
!
vgs
gm vgs
gm vgs
ro
#
#
S
S
(b)
(a)
Figure 5.37 H3"775($&%"7'30+,7(':06')-,'FGHIJ9D'1(2'%,&7,/)$%&')-,'+,<,%+,%/,'0:'+('0%'v()'$%'(")*6"5
)$0%'E)-,'/-"%%,757,%&)-'30+*7")$0%',::,/)Ka'"%+'1/2'$%/7*+$%&')-,',::,/)'0:'/-"%%,757,%&)-'30+*7")$0%1'30+5
,7,+'4;'0*)<*)'6,($()"%/,' 6 $ = 8 G ⁄ ? ( 8
/$6/*$)'6,(*7)$%&'/"%')-,%'4,'*(,+')0'<,6:063'"%;'6,O*$6,+'($&%"7'"%"7;($(1'(*/-'"('/"7/*7")$%&
#07)"&,'&"$%8
9-,' 30()' (,6$0*(' (-06)/03$%&' 0:' )-,' (3"775($&%"7' 30+,7' 0:' I$&8' W8CfE"K' $(' )-")' $)
"((*3,(' )-,' +6"$%' /*66,%)' $%' (")*6")$0%' )0' 4,' $%+,<,%+,%)' 0:' )-,' +6"$%' #07)"&,8' I603' 0*6
()*+;'0:')-,'FGHIJ9'/-"6"/),6$()$/('$%'(")*6")$0%1'2,'P%02')-")')-,'+6"$%'/*66,%)'+0,('$%
:"/)'+,<,%+'0%'v()'$%'"'7$%,"6'3"%%,68'H*/-'+,<,%+,%/,'2"('30+,7,+'4;'"':$%$),'6,($()"%/,'6$
4,)2,,%'+6"$%'"%+'(0*6/,1'2-0(,'#"7*,'2"('&$#,%'4;'JO8'EW8QfK'$%'H,/)$0%'W8Q8b1'2-$/-'2,
6,<,")'-,6,'"(
8G
5
6 $ = 55555555
?(
EW8WQK
2-,6,' 8 G = @/ λ ' $('"'FGHIJ9'<"6"3,),6')-")',$)-,6'$('(<,/$:$,+'06' /"%'4,'3,"(*6,+8' =)
(-0*7+'4,'6,/"77,+')-")':06'"'&$#,%'<60/,(('),/-%070&;1'8G'$('<60<06)$0%"7')0')-,'FGHIJ9
/-"%%,7'7,%&)-8'9-,'/*66,%)'?('$(')-,'#"7*,'0:')-,'+/'+6"$%'/*66,%)'2$)-0*)')-,'/-"%%,757,%&)30+*7")$0%')"P,%'$%)0'"//0*%)a')-")'$(1
@
Q
? ( = 555 > !'8 :8
Q
EW8WCK
9;<$/"77;1'6$'$('$%')-,'6"%&,'0:'@Z'PΩ')0'@ZZZ'PΩ. =)':07702(')-")')-,'"//*6"/;'0:')-,'(3"775
($&%"7' 30+,7' /"%' 4,' $3<60#,+' 4;' $%/7*+$%&' 6$' $%' <"6"77,7' 2$)-' )-,' /0%)6077,+' (0*6/,1' "(
(-02%'$%'I$&8'W8CfE4K8
=)'$('$3<06)"%)')0'%0),')-")')-,'(3"775($&%"7'30+,7'<"6"3,),6('7@'"%+'6$'+,<,%+'0%')-,'+/
4$"('<0$%)'0:')-,'FGHIJ98
i,)*6%$%&' )0' )-,' "3<7$:$,6' 0:' I$&8' W8Cb1' 2,' :$%+' )-")' 6,<7"/$%&' )-,' FGHIJ9' 2$)-' )-,
(3"775($&%"7'30+,7'0:'I$&8'W8CfE4K'6,(*7)('$%')-,'#07)"&,5&"$%',B<6,(($0%
v
,1
5 = ' 7 @ ( F ( ll 6 $ )
G v = 55555
v 71
EW8WbK
9-*(1')-,':$%$),'0*)<*)'6,($()"%/,'6$'6,(*7)('$%'"'6,+*/)$0%'$%')-,'3"&%$)*+,'0:')-,'#07)"&,'&"$%8
A7)-0*&-')-,'"%"7;($('"40#,'$('<,6:063,+'0%'"%'`FGH')6"%($()061')-,'6,(*7)(1'"%+')-,
,O*$#"7,%)'/$6/*$)'30+,7('0:'I$&8'W8Cf1'"<<7;',O*"77;'2,77')0'_FGH'+,#$/,(1',B/,<)':06'*($%&
8 *) 1' 8 # 1' 8 :8 1 '"%+' 8 G '"%+'6,<7"/$%&' > !'2$)-' > " 8
281
282 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.5.6 The Transconductance gm
U,'(-"77'%02')"P,'"'/70(,6'700P'")')-,'FGHIJ9')6"%(/0%+*/)"%/,'&$#,%'4;'JO8'EW8bfK1'2-$/2,'6,26$),'2$)-' > ! & > !′ 0('c&) "(':07702(D
7 @ = > !′ ( ' ⁄ & ) ( 8 *) ' 8 # ) = > !′ ( ' ⁄ & )8 :8
EW8WWK
9-$('6,7")$0%(-$<'$%+$/"),(')-")'7@'$('<60<06)$0%"7')0')-,'<60/,((')6"%(/0%+*/)"%/,'<"6"3,),6
> !′ = µ ! < $% "%+')0')-,''/ &'6")$0'0:')-,'FGH')6"%($()06a'-,%/,')0'04)"$%'6,7")$#,7;'7"6&,')6"%(5
/0%+*/)"%/,')-,'+,#$/,'3*()'4,'(-06)'"%+'2$+,8'U,'"7(0'04(,6#,')-")':06'"'&$#,%'+,#$/,')-,
)6"%(/0%+*/)"%/,'$('<60<06)$0%"7')0')-,'0#,6+6$#,'#07)"&,1' 8 :8 = 8 *) ' 8 # 1')-,'"30*%)'4;
2-$/-')-,'4$"('#07)"&,'8*)',B/,,+(')-,')-6,(-07+'#07)"&,'8#8'`0),1'-02,#,61')-")'$%/6,"(5
$%&'7@'4;'4$"($%&')-,'+,#$/,'")'"'7"6&,6'8*)'-"(')-,'+$("+#"%)"&,'0:'6,+*/$%&')-,'"7702"47,
#07)"&,'($&%"7'(2$%&'")')-,'+6"$%8
A%0)-,6'*(,:*7',B<6,(($0%':06'7@'/"%'4,'04)"$%,+'4;'(*4()$)*)$%&':06'8:8'$%'JO8'EW8WWK'
4;' Q? ( ⁄ E> !′ ( ' ⁄ & )K 'q:603'JO8'EW8bZKrD
7@ =
Q> !′ ' ⁄ & ? (
EW8WNK
9-$(',B<6,(($0%'(-02(')20')-$%&(D
1. I06'"'&$#,%'FGHIJ91'7@'$('<60<06)$0%"7')0')-,'(O*"6,'600)'0:')-,'+/'4$"('/*66,%)8
2. A)'"'&$#,%'4$"('/*66,%)1'7@'$('<60<06)$0%"7')0' ' ⁄ &8
=%' /0%)6"()1' )-,' )6"%(/0%+*/)"%/,' 0:' )-,' 4$<07"6' .*%/)$0%' )6"%($()06' ELM9K' ()*+$,+' $%
?-"<),6 N' $(' <60<06)$0%"7' )0' )-,' 4$"(' /*66,%)' "%+' $(' $%+,<,%+,%)' 0:' )-,' <-;($/"7' ($>,' "%+
&,03,)6;'0:')-,'+,#$/,8
90'&"$%'(03,'$%($&-)'$%)0')-,'#"7*,('0:'7@'04)"$%,+'$%'FGHIJ9('/0%($+,6'"%'$%),5
Q
&6"),+5/$6/*$)' +,#$/,' 0<,6")$%&' ")' ?(' =' Z8W' 3A' "%+' -"#$%&' > !′ = @QZ'µAcS 8' JO*")$0%
EW8WNK'(-02(')-")':06''/ &' ='@1'7@' = 'Z8CW'3AcS1'2-,6,"('"'+,#$/,':06'2-$/-''/ &'='@ZZ
-"('7@'='C8W 3AcS8'=%'/0%)6"()1'"'LM9'0<,6")$%&'")'"'/077,/)06'/*66,%)'0:'Z8W'3A'-"('7@'=
QZ'3AcS8
u,)'"%0)-,6'*(,:*7',B<6,(($0%':06'7@'0:')-,'FGHIJ9'/"%'4,'04)"$%,+'4;'(*4()$)*)$%&':06
> !′ E'/ &K'$%'JO8'EW8WWK'4;'Q?( /E8*)'−'8#KQD
Q?
Q? (
5 = 55555555(5
7 @ = 55555555555555555555
8 *) ' 8 #
8 :8
EW8WfK
A'/0%#,%$,%)'&6"<-$/"7'/0%()6*/)$0%')-")'/7,"67;'$77*()6"),(')-$('6,7")$0%(-$<'$('(-02%'$%'I$&8'W8Cd8
=%' (*33"6;1' )-,6,' "6,' )-6,,' +$::,6,%)' 6,7")$0%(-$<(' :06' +,),63$%$%&' 7@pJO(8' EW8WWK1
EW8WNK1'"%+'EW8WfKp"%+')-,6,'"6,')-6,,'+,($&%'<"6"3,),6(pE'/ &K1'8:81'"%+'?(1'"%;')20'0:
2-$/-'/"%'4,'/-0(,%'$%+,<,%+,%)7;8'9-")'$(1')-,'+,($&%,6'3";'/-00(,')0'0<,6"),')-,'FGHIJ9
2$)-'"'/,6)"$%'0#,6+6$#,'#07)"&,'8:8'"%+'")'"'<"6)$/*7"6'/*66,%)'?(a')-,'6,O*$6,+''/ &'6")$0'/"%
)-,%'4,':0*%+'"%+')-,'6,(*7)$%&'7@'+,),63$%,+8
5.5 Small-Signal Operation and Models
iD
Q
ID
Slope
ID
!gm = 1
VOV
2
0
Figure 5.38
7me?( cE @Q555 V:8K8
1
2 VOV
VOV
vOV
9-,'(70<,'0:')-,')"%&,%)'")')-,'4$"('<0$%)'s'$%),6(,/)(')-,'v:8'"B$('")' @55Q5 V:8 8'9-*(1
Example 5.10
I$&*6,'W8C[E"K'(-02('"'+$(/6,),'/0330%5(0*6/,'FGHIJ9'"3<7$:$,6'*)$7$>$%&'"'+6"$%5)05&"),'6,($()"%/,
F*':06'4$"($%&'<*6<0(,(8'H*/-'"'4$"($%&'"66"%&,3,%)'2$77'4,'()*+$,+'$%'H,/)$0%'W8f8'9-,'$%<*)'($&%"7' v+'$(
/0*<7,+')0')-,'&"),'#$"'"'7"6&,'/"<"/$)061'"%+')-,'0*)<*)'($&%"7'")')-,'+6"$%'$('/0*<7,+')0')-,'70"+'6,($()"%/,
F&'#$"'"%0)-,6'7"6&,'/"<"/$)068'U,'2$(-')0'"%"7;>,')-$('"3<7$:$,6'/$6/*$)')0'+,),63$%,'$)('(3"775($&%"7'#07)5
"&,'&"$%1'$)('$%<*)'6,($()"%/,1'"%+')-,'7"6&,()'"7702"47,'$%<*)'($&%"78'9-,')6"%($()06'-"('8#'='@8W'S1' > !′ E'/&K
='Z8QW'3AcSQ1'"%+'8G'='WZ'S8'A((*3,')-,'/0*<7$%&'/"<"/$)06(')0'4,'(*::$/$,%)7;'7"6&,'(0'"(')0'"/)'"('(-06)
/$6/*$)('")')-,'($&%"7':6,O*,%/$,('0:'$%),6,()8
VDD =
(a)
283
284 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.10 continued
VDD
ID
RD
ID
RG
IG = 0
!
VDS
#
!
VGS
#
(b)
(c)
ii
(ii−gmvgs)
RG
!
vi
!
#
vgs=vi
gmvgs
vo
#
#
Rin=
R)L
R)L=RL || RD || ro
vi
ii
(d)
Figure 5.39 JB"3<7,'W8@ZD'1(2'"3<7$:$,6'/$6/*$)a'1/2'/$6/*$)':06'+,),63$%$%&')-,'+/'0<,6")$%&'<0$%)a'1%2+)-,+'"3<7$:$,6'
(3"775($&%"7',O*$#"7,%)'/$6/*$)a'1'2'"'($3<7$:$,+'#,6($0%'0:')-,'/$6/*$)'$%'E%K8
5.5 Small-Signal Operation and Models
Solution
U,':$6()'+,),63$%,')-,'+/'0<,6")$%&'<0$%)8'I06')-$('<*6<0(,1'2,',7$3$%"),')-,'$%<*)'($&%"7' v + 1'"%+'0<,%5
/$6/*$)')-,')20'/0*<7$%&'/"<"/$)06('E($%/,')-,;'470/P'+/'/*66,%)(K8'9-,'6,(*7)'$(')-,'/$6/*$)'(-02%'$%'I$&8
W8C[E4K8'U,'%0),')-")'($%/,' ? * & Z 1')-,'+/'#07)"&,'+60<'"/60((' F * '2$77'4,'>,601'"%+'
8 *) & 8 () & 8 (( ' F ( ? (
EW8WdK
U$)-' 8 () & 8 *) 1')-,'`FGH')6"%($()06'2$77'4,'0<,6")$%&'$%'(")*6")$0%8'9-*(1
@
Q
? ( & 555 > ! ( 8 *) ' 8 # )
Q
EW8W[K
2-,6,1' :06' ($3<7$/$);1' 2,' -"#,' %,&7,/),+' )-,' ,::,/)' 0:' /-"%%,757,%&)-' 30+*7")$0%' 0%' )-,' +/' 0<,6")$%&
<0$%)8'H*4()$)*)$%&' 8 (( & @W 'S1' F ( & @Z 'P Ω1' > ! & Z8QW '3AcSQ1'"%+' 8 # & @8W 'S'$%'JO(8'EW8WdK'"%+
EW8W[K1'"%+'(*4()$)*)$%&':06' 8 *) ':603'JO8'EW8WdK'$%)0'JO8'EW8W[K'6,(*7)('$%'"'O*"+6")$/',O*")$0%'$%' ? ( 8'H07#5
$%&')-,'7")),6'"%+'+$(/"6+$%&')-,'600)')-")'$('%0)'<-;($/"77;'3,"%$%&:*7';$,7+(')-,'(07*)$0%
? ( & @8ZN '3A
2-$/-'/066,(<0%+(')0
8 *) & 8 () & b8b 'S
"%+
8 :8 & b8b ' @8W & Q8[ 'S
`,B)' 2,' <60/,,+' 2$)-' )-,' (3"775($&%"7' "%"7;($(' 0:' )-,' "3<7$:$,68' 902"6+' )-")' ,%+' 2,' 6,<7"/,' )-,
FGHIJ9'2$)-'$)('(3"775($&%"7'30+,7')0'04)"$%')-,'(3"775($&%"7',O*$#"7,%)'/$6/*$)'0:')-,'"3<7$:$,61'(-02%
$%'I$&8'W8C[E/K8'G4(,6#,')-")'2,'-"#,'6,<7"/,+')-,'/0*<7$%&'/"<"/$)06('2$)-'(-06)'/$6/*$)(8'9-,'+/'#07)"&,
(*<<7;'8 (('-"('"7(0'4,,%'6,<7"/,+'2$)-'"'(-06)'/$6/*$)')0'&60*%+8
9-,'#"7*,('0:')-,')6"%($()06'(3"775($&%"7'<"6"3,),6(' 7 @ '"%+' 6 $ '/"%'4,'+,),63$%,+'4;'*($%&')-,'+/
4$"('O*"%)$)$,(':0*%+'"40#,1'"(':07702(D
7 @ & > ! 8 :8
& Z8QW × Q8[ & Z8fQW '3AcS
8
WZ
6 $ & 55555G5 & 5555555555 & bf 'P Ω '
@8ZN
?(
`,B)'2,'*(,')-,' ,O*$#"7,%)'/$6/*$)'0:'I$&8'W8C[E/K' )0'+,),63$%,' )-,'$%<*)' 6,($()"%/,' F $% ≡ v + ⁄ + + ' "%+')-,
#07)"&,'&"$%' G v & v $ ⁄ v + 8 '902"6+')-")',%+'2,'($3<7$:;')-,'/$6/*$)'4;'/034$%$%&')-,')-6,,'<"6"77,7'6,($(5
)"%/,(' 6 $1' F (1'"%+' F &'$%'"'($%&7,'6,($()"%/,' F′& 1
F′& & F & F ( 6 $
& @Z @Z bf & b8WQ 'PΩ
"('(-02%'$%'I$&8'W8C[E+K8'I06')-,'7")),6'/$6/*$)'2,'/"%'26$),')-,')20',O*")$0%('
v $ & ( + + ' 7 @ v 71 )F′&
EW8NZK
285
286 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
e
x
Example 5.10 continued
"%+
v7 1 ' v$
+ + & 5555555555555555
5
F*
EW8N@K
H*4()$)*)$%&':06' + + ':603'JO8'EW8N@K'$%)0'JO8'EW8NZK'6,(*7)('$%')-,':07702$%&',B<6,(($0%':06')-,'#07)"&,'&"$%
G v ≡ v $ ⁄ v + & v $ ⁄ v 71 D
@ '( @ ⁄ 7@ F* )
' G v & ' 7 @ F′& 5555555555555555555555555555555
@ ( ( F′& ⁄ F * )
H$%/,' F * ' $(' #,6;' 7"6&,1' 7 @ F * / @' "%+' F′& ⁄ F * - @' E)-,' 6,"+,6' /"%' ,"($7;' #,6$:;' )-$(K1' "%+' )-,' &"$%
,B<6,(($0%'/"%'4,'"<<60B$3"),+'"(
Gv " ' 7 @ F′&
EW8NQK
H*4()$)*)$%&1' 7 @ & Z8fQW'3AcS'"%+' F′& & b8WQ 'P Ω ';$,7+(
G v & ' C8C'ScS
90' 04)"$%' )-,' $%<*)' 6,($()"%/,1' 2,' (*4()$)*),' $%' JO8' EW8N@K' :06' v $ & G v v 71 & ' 7 @ F′& v 71 1' )-,%' *(,
F $% ≡ v + ⁄ + + & v 71 ⁄ + + ')0'04)"$%
F*
F $% & 555555555555555555555
@ ( 7 @ F′&
EW8NCK
9-$('$('"%'$%),6,()$%&'6,7")$0%(-$<D'9-,'$%<*)'6,($()"%/,'+,/6,"(,('"(')-,'&"$%' ( 7 @ F′& ) '$('$%/6,"(,+8'9-,
#"7*,'0:' F $% '/"%'%02'4,'+,),63$%,+a'$)'$(
@Z'FΩ
F $% & 555555555555555555 & Q8CC'FΩ
@ ( C8C
2-$/-'$('()$77'#,6;'7"6&,8
9-,'7"6&,()'"7702"47,'$%<*)'($&%"7' vt + '$('/0%()6"$%,+'4;')-,'%,,+')0'P,,<')-,')6"%($()06'$%'(")*6")$0%'")
"77')$3,(a')-")'$(1
v () ≥ v *) ' 8 #
J%:06/$%&')-$('/0%+$)$0%'2$)-',O*"7$);'")')-,'<0$%)' v *) '$('3"B$3*3'"%+' v () '$('3$%$3*31'2,'26$),
v ()3$% ' & v *)3"B ' 8 #
8 () ' G v vt + & 8 *) ( vt + ' 8 #
H$%/,' 8 () & 8 *) 1'2,'04)"$%
8
Gv ( @
9-$('$('"'&,%,6"7'6,7")$0%(-$<')-")'"<<7$,(')0')-$('/$6/*$)'$66,(<,/)$#,'0:')-,'/03<0%,%)'#"7*,(8'G4(,6#,')-")
$)'($3<7;'()"),(')-")')-,'3"B$3*3'($&%"7'(2$%&'$('+,),63$%,+'4;')-,':"/)')-")')-,'4$"('"66"%&,3,%)'3"P,(
8 ( & 8 * '"%+')-*(1')0'P,,<')-,'FGHIJ9'0*)'0:')-,')6$0+,'6,&$0%1')-,'($&%"7'4,)2,,%'^'"%+']'$('/0%5
()6"$%,+')0'4,',O*"7'')0' 8 # 8'I06'0*6'<"6)$/*7"6'+,($&%1'
#
vt + & 55555555555555555
5
@8W
vt + & 5555555555555555 & Z8CW'S
C8C ( @
A'30+$:$/")$0%'0:')-$('/$6/*$)')-")'$%/6,"(,(')-,'"7702"47,'($&%"7'(2$%&'$('$%#,()$&"),+'$%'_6047,3'W8dZ8
5.5 Small-Signal Operation and Models
EXERCISE
D5.18' ?0%($+,6' )-,' "3<7$:$,6' /$6/*$)' 0:' I$&8' W8C[E"K' 2$)-0*)' )-,' 70"+' 6,($()"%/,' F &' "%+' 2$)-' /-"%%,7
7,%&)-'30+*7")$0%'%,&7,/),+8'T,)' 8 (( & W'S1'8 # & Z8f'S1'"%+'> ! & @'3AcSQ8'I$%+'8 :8 1' ? ( 1 ' F ( 1
"%+' F * ')0'04)"$%'"'#07)"&,'&"$%'0:'QW'ScS'"%+'"%'$%<*)'6,($()"%/,'0:'Z8W'FΩ 8'U-")'$(')-,'3"B$5
3*3'"7702"47,'$%<*)'($&%"71' vt + g
Ans. Z8C@['Sa'WZ8f'µAa'fd8W'PΩ a'@C'FΩ a'Qf'3S
5.5.7 The T Equivalent-Circuit Model
9-60*&-'"'($3<7,'/$6/*$)')6"%(:063")$0%'$)'$('<0(($47,')0'+,#,70<'"%'"7),6%")$#,',O*$#"5
7,%)5/$6/*$)'30+,7':06')-,'FGHIJ98'9-,'+,#,70<3,%)'0:'(*/-'"'30+,71'P%02%'"(')-,'9
30+,71' $(' $77*()6"),+' $%' I$&8' W8bZ8' I$&*6,' W8bZE"K' (-02(' )-,' ,O*$#"7,%)' /$6/*$)' ()*+$,+
ig " 0
G
gmvgs
ig " 0
id
D
X
G
!
D
id
!
vgs
gmvgs
vgs
#
gmvgs
#
is
is
S
S
(a)
(b)
D
id
gmvgs
ig " 0
G
ig " 0
X
G
D
id
!
vgs
!
vgs
gmvgs
gmvgs
#
1/gm
#
is
is
S
S
(d)
(c)
Figure 5.40 ^,#,70<3,%)'0:')-,'9',O*$#"7,%)5/$6/*$)'30+,7':06')-,'FGHIJ98'I06'($3<7$/$);1'6$'-"('4,,%
03$)),+a'-02,#,61'$)'3";'4,'"++,+'4,)2,,%'^'"%+'H'$%')-,'9'30+,7'0:'1'28
287
288 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
D
D
gm vgs
G
10i
ro
!
vgs
G
ro
i
1/g m
1/g m
#
S
S
(a)
(b)
Figure 5.41 1(2'9-,'9'30+,7'0:')-,'FGHIJ9'"*&3,%),+'2$)-')-,'+6"$%5)05(0*6/,'6,($()"%/,'6$8'1/2'A%'
"7),6%")$#,'6,<6,(,%)")$0%'0:')-,'9'30+,78
"40#,'2$)-0*)'6$8'=%'I$&8'W8bZE4K'2,'-"#,'"++,+'"'(,/0%+'7@v71'/*66,%)'(0*6/,'$%'(,6$,(
2$)-')-,'06$&$%"7'/0%)6077,+'(0*6/,8'9-$('"++$)$0%'04#$0*(7;'+0,('%0)'/-"%&,')-,'),63$5
%"7'/*66,%)('"%+'$(')-*('"7702,+8'9-,'%,27;'/6,"),+'/$6/*$)'%0+,1'7"4,7,+'v1'$('.0$%,+')0
)-,'&"),'),63$%"7']'$%'I$&8 W8bZE/K8'G4(,6#,')-")')-,'&"),'/*66,%)'+0,('%0)'/-"%&,p)-")
$(1'$)'6,3"$%(',O*"7')0'>,60p"%+')-*(')-$('/0%%,/)$0%'+0,('%0)'"7),6')-,'),63$%"7'/-"6"/5
),6$()$/(8'U,'%02'%0),')-")'2,'-"#,'"'/0%)6077,+'/*66,%)'(0*6/,'7@v71'/0%%,/),+'"/60((
$)('/0%)607'#07)"&,' v718'U,'/"%'6,<7"/,')-$('/0%)6077,+'(0*6/,'4;'"'6,($()"%/,'"('70%&'"(
)-$('6,($()"%/,'+6"2('"%',O*"7'/*66,%)'"(')-,'(0*6/,8'EH,,')-,'(0*6/,5"4(06<)$0%')-,06,3
$%'A<<,%+$B'^8K'9-*(')-,'#"7*,'0:')-,'6,($()"%/,'$(' v 71 ⁄ 7 @ v 71 = @ ⁄ 7 @8'9-$('6,<7"/,3,%)
$(' (-02%' $%' I$&8' W8bZE+K1' 2-$/-' +,<$/)(' )-,' "7),6%")$#,' 30+,78' G4(,6#,' )-")' +7' $(' ()$77
>,601' + , = 7 @ v 71 1'"%+'+ 1 = v 71 ⁄ ( @ ⁄ 7 @ ) = 7 @ v 71 1'"77')-,'("3,'"('$%')-,'06$&$%"7'30+,7'$%
I$&8'W8bZE"K8
9-,'30+,7'0:'I$&8'W8bZE+K'(-02(')-")')-,'6,($()"%/,'4,)2,,%'&"),'"%+'(0*6/,'700P5
$%&' $%)0' )-,' (0*6/,' $(' @ ⁄ 7 @ 8' 9-$(' 04(,6#")$0%' "%+' )-,' 9' 30+,7' <60#,' *(,:*7' $%' 3"%;
"<<7$/")$0%(8'`0),')-")')-,'6,($()"%/,'4,)2,,%'&"),'"%+'(0*6/,1'700P$%&'$%)0')-,'&"),1'$(
$%:$%$),8
=%'+,#,70<$%&')-,'9'30+,7'2,'+$+'%0)'$%/7*+,'6$8'=:'+,($6,+1')-$('/"%'4,'+0%,'4;'$%/065
<06")$%&'$%')-,'/$6/*$)'0:'I$&8'W8bZE+K'"'6,($()"%/,'6$'4,)2,,%'+6"$%'"%+'(0*6/,1'"('(-02%'$%
I$&8'W8b@E"K8'A%'"7),6%")$#,'6,<6,(,%)")$0%'0:')-,'9'30+,71'$%'2-$/-')-,'#07)"&,5/0%)6077,+
/*66,%)'(0*6/,'$('6,<7"/,+'2$)-'"'/*66,%)5/0%)6077,+'/*66,%)'(0*6/,1'$('(-02%'$%'I$&8'W8b@E4K8
I$%"77;1'2,'(-0*7+'%0),')-")'$%'06+,6')0'+$()$%&*$(-')-,'30+,7'0:'I$&8'W8CfE4K':603')-,
,O*$#"7,%)'9'30+,71')-,':063,6'$('(03,)$3,('6,:,66,+')0'"(')-,'90/$)'3π+B"'&.1'"'/"66;0#,6
:603')-, 4$<07"6')6"%($()06'7$),6")*6,8'9-,'06$&$%'0:')-$('%"3,'2$77'4,',B<7"$%,+'$%')-,'%,B)
/-"<),68
Example 5.11
I$&*6,'W8bQE"K'(-02('"'FGHIJ9'"3<7$:$,6'4$"(,+'4;'"'/0%()"%)5/*66,%)'(0*6/,'?8'A((*3,')-")')-,'#"7*,(
0:'?'"%+' F ( '"6,'(*/-')-")')-,'FGHIJ9'0<,6"),('$%')-,'(")*6")$0%'6,&$0%8'9-,'$%<*)'($&%"7' v + '$('/0*<7,+')0
5.5 Small-Signal Operation and Models
)-,'(0*6/,'),63$%"7'4;'*)$7$>$%&'"'7"6&,'/"<"/$)06' < <@8'H$3$7"67;1')-,'0*)<*)'($&%"7'")')-,'+6"$%'$(')"P,%
)-60*&-'"'7"6&,'/0*<7$%&'/"<"/$)06'< <Q8'I$%+')-,'$%<*)'6,($()"%/,' F $% '"%+')-,'#07)"&,'&"$%' v $ ⁄ v + 8'`,&7,/)
/-"%%,757,%&)-'30+*7")$0%8
VDD
D
!
10i
RD
vo
RD
G
CC2
#
i
S
CC1
vi
!
#
I
Rin
vo
vi
1
gm
!
#
Rin
−VSS
(a)
(b)
Figure 5.42 E(K'A3<7$:$,6'/$6/*$)':06'JB"3<7,'W8@@a'E/K'H3"775($&%"7',O*$#"7,%)'/$6/*$)'0:')-,'"3<7$:$,6'$%'E"K8
Solution
i,<7"/$%&' )-,' FGHIJ9' 2$)-' $)(' 9' ,O*$#"7,%)5/$6/*$)' 30+,7' 6,(*7)(' $%' )-,' "3<7$:$,6' ,O*$#"7,%)' /$6/*$)
(-02%'$%'I$&8'W8bQE4K8'G4(,6#,')-")')-,'+/'/*66,%)'(0*6/,'?'$('6,<7"/,+'2$)-'"%'0<,%'/$6/*$)'"%+')-,'+/
#07)"&,'(0*6/,' 8 (( '$('6,<7"/,+'4;'"'(-06)'/$6/*$)8'9-,'7"6&,'/0*<7$%&'/"<"/$)06('-"#,'4,,%'6,<7"/,+'4;
(-06)'/$6/*$)(8'I603')-,',O*$#"7,%)'/$6/*$)530+,7'2,'+,),63$%,
v
F $% & 5555+ & @ ⁄ 7 @
'+
"%+
v+
v $ & ' +F ( & 5555555555555 F ( & 7 @ F ( v +
@ ⁄ 7@
9-*(1
v
' G v ≡ 5555$ & 7 @ F (
v+
U,'%0),')-")')-$('"3<7$:$,61'P%02%'"(')-,'/0330%5&"),'"3<7$:$,6'4,/"*(,')-,'&"),'")'&60*%+'<0),%)$"7'$(
/0330%')0'40)-')-,'$%<*)'"%+'0*)<*)'<06)(1'-"('"'702'$%<*)'6,($()"%/,' ( @ ⁄ 7 @ )'"%+'"'%0%$%#,6)$%&'&"$%8
U,'(-"77'()*+;')-$('"3<7$:$,6');<,'$%'H,/)$0%'W8N8W8
EXERCISE
5.19 n(,')-,'9030+,7'0:'I$&8'W8b@E4K')0'(-02')-")'"'FGHIJ9'2-0(,'+6"$%'$('/0%%,/),+')0'$)('&"),',B-$45
$)('"%'$%/6,3,%)"7'6,($()"%/,',O*"7')0'[ ( @ ⁄ 7 @ ) || 6 $ ]8
Ans. H,,'I$&8'JW8@[8
289
290 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
0
i
ro
Q
i
1
gm
r " ( g1 )|| ro Figure E5.19 ?$6/*$)(':06'JB,6/$(,'W8@[8'`0),')-")')-,'
m
4$"('"66"%&,3,%)'0:';'$('%0)'(-02%8
(b)
(a)
5.5.8 Summary
U,'/0%/7*+,')-$('(,/)$0%'4;'<6,(,%)$%&'$%'9"47,'W8C'"'(*33"6;'0:')-,':063*7"(':06'/"7/*7")$%&
)-,'#"7*,('0:')-,'(3"775($&%"7'FGHIJ9'<"6"3,),6(8'G4(,6#,')-")':06'7@'2,'-"#,')-6,,'+$::,6,%)
:063*7"(1',"/-'<60#$+$%&')-,'/$6/*$)'+,($&%,6'2$)-'$%($&-)'6,&"6+$%&'+,($&%'/-0$/,(8'U,'(-"77
3"P,':6,O*,%)'/033,%)('0%')-,(,'$%'7"),6'(,/)$0%('"%+'/-"<),6(8
Table 5.3 Small-Signal Equivalent-Circuit Models for the MOSFET
"#$%%&"'(!$%)*$+$#,-,+.
=:;<+-$(*!)!-"$!
96"%(/0%+*/)"%/,D
'
7 @ = µ ! < $% 55555 8 :8 =
&
G*)<*)'6,($()"%/,D
Q?
'
Q µ ! < $% 55555 ? ( = 55555555(5
&
8 :8
6$ = 8G ⁄ ?( = @ ⁄ λ ?(
F:;<+-$(*!)!-"$!
H"3,':063*7"('"(':06'`FGH'/%./"#'*($%&'|8:8 |1'|8G|1'"%+'6,<7"/$%&'µ!'2$)-'µ"8
)
"#$%%&"'(!$%)/01'2$%,!-)3'+41'-)567,%.
D
G
D
vgs
gmvgs
ro
S
!;46$+5π'30+,7
D
i
gmvgs
G
ro
1
gm
vgs
G
ro
1
gm
i
S
S
9'30+,7(
5.6 Basic MOSFET Amplifier Configurations
EXERCISES
5.20' I06')-,'"3<7$:$,6'$%'I$&8'W8Cb1'7,)'8(('='W'S1'F('='@Z'PΩ1'8#'='@'S1' >′! & QZ 'µA/SQ1''/&'='QZ1
8*) = Q S1'"%+'λ'='Z8'
E"K'I$%+')-,'+/'/*66,%)'?('"%+')-,'+/'#07)"&,'8()8'
E4K'I$%+'7@8'
E/K'I$%+')-,'#07)"&,'&"$%8'
E+K'=:'v71'='Z8Q'($%'ω #'#07)(1':$%+'v,1'"((*3$%&')-")')-,'(3"775($&%"7'"<<60B$3")$0%'-07+(8'U-")'"6,
)-,'3$%$3*3'"%+'3"B$3*3'#"7*,('0:'v()g'
E,K'n(,'JO8'EW8bCK')0'+,),63$%,')-,'#"6$0*('/03<0%,%)('0:'+(8'n($%&')-,'$+,%)$);'E($%Q ω #'=' @55Q5 ' @55Q5 /0(
Qω #K1'(-02')-")')-,6,'$('"'(7$&-)'(-$:)'$%'?('E4;'-02'3*/-gK'"%+')-")')-,6,'$('"'(,/0%+5-"630%$/'/035
<0%,%)'E$8,81'"'/03<0%,%)'2$)-':6,O*,%/;'QωK8'JB<6,((')-,'"3<7$)*+,'0:')-,'(,/0%+5-"630%$/'/035
<0%,%)'"('"'<,6/,%)"&,'0:')-,'"3<7$)*+,'0:')-,':*%+"3,%)"78'E9-$('#"7*,'$('P%02%'"(')-,'(,/0%+5
-"630%$/'+$()06)$0%8K
Ans. E"K'QZZ'µA1'C'Sa'E4K'Z8b'3A/Sa'E/K'−b'S/Sa'E+K'v,1'='−Z8d'($% ω #'#07)(1'Q8Q'S1'C8d'Sa'E,K
+('='EQZb'+'dZ'($% ω #'−'b'/0('Q ω #K'µA1'W%
5.21' A%'`FGH')6"%($()06'-"('µ!<$%'='NZ'µAcSQ1''/&'='bZ1'8#'='@'S1'"%+'8G'='@W'S8'I$%+'7@'"%+'6$'2-,%
E"K )-,'4$"('#07)"&,'8*)'='@8W'S1'E4K')-,'4$"('/*66,%)'?('='Z8W'3A8
Ans. E"K'@8Q'3A/S1'WZ'PΩa'E4K'@8WW'3A/S1'CZ'PΩ
5.22' A'FGHIJ9'$(')0'0<,6"),'")'?('='Z8@'3A'"%+'$(')0'-"#,'7@'='@'3AcS8'=:' > !′ ='WZ'µA/SQ1':$%+')-,
6,O*$6,+''/&'6")$0'"%+')-,'0#,6+6$#,'#07)"&,8
Ans. @ZZa'Z8Q'S
5.23' I06'"':"46$/")$0%'<60/,((':06'2-$/-'µ"'"'Z8bµ!1':$%+')-,'6")$0'0:')-,'2$+)-'0:'"'_FGH')6"%($()06')0
)-,'2$+)-'0:'"%'`FGH')6"%($()06'(0')-")')-,')20'+,#$/,('-"#,',O*"7'7@':06')-,'("3,'4$"('/0%+$)$0%(8
9-,')20'+,#$/,('-"#,',O*"7'/-"%%,7'7,%&)-(8
Ans. Q8W
5.24' A'_FGH')6"%($()06'-"('8#'='−@'S1' > "′ ='NZ'µA/SQ1'"%+''/&'='@N' µ3 ⁄ Z8d'µ38'I$%+'?('"%+'7@'2-,%
)-,'+,#$/,'$('4$"(,+'")'8*)'='−@8N'S8'A7(01':$%+')-,'#"7*,'0:'6$'$:'λ'E")'&'='@'µ3K'='−Z8Zb'S −@8
Ans. Q@N'µAa'Z8fQ'3A/Sa'[Q8N'PΩ
5.25' n(,')-,':063*7"('$%'9"47,'W8C')0'+,6$#,'"%',B<6,(($0%':06'E7@6$K'$%'),63('0:'8G'"%+'8:88'A('2,'(-"77
(,,'$%'?-"<),6'f1')-$('$('"%'$3<06)"%)')6"%($()06'<"6"3,),6'"%+'$('P%02%'"(')-,'$%)6$%($/'&"$%8'J#"7*"),
)-,'#"7*,'0:'7@6$':06'"%'`FGH')6"%($()06':"46$/"),+'$%'"'Z8d5µ3'?FGH'<60/,((':06'2-$/-' 8G′ '='@Q8W
S/µ3'0:'/-"%%,7'7,%&)-8'T,)')-,'+,#$/,'-"#,'3$%$3*3'/-"%%,7'7,%&)-'"%+'4,'0<,6"),+'")'"%'0#,6+6$#,
#07)"&,'0:'Z8Q'S8
Ans. 7 @ 6 $ = Q8 G ⁄ 8 :8 a @ZZ'S/S
5.6 Basic MOSFET Amplifier Configurations
=)'$('*(,:*7'")')-$('<0$%)')0')"P,'()0/P'0:'2-,6,'2,'"6,'"%+'2-,6,'2,'"6,'&0$%&'$%'0*6'()*+;
0:'FGHIJ9'"3<7$:$,6(8'=%'H,/)$0%'W8b'2,',B"3$%,+')-,',((,%/,'0:')-,'*(,'0:')-,'FGH5
IJ9'"('"%'"3<7$:$,68'9-,6,'2,':0*%+')-")'"730()57$%,"6'"3<7$:$/")$0%'/"%'4,'04)"$%,+'4;
4$"($%&')-,'FGHIJ9'")'"%'"<<60<6$"),'<0$%)'$%'$)('(")*6")$0%'6,&$0%'0:'0<,6")$0%'"%+'4;
P,,<$%&')-,'($&%"7' v 71'(3"778'U,')-,%')00P'"'/70(,6'700P'")')-,'(3"775($&%"7'0<,6")$0%'0:
)-,'FGHIJ9'$%'H,/)$0%'W8W'"%+'+,#,70<,+'/$6/*$)'30+,7(')0'6,<6,(,%)')-,')6"%($()061')-*(
:"/$7$)")$%&')-,'+,),63$%")$0%'0:'"3<7$:$,6'<"6"3,),6('(*/-'"('#07)"&,'&"$%'"%+'$%<*)'"%+
0*)<*)'6,($()"%/,(8'
291
292 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
U,'"6,'%02'6,"+;')0'/0%($+,6')-,'#"6$0*('<0(($47,'/0%:$&*6")$0%('0:'FGHIJ9'"3<7$:$,6(1
"%+'2,'2$77'+0')-")'$%')-,'<6,(,%)'(,/)$0%8'90':0/*('0*6'")),%)$0%'0%')-,'("7$,%)':,")*6,('0:')-,'#"65
$0*(' /0%:$&*6")$0%(1' 2,' (-"77' <6,(,%)' )-,3' $%' )-,$6' 30()' ($3<7,1' 06' X()6$<<,+' +02%Y' #,6($0%8
9-*(1'2,'2$77'%0)'(-02')-,'+/'4$"($%&'"66"%&,3,%)(1'7,"#$%&')-,'()*+;'0:'4$"('+,($&%')0')-,'%,B)
(,/)$0%8'I$%"77;1'$%'H,/)$0%'W8d'2,'2$77'46$%&',#,6;)-$%&')0&,)-,6'"%+'<6,(,%)'<6"/)$/"7'/$6/*$)(':06
+$(/6,),5/$6/*$)' FGHIJ9' "3<7$:$,6(a' %"3,7;1' )-0(,' "3<7$:,6' /$6/*$)(' )-")' /"%' 4,' /0%()6*/),+
*($%&'+$(/6,),'/03<0%,%)(8'9-,'()*+;'0:'$%),&6"),+5/$6/*$)'"3<7$:$,6('4,&$%('$%'?-"<),6'f8
5.6.1 The Three Basic Configurations
9-,6,'"6,')-6,,'4"($/'/0%:$&*6")$0%(':06'/0%%,/)$%&')-,'FGHIJ9'"('"%'"3<7$:$,68'J"/-'0:')-,(,
/0%:$&*6")$0%('$('04)"$%,+'4;'/0%%,/)$%&'0%,'0:')-,')-6,,'FGHIJ9'),63$%"7(')0'&60*%+1')-*('/6,5
")$%&'"')205<06)'%,)206P'2$)-')-,'&60*%+,+'),63$%"7'4,$%&'.$@@$!')0')-,'$%<*)'"%+'0*)<*)'<06)(8
I$&*6,'W8bC'(-02(')-,'6,(*7)$%&')-6,,'/0%:$&*6")$0%('2$)-')-,'4$"($%&'"66"%&,3,%)('03$)),+8
=%')-,'/$6/*$)'0:'I$&8'W8bCE"K')-,'(0*6/,'),63$%"7'$('/0%%,/),+')0'&60*%+1')-,'$%<*)'#07)"&,'($&5
%"7' v + '$('"<<7$,+'4,)2,,%')-,'&"),'"%+'&60*%+1'"%+')-,'0*)<*)'#07)"&,'($&%"7' v $'$(')"P,%'4,)2,,%
)-,' +6"$%' "%+' &60*%+1' "/60((' )-,' 6,($()"%/,' F ( 8' 9-$(' /0%:$&*6")$0%1' )-,6,:06,1' $(' /"77,+' )-,
&60*%+,+5(0*6/,'06'%"BB"*3!"#$%&+1C<2+"3<7$:$,68'=)'$('4;':"6')-,'30()'<0<*7"6'FGH'"3<7$:$,6
/0%:$&*6")$0%'"%+'$(')-,'0%,'2,'*)$7$>,+'$%'H,/)$0%('W8b'"%+'W8W')0'()*+;'FGH'"3<7$:$,6'0<,6")$0%8
9-,' %"BB"*3,(-&+ 1C82' 06' &60*%+,+5&"),' "3<7$:$,6' $(' (-02%' $%' I$&8' W8bCE4K8' =)' $(
04)"$%,+' 4;' /0%%,/)$%&' )-,' &"),' )0' &60*%+1' "<<7;$%&' )-,' $%<*)' v + ' 4,)2,,%' )-,' (0*6/,' "%+
!
RD
!
RD
vi
vo
!
#
vo
#
vi
!
#
#
(a) Common Source (CS)
vi
(b) Common Gate (CG)
!
#
!
RL
vo
#
(c) Common Drain (CD)
Figure 5.43 9-,')-6,,'4"($/'FGHIJ9'"3<7$:$,6'/0%:$&*6")$0%(8
5.6 Basic MOSFET Amplifier Configurations
&60*%+1'"%+')"P$%&')-,'0*)<*)' v $'"/60((')-,'6,($()"%/,' F ( '/0%%,/),+'4,)2,,%')-,'+6"$%'"%+
&60*%+8'U,',%/0*%),6,+'"'?]'"3<7$:$,6'$%'JB"3<7,'W8@@8
I$%"77;1'I$&8'W8bCE/K'(-02(')-,'%"BB"*3'$()*+1CG2'06'&60*%+,+5+6"$%'"3<7$:$,68'=)'$(
04)"$%,+' 4;' /0%%,/)$%&' )-,' +6"$%' ),63$%"7' )0' &60*%+1' "<<7;$%&' )-,' $%<*)' #07)"&,' ($&%"7' v +
4,)2,,%' &"),' "%+' &60*%+1' "%+' )"P$%&' )-,' 0*)<*)' #07)"&,' ($&%"7' 4,)2,,%' )-,' (0*6/,' "%+
&60*%+1'"/60(('"'70"+'6,($()"%/,' F & 8'I06'6,"(0%(')-")'2$77'4,/03,'"<<"6,%)'(-06)7;1')-$('/0%5
:$&*6")$0%'$('306,'/0330%7;'/"77,+')-,'!"#$%&+?".."D&$8'
G*6'()*+;'0:')-,')-6,,'4"($/'FGH'"3<7$:$,6'/0%:$&*6")$0%('2$77'6,#,"7')-")',"/-'-"('+$(5
)$%/)7;'+$::,6,%)'"))6$4*),('"%+'-,%/,'"6,"('0:'"<<7$/")$0%8
5.6.2 Characterizing Amplifiers
L,:06,'2,'4,&$%'0*6'()*+;'0:')-,'+$::,6,%)'FGHIJ9'"3<7$:$,6'/0%:$&*6")$0%(1'2,'/0%($+,6
-02')0'/-"6"/),6$>,')-,'<,6:063"%/,'0:'"%'"3<7$:$,6'"('"'/$6/*$)'4*$7+$%&'470/P8'A%'$%)60+*/5
)$0%')0')-$(')0<$/'2"('<6,(,%),+'$%'H,/)$0%'@8W8
I$&*6,'W8bbE"K'(-02('"%'"3<7$:$,6':,+'2$)-'"'($&%"7'(0*6/,'-"#$%&'"%'0<,%5/$6/*$)'#07)5
"&,' v ($&'"%+'"%'$%),6%"7'6,($()"%/,' F ($&8'9-,(,'/"%'4,')-,'<"6"3,),6('0:'"%'"/)*"7'($&%"7'(0*6/,
061'$%'"'/"(/"+,'"3<7$:$,61')-,'9-w#,%$%',O*$#"7,%)'0:')-,'0*)<*)'/$6/*$)'0:'"%0)-,6'"3<7$:$,6
()"&,' <6,/,+$%&' )-,' 0%,' *%+,6' ()*+;8' 9-,' "3<7$:$,6' $(' (-02%' 2$)-' "' 70"+' 6,($()"%/,' F &
ii
Rsig
vsig
!
#
io
!
!
vi
RL vo
#
#
(a)
Rsig
vsig
!
#
ii
Ro
!
vi
io
!
Rin
Avovi
!
#
RL
#
vo
#
(b)
!
vi "0
!
vx
#
#
RL ix
Ro
(c)
Figure 5.44 ?-"6"/),6$>")$0%'0:')-,'"3<7$:$,6'"('"':*%/)$0%"7'470/PD'E(K'A%'"3<7$:$,6':,+'2$)-'"'#07)"&,
($&%"7'v($&'-"#$%&'"'(0*6/,'6,($()"%/,'F($&1'"%+':,,+$%&'"'70"+'6,($()"%/,'F&a'E/K'JO*$#"7,%)5/$6/*$)'6,<6,(,%)"5
)$0%'0:')-,'/$6/*$)'$%'E"Ka'E%K'^,),63$%$%&')-,'"3<7$:$,6'0*)<*)'6,($()"%/,'F$8
293
294 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
/0%%,/),+')0')-,'0*)<*)'),63$%"78'!,6,1' F &'/"%'4,'"%'"/)*"7'70"+'6,($()"%/,'06')-,'$%<*)'6,($(5
)"%/,'0:'"'(*//,,+$%&'"3<7$:$,6'()"&,'$%'"'/"(/"+,'"3<7$:$,68
I$&*6,'W8bbE4K'(-02(')-,'"3<7$:$,6'/$6/*$)'2$)-')-,'"3<7$:$,6'470/P'6,<7"/,+'4;'$)(',O*$#5
"7,%)5/$6/*$)'30+,78'9-,'$%<*)'6,($()"%/,' F $% '6,<6,(,%)(')-,'70"+$%&',::,/)'0:')-,'"3<7$:$,6
$%<*)'0%')-,'($&%"7'(0*6/,8'=)'$(':0*%+':603
v
F $% ≡ 5555+
++
"%+')0&,)-,6'2$)-')-,'6,($()"%/,' F ($& ':063('"'#07)"&,'+$#$+,6')-")'6,+*/,(' v ($&')0')-,'#"7*,' v +
)-")'"<<,"6('")')-,'"3<7$:$,6'$%<*)1
F $%
F $% ( F ($&
v + & 5555555555555555555555 v ($&
EW8NWK
A77')-,'"3<7$:$,6'/$6/*$)('()*+$,+'$%')-$('(,/)$0%'"6,'#*).(-&$(.8'9-")'$(1')-,;'+0'%0)'/0%)"$%
$%),6%"7':,,+4"/P1'"%+')-*(' F $%'2$77'4,'$%+,<,%+,%)'0:' F &8'!02,#,61'"('2$77'4,'(,,%'$%'(*4(,5
O*,%)'/-"<),6(1')-$('$('%0)'"72";(')-,'/"(,8
9-,'(,/0%+'<"6"3,),6'$%'/-"6"/),6$>$%&'"3<7$:$,6'<,6:063"%/,'$(')-,'"A&*3%)$%#)-+>".-3
(,&+,()*+ G v$ 1++,:$%,+'"(
v
G v$ ≡ 5555$
v+
F& & ∞
9-,')-$6+'"%+':$%"7'<"6"3,),6'$(')-,'0*)<*)'6,($()"%/,' F $8'G4(,6#,':603'I$&8'W8bbE4K')-")
F $ '$(')-,'6,($()"%/,'(,,%'700P$%&'4"/P'$%)0')-,'"3<7$:$,6'0*)<*)'),63$%"7'2$)-' v + '(,)')0'>,608
9-*(' F $'/"%'4,'+,),63$%,+1'")'7,"()'/0%/,<)*"77;1'"('$%+$/"),+'$%'I$&8'W8bbE/K'2$)v
F $ & 5555%
+%
9-,'/0%)6077,+'(0*6/,' G v$ v + '"%+')-,'0*)<*)'6,($()"%/,' F $'6,<6,(,%)')-,'9-w#,%$%',O*$#"5
7,%)'0:')-,'"3<7$:$,6'0*)<*)'/$6/*$)1'"%+')-,'0*)<*)'#07)"&,'v $'/"%'4,':0*%+':603
F&
F& ( F$
v $ ' & 555555555555555555 G v$ v +
EW8NNK
9-*(')-,'#07)"&,'&"$%'0:')-,'"3<7$:$,6'<60<,61' G v 1'/"%'4,':0*%+'"(
v
F&
5
G v ≡ 5555$ & G v$ 55555555555555555
v+
F& ( F$
"%+')-,'0#,6"77'#07)"&,'&"$%' * v1
EW8NfK
v
* v ≡ 555555$5
v ($&
/"%'4,'+,),63$%,+'4;'/034$%$%&'JO(8'EW8NWK'"%+'EW8NfKD
F $%
F&
5 G v$ 55555555555555555
5
* v & 555555555555555555555
F $% ( F ($&
F& ( F$
EW8NdK
5.6.3 The Common-Source (CS) Amplifier
G:' )-,' )-6,,' 4"($/' FGH' "3<7$:$,6' /0%:$&*6")$0%(1' )-,' /0330%' (0*6/,' $(' )-,' 30()' 2$+,7;
*(,+8' 9;<$/"77;1' $%' "%' "3<7$:$,6' :063,+' 4;' /"(/"+$%&' "' %*34,6' 0:' ()"&,(1' )-,' 4*7P' 0:' )-,
#07)"&,'&"$%'$('04)"$%,+'4;'*($%&'0%,'06'306,'/0330%5(0*6/,'()"&,('$%')-,'/"(/"+,8
5.6 Basic MOSFET Amplifier Configurations
!
Rsig
vsig
vo
RD
!
vi
#
!
#
#
Rin
Ro
(a)
Rsig
!
!
vsig
!
#
vgs " vi
gmvgs
ro
#
RD
vo
#
Rin"+
Ro"RD || ro
(b)
Figure 5.45 E(K'?0330%5(0*6/,'"3<7$:$,6':,+'2$)-'"'($&%"7'v($&':603'"'&,%,6")06'2$)-'"'6,($()"%/,'F($&8'9-,
4$"('/$6/*$)'$('03$)),+8'E/K'9-,'/0330%5(0*6/,'"3<7$:$,6'2$)-')-,'FGHIJ9'6,<7"/,+'2$)-'$)('-;46$+5π'30+,78
I$&*6,'W8bWE"K'(-02('"'/0330%5(0*6/,'"3<7$:$,6'E2$)-')-,'4$"($%&'"66"%&,3,%)'03$)),+K
:,+'2$)-'"'($&%"7'(0*6/,' v ($&'-"#$%&'"'(0*6/,'6,($()"%/,' F ($&8'U,'2$(-')0'"%"7;>,')-$('/$6/*$)
)0'+,),63$%,' F $%1' G v$1' F $1'"%+' * v8'I06')-$('<*6<0(,'2,'(-"77'"((*3,')-")' F ('$('<"6)'0:')-,
"3<7$:$,6a')-*('$:'"'70"+'6,($()"%/,' F &'$('/0%%,/),+')0')-,'"3<7$:$,6'0*)<*)1'$)'"<<,"6('$%'<"65
"77,7'2$)-' F (8
Characteristic Parameters of the CS Amplifier i,<7"/$%&' )-,' FGHIJ9' 2$)-' $)(
-;46$+5π'30+,71'2,'04)"$%')-,'?H'"3<7$:$,6',O*$#"7,%)'/$6/*$)'(-02%'$%'I$&'W8bWE4K8'U,'(-"77
*(,' )-$(' ,O*$#"7,%)' /$6/*$)' )0' +,),63$%,' )-,' /-"6"/),6$()$/' <"6"3,),6(' F $% 1 ' G v$ 1 ' "%+' F $ ' "(
:07702(8
9-,'$%<*)'6,($()"%/,' F $%'$('04#$0*(7;'$%:$%$),1
F $% ' & ∞
EW8N[K
9-,' 0*)<*)' #07)"&,' v $' $(' :0*%+' 4;' 3*7)$<7;$%&' )-,' /*66,%)' ( 7 @ v 71 ) ' 4;' )-,' )0)"7' 6,($()"%/,
4,)2,,%')-,'0*)<*)'%0+,'"%+'&60*%+1
v $ ' & ' ( 7 @ v 71 ) ( F ( || 6 $ )
H$%/,' v 71 ' & v + 1')-,'0<,%5/$6/*$)'#07)"&,'&"$%' G v$ ≡ v $ ⁄ v + '/"%'4,'04)"$%,+'"('
G v$ ' & ' 7 @ ( F ( || 6 $ )
EW8fZK
G4(,6#,')-")')-,')6"%($()06'0*)<*)'6,($()"%/,'6 $'6,+*/,(')-,'3"&%$)*+,'0:')-,'#07)"&,'&"$%8'=%
+$(/6,),5/$6/*$)' "3<7$:$,6(1' 2-$/-' "6,' 0:' $%),6,()' )0' *(' $%' )-$(' /-"<),61' F ( ' $(' *(*"77;' 3*/-
295
296 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
702,6')-"%' 6 $'"%+')-,',::,/)'0:' 6 $'0%'6,+*/$%&' G v$ '$('(7$&-)'E7,((')-"%'@Zo'06'(0K8'9-*('$%
3"%;'/"(,('2,'/"%'%,&7,/)' 6 $'"%+',B<6,((' G v$ '($3<7;'"('
G v$ " ( ' 7 @ F ( )
EW8f@K
9-,' 6,"+,6' $(' /"*)$0%,+1' -02,#,61' )-")' %,&7,/)$%&' 6 $' $(' "7702,+' 0%7;' $%' +$(/6,),5/$6/*$)
+,($&%8'A('2$77'4,'(,,%'$%'?-"<),6'f1' 6 $'<7";('"'/,%)6"7'607,'$%'=?'"3<7$:$,6(8'
9-,' 0*)<*)' 6,($()"%/,' F $ ' $(' )-,' 6,($()"%/,' (,,%' 700P$%&' 4"/P' $%)0' )-,' 0*)<*)' ),63$%"7
2$)-'v +'(,)')0'>,608'I603'I$&8'W8bWE4K'2,'(,,')-")'2$)-'v + '(,)')0'>,601' v 71'2$77'4,'>,601'"%+')-*(
7 @ v 71 '2$77'4,'>,601'6,(*7)$%&'$%'
F $ ' & F ( || 6 $
EW8fQK
!,6,1' 6 $'-"(')-,'4,%,:$/$"7',::,/)'0:'6,+*/$%&')-,'#"7*,'0:' F $ 8'=%'+$(/6,),'/$6/*$)(1'-02,#,61
)-$(',::,/)'$('(7$&-)'"%+'2,'/"%'3"P,')-,'"<<60B$3")$0%
F$ " F(
EW8fCK
9-$('/0%/7*+,(')-,'"%"7;($('0:')-,'?H'"3<7$:$,6'<60<,68'U,'/"%'%02'3"P,')-,':07702$%&
04(,6#")$0%(8
1. 9-,'$%<*)'6,($()"%/,'$('$+,"77;'$%:$%$),8
2. 9-,'0*)<*)'6,($()"%/,'$('30+,6"),')0'-$&-'E$%')-,'P$70-3(')0'),%('0:'P$70-3('6"%&,K8
i,+*/$%&' F ( ')0'702,6' F $ '$('%0)'"'#$"47,'<60<0($)$0%1'($%/,')-,'#07)"&,'&"$%'$('"7(0
6,+*/,+8' A7),6%")$#,7;1' $:' "' 702' 0*)<*)' 6,($()"%/,' E$%' )-,' 0-3(' )0' ),%(' 0:' 0-3(
6"%&,K' $(' %,,+,+1' "' (0*6/,' :07702,6' ()"&,' $(' /"77,+' :061' "(' 2$77' 4,' +$(/*((,+' $%
H,/)$0%'W8N8N8
3. 9-,'0<,%5/$6/*$)'#07)"&,'&"$%' G v$'/"%'4,'-$&-1'3"P$%&')-,'?H'/0%:$&*6")$0%')-,'206P5
-06(,'$%'FGH'"3<7$:$,6'+,($&%8'n%:06)*%"),7;1'-02,#,61')-,'4"%+2$+)-'0:')-,'?H'"3<7$5
:$,6'$('(,#,6,7;'7$3$),+8'U,'(-"77'()*+;'"3<7$:$,6':6,O*,%/;'6,(<0%(,'$%'?-"<),6'[8
Overall Voltage Gain 90'+,),63$%,')-,'0#,6"77'#07)"&,'&"$%' * v 1'2,':$6()'%0),')-")')-,
$%:$%$),'$%<*)'6,($()"%/,'2$77'3"P,')-,',%)$6,'($&%"7' v ($& '"<<,"6'")')-,'"3<7$:$,6'$%<*)1
v + ' & v ($&
EW8fbK
"%'04#$0*(7;'$+,"7'($)*")$0%8'A)')-$('<0$%)'2,'(-0*7+'6,3$%+')-,'6,"+,6')-")')0'3"$%)"$%'"'6,"5
(0%"47;'7$%,"6'0<,6")$0%1' v + '"%+'-,%/,' v ($&'(-0*7+'4,'P,<)'3*/-'(3"77,6')-"%' Q8 :8 8
=:'"'70"+'6,($()"%/,' F & '$('/0%%,/),+')0')-,'0*)<*)'),63$%"7'0:')-,'"3<7$:$,61')-$('6,($(5
)"%/,'2$77'"<<,"6'$%'<"6"77,7'2$)-' F ( 8 '=)':07702(')-")')-,'#07)"&,'&"$%' G v'/"%'4,'04)"$%,+'4;
($3<7;'6,<7"/$%&' F ( '$%')-,',B<6,(($0%':06' G v$'$%'JO8'EW8fZK'4;' F ( || F & 1
G v ' & ' 7 @ ( F ( || F & || 6 $ )
EW8fWK
9-$(',B<6,(($0%')0&,)-,6'2$)-')-,':"/)')-")' v + ' & v ($& 1'<60#$+,(')-,'0#,6"77'#07)"&,'&"$%1
* v & G v & ' 7 @ ( F ( || F & || 6 $ )
EW8fNK
EXERCISE
5.26 n(,' G v$ '$%'JO8'EW8fZK')0&,)-,6'2$)-' F $ '$%'JO8'EW8fQK')0'04)"$%' G v 8 'H-02')-")')-,'6,(*7)'$('$+,%)$/"7
)0')-")'$%'JO8'EW8fWK8
5.6 Basic MOSFET Amplifier Configurations
Rsig
gmvgs
!
vsig !
#
!
0
vgs " vi
#
Rin"+
vgs " vsig
ro
RD
vo
#
Ro"RD || ro
(
vo " #gmvgs RD || ro
)
Figure 5.46 _,6:063$%&')-,'"%"7;($('+$6,/)7;'0%')-,'/$6/*$)'+$"&6"3'2$)-')-,'FGHIJ9'30+,7'*(,+'$3<7$/$)7;8
Performing the Analysis Directly on the Circuit Diagram A7)-0*&- (3"775($&%"71
,O*$#"7,%)5/$6/*$)'30+,7('<60#$+,'"'(;(),3")$/'<60/,((':06')-,'"%"7;($('0:'"%;'"3<7$:$,6'/$65
/*$)1')-,',::06)'$%#07#,+'$%'+6"2$%&')-,',O*$#"7,%)'/$6/*$)'$('(03,)$3,('%0)'.*()$:$,+8'9-")'$(1
$%'($3<7,'($)*")$0%('"%+'":),6'"'70)'0:'<6"/)$/,1'0%,'/"%'<,6:063')-,'(3"775($&%"7'"%"7;($(
+$6,/)7;'0%')-,'/$6/*$)'(/-,3")$/8'L,/"*(,'$%')-$('2";'0%,'6,3"$%('/70(,6')0')-,'"/)*"7'/$65
/*$)1')-,'+$6,/)'"%"7;($('/"%';$,7+'&6,"),6'$%($&-)'$%)0'/$6/*$)'0<,6")$0%8'I$&*6,'W8bN'(-02(')-,
+$6,/)'"%"7;($('0:')-,'?H'"3<7$:$,68'G4(,6#,')-")'2,'-"#,'X<*77,+'0*)Y')-,'6,($()"%/,' 6 $ ':603
)-,')6"%($()061')-*('3"P$%&')-,')6"%($()06'+6"$%'/0%+*/)' 7 @ v 71 '2-$7,'()$77'"//0*%)$%&':06')-,
,::,/)'0:' 6 $8
EXERCISE
5.27 A'?H'"3<7$:$,6'*)$7$>,('"'FGHIJ9'4$"(,+'")' ? ( ' & Z8QW'3A'2$)-'8 :8 ' & Z8QW'S'"%+' F ( & QZ 'P Ω8
9-,'+,#$/,'-"(' 8 G & WZ'S8'9-,'"3<7$:$,6'$(':,+'2$)-'"'(0*6/,'-"#$%&' F ($& ' & @ZZ 'PΩ1'"%+'"'QZ5PΩ
70"+'$('/0%%,/),+')0')-,'0*)<*)8'I$%+' F $% 1' G v$ 1' F $ 1' G v1'"%+'* v 8'=:')0'3"$%)"$%'6,"(0%"47,'7$%,"6$);1
)-,'<,"P'0:')-,'$%<*)'($%,52"#,'($&%"7'$('7$3$),+')0'@Zo'0:' ( Q8 :8 )'2-")'$(')-,'<,"P'0:')-,'($%,5
2"#,'#07)"&,'")')-,'0*)<*)g
Ans. ∞a' ' CN8b 'ScSa'@d8Q'PΩa' ' @['ScSa' ' @['ScSa'Z8[W'S
5.6.4 The Common-Source Amplifier with a Source Resistance
=)'$('0:),%'4,%,:$/$"7')0'$%(,6)'"'6,($()"%/,' F 1 '$%')-,'(0*6/,'7,"+'0:')-,'/0330%5(0*6/,'"3<7$5
:$,6'"('(-02%'$%'I$&8'W8bfE"K8'9-,'/066,(<0%+$%&'(3"775($&%"7',O*$#"7,%)'/$6/*$)'$('(-02%'$%
I$&8'W8bfE4K1'2-,6,'2,'%0),')-")')-,'FGHIJ9'-"('4,,%'6,<7"/,+'2$)-'$)('9',O*$#"7,%)5/$65
/*$)'30+,78'9-,'9'30+,7'$('*(,+'$%'<6,:,6,%/,')0')-,' π'30+,7'4,/"*(,'$)'3"P,(')-,'"%"7;($(
$%')-$('/"(,'(03,2-")'($3<7,68'=%'&,%,6"71'CB/!/5/60206/1+1#2!./0+10.$!!/.#/,0+!0#B/01$-6./
3/2,L0#B/090@$,/30+10"6/M/66/,8'9-,'(0*6/,'6,($()"%/,')-,%'($3<7;'"<<,"6('$%'(,6$,('2$)-')-,
6,($()"%/,' @ ⁄ 7 @ '"%+'/"%'4,'"++,+')0'$)8
=)' (-0*7+' 4,' %0),+' )-")' 2,' -"#,' %0)' $%/7*+,+' 6 $ ' $%' )-,' ,O*$#"7,%)5/$6/*$)' 30+,78
=%/7*+$%&' 6 $ '20*7+'/03<7$/"),')-,'"%"7;($('/0%($+,6"47;a' 6 $ '20*7+'/0%%,/)')-,'0*)<*)
%0+,'0:')-,'"3<7$:$,6')0')-,'$%<*)'($+,'"%+')-*('20*7+'3"P,')-,'"3<7$:$,6'!$!-!+32#/6238
297
298 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Rsig
vsig
!
!
vi
#
!
#
vo
RD
Rs
#
Rin
Ro
(a)
D
i
Rsig
vsig
!
#
G
0
!
!
vgs
#
!
RD
vo
i
1
gm
vi
#
Ro"RD
S
Rs
#
Rin"+
(b)
Figure 5.47 9-,'?H'"3<7$:$,6'2$)-'"'(0*6/,'6,($()"%/,'F1D'E(K'?$6/*$)'2$)-0*)'4$"('+,)"$7(a'E/K'JO*$#"7,%)'/$65
/*$)'2$)-')-,'FGHIJ9'6,<6,(,%),+'4;'$)('9'30+,78
I06)*%"),7;1' $)' )*6%(' 0*)' )-")' )-,' ,::,/)' 0:' 6 $ ' 0%' )-,' 0<,6")$0%' 0:' )-,' +$(/6,),5/$6/*$)
"3<7$:$,6' $(' %0)' $3<06)"%)8' 9-$(' /"%' 4,' #,6$:$,+' 4;' /03<*),6' ($3*7")$0%1' *($%&' :06
$%()"%/,'H_=?J8'9-$('$('%0)')-,'/"(,1'-02,#,61':06')-,'$%),&6"),+5/$6/*$)'#,6($0%'0:')-,
/$6/*$)1'2-,6,' 6 $ '<7";('"'3".06'607,'"%+'3*()'4,')"P,%'$%)0'"//0*%)1'"('2,'(-"77'+0'$%
?-"<),6'f8
I603' I$&8' W8bfE4K' 2,' (,,' )-")' )-,' $%<*)' 6,($()"%/,' F $% ' $(' $%:$%$),' "%+' )-*(' v + & v ($& 8
n%7$P,')-,'?H'"3<7$:$,61'-02,#,61'-,6,'0%7;'"':6"/)$0%'0:' v + '"<<,"6('4,)2,,%'&"),'"%+'(0*6/,
"(' v 71 8'=)'/"%'4,'+,),63$%,+':603')-,'#07)"&,'+$#$+,6'/03<0(,+'0:'@ ⁄ 7 @'"%+' F 1 ')-")'"<<,"6(
"/60((')-,'"3<7$:$,6'$%<*)1'"(':07702(D
@ ⁄ 7@
v+
v 71 ' & v + 5555555555555555555555555 & 55555555555555555555
5
@ ⁄ 7@ ( F1
@ ( 7@ F1
EW8ffK
9-*(' 2,' /"%' *(,' )-,' #"7*,' 0:' F 1 ' )0' /0%)607' )-,' 3"&%$)*+,' 0:' )-,' ($&%"7' v 71 ' "%+' )-,6,4;
,%(*6,')-")' v 71 '+0,('%0)'4,/03,')00'7"6&,'"%+'/"*(,'*%"//,<)"47;'-$&-'%0%7$%,"6'+$()06)$0%8
9-$('$(')-,':$6()'4,%,:$)'0:'$%/7*+$%&'6,($()06' F 1 8'G)-,6'4,%,:$)('2$77'4,',%/0*%),6,+'$%'7"),6
(,/)$0%('"%+'/-"<),6(8'I06'$%()"%/,1'$)'2$77'4,'(-02%'$%'?-"<),6'[')-")' F 1 '/"*(,(')-,'*(,:*7
4"%+2$+)-' 0:' )-,' "3<7$:$,6' )0' 4,' ,B),%+,+8' 9-,' 3,/-"%$(3' 4;' 2-$/-' F 1 ' /"*(,(' (*/$3<60#,3,%)(' $%' "3<7$:$,6' <,6:063"%/,' $(' %,&")$#,' :,,+4"/P8' 90' (,,' -02' F 1 ' $%)60+*/,(
5.6 Basic MOSFET Amplifier Configurations
%,&")$#,':,,+4"/P1'6,:,6')0'I$&8'W8bfE"KD'=:'2-$7,'P,,<$%&' v + '/0%()"%)1':06'(03,'6,"(0%')-,
+6"$%'/*66,%)'$%/6,"(,(1')-,'(0*6/,'/*66,%)'"7(0'2$77'$%/6,"(,1'6,(*7)$%&'$%'"%'$%/6,"(,+'#07)5
"&,'+60<'"/60((' F 18'9-*(')-,'(0*6/,'#07)"&,'6$(,(1'"%+')-,'&"),5)05(0*6/,'#07)"&,'+,/6,"(,(8
9-,' 7")),6' ,::,/)' /"*(,(' )-,' +6"$%' /*66,%)' )0' +,/6,"(,1' /0*%),6"/)$%&' )-,' $%$)$"77;' "((*3,+
/-"%&,1' "%' $%+$/")$0%' 0:' )-,' <6,(,%/,' 0:' %,&")$#,' :,,+4"/P8' =%'?-"<),6' @Z' 2,' (-"77'()*+;
%,&")$#,':,,+4"/P':063"77;8'9-,6,'2,'2$77'7,"6%')-")')-,'$3<60#,3,%)(')-")'%,&")$#,':,,+5
4"/P'<60#$+,('"6,'04)"$%,+'")')-,',B<,%(,'0:'"'6,+*/)$0%'$%'&"$%8'U,'2$77'%02'(-02')-$(')0
4,')-,'/"(,'$%')-,'/$6/*$)'0:'I$&8'W8bf8
9-,'0*)<*)'#07)"&,' v $ '$('04)"$%,+'4;'3*7)$<7;$%&')-,'/0%)6077,+5(0*6/,'/*66,%)'+'4;' F (1
v$ & '+ F(
9-,'/*66,%)0+'$%')-,'(0*6/,'7,"+'/"%'4,':0*%+'4;'+$#$+$%&' v + '4;')-,')0)"7'6,($()"%/,'$%')-,'(0*6/,1
v+
7@ 5 & 55555555555555555555
5 v
+' & 555555555555555555555555
@ ⁄ 7@ ( F1
@ ( 7@ F1 +
EW8fdK
9-*(1')-,'#07)"&,'&"$%' G v$ '/"%'4,':0*%+'"('
v
F(
G v$ ' & 5555$ & ' 555555555555555555555555
5
v+
@ ⁄ 7@ ( F1
EW8f[K
7@ F(
G v$ ' & ' 55555555555555555555
5
@ ( 7@ F1
EW8dZK
2-$/-'/"%'"7(0'4,',B<6,((,+'"(
JO*")$0%'EW8dZK'$%+$/"),(')-")'$%/7*+$%&')-,'6,($()"%/,' F 1 '6,+*/,(')-,'#07)"&,'&"$%'4;')-,
:"/)06' ( @ ( 7 @ F 1 )8'9-$('$(')-,'<6$/,'<"$+':06')-,'$3<60#,3,%)(')-")'"//6*,'"('"'6,(*7)'0:' F 1 8 '=)
$(' $%),6,()$%&' )0' %0),' )-")' $%' ?-"<),6' @Z1' 2,' 2$77' :$%+' )-")' )-,' :"/)06' ( @ ( 7 @ F 1 ) ' $(' )-,
X"30*%)'0:'%,&")$#,':,,+4"/PY'$%)60+*/,+'4;' F 1 8'=)'$('"7(0')-,'("3,':"/)06'4;'2-$/-'4"%+5
2$+)-'"%+'0)-,6'<,6:063"%/,'<"6"3,),6('$3<60#,8'L,/"*(,'0:')-,'%,&")$#,5:,,+4"/P'"/)$0%
0:' F 1 '$)'$('P%02%'"('"'!"#$%&3'&,&*&$(-)"*+$&!)!-(*%&8'
9-,6,' $(' "%0)-,6' *(,:*7' $%),6<6,)")$0%' 0:' )-,' ,B<6,(($0%' :06' )-,' +6"$%' /*66,%)' $%' JO8
EW8fdKD'9-,'O*"%)$);'4,)2,,%'46"/P,)('0%')-,'6$&-)5-"%+'($+,'/"%'4,')-0*&-)'0:'"(')-,'X,::,/5
)$#,')6"%(/0%+*/)"%/,'2$)-' F 1'$%/7*+,+8Y'9-*(1'$%/7*+$%&' F 1 '6,+*/,(')-,')6"%(/0%+*/)"%/,'4;
)-,' :"/)06' ( @ ( 7 @ F 1 )8 ' 9-$(1' 0:' /0*6(,1' $(' ($3<7;' )-,' 6,(*7)' 0:' )-,' :"/)' )-")' 0%7;' "' :6"/)$0%
@ ⁄ ( @ ( 7 @ F 1 ) '0:' v + '"<<,"6('"(' v 71 'E(,,'JO8'W8ff8K8
9-,'"7),6%")$#,'&"$%',B<6,(($0%'$%'JO8'EW8f[K'-"('"'<02,6:*7'"%+'$%($&-):*7'$%),6<6,)")$0%D
9-,'#07)"&,'&"$%'4,)2,,%'&"),'"%+'+6"$%'$(',O*"7')0')-,'6")$0'0:')-,')0)"7'6,($()"%/,'$%')-,
+6"$%'( F ( )')0')-,')0)"7'6,($()"%/,'$%')-,'(0*6/,'( @ ⁄ 7 @ ( F 1 )1
90)"7'6,($()"%/,'$%'+6"$%
S07)"&,'&"$%':603'&"),')0'+6"$%'e' ' 555555555555555555555555555555555555555555555555555555555555
5
90)"7'6,($()"%/,'$%'(0*6/,
EW8d@K
9-$('$('"'&,%,6"7',B<6,(($0%8'I06'$%()"%/,1'(,))$%&' F 1 & Z '$%'JO8'EW8f[K';$,7+(' G v$ '0:')-,'?H
"3<7$:$,68
I$%"77;1'2,'/0%($+,6')-,'($)*")$0%'0:'"'70"+'6,($()"%/,' F & '/0%%,/),+'")')-,'0*)<*)8'U,
/"%'04)"$%')-,'&"$%' G v '*($%&')-,'0<,%5/$6/*$)'#07)"&,'&"$%' G v$ ')0&,)-,6'2$)-')-,'0*)<*)'6,($(5
)"%/,' F $ 1 '2-$/-'/"%'4,':0*%+'4;'$%(<,/)$0%')0'4,
F$ ' & F(
299
300 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
A7),6%")$#,7;1' G v' /"%' 4,' 04)"$%,+' 4;' ($3<7;' 6,<7"/$%&' F ( ' $%' JO8' EW8f[K' 06' EW8dZK' 4;
( F ( || F & )a')-*(1
06
F ( || F &
G v ' & ' 555555555555555555555555
5
@ ⁄ 7@ ( F1
EW8dQK
7 @ ( F ( || F & )
' G v ' & ' 55555555555555555555555555555
@ ( 7@ F1
EW8dCK
G4(,6#,')-")'JO8'EW8dQK'$('"'+$6,/)'"<<7$/")$0%'0:')-,'6")$0'0:')0)"7'6,($()"%/,'6*7,'0:'JO8'EW8d@K8
I$%"77;1'%0),')-")'4,/"*(,' F $% '$('$%:$%$),1' v + & v ($&'"%+')-,'0#,6"77'#07)"&,'&"$%' * v'$(',O*"7')0' G v8
EXERCISE
5.28 =%'JB,6/$(,'W8Qf'2,'"<<7$,+'"%'$%<*)'($&%"7' v ($& '0:'WZ'3S'<,"P'"%+'04)"$%,+'"%'0*)<*)'($&%"7'0:
"<<60B$3"),7;'@ S'<,"P8'A((*3,')-")':06'(03,'6,"(0%'2,'%02'-"#,'"%'$%<*)'($&%"7' v ($& ')-")'$('Z8Q
S'<,"P'"%+')-")'2,'2$(-')0'30+$:;')-,'/$6/*$)')0'P,,<' v 71 '*%/-"%&,+1'"%+')-*('P,,<')-,'%0%7$%,"6
+$()06)$0%':603'$%/6,"($%&8'U-")'#"7*,'(-0*7+'2,'*(,':06' F 1 g'U-")'#"7*,'0:' * v'2$77'6,(*7)g'U-")
2$77')-,'<,"P'($&%"7'")')-,'0*)<*)'4,/03,g'A((*3,' 6 $ & ∞8
Ans. @8W'PΩa' ' W'ScSa'@'S
5.6.5 The Common-Gate (CG) Amplifier
I$&*6,'W8bdE"K'(-02('"'/0330%5&"),'"3<7$:$,6'2$)-')-,'4$"($%&'/$6/*$)'03$)),+8'9-,'"3<7$:$,6
$(':,+'2$)-'"'($&%"7'(0*6/,'/-"6"/),6$>,+'4;' v ($& '"%+' F ($&8'H$%/,' F ($& '"<<,"6('$%'(,6$,('2$)-')-,
(0*6/,1' $)' $(' 306,' /0%#,%$,%)' )0' 6,<6,(,%)' )-,' )6"%($()06' 2$)-' )-,' 9' 30+,7' )-"%' 2$)-' )-,' π
30+,78'^0$%&')-$(1'2,'04)"$%')-,'"3<7$:$,6',O*$#"7,%)'/$6/*$)'(-02%'$%'I$&8'W8bdE4K8'`0),')-")
2,' -"#,' %0)' $%/7*+,+' 6 $D ' 9-$(' 20*7+' -"#,' /03<7$/"),+' )-,' "%"7;($(' /0%($+,6"47;1' :06' 6 $
20*7+'-"#,'"<<,"6,+'4,)2,,%')-,'0*)<*)'"%+')-,'$%<*)'($+,'0:')-,'"3<7$:$,68'I06)*%"),7;1'$)
D
!
RD
Rsig
vsig
G
vo
#
!
!
#
i
vi
Rsig
Ro
S
i
1/gm
RD
!
vo
#
Ro " RD
!
#
vsig
Rin
!
#
vi
#
Rin"1/gm
(a)
(b)
Figure 5.48 E(K'?0330%5&"),'E?]K'"3<7$:$,6'2$)-'4$"('"66"%&,3,%)'03$)),+8'E/K'JO*$#"7,%)'/$6/*$)'0:')-,'?]
"3<7$:$,6'2$)-')-,'FGHIJ9'6,<7"/,+'2$)-'$)('9'30+,78
5.6 Basic MOSFET Amplifier Configurations
)*6%('0*)')-")')-,',::,/)'0:' 6 $'0%')-,'<,6:063"%/,'0:'"'+$(/6,),'?]'"3<7$:$,6'$('#,6;'(3"778'U,
2$77'/0%($+,6')-,',::,/)'0:' 6 $ '2-,%'2,'()*+;')-,'=?':063'0:')-,'?]'"3<7$:$,6'$%'?-"<),6'f8
I603'$%(<,/)$0%'0:')-,',O*$#"7,%)'/$6/*$)'0:'I$&8'W8bdE4K1'2,'(,,')-")')-,'$%<*)'6,($()"%/,
@
F $% & 555555
7@
EW8dbK
9-$('(-0*7+'-"#,'4,,%',B<,/),+1'($%/,'2,'"6,'700P$%&'$%)0')-,'(0*6/,'"%+')-,'&"),'$('&60*%+,+8
9;<$/"77;'@ ⁄ 7 @'$('"':,2'-*%+6,+'0-3(a')-*(')-,'?]'"3<7$:$,6'-"('"'702'$%<*)'6,($()"%/,8'
90'+,),63$%,')-,'#07)"&,'&"$%' G v$1'2,'26$),'")')-,'+6"$%'%0+,'
v $ & ' +F (
"%+'(*4()$)*),':06')-,'(0*6/,'/*66,%)'+0:603
v
+
+ & ' 555555555555
5
@ ⁄ 7@
)0'04)"$%
v
G v$ ≡ 5555$ & 7 @ F (
v+
EW8dWK
2-$/-',B/,<)':06')-,'<0($)$#,'($&%'$('$+,%)$/"7')0')-,',B<6,(($0%':06' G v$ '0:')-,'?H'"3<7$:$,6
E2-,%' 6 $'$('%,&7,/),+K8'
9-,'0*)<*)'6,($()"%/,'0:')-,'?]'/$6/*$)'/"%'4,':0*%+'4;'$%(<,/)$0%'0:')-,'/$6/*$)'$%'I$&8
W8bdE4K'"(
EW8dNK
F$ & F(
2-$/-'$(')-,'("3,'"('$%')-,'/"(,'0:')-,'?H'"3<7$:$,6'E2$)-' 6 $'%,&7,/),+K8
A7)-0*&-')-,'&"$%'0:')-,'?]'"3<7$:$,6'<60<,6'-"(')-,'("3,'3"&%$)*+,'"(')-")'0:')-,'?H
"3<7$:$,61')-$('$('*(*"77;'%0)')-,'/"(,'"(':"6'"(')-,'0#,6"77'#07)"&,'&"$%'$('/0%/,6%,+8'9-,'702'$%<*)
6,($()"%/,'0:')-,'?]'"3<7$:$,6'/"%'/"*(,')-,'$%<*)'($&%"7')0'4,'(,#,6,7;'")),%*"),+8'H<,/$:$/"77;1
v
F $%
@ ⁄ 7@
555555+5 ' & 555555555555555555555
5 ' & 555555555555555555555555555
5
v ($&
F $% ( F ($& @ ⁄ 7 @ ( F ($&
EW8dfK
:603'2-$/-'2,'(,,')-")',B/,<)':06'($)*")$0%('$%'2-$/-' F ($&'$('0%')-,'06+,6'0:'@ ⁄ 7 @1')-,'($&%"7
)6"%(3$(($0%':"/)06' v + ⁄ v ($& '/"%'4,'#,6;'(3"77'"%+')-,'0#,6"77'#07)"&,'&"$%' * v'/"%'4,'/066,5
(<0%+$%&7;'(3"778'H<,/$:$/"77;1'2$)-'"'6,($()"%/,' F &'/0%%,/),+'")')-,'0*)<*)'
@ ⁄ 7@
5 [ 7 ( F || F & ) ]
* v ' & 555555555555555555555555555
F ($& ( @ ⁄ 7 @ @ (
9-*(1
( F ( || F & )
* v & 555555555555555555555555555
5
F ($& ( @ ⁄ 7 @
EW8ddK
G4(,6#,')-")'#B/0$5/623305$3#27/072+!0+101+@"340#B/062#+$0$M0#B/0#$#2306/1+1#2!./0+!0#B/0,62+!
.+6.-+#0#$0#B/0#$#2306/1+1#2!./0+!0#B/01$-6./0.+6.-+#8'=:' F ($&'$('0:')-,'("3,'06+,6'"(' F ('"%+' F &1
* v '2$77'4,'#,6;'(3"778
L,/"*(,'0:'$)('702'$%<*)'6,($()"%/,1')-,'?]'"3<7$:$,6'"70%,'-"('#,6;'7$3$),+'"<<7$/")$0%8
G%,'(*/-'"<<7$/")$0%'$(')0'"3<7$:;'-$&-5:6,O*,%/;'($&%"7(')-")'/03,':603'(0*6/,('2$)-'6,7"5
)$#,7;' 702' 6,($()"%/,(8' 9-,(,' $%/7*+,' /"47,(1' 2-,6,' $)' $(' *(*"77;' %,/,(("6;' :06' )-,' $%<*)
301
302 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
6,($()"%/,'0:')-,'"3<7$:$,6')0'3")/-')-,'/-"6"/),6$()$/'6,($()"%/,'0:')-,'/"47,8'A('2$77'4,'(-02%
$%'?-"<),6'[1')-,'?]'"3<7$:$,6'-"(',B/,77,%)'-$&-5:6,O*,%/;'6,(<0%(,8'9-*('$)'/"%'4,'/035
4$%,+'2$)-')-,'?H'"3<7$:$,6'$%'"'#,6;'4,%,:$/$"7'2";')-")')"P,('"+#"%)"&,'0:')-,'4,()':,")*6,(
0:' ,"/-' 0:' )-,' )20' /0%:$&*6")$0%(8' A' #,6;' ($&%$:$/"%)' /$6/*$)' 0:' )-$(' P$%+' 2$77' 4,' ()*+$,+' $%
?-"<),6'f8
8
EXERCISE
5.29 A'?]'"3<7$:$,6'$('6,O*$6,+')0'3")/-'"'($&%"7'(0*6/,'2$)-'F ($& & @ZZ'Ω8'A)'2-")'/*66,%)' ? ( '(-0*7+
)-,'FGHIJ9'4,'4$"(,+'$:'$)'$('0<,6"),+'")'"%'0#,6+6$#,'#07)"&,'0:'Z8QZ'Sg'=:')-,')0)"7'6,($()"%/,'$%
)-,'+6"$%'/$6/*$)'$('Q'PΩ1'2-")'0#,6"77'#07)"&,'&"$%'$('6,"7$>,+g
Ans. @'3Aa'@Z'ScS
5.6.6 The Common-Drain Amplifier or Source Follower
9-,'7"()'0:')-,'4"($/'FGHIJ9'"3<7$:$,6'/0%:$&*6")$0%('$(')-,'/0330%5+6"$%'"3<7$:$,61'"%
$3<06)"%)'/$6/*$)')-")':$%+('"<<7$/")$0%'$%')-,'+,($&%'0:'40)-'(3"775($&%"7'"3<7$:$,6('"('2,77
"('"3<7$:$,6(')-")'"6,'6,O*$6,+')0'-"%+7,'7"6&,'($&%"7('"%+'+,7$#,6'(*4()"%)$"7'"30*%)('0:'($&5
%"7'<02,6')0'"'70"+8'9-$(' 7")),6'#"6$,);'2$77' 4,'()*+$,+' $%' ?-"<),6'@@8'9-,'/0330%' +6"$%
"3<7$:$,6' $(' 306,' /0330%7;' P%02%' "(' )-,' 1$-6./0 M$33$C/68' 9-,' 6,"(0%' 4,-$%+' )-$(' %"3,
2$77'4,/03,'"<<"6,%)'(-06)7;8
The Need for Voltage Buffers L,:06,' ,34"6P$%&' 0%' )-,' "%"7;($(' 0:' )-,' (0*6/,' :075
702,61'$)'$('*(,:*7')0'700P'")'0%,'0:'$)('306,'/0330%'"<<7$/")$0%(8'?0%($+,6')-,'($)*")$0%
+,<$/),+' $%' I$&8' W8b[E"K8' A' ($&%"7' (0*6/,' +,7$#,6$%&' "' ($&%"7' 0:' 6,"(0%"47,' ()6,%&)-' E@' SK
Rsig " 1 M(
Rsig " 1 M(
RL
1 k(
vsig " 1V !
#
!
#
vsig " 1V
RL
1 k(
!
vo " 1 mV
#
(a)
(b)
Rsig " 1 M( " 1V
Ro " 100(
Avo"1
RL
1 k(
!
vsig " 1V #
!
vo " 0.9V
#
Rin very large
(c)
Figure 5.49 =77*()6")$%&')-,'%,,+':06'"'*%$);5&"$%'4*::,6'"3<7$:$,68
5.6 Basic MOSFET Amplifier Configurations
2$)-'"%'$%),6%"7'6,($()"%/,'0:'@'FΩ'$(')0'4,'/0%%,/),+')0'"'@5PΩ'70"+'6,($()"%/,8'?0%%,/)$%&
)-,'(0*6/,')0')-,'70"+'+$6,/)7;'"('$%'I$&8'W8b[E4K'20*7+'6,(*7)'$%'(,#,6,'")),%*")$0%'0:')-,'($&5
%"7a' )-,' ($&%"7' "<<,"6$%&' "/60((' )-,' 70"+' 2$77' 4,' 0%7;' @ ⁄ ( @ZZZ ( @ )' 0:' )-,' $%<*)' ($&%"7' 06
"40*)'@'3S8'A%'"7),6%")$#,'/0*6(,'0:'"/)$0%'$('(*&&,(),+'$%'I$&8'W8b[E/K8'!,6,'2,'-"#,'$%),65
<0(,+'"%'"3<7$:$,6'4,)2,,%')-,'(0*6/,'"%+')-,'70"+8'G*6'"3<7$:$,61'-02,#,61'$('*%7$P,')-,
"3<7$:$,6('2,'-"#,'4,,%'()*+;$%&'$%')-$('/-"<),6')-*(':"6a'$)'-"('"'#07)"&,'&"$%'0:'0%7;'*%$);8
9-$('$('4,/"*(,'0*6'($&%"7'$('"76,"+;'0:'(*::$/$,%)'()6,%&)-'"%+'2,'+0'%0)'%,,+')0'$%/6,"(,'$)(
"3<7$)*+,8'`0),1'-02,#,61')-")'0*6'"3<7$:$,6'-"('"'#,6;'7"6&,'$%<*)'6,($()"%/,1')-*('"730()
"77'0:' v ($&'E$8,81'@'SK'2$77'"<<,"6'")')-,'$%<*)'0:')-,'"3<7$:$,6'<60<,68'H$%/,')-,'"3<7$:$,6'-"('"
702'0*)<*)'6,($()"%/,'E@ZZ'ΩK1'[Zo'0:')-$('($&%"7'EZ8['SK'2$77'"<<,"6'")')-,'0*)<*)1'04#$0*(7;
"' #,6;' ($&%$:$/"%)' $3<60#,3,%)' 0#,6' )-,' ($)*")$0%' 2$)-0*)' )-,' "3<7$:$,68' A(' 2$77' 4,' (,,%
(-06)7;1')-,'(0*6/,':07702,6'/"%',"($7;'$3<7,3,%)')-,'*%$);5&"$%'4*::,6'"3<7$:$,6'(-02%'$%
I$&8'W8b[E/K8
Characteristic Parameters of the Source Follower I$&*6,' W8WZE"K' (-02(' "' (0*6/,
:07702,6' 2$)-' )-,' 4$"(' /$6/*$)' 03$)),+8' 9-,' (0*6/,' :07702,6' $(' :,+' 2$)-' "' ($&%"7' &,%,6")06
E v ($& 1' F ($&K'"%+'-"('"'70"+'6,($()"%/,' F &'/0%%,/),+'4,)2,,%')-,'(0*6/,'),63$%"7'"%+'&60*%+8
U,'(-"77'"((*3,')-")' F &'$%/7*+,('40)-')-,'"/)*"7'70"+'"%+'"%;'0)-,6'6,($()"%/,')-")'3";'4,
<6,(,%)'4,)2,,%')-,'(0*6/,'),63$%"7'"%+'&60*%+'E,8&81':06'4$"($%&'<*6<0(,(K8'`063"77;1')-,
"/)*"7'70"+'6,($()"%/,'20*7+'4,'3*/-'702,6'$%'#"7*,')-"%'(*/-'0)-,6'6,($()"%/,('"%+')-*(
20*7+'+03$%"),8
H$%/,')-,'FGHIJ9'-"('"'6,($()"%/,' F &'/0%%,/),+'$%'$)('(0*6/,'),63$%"71'$)'$('30()'/0%5
#,%$,%)')0'*(,')-,'9'30+,71'"('(-02%'$%'I$&8'W8WZE4K8'`0),')-")'2,'-"#,'$%/7*+,+' 6 $1'($3<7;
4,/"*(,'$)'$('#,6;',"(;')0'+0'(08'!02,#,61'($%/,' 6 $'$%',::,/)'"<<,"6('$%'<"6"77,7'2$)-' F &1'"%+
($%/,'$%'+$(/6,),'/$6/*$)(' 6 $ / F & 1'2,'/"%'%,&7,/)' 6 $'"%+'04)"$%')-,'($3<7$:$,+',O*$#"7,%)'/$65
/*$)'(-02%'$%'I$&8'W8WZE/K8'I603')-,'7")),6'/$6/*$)'2,'/"%'26$),'4;'$%(<,/)$0%
F $% & ∞
"%+'04)"$%' G v':603')-,'#07)"&,'+$#$+,6':063,+'4;'@ ⁄ 7 @'"%+' F &'"('
v
F&
G v ≡ 5555$ & 555555555555555555555555
5
v+
F& ( @ ⁄ 7@
EW8d[K
G v$ & @
EW8[ZK
H,))$%&'F & & ∞'2,'04)"$%
9-,'0*)<*)'6,($()"%/,' F $ '$(':0*%+'4;'(,))$%&' v + ' & Z'E$8,81'4;'&60*%+$%&')-,'&"),K8'`02'700P5
$%&'4"/P'$%)0')-,'0*)<*)'),63$%"71',B/7*+$%&'F &1'2,'($3<7;'(,,'@ ⁄ 7 @1')-*(
F$ & @ ⁄ 7@
EW8[@K
9-,'*%$);'0<,%5/$6/*$)'#07)"&,'&"$%')0&,)-,6'2$)-' F $'$%'JO8'EW8[@K'/"%'4,'*(,+')0':$%+' G v
2-,%'"'70"+'6,($()"%/,' F &'$('/0%%,/),+8'9-,'6,(*7)'$('($3<7;')-,',B<6,(($0%'$%'JO8'EW8d[K8
I$%"77;1'4,/"*(,'0:')-,'$%:$%$),' F $% 1' v + & v ($& 1'"%+')-,'0#,6"77'#07)"&,'&"$%'$(
F&
5
* v ' & G v ' & 555555555555555555555555
F& ( @ ⁄ 7@
EW8[QK
9-*('* v '2$77'4,'702,6')-"%'*%$);8'!02,#,61'4,/"*(,'@ ⁄ 7 @'$('*(*"77;'7021')-,'#07)"&,'&"$%
/"%'4,'/70(,')0'*%$);8'9-,'*%$);'0<,%5/$6/*$)'#07)"&,'&"$%'$%'JO8'EW8[ZK'$%+$/"),(')-")')-,
303
304 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Rsig
!
vsig
vi
!
#
!
#
vo
RL
Rin
#
Ro
(a)
i
ro
0
Rsig
!
vsig !
#
1
gm
vi
#
i
RL
!
vo
#
(b)
i
0
Rsig
i
!
vsig !
#
1
gm
Ro " 1
gm
vi
!
RL
#
vo
#
Rin " +
(c)
Figure 5.50 E(K' ?0330%5+6"$%' "3<7$:$,6' 06' (0*6/,' :07702,68' ' E/K' JO*$#"7,%)' /$6/*$)' 0:' )-,' (0*6/,
:07702,6'04)"$%,+'4;'6,<7"/$%&')-,'FGHIJ9'2$)-'$)('9'30+,78'`0),')-")'6$0"<<,"6('$%'<"6"77,7'2$)-'F&0'"%+'$%
+$(/6,),'/$6/*$)(1'6$0/0F& 8'`,&7,/)$%&'6$ 1'2,'04)"$%')-,'($3<7$:$,+',O*$#"7,%)'/$6/*$)'$%'E%K8
5.6 Basic MOSFET Amplifier Configurations
#07)"&,' ")' )-,' (0*6/,' ),63$%"7' 2$77' :07702' )-")' ")' )-,' $%<*)1' -,%/,' )-,' %"3,' 1$-6./0 M$3D
3$C/68
=%'/0%/7*($0%1')-,'(0*6/,':07702,6':,")*6,('"'#,6;'-$&-'$%<*)'6,($()"%/,'E$+,"77;1'$%:$5
%$),K1'"'6,7")$#,7;'702'0*)<*)'6,($()"%/,1'"%+'"%'0<,%5/$6/*$)'#07)"&,'&"$%')-")'$('%,"6'*%$);
E$+,"77;1'*%$);K8'9-*(')-,'(0*6/,':07702,6'$('$+,"77;'(*$),+':06'$3<7,3,%)$%&')-,'*%$);5&"$%
#07)"&,' 4*::,6' 0:' I$&8' W8b[E/K8' 9-,' (0*6/,' :07702,6' $(' "7(0' *(,+' "(' )-,' 0*)<*)' E$8,81' 7"()K
()"&,'$%'"'3*7)$()"&,'"3<7$:$,61'2-,6,'$)(':*%/)$0%'$(')0',O*$<')-,'0#,6"77'"3<7$:$,6'2$)-'"
702'0*)<*)'6,($()"%/,1')-*(',%"47$%&'$)')0'(*<<7;'6,7")$#,7;'7"6&,'70"+'/*66,%)('2$)-0*)'70((
0:' &"$%' E$8,81' 2$)-' 7$))7,' 6,+*/)$0%' 0:' 0*)<*)' ($&%"7' 7,#,7K8' 9-,' +,($&%' 0:' 0*)<*)' ()"&,(' $(
()*+$,+'$%'?-"<),6'@@8
EXERCISES
D5.30 =)' $(' 6,O*$6,+' )0' +,($&%' "' (0*6/,' :07702,6' )-")' $3<7,3,%)(' )-,' 4*::,6' "3<7$:$,6' (-02%' $%' I$&8
W8b[E/K8'=:')-,'FGHIJ9'$('0<,6"),+'2$)-'"%'0#,6+6$#,'#07)"&,' 8 :8 & Z8QW'S1'")'2-")'+6"$%'/*65
6,%)'(-0*7+'$)'4,'4$"(,+g'I$%+')-,'0*)<*)'($&%"7'"3<7$)*+,'"%+')-,'($&%"7'"3<7$)*+,'4,)2,,%'&"),
"%+'(0*6/,8
Ans. @8QW'3Aa'Z8[@'Sa'[@'3S
D5.31 A'FGHIJ9'$('/0%%,/),+'$%')-,'(0*6/,5:07702,6'/0%:$&*6")$0%'"%+',3<70;,+'"(')-,'0*)<*)'()"&,
0:'"'/"(/"+,'"3<7$:$,68'=)'$('6,O*$6,+')0'<60#$+,'"%'0*)<*)'6,($()"%/,'0:'QZZ' Ω 8'=:')-,'FGHIJ9
-"(' >′! & Z8b '3AcSQ'"%+'$('0<,6"),+'")' 8 :8 ' & Z8QW 'S1':$%+')-,'6,O*$6,+''c&'6")$08'A7(0'(<,/$:;
)-,'+/'4$"('/*66,%)' ? ( 8 '=:')-,'"3<7$:$,6'70"+'6,($()"%/,'#"6$,('0#,6')-,'6"%&,'@'P Ω ')0'@Z'P Ω1
2-")'$(')-,'6"%&,'0:' * v '0:')-,'(0*6/,':07702,6g
Ans. WZa'Z8NQW'3Aa'Z8dC'ScS')0'Z8[d'ScS
5.32 i,:,6')0'I$&8'W8WZE4K8'H-02')-")')"P$%&' 6 $ '$%)0'"//0*%)'6,(*7)('$%
6$
G v$ ' & 55555555555555555555555
5
6$ ( @ ⁄ 7@
`021'6,/"77$%&')-")' 6 $ & 8 G ⁄ ? ( '"%+' 7 @ & Q? ( ⁄ 8 :8 1':$%+' G v$ '$%'),63('0:' 8 G '"%+' 8 :8 8'I06'"
),/-%070&;':06'2-$/-'8 G & QZ 'S1'2-")'$(')-,'3"B$3*3' 8 :8 '")'2-$/-')-,')6"%($()06'/"%'4,'0<,65
"),+'2-$7,'04)"$%$%&' G v$ ≥ Z8[[ 'ScSg
Ans.' G v$ & @ ⁄ [ @ ( 8 :8 ⁄ Q8 G ]a'Z8b'S
5.6.7 Summary and Comparisons
I06',"(;'6,:,6,%/,'"%+')0',%"47,'/03<"6$(0%(1'2,'<6,(,%)'$%'9"47,'W8b')-,':063*7"(':06'+,),65
3$%$%&' )-,' /-"6"/),6$()$/' <"6"3,),6(' 0:' +$(/6,),' FGH' "3<7$:$,6(8' `0),' )-")' 6 $' -"(' 4,,%
%,&7,/),+')-60*&-0*)8'9-$('$('4,/"*(,'0*6'$%),6,()'$%')-$('/-"<),6'$('<6$3"6$7;'$%'+$(/6,),5/$6/*$)
"3<7$:$,6(8'A('"76,"+;'3,%)$0%,+1' 6 $'-"('"'6,7")$#,7;'(3"77',::,/)'0%')-,'<,6:063"%/,'0:'+$(5
/6,),5/$6/*$)'"3<7$:$,6('"%+'/"%'*(*"77;'4,'%,&7,/),+8'=%'(03,'/"(,(1'-02,#,61'$)'$('#,6;',"(;')0
)"P,' 6 $'$%)0'"//0*%)1'(*/-'"('$%')-,'/"(,'0:')-,'?H'"%+'?^'"3<7$:$,6(1'"%+'0%,'$(',%/0*6"&,+')0
+0'(08'I06'$%),&6"),+5/$6/*$)'"3<7$:$,6(1'6 $'@-1#0"72";('4,')"P,%'$%)0'"//0*%)8
305
306 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
'
Table 5.4 Characteristics of MOSFET Amplifiers
38$+$4-,+'.-'4."1)4
9#:%';',+)-<:,
?0330%'(0*6/,
EI$&8'W8bWK
?0330%'(0*6/,'
2$)-' F 1 'EI$&8'
W8bfK
?0330%'&"),'
EI$&8'W8bdK
'H0*6/,':07702,6'
EI$&8'W8WZK
F $%
G v$
F$
Gv
*v
∞
'7@ F(
F(
' 7 @ ( F ( || F & )
' 7 @ ( F ( || F & )
∞
7@ F(
' 55555555555555555555
5
@ ( 7@ F1
F(
' 7 @ ( F ( || F & )
555555555555555555555555555555555
@ ( 7@ F1
7 @ ( F ( || F & )
' 55555555555555555555555555555
@ ( 7@ F1
F ( || F &
' 555555555555555555555555
5
@ ⁄ 7@ ( F1
F ( || F &
5
' 555555555555555555555555
@ ⁄ 7@ ( F1
@5
55555
7@
7@ F(
F(
7 @ ( F ( || F & )
F ( || F &
555555555555555555555555555
5
F ($& ( @ ⁄ 7 @
∞
@
@5
55555
7@
F&
555555555555555555555555
5
F& ( @ ⁄ 7@
F&
555555555555555555555555
5
F& ( @ ⁄ 7@
"
''I06')-,'$%),6<6,)")$0%'0:'F$%1'Gv$1'"%+'F$1'6,:,6')0'I$&8'W8bbE4K8
''9-,'FGHIJ9'0*)<*)'6,($()"%/,'6$'-"('4,,%'%,&7,/),+1'"('$('<,63$)),+'$%')-,'+$(/6,),5/$6/*$)'"3<7$:$,6('()*+$,+'$%')-$('
4
/-"<),68'I06'=?'"3<7$:$,6(1'6$'3*()'"72";('4,')"P,%'$%)0'"//0*%)8
=%'"++$)$0%')0')-,'6,3"6P('"76,"+;'3"+,')-60*&-0*)')-$('(,/)$0%'"40*)')-,'/-"6"/),6$()$/('"%+
"6,"('0:'"<<7$/"4$7$);'0:')-,'#"6$0*('/0%:$&*6")$0%(1'2,'3"P,')-,':07702$%&'/0%/7*+$%&'<0$%)(D
1. 9-,'?H'/0%:$&*6")$0%'$(')-,'4,()'(*$),+':06'6,"7$>$%&')-,'4*7P'0:')-,'&"$%'6,O*$6,+'$%
"%'"3<7$:$,68'^,<,%+$%&'0%')-,'3"&%$)*+,'0:')-,'&"$%'6,O*$6,+1',$)-,6'"'($%&7,'()"&,
06'"'/"(/"+,'0:')20'06')-6,,'()"&,('/"%'4,'*(,+8
2. =%/7*+$%&'"'6,($()06' F 1'$%')-,'(0*6/,'7,"+'0:')-,'?H'()"&,'<60#$+,('"'%*34,6'0:'<,65
:063"%/,'$3<60#,3,%)('")')-,',B<,%(,'0:'&"$%'6,+*/)$0%8
3. 9-,'702'$%<*)'6,($()"%/,'0:')-,'?]'"3<7$:$,6'3"P,('$)'*(,:*7'0%7;'$%'(<,/$:$/'"<<7$/")$0%(8
A('2,'(-"77'(,,'$%'?-"<),6'[1'$)'-"('"'3*/-'4,)),6'-$&-5:6,O*,%/;'6,(<0%(,')-"%')-,'?H
"3<7$:$,68'9-$('(*<,6$06$);'3"P,('$)'*(,:*7'"('"'-$&-5:6,O*,%/;'"3<7$:$,61',(<,/$"77;'2-,%
/034$%,+'2$)-')-,'?H'/$6/*$)8'U,'(-"77'(,,'0%,'(*/-'/034$%")$0%'$%'?-"<),6'f8
4. 9-,' (0*6/,' :07702,6' :$%+(' "<<7$/")$0%' "(' "' #07)"&,' 4*::,6' :06' /0%%,/)$%&' "' -$&-5
6,($()"%/,' (0*6/,' )0' "' 70256,($()"%/,' 70"+' "%+' "(' )-,' 0*)<*)' ()"&,' $%' "' 3*7)$()"&,
"3<7$:$,6'2-,6,'$)('<*6<0(,'$(')0',O*$<')-,'"3<7$:$,6'2$)-'"'702'0*)<*)'6,($()"%/,8
5.7 Biasing in MOS Amplifier Circuits
A('+$(/*((,+'$%'H,/)$0%'W8b1'"%',((,%)$"7'(),<'$%')-,'+,($&%'0:'"'FGHIJ9'"3<7$:$,6'/$6/*$)'$(
)-,' ,()"47$(-3,%)' 0:' "%' "<<60<6$"),' +/' 0<,6")$%&' <0$%)' :06' )-,' )6"%($()068' 9-$(' $(' )-,' (),<
P%02%'"('4$"($%&'06'4$"('+,($&%8'A%'"<<60<6$"),'+/'0<,6")$%&'<0$%)'06'4$"('<0$%)'$('/-"6"/5
),6$>,+'4;'"'()"47,'"%+'<6,+$/)"47,'+/'+6"$%'/*66,%)'?('"%+'4;'"'+/'+6"$%5)05(0*6/,'#07)"&,'8()
)-")',%(*6,('0<,6")$0%'$%')-,'(")*6")$0%'6,&$0%':06'"77',B<,/),+'$%<*)5($&%"7'7,#,7(8'
5.7 Biasing in MOS Amplifier Circuits
5.7.1 Biasing by Fixing VGS
9-,'30()'()6"$&-):062"6+'"<<60"/-')0'4$"($%&'"'FGHIJ9'$(')0':$B'$)('&"),5)05(0*6/,'#07)"&,
8*)')0')-,'#"7*,'6,O*$6,+[')0'<60#$+,')-,'+,($6,+'?(8'9-$('#07)"&,'#"7*,'/"%'4,'+,6$#,+':603
)-,'<02,65(*<<7;'#07)"&,'8((')-60*&-')-,'*(,'0:'"%'"<<60<6$"),'#07)"&,'+$#$+,68'A7),6%")$#,7;1
$)'/"%'4,'+,6$#,+':603'"%0)-,6'(*$)"47,'6,:,6,%/,'#07)"&,')-")'3$&-)'4,'"#"$7"47,'$%')-,'(;(),38
=%+,<,%+,%)'0:'-02')-,'#07)"&,'8*)'3";'4,'&,%,6"),+1')-$('$('!$#'"'&00+'"<<60"/-')0'4$"($%&
"'FGHIJ98'90'*%+,6()"%+')-,'6,"(0%':06')-$('()"),3,%)1'6,/"77')-")'
@
'
Q
? ( = 555 µ ! < $% 55555 ( 8 *) ' 8 # )
Q
&
"%+' %0),' )-")' )-,' #"7*,(' 0:' )-,' )-6,(-07+' #07)"&,' 8# 1' )-,' 0B$+,5/"<"/$)"%/,' <$% 1' "%+' E)0' "
7,((,6',B),%)K')-,')6"%($()06'"(<,/)'6")$0 ' ⁄ & #"6;'2$+,7;'"30%&'+,#$/,('0:'(*<<0(,+7;')-,'("3,
($>,'"%+');<,8'9-$('$('/,6)"$%7;')-,'/"(,':06'+$(/6,),'+,#$/,(1'$%'2-$/-'7"6&,'(<6,"+('$%')-,
#"7*,('0:')-,(,'<"6"3,),6('0//*6'"30%&'+,#$/,('0:')-,'("3,'3"%*:"/)*6,6m('<"6)'%*34,68
9-,'(<6,"+'$('"7(0'7"6&,'$%'$%),&6"),+'/$6/*$)(1',(<,/$"77;'"30%&'+,#$/,(':"46$/"),+'0%'+$::,65
,%)'2":,6('"%+'/,6)"$%7;'4,)2,,%'+$::,6,%)'4")/-,('0:'2":,6(8'I*6)-,6306,1'40)-'8#'"%+'µ!
+,<,%+'0%'),3<,6")*6,1'2$)-')-,'6,(*7)')-")'$:'2,':$B')-,'#"7*,'0:'8*)1')-,'+6"$%'/*66,%)'?(
4,/03,('#,6;'3*/-'),3<,6")*6,'+,<,%+,%)8
90',3<-"($>,')-,'<0$%)')-")'4$"($%&'4;':$B$%&'8*)'$('%0)'"'&00+'),/-%$O*,1'2,'(-02'$%
I$&8'W8W@')20'+(Vv*)'/-"6"/),6$()$/'/*6#,('6,<6,(,%)$%&',B)6,3,'#"7*,('$%'"'4")/-'0:'FGHIJ9(
0:')-,'("3,');<,8'G4(,6#,')-")':06')-,':$B,+'#"7*,'0:'8*)1')-,'6,(*7)"%)'(<6,"+'$%')-,'#"7*,('0:
)-,'+6"$%'/*66,%)'/"%'4,'(*4()"%)$"78
iD
Device 2
Device 1
ID2
ID1
0
VGS
vGS
Figure 5.51 9-,'*(,'0:':$B,+'4$"('E/0%()"%)'8*)K'/"%'6,(*7)'$%'"'7"6&,'#"6$"4$7$);'$%')-,'#"7*,'0:'?(8'^,#$/,(
@'"%+'Q'6,<6,(,%)',B)6,3,('"30%&'*%$)('0:')-,'("3,');<,8
[
9-")'$('$%+,,+'2-")'2,'2,6,'+0$%&'$%'H,/)$0%'W8b8'!02,#,61')-,'"3<7$:$,6'/$6/*$)('()*+$,+')-,6,'2,6,
/0%/,<)*"7'0%,(1'%0)'"/)*"7'<6"/)$/"7'/$6/*$)(8'G*6'<*6<0(,'$%')-$('(,/)$0%'$(')0'()*+;')-,'7")),68
307
308 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.7.2 Biasing by Fixing VG and Connecting a Resistance
in the Source
A%',B/,77,%)'4$"($%&'),/-%$O*,':06'+$(/6,),'FGHIJ9'/$6/*$)('/0%($()('0:':$B$%&')-,'+/'#07)5
"&,'")')-,'&"),1'8*1'"%+'/0%%,/)$%&'"'6,($()"%/,'$%')-,'(0*6/,'7,"+1'"('(-02%'$%'I$&8'W8WQE"K8
I06')-$('/$6/*$)'2,'/"%'26$),
8 * = 8 *) + F ) ? (
EW8[CK
`021'$:'8*'$('3*/-'&6,"),6')-"%'8*) 1'?('2$77'4,'30()7;'+,),63$%,+'4;')-,'#"7*,('0:'8*'"%+
F)8'!02,#,61',#,%'$:'8*'$('%0)'3*/-'7"6&,6')-"%'8*)1'6,($()06'F)'<60#$+,('!/72#+5/0M//,K2.>L
2-$/-'"/)(')0'()"4$7$>,')-,'#"7*,'0:')-,'4$"('/*66,%)'?(8'90'(,,'-02')-$('/03,('"40*)1'/0%($+,6
2-")'-"<<,%('2-,%'?('$%/6,"(,(':06'2-"),#,6'6,"(0%8'JO*")$0%'EW8[CK'$%+$/"),(')-")'($%/,'8*
$('/0%()"%)1'8*)'2$77'-"#,')0'+,/6,"(,8'9-$('$%')*6%'6,(*7)('$%'"'+,/6,"(,'$%'?(1'"'/-"%&,')-")'$(
iD
ID
!
!
VGS
Device 1
ID
#
VG
Device 2
ID2
ID1
RS
Slope " #1$RS
#
0
VGS2
VG vGS
VGS1
(a)
(b)
VDD
VDD
VDD
RG1
RD
ID
0
VG
RG1
Rsig
!
CC1
ID
0
RD
RG
!
VGS
ID
VGS
#
RG2
RD
RS
ID
#
vsig !
#
RG2
RS
RS
#VSS
(c)
(d)
(e)
Figure 5.52 L$"($%&'*($%&'"':$B,+'#07)"&,'")')-,'&"),1'8*1'"%+'"'6,($()"%/,'$%')-,'(0*6/,'7,"+1'F) D'1(2'4"($/
"66"%&,3,%)a'1/2'6,+*/,+'#"6$"4$7$);'$%'?( a'1%2'<6"/)$/"7'$3<7,3,%)")$0%'*($%&'"'($%&7,'(*<<7;a'1'2'/0*<7$%&'0:'"
($&%"7'(0*6/,')0')-,'&"),'*($%&'"'/"<"/$)06'<<@a'1&2'<6"/)$/"7'$3<7,3,%)")$0%'*($%&')20'(*<<7$,(8
5.7 Biasing in MOS Amplifier Circuits
309
0<<0($),')0')-")'$%$)$"77;'"((*3,+8'9-*(')-,'"/)$0%'0:'F)'206P(')0'P,,<'?('"('/0%()"%)'"('<0(5
($47,8' 9-$(' %,&")$#,' :,,+4"/P' "/)$0%' 0:' F)' &$#,(' $)' )-,' %"3,' '&,&*&$(-)"*+ $&!)!-(*%&1' "
%"3,')-")'2,'2$77'"<<6,/$"),'3*/-'4,)),6'")'"'7"),6'<0$%)'$%')-$('),B)8@Z
I$&*6,' W8WQE4K' <60#$+,(' "' &6"<-$/"7' $77*()6")$0%' 0:' )-,' ,::,/)$#,%,((' 0:' )-$(' 4$"($%&
(/-,3,8' !,6,' )00' 2,' (-02' )-,' +(Vv*)' /-"6"/),6$()$/(' :06' )20' +,#$/,(' )-")' 6,<6,(,%)' )-,
,B)6,3,('0:'"'4")/-'0:'FGHIJ9(8'H*<,6$3<0(,+'0%')-,'+,#$/,'/-"6"/),6$()$/('$('"'()6"$&-)
7$%,')-")'6,<6,(,%)(')-,'/0%()6"$%)'$3<0(,+'4;')-,'4$"('/$6/*$)p%"3,7;1'JO8'EW8[CK8'9-,'$%),65
(,/)$0%'0:')-$('()6"$&-)'7$%,'2$)-')-,'+(Vv*)'/-"6"/),6$()$/'/*6#,'<60#$+,(')-,'/006+$%"),('E?(
"%+'8*)K'0:')-,'4$"('<0$%)8'G4(,6#,')-")'/03<"6,+')0')-,'/"(,'0:':$B,+'8*)1'-,6,')-,'#"6$"4$75
$);'04)"$%,+'$%'?('$('3*/-'(3"77,68'A7(01'%0),')-")')-,'#"6$"4$7$);'+,/6,"(,('"('8*'"%+'F)'"6,
3"+,'7"6&,6'E)-*('<60#$+$%&'"'4$"('7$%,')-")'$('7,(('(),,<K8
920' <0(($47,' <6"/)$/"7' +$(/6,),' $3<7,3,%)")$0%(' 0:' )-$(' 4$"(' (/-,3,' "6,' (-02%' $%
I$&8'W8WQE/K'"%+'E,K8'9-,'/$6/*$)'$%'I$&8'W8WQE/K'*)$7$>,('0%,'<02,65(*<<7;'8(('"%+'+,6$#,(
8*')-60*&-'"'#07)"&,'+$#$+,6'EF*@1'F*QK8'H$%/,'?*'='Z1'F*@'"%+'F*Q'/"%'4,'(,7,/),+')0'4,
#,6;'7"6&,'E$%')-,'3,&0-3'6"%&,K1'"7702$%&')-,'FGHIJ9')0'<6,(,%)'"'7"6&,'$%<*)'6,($(5
)"%/,')0'"'($&%"7'(0*6/,')-")'3";'4,'/0%%,/),+')0')-,'&"),')-60*&-'"'/0*<7$%&'/"<"/$)061
"('(-02%'$%'I$&8 W8WQE+K8'!,6,'/"<"/$)06'<<@'470/P('+/'"%+')-*('"7702('*(')0'/0*<7,')-,
($&%"7'v($&')0')-, "3<7$:$,6'$%<*)'2$)-0*)'+$()*64$%&')-,'FGHIJ9'+/'4$"('<0$%)8'9-,'#"7*,
0:' <<@' (-0*7+' 4,' (,7,/),+' 7"6&,' ,%0*&-' )0' "<<60B$3"),' "' (-06)' /$6/*$)' ")' "77' ($&%"7' :6,5
O*,%/$,('0:'$%),6,()8'U,'(-"77'()*+;'/"<"/$)$#,7;'/0*<7,+'FGHIJ9'"3<7$:$,6(1'2-$/-'"6,
(*$)"47,'0%7;'$%'+$(/6,),'/$6/*$)'+,($&%1'$%'H,/)$0%'W8d8'I$%"77;1'%0),')-")'$%')-,'/$6/*$)'0:
I$&8'W8WQE/K1'6,($()06'F('$('(,7,/),+')0'4,'"('7"6&,'"('<0(($47,')0'04)"$%'-$&-'&"$%'4*)'(3"77
,%0*&-')0'"7702':06')-,'+,($6,+'($&%"7'(2$%&'")')-,'+6"$%'2-$7,'P,,<$%&')-,'FGHIJ9'$%
(")*6")$0%'")'"77')$3,(8'
U-,%')20'<02,6'(*<<7$,('"6,'"#"$7"47,1'"('$('0:),%')-,'/"(,1')-,'(03,2-")'($3<7,6'4$"(
"66"%&,3,%)'0:'I$&8'W8WQE,K'/"%'4,'*)$7$>,+8'9-$('/$6/*$)'$('"%'$3<7,3,%)")$0%'0:'JO8'EW8[CK1
2$)-'8*'6,<7"/,+'4;'8))8'i,($()06'F*',()"47$(-,('"'+/'&60*%+'")')-,'&"),'"%+'<6,(,%)('"'-$&$%<*)' 6,($()"%/,' )0' "' ($&%"7' (0*6/,' )-")' 3";' 4,' /0%%,/),+' )0' )-,' &"),' )-60*&-' "' /0*<7$%&
/"<"/$)068
Example 5.12
=)'$('6,O*$6,+')0'+,($&%')-,'/$6/*$)'0:'I$&8'W8WQE/K')0',()"47$(-'"'+/'+6"$%'/*66,%)'?('='Z8W'3A8'9-,'FGHIJ9'$(
Q
(<,/$:$,+')0'-"#,'8#'='@'S'"%+ > !′' ⁄ & = @'3AcS 8'I06'($3<7$/$);1'%,&7,/)')-,'/-"%%,757,%&)-'30+*7")$0%
,::,/)'E$8,81'"((*3,'λ = 0K8'n(,'"'<02,65(*<<7;'8(('='@W'S8'?"7/*7"),')-,'<,6/,%)"&,'/-"%&,'$%')-,'#"7*,'0:
?('04)"$%,+'2-,%')-,'FGHIJ9'$('6,<7"/,+'2$)-'"%0)-,6'*%$)'-"#$%&')-,'("3, > !′' ⁄ &'4*)'8#'='@8W'S8
Solution
A('"'6*7,'0:')-*34':06'+,($&%$%&')-$('/7"(($/"7'4$"($%&'/$6/*$)1'2,'/-00(,'F('"%+'F)')0'<60#$+,'0%,5)-$6+'0:
)-,'<02,65(*<<7;'#07)"&,'8(('"('"'+60<'"/60((',"/-'0:'F(1')-,')6"%($()06'E$8,81'8()K'"%+'F)8'I06'8(('='@W'S1
9-,'"/)$0%'0:' F ) '$%'()"4$7$>$%&')-,'#"7*,'0:')-,'4$"('/*66,%)' ? ('$('%0)'*%7$P,')-")'0:')-,'6,($()"%/,' F 11
2-$/-'2,'$%/7*+,+'$%')-,'(0*6/,'7,"+'0:'"'?H'"3<7$:$,6'$%'H,/)$0%'W8N8b8'=%')-,'7")),6'/"(,'"7(01' F 1'206P(
)0'6,+*/,')-,'/-"%&,'$%' + ('2$)-')-,'6,(*7)')-")')-,'"3<7$:$,6'&"$%'$('6,+*/,+8
@Z
310 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Example 5.12 continued
)-$('/-0$/,'3"P,('8('='+@Z'S'"%+'8)'='+W'S8'`021'($%/,'?('$('6,O*$6,+')0'4,'Z8W'3A1'2,'/"%':$%+')-,'#"75
*,('0:'F('"%+'F)'"(':07702(D
8 (( ' 8 (
@W ' @Z
5 = 555555555555555555 = @Z'PΩ
F ( = 5555555555555555555555
?(
Z8W
8
W
F ) = 55555) = 5555555 = @Z'PΩ
Z8W
F)
9-,'6,O*$6,+'#"7*,'0:'8*)'/"%'4,'+,),63$%,+'4;':$6()'/"7/*7")$%&')-,'0#,6+6$#,'#07)"&,'8:8':603
Q
? ( = @55Q5 > !′ ( ' ⁄ & )8 :8
Q
Z8W = @55Q5 × @ × 8 :8
2-$/-';$,7+('8:8'e'@'S1'"%+')-*(1'
8 *) = 8 # + 8 :8 = @ + @ = Q'S
`021'($%/,'8)'='+W'S1'8*'3*()'4,
8 * = 8 ) + 8 *) = W + Q = f'S
90',()"47$(-')-$('#07)"&,'")')-,'&"),'2,'3";'(,7,/)'F*@'='d'FΩ'"%+'F*Q'='f'FΩ8'9-,':$%"7'/$6/*$)'$('(-02%
$%'I$&8'W8WC8'G4(,6#,')-")')-,'+/'#07)"&,'")')-,'+6"$%'E+@Z'SK'"7702(':06'"'<0($)$#,'($&%"7'(2$%&'0:'+W'S
E$8,81'*<')0'8((K'"%+'"'%,&")$#,'($&%"7'(2$%&'0:'Vb'S'q$8,81'+02%')0'E8*'V'8#Kr8'
VDD " !15 V
ID "
0.5 mA
8 M(
RD " 10 k(
VD " !10 V
VG " !7 V
VS " !5 V
ID "
0.5 mA
7 M(
RS " 10 k(
Figure 5.53 ?$6/*$)':06'JB"3<7,'W8@Q8
5.7 Biasing in MOS Amplifier Circuits
=:')-,'`FGH')6"%($()06'$('6,<7"/,+'2$)-'"%0)-,6'-"#$%&'8#'='@8W'S1')-,'%,2'#"7*,'0:'?('/"%'4,':0*%+
"(':07702(D
? ( = @55Q5 × @ × ( 8 *) ' @8W )
Q
EW8[bK
8 * = 8 *) + ? ( F )
f = 8 *) + @Z? (
EW8[WK
H07#$%&'JO(8'EW8[bK'"%+'EW8[WK')0&,)-,6';$,7+(
? ( = Z8bWW'3A
9-*(')-,'/-"%&,'$%'?('$(
∆? ( = Z8bWW ' Z8W = ' Z8ZbW'3A
' Z8ZbW
2-$/-'$(' 55555555555555555 × @ZZ = ' [o'/-"%&,8
Z8W
EXERCISES
5.33' ?0%($+,6')-,'FGHIJ9'$%'JB"3<7,'W8@Q'2-,%':$B,+58*)'4$"('$('*(,+8'I$%+')-,'6,O*$6,+'#"7*,'0:'8*)
)0 ,()"47$(-'"'+/'4$"('/*66,%)'?('='Z8W'3A8'i,/"77')-")')-,'+,#$/,'<"6"3,),6('"6,'8#'='@'S1 > !′' ⁄ & =
Q
@'3AcS 1 "%+'λ'='Z8'U-")'$(')-,'<,6/,%)"&,'/-"%&,'$%'?('04)"$%,+'2-,%')-,')6"%($()06'$('6,<7"/,+
2$)-'"%0)-,6'-"#$%&'8#'='@8W'Sg
Ans. 8*)'='Q'Sa'−fWo
D5.34' ^,($&%')-,'/$6/*$)'0:'I$&8'W8WQE,K')0'0<,6"),'")'"'+/'+6"$%'/*66,%)'0:'Z8W'3A'"%+'8('='+Q'S8'T,)'8#
Q
='@ S1''> !′' ⁄ & = @'3AcS 1 λ'='Z1'8(('='8))'='W'S8'n(,'()"%+"6+'Wo'6,($()06'#"7*,('E(,,'A<<,%+$B
]K1'"%+'&$#,')-,'6,(*7)$%&'#"7*,('0:''?(1'8(1'"%+'8)8
Ans. F('='F)'='N8Q'PΩa'?('='Z8b['3A1'8)'='−@8[N'S1'"%+'8('='+@8[N'S8'F*'/"%'4,'(,7,/),+'$%')-,
6"%&,'0:'@'FΩ')0'@Z'FΩ.
5.7.3 Biasing Using a Drain-to-Gate Feedback Resistor
A'($3<7,'"%+',::,/)$#,'+$(/6,),5/$6/*$)'4$"($%&'"66"%&,3,%)'*)$7$>$%&'"':,,+4"/P'6,($()06'/0%5
%,/),+'4,)2,,%')-,'+6"$%'"%+')-,'&"),'$('(-02%'$%'I$&8'W8Wb8'!,6,')-,'7"6&,':,,+4"/P'6,($(5
)"%/,'F*'E*(*"77;'$%')-,'3,&0-3'6"%&,K':06/,(')-,'+/'#07)"&,'")')-,'&"),')0'4,',O*"7')0')-")'")
)-,'+6"$%'E4,/"*(,'?*'='ZK8'9-*('2,'/"%'26$),
8 *) = 8 () = 8 (( ' F ( ? (
2-$/-'/"%'4,'6,26$)),%'$%')-,':063
8 (( = 8 *) + F ( ? (
EW8[NK
311
312 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
2-$/-'$('$+,%)$/"7'$%':063')0'JO8'EW8[CK1'2-$/-'+,(/6$4,(')-,'0<,6")$0%'0:')-,'4$"('(/-,3,
+$(/*((,+' "40#,' q)-")' $%' I$&8' W8WQE"Kr8' 9-*(1' -,6,' )001' $:' ?(' :06' (03,' 6,"(0%' /-"%&,(1' (";
$%/6,"(,(1' )-,%' JO8' EW8[NK' $%+$/"),(' )-")' 8*)' 3*()' +,/6,"(,8' 9-,' +,/6,"(,' $%' 8*)' $%' )*6%
/"*(,('"'+,/6,"(,'$%'?( 1'"'/-"%&,')-")'$('0<<0($),'$%'+$6,/)$0%')0')-,'0%,'06$&$%"77;'"((*3,+8
9-*(')-,'%,&")$#,':,,+4"/P'06'+,&,%,6")$0%'<60#$+,+'4;'F*'206P(')0'P,,<')-,'#"7*,'0:'?('"(
/0%()"%)'"('<0(($47,8
9-,'/$6/*$)'0:'I$&8'W8Wb'/"%'4,'*)$7$>,+'"('"%'"3<7$:$,6'4;'"<<7;$%&')-,'$%<*)'#07)"&,'($&%"7
)0')-,'&"),'#$"'"'/0*<7$%&'/"<"/$)06'(0'"('%0)')0'+$()*64')-,'+/'4$"('/0%+$)$0%('"76,"+;',()"45
7$(-,+8'9-,'"3<7$:$,+'0*)<*)'($&%"7'")')-,'+6"$%'/"%'4,'/0*<7,+')0'"%0)-,6'<"6)'0:')-,'/$6/*$)1
"&"$%'#$"'"'/"<"/$)068'U,'-"#,'/0%($+,6,+'(*/-'"%'"3<7$:$,6'/$6/*$)'$%'H,/)$0%'W8W'EJB"3<7,
W8@ZK8
VDD
RD
0
ID
RG
ID !
VDS
!
VGS
#
#
Figure 5.54 L$"($%&')-,'FGHIJ9'*($%&'"'7"6&,'+6"$%5)05&"),':,,+4"/P'6,($()"%/,1'F* 8
EXERCISE
D5.35' ^,($&%' )-,' /$6/*$)' $%' I$&8' W8Wb' )0' 0<,6"),' ")' "' +/' +6"$%' /*66,%)' 0:' Z8W' 3A8' A((*3,'8((' =' +W
Q
S1 >′! ' ⁄ & = @'3AcS 1 '8#'='@'S1'"%+'λ'='Z8'n(,'"'()"%+"6+'Wo'6,($()"%/,'#"7*,':06'F(1'"%+'&$#,
)-,'"/)*"7'#"7*,('04)"$%,+':06'?('"%+'8(8
Ans. F('='N8Q'PΩa' ? ( " Z8b['3Aa 8 ( " @8[N'S
5.7.4 Biasing Using a Constant-Current Source
9-,'30()',::,/)$#,'(/-,3,':06'4$"($%&'"'FGHIJ9'"3<7$:$,6'$(')-")'*($%&'"'/0%()"%)5/*66,%)
(0*6/,8'I$&*6,'W8WWE"K'(-02('(*/-'"%'"66"%&,3,%)'"<<7$,+')0'"'+$(/6,),'FGHIJ98'!,6,'F*
E*(*"77;'$%')-,'3,&0-3'6"%&,K',()"47$(-,('"'+/'&60*%+'")')-,'&"),'"%+'<6,(,%)('"'7"6&,'6,($(5
)"%/,' )0' "%' $%<*)' ($&%"7' (0*6/,' )-")' /"%' 4,' /"<"/$)$#,7;' /0*<7,+' )0' )-,' &"),8' i,($()06' F(
,()"47$(-,(' "%' "<<60<6$"),' +/' #07)"&,' ")' )-,' +6"$%' )0' "7702' :06' )-,' 6,O*$6,+' 0*)<*)' ($&%"7
(2$%&'2-$7,',%(*6$%&')-")')-,')6"%($()06'"72";('6,3"$%('$%')-,'(")*6")$0%'6,&$0%8
5.7 Biasing in MOS Amplifier Circuits
VDD
VDD
RD
ID " I
Q
To source of
transistor Q
in Fig. 5.55 (a)
R
IREF
0
ID2
ID1
RG
Q1
I
#VSS
!
VGS
#
Q2
#VSS
(a)
(b)
Figure 5.55 1(2' L$"($%&' )-,' FGHIJ9' *($%&' "' /0%()"%)5/*66,%)' (0*6/,' ?8' 1/2' =3<7,3,%)")$0%' 0:' )-,
/0%()"%)5/*66,%)'(0*6/,'?'*($%&'"'/*66,%)'3$66068
A'/$6/*$)':06'$3<7,3,%)$%&')-,'/0%()"%)5/*66,%)'(0*6/,'?'$('(-02%'$%'I$&8'W8WWE4K8'9-,
-,"6)'0:')-,'/$6/*$)'$(')6"%($()06';@1'2-0(,'+6"$%'$('(-06),+')0'$)('&"),1'"%+')-*('$('0<,6")$%&'$%
)-,'(")*6")$0%'6,&$0%1'(*/-')-")'
@
'
Q
? (@ = 555 > !′ 55555 ( 8 *) ' 8 # ) '
Q & @
EW8[fK
2-,6,'2,'-"#,'%,&7,/),+'/-"%%,757,%&)-'30+*7")$0%'E$8,81'"((*3,+'λ'='ZK8'9-,'+6"$%'/*66,%)
0:';@'$('(*<<7$,+'4;'8((')-60*&-'6,($()06'F8'H$%/,')-,'&"),'/*66,%)('"6,'>,601
8 (( + 8 )) ' 8 *)
5
? (@ = ? iJI = 5555555555555555555555555555555555555
F
EW8[dK
2-,6,')-,'/*66,%)')-60*&-'F'$('/0%($+,6,+')0'4,')-,'6/M/6/!./0.-66/!#'0:')-,'/*66,%)'(0*6/,
"%+'$('+,%0),+'?iJI8']$#,%')-,'<"6"3,),6'#"7*,('0:';@'"%+'"'+,($6,+'#"7*,':06'?iJI1'JO(8'EW8[fK
"%+'EW8[dK'/"%'4,'*(,+')0'+,),63$%,')-,'#"7*,'0:'F8'`02'/0%($+,6')6"%($()06';QD'=)'-"(')-,
("3,'8*)'"(';@a')-*('$:'2,'"((*3,')-")'$)'$('0<,6")$%&'$%'(")*6")$0%1'$)('+6"$%'/*66,%)1'2-$/-'$(
)-,'+,($6,+'/*66,%)'?'0:')-,'/*66,%)'(0*6/,1'2$77'4,
@
'
Q
? = ? (Q = 555 > !′ 55555 ( 8 *) ' 8 # )
Q & Q
EW8[[K
2-,6,'2,'-"#,'%,&7,/),+'/-"%%,757,%&)-'30+*7")$0%8'JO*")$0%('EW8[dK'"%+'EW8[[K',%"47,'*(
)0'6,7"),')-,'/*66,%)'?')0')-,'6,:,6,%/,'/*66,%)'?iJI1
(' ⁄ &)
? = ? iJI 5555555555555555555Q
( ' ⁄ & )@
EW8@ZZK
9-*('?'$('6,7"),+')0'?iJI'4;')-,'6")$0'0:')-,'"(<,/)'6")$0('0:';@'"%+';Q8'9-$('/$6/*$)1'P%02%'"('"
%#$$&*-+B)$$"$1'$('#,6;'<0<*7"6'$%')-,'+,($&%'0:'=?'FGH'"3<7$:$,6('"%+'2$77'4,'()*+$,+'$%
&6,")'+,)"$7'$%'?-"<),6'f8
313
314 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
EXERCISE
D5.36 n($%&')20')6"%($()06(';@'"%+';Q'-"#$%&',O*"7'7,%&)-('4*)'2$+)-('6,7"),+'4;'' Q ⁄ ' @ = W1'+,($&%')-,
Q
/$6/*$)'0:'I$&8'W8WWE4K')0'04)"$%'?'='Z8W'3A8'T,)'8(('=' −8))' =' W'S1 > !′ ( ' ⁄ & ) @ = Z8d'3AcS 108#'=
@ S1'"%+'λ'='Z8'I$%+')-,'6,O*$6,+'#"7*,':06'F8'U-")'$(')-,'#07)"&,'")')-,'&"),('0:';@'"%+';Qg'U-")
$(')-,'702,()'#07)"&,'"7702,+'")')-,'+6"$%'0:';Q'2-$7,';Q'6,3"$%('$%')-,'(")*6")$0%'6,&$0%g
Ans. dW'PΩa'−C8W'Sa'−b8W'S
5.7.5 A Final Remark
9-,' 4$"(' /$6/*$)(' ()*+$,+' $%' )-$(' (,/)$0%' "6,' $%),%+,+' :06' +$(/6,),5/$6/*$)' "<<7$/")$0%(8
9-,' 0%7;' ,B/,<)$0%' $(' )-,' /*66,%)' 3$6606' /$6/*$)' 0:' I$&8' W8WWE4K' 2-$/-1' "(' 3,%)$0%,+
"40#,1'$(',B),%($#,7;'*(,+'$%'=?'+,($&%8'L$"('"66"%&,3,%)(':06'=?'FGH'"3<7$:$,6('2$77
4,'()*+$,+'$%'?-"<),6'f8
5.8 Discrete-Circuit MOS Amplifiers
U$)-' 0*6' ()*+;' 0:' FGH' "3<7$:$,6' 4"($/(' /03<7,),1' 2,' %02' <*)' ,#,6;)-$%&' )0&,)-,6' 4;
<6,(,%)$%&' <6"/)$/"7' /$6/*$)(' :06' +$(/6,),5/$6/*$)' "3<7$:$,6(8' 9-,(,' /$6/*$)(1' 2-$/-' *)$7$>,
)-,'"3<7$:$,6'/0%:$&*6")$0%('()*+$,+'$%'H,/)$0%'W8N'"%+'0%,'0:')-,'4$"($%&'3,)-0+('0:'H,/5
)$0%' W8f1' /"%' 4,' "((,347,+' *($%&' 0::5)-,5(-,7:' +$(/6,),' )6"%($()06(1' 6,($()06(1' "%+' /"<"/$5
)06(8' 9-0*&-' <6"/)$/"7' "%+' /"6,:*77;' (,7,/),+' )0' $77*()6"),' (03,' $3<06)"%)' <0$%)(1' )-,
/$6/*$)('<6,(,%),+'$%')-$('(,/)$0%'(-0*7+'4,'6,&"6+,+'0%7;'"(',B"3<7,('0:'+$(/6,),5/$6/*$)
FGH'"3<7$:$,6(8'=%+,,+1')-,6,'$('"'&6,")'#"6$,);'0:'(*/-'/$6/*$)(1'"'%*34,6'0:'2-$/-'"6,
,B<706,+' $%' )-,' ,%+50:5/-"<),6' <6047,3(8' U,' (-0*7+1' -02,#,61' /"*)$0%' )-,' 6,"+,6' )-")
FGH')6"%($()06('"6,'<6$3"6$7;'*(,+'$%'$%),&6"),+'/$6/*$)'+,($&%1'"('2,'(-"77'(,,'$%'?-"<),6
f'"%+'4,;0%+8
=%')-$('(,/)$0%'2,'<6,(,%)'"'(,6$,('0:',B,6/$(,'<6047,3(1'JB,6/$(,('W8Cf')0'W8b@1')-")'"6,
/"6,:*77;'+,($&%,+')0'$77*()6"),'$3<06)"%)'"(<,/)('0:')-,'"3<7$:$,6'/$6/*$)('()*+$,+8'9-,(,',B,65
/$(,('"6,'"7(0'$%),%+,+')0',%"47,')-,'6,"+,6')0'(,,'306,'/7,"67;')-,'+$::,6,%/,('4,)2,,%')-,
#"6$0*('/$6/*$)'/0%:$&*6")$0%(8'U,'()60%&7;'*6&,')-,'6,"+,6')0'(07#,')-,(,',B,6/$(,(8'A('*(*"71
)-,'"%(2,6('"6,'<60#$+,+8
5.8.1 The Basic Structure
I$&*6,'W8WN'(-02(')-,'4"($/'/$6/*$)'2,'(-"77'*)$7$>,')0'$3<7,3,%)')-,'#"6$0*('/0%:$&*6")$0%(
0:'+$(/6,),5/$6/*$)'FGH'"3<7$:$,6(8'A30%&')-,'#"6$0*('(/-,3,(':06'4$"($%&'FGH'"3<7$:$,6(
EH,/)$0%'W8fK1'2,'-"#,'(,7,/),+1':06'40)-'$)(',::,/)$#,%,(('"%+'$)('($3<7$/$);1')-,'0%,',3<70;5
$%&'/0%()"%)5/*66,%)'4$"($%&8'I$&*6,'W8WN'$%+$/"),(')-,'+/'/*66,%)'"%+')-,'+/'#07)"&,('6,(*7)5
$%&'")'#"6$0*('%0+,(8
5.8 Discrete-Circuit MOS Amplifiers
EXERCISE
e
x
5.37'?0%($+,6')-,'/$6/*$)'0:'I$&8'W8WN':06')-,'/"(,'8(('='8))'='@Z'S1'?'='Z8W'3A1'F*'='b8f'FΩ1'F('='@W
PΩ1'8#'='@8W'S1'"%+' > !′ E'/&K'='@'3A/SQ8'I$%+'8:81'8*)1'8*1'8)1'"%+'8(8'A7(01'/"7/*7"),')-,'#"7*,('0:
7@'"%+'6$1'"((*3$%&')-")'8G'='fW'S8'U-")'$(')-,'3"B$3*3'<0(($47,'($&%"7'(2$%&'")')-,'+6"$%':06
2-$/-')-,'FGHIJ9'6,3"$%('$%'(")*6")$0%g
Ans. H,,'I$&8'JW8Cfa'2$)-0*)')"P$%&'$%)0'"//0*%)')-,'($&%"7'(2$%&'")')-,'&"),1')-,'+6"$%'/"%'(2$%&')0
−@8W'S1'"'%,&")$#,'($&%"7'(2$%&'0:'b'S
)
VD
min=
change:
-4
!10 V
0.5 mA
15 k(
!2.5 V
0 mA
0V
VOV " 1 V
VGS " 2.5 V
#2.5 V
4.7 M(
0.5 mA
#10 V
(a)
D
G
D
!
vgs
gmvgs
ro
#
gm " 1 mA.V
ro " 150 k(
1$gm " 1 k(
i
ro
G
S
(b)
Figure E5.37
i
1
gm
S
(c)
315
316 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.8.2 The Common-Source (CS) Amplifier
A('3,%)$0%,+'$%'H,/)$0%'W8N1')-,'/0330%5(0*6/,'E?HK'/0%:$&*6")$0%'$(')-,'30()'2$+,7;'*(,+
0:'"77'FGHIJ9'"3<7$:$,6'/$6/*$)(8'A'/0330%5(0*6/,'"3<7$:$,6'6,"7$>,+'*($%&')-,'/$6/*$)'0:
I$&8 W8WN'$('(-02%'$%'I$&8'W8WfE"K8'G4(,6#,')-")')0',()"47$(-'"'!),*(.+,$"#*'1'06'"%'(%+,$"#*'
"('$)'$('(03,)$3,('/"77,+1'")')-,'(0*6/,1'2,'-"#,'/0%%,/),+'"'7"6&,'/"<"/$)061'<)1'4,)2,,%')-,
(0*6/,'"%+'&60*%+8'9-$('/"<"/$)061'*(*"77;'$%')-,'3$/60:"6"+'6"%&,1'$('6,O*$6,+')0'<60#$+,'"
#,6;'(3"77'$3<,+"%/,'E$+,"77;1'>,60'$3<,+"%/,a'$8,81'$%',::,/)1'"'(-06)'/$6/*$)K'")'"77'($&%"7':6,5
O*,%/$,(' 0:' $%),6,()8' =%' )-$(' 2";1' )-,' ($&%"7' /*66,%)' <"((,(' )-60*&-' <)' )0' &60*%+' "%+' )-*(
K4"211/1')-,'0*)<*)'6,($()"%/,'0:'/*66,%)'(0*6/,'?'E"%+'"%;'0)-,6'/$6/*$)'/03<0%,%)')-")'3$&-)
4,'/0%%,/),+')0')-,'FGHIJ9'(0*6/,Ka'-,%/,1'<)'$('/"77,+'"'/0A(!!+%(A(%)-"$8'G4#$0*(7;1')-,
702,6')-,'($&%"7':6,O*,%/;1')-,'7,((',::,/)$#,')-,'4;<"(('/"<"/$)06'4,/03,(8'9-$('$((*,'2$77'4,
()*+$,+'$%'H,/)$0%'[8@8'I06'0*6'<*6<0(,('-,6,'2,'(-"77'"((*3,')-")'<)'$('"/)$%&'"('"'<,6:,/)
(-06)'/$6/*$)'"%+')-*('$(',()"47$(-$%&'"'>,60'($&%"7'#07)"&,'")')-,'FGHIJ9'(0*6/,8
=%' 06+,6' %0)' )0' +$()*64' )-,' +/' 4$"(' /*66,%)' "%+' #07)"&,(1' )-,' ($&%"7' )0' 4,' "3<7$:$,+1
(-02%'"('#07)"&,'(0*6/,'v($&'2$)-'"%'$%),6%"7'6,($()"%/,'F($&1'$('/0%%,/),+')0')-,'&"),')-60*&"'7"6&,'/"<"/$)06'<<@8'?"<"/$)06'<<@1'P%02%'"('"'%"#A.)*,+%(A(%)-"$1'$('6,O*$6,+')0'"/)'"('"
<,6:,/)'(-06)'/$6/*$)'")'"77'($&%"7':6,O*,%/$,('0:'$%),6,()'2-$7,'470/P$%&'+/8'!,6,'"&"$%1'2,
%0),' )-")' "(' )-,' ($&%"7' :6,O*,%/;' $(' 702,6,+1' )-,' $3<,+"%/,' 0:' <<@' E$8,81' @ ⁄ N ω < <@K' 2$77
$%/6,"(,'"%+'$)(',::,/)$#,%,(('"('"'/0*<7$%&'/"<"/$)06'2$77'4,'/066,(<0%+$%&7;'6,+*/,+8'9-$(
<6047,3')00'2$77'4,'/0%($+,6,+'$%'H,/)$0%'[8@'2-,%')-,'+,<,%+,%/,'0:')-,'"3<7$:$,6'0<,6")$0%
0%':6,O*,%/;'$('()*+$,+8'I06'0*6'<*6<0(,('-,6,'2,'(-"77'"((*3,'<<@'$('"/)$%&'"('"'<,6:,/)'(-06)
/$6/*$)'"(':"6'"(')-,'($&%"7'$('/0%/,6%,+8'L,:06,'7,"#$%&'<<@1'2,'(-0*7+'<0$%)'0*)')-")'2-,%')-,
($&%"7'(0*6/,'/"%'<60#$+,'"%'"<<60<6$"),'+/'<")-')0'&60*%+1')-,'&"),'/"%'4,'/0%%,/),+'+$6,/)7;
)0')-,'($&%"7'(0*6/,'"%+'40)-'F*'"%+'<<@'/"%'4,'+$(<,%(,+'2$)-8
9-,'#07)"&,'($&%"7'6,(*7)$%&'")')-,'+6"$%'$('/0*<7,+')0')-,'70"+'6,($()"%/,'F&'#$"'"%0)-,6
/0*<7$%&'/"<"/$)06'<<Q8'U,'(-"77'"((*3,')-")'<<Q'"/)('"('"'<,6:,/)'(-06)'/$6/*$)'")'"77'($&%"7
:6,O*,%/$,('0:'$%),6,()'"%+')-*(')-")')-,'0*)<*)'#07)"&,'v$'='v,8'`0),')-")'F&'/"%'4,',$)-,6'"%
"/)*"7'70"+'6,($()061')0'2-$/-')-,'"3<7$:$,6'$('6,O*$6,+')0'<60#$+,'$)('0*)<*)'#07)"&,'($&%"71'06
$)'/"%'4,')-,'$%<*)'6,($()"%/,'0:'"%0)-,6'"3<7$:$,6'()"&,'$%'/"(,('2-,6,'306,')-"%'0%,'()"&,'0:
"3<7$:$/")$0%'$('%,,+,+8'EU,'2$77'()*+;'3*7)$()"&,'"3<7$:$,6('$%'?-"<),6'd8K'
VDD
RD
ID " I
VD " VDD # RD ID
0V
!
VGS
RG
VGS " Vt ! VOV
#
I
#VSS
VOV " 2I$k)n W
L
Figure 5.56 L"($/'()6*/)*6,'0:')-,'/$6/*$)'*(,+')0
6,"7$>,' ($%&7,5()"&,1' +$(/6,),5/$6/*$)' FGH' "3<7$:$,6
/0%:$&*6")$0%(8
5.8 Discrete-Circuit MOS Amplifiers
VDD (0 V)
RD
CC1 i
i
Rsig
CC2
vd
vo
0
RL
!
vsig
!
#
!
vgs = vi
vi
RG
0V
#
CS
I
#
Ro
Rin
#VSS
(a)
Rsig
ii
ig " 0
!
!
vsig !
#
vi
#
Rin " RG
D vo = #gm vgs (RD 11 RL 11 ro)
G
RG
vgs
gmvgs
ro
RD
RL
#
S
Ro = RD 11 ro
(b)
Figure 5.57 1(2'?0330%5(0*6/,'"3<7$:$,6'4"(,+'0%')-,'/$6/*$)'0:'I$&8'W8WN8'1/2'JO*$#"7,%)'/$6/*$)'0:')-,
"3<7$:$,6':06'(3"775($&%"7'"%"7;($(8
90'+,),63$%,')-,'),63$%"7'/-"6"/),6$()$/('0:')-,'?H'"3<7$:$,6p)-")'$(1'$)('$%<*)'6,($()"%/,1
#07)"&,'&"$%1'"%+'0*)<*)'6,($()"%/,p2,'6,<7"/,')-,'FGHIJ9'2$)-'$)('(3"775($&%"7'30+,78
9-,'6,(*7)$%&'/$6/*$)'$('(-02%'$%'I$&8'W8WfE4K8
U,'04(,6#,')-")')-,'0%7;'+$::,6,%/,'4,)2,,%')-$('/$6/*$)'"%+')-,'()6$<<,+5+02%'#,6($0%
()*+$,+' $%' H,/)$0%' W8N8C' EI$&8' W8bWK' $(' )-")' -,6,' 2,' -"#,' )-,' 4$"(' 6,($()"%/,' F *8' H$%/,' F *
"<<,"6(' "/60((' )-,' $%<*)' ),63$%"7(' 0:' )-,' "3<7$:$,61' )-,' $%<*)' 6,($()"%/,' 2$77' %0' 70%&,6' 4,
$%:$%$),1'6")-,6'
F $% ' & F *
90'P,,<' F $%'-$&-1'"'7"6&,'#"7*,'0:' F *'E$%')-,'3,&0-3'6"%&,K'$('*(*"77;'(,7,/),+8'9-,':$%$),
F $%'2$77'"::,/)')-,'0#,6"77'#07)"&,'&"$%' * v'2-$/-'4,/03,(
F*
* v ' & ' 555555555555555555555
7 ( F || F & || 6 $ )
F * ( F ($& @ (
EW8@Z@K
I$%"77;1')0',%/0*6"&,')-,'6,"+,6')0'+0')-,'"%"7;($('+$6,/)7;'0%')-,'/$6/*$)'+$"&6"31'2$)-')-,
FGHIJ9'30+,7'*(,+'$3<7$/$)7;1'2,'(-02'(03,'0:')-,'"%"7;($('0%')-,'/$6/*$)'$%'I$&8'W8WfE"K8
317
318 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
EXERCISE
5.38' ?0%($+,6'"'?H'"3<7$:$,6'4"(,+'0%')-,'/$6/*$)'"%"7;>,+'$%'JB,6/$(,'W8Cf8'H<,/$:$/"77;1'6,:,6')0')-,
6,(*7)('0:')-")',B,6/$(,'(-02%'$%'I$&8'JW8Cf8'I$%+'F$%1'Gv$1'"%+'F$1'40)-'2$)-0*)'"%+'2$)-'6$')"P,%
$%)0'"//0*%)8'9-,%'/"7/*7"),')-,'0#,6"77'#07)"&,'&"$%'*v 1'2$)-'6$')"P,%'$%)0'"//0*%)1':06')-,'/"(,
F($& = @ZZ'PΩ'"%+'F& ='@W'PΩ8'=:'v($&'$('"'Z8b5S'<,"P5)05<,"P'($%*(0$+1'2-")'0*)<*)'($&%"7'v$'6,(*7)(g
Ans. U$)-0*)'6$D'F$%'='b8f'FΩ1'Gv$'=''−@W'ScS1'"%+'F$ ='@W'PΩa'2$)-'6$D'F$%'='b8f'FΩ 1'Gv$'='−@C8N
ScS1'"%+'F$ ='@C8N'PΩa'* v = ' f'ScSa'v$'$('"'Q8d5S'<,"P5)05<,"P'($%*(0$+'(*<,6$3<0(,+'0%'"'+/
+6"$%'#07)"&,'0:'+Q8W'S8
5.8.3 The Common-Source Amplifier with a Source Resistance
A('+,30%()6"),+'$%'H,/)$0%'W8N8b1'"'%*34,6'0:'4,%,:$/$"7'6,(*7)('/"%'4,'04)"$%,+'4;'/0%%,/)$%&
"'6,($()"%/,' F 1'$%')-,'(0*6/,'7,"+'0:')-,')6"%($()06'$%')-,'?H'"3<7$:$,68'9-$('$('(-02%'$%'I$&8
W8WdE"K1'2-,6,' F 1'$(1'0:'/0*6(,1'*%4;<"((,+8'I$&*6,'W8WdE4K'(-02(')-,'(3"775($&%"7',O*$#"7,%)5
/$6/*$)'30+,78'G4(,6#,')-")')-,'0%7;'+$::,6,%/,'4,)2,,%')-$('/$6/*$)'"%+')-,'($3<7$:$,+'#,6($0%
()*+$,+'$%'H,/)$0%'W8N8b'$(')-,'4$"('6,($()"%/,' F *')-")'"<<,"6('"/60((')-,'$%<*)'),63$%"7('"%+
3"P,(' F $%':$%$),8'9-$('2$77'$%')*6%'"::,/)')-,'0#,6"77'#07)"&,'&"$%'* v1'2-$/-'4,/03,(
F*
F ( || F &
555555555555555555555555
5'
* v & ' 555555555555555555555
F * ( F ($& @ ⁄ 7 @ ( F 1
EW8@ZQK
I$%"77;1'%0),')-")'3*/-'0:')-,'"%"7;($('$('(-02%'40)-'0%')-,'"/)*"7'/$6/*$)'$%'I$&8'W8WdE"K'"%+
0%')-,',O*$#"7,%)'/$6/*$)'$%'I$&8'W8WdE4K8
EXERCISE
5.39' =%'JB,6/$(,'W8Cd'2,'"<<7$,+'"%'$%<*)'($&%"7'0:'Z8b'S'<,"P5)05<,"P1'2-$/-'6,(*7),+'$%'"%'0*)<*)'($&5
%"7'0:')-,'?H'"3<7$:$,6'0:'Q8d'S'<,"P5)05<,"P8'A((*3,')-")':06'(03,'6,"(0%'2,'%02'-"#,'"%'$%<*)
($&%"7')-6,,')$3,('"('7"6&,'"('4,:06,'E$8,81'@8Q'S'<5<K'"%+')-")'2,'2$(-')0'30+$:;')-,'/$6/*$)')0'P,,<
)-,'0*)<*)'($&%"7'7,#,7'*%/-"%&,+8'U-")'#"7*,'(-0*7+'2,'*(,':06'F1g
Ans. Q8@W'PΩ
5.8.4 The Common-Gate (CG) Amplifier
I$&*6,'W8W[E"K'(-02('"'?]'"3<7$:$,6'04)"$%,+':603')-,'/$6/*$)'0:'I$&8'W8WN8'G4(,6#,')-")'($%/,
40)-')-,'+/'"%+'"/'#07)"&,('")')-,'&"), "6,')0'4,'>,601'2,'-"#,'/0%%,/),+')-,'&"),'+$6,/)7;')0
&60*%+1')-*(',7$3$%")$%&'6,($()06'F*'"7)0&,)-,68'?0*<7$%&'/"<"/$)06('<<@'"%+'<<Q'<,6:063'($3$5
7"6':*%/)$0%(')0')-0(,'$%')-,'?H'/$6/*$)8'
9-,'(3"775($&%"71',O*$#"7,%)'/$6/*$)'30+,7'0:')-,'?]'"3<7$:$,6'$('(-02%'$%'I$&8'W8W[E4K8
U,'%0),')-")')-$('/$6/*$)'$('$+,%)$/"7')0')-,',O*$#"7,%)'/$6/*$)'0:')-,'()6$<<,+5+02%'#,6($0%'0:
)-,'?]'"3<7$:$,61'$%'I$&8'W8bdE4K8'9-*(')-,'"%"7;($('<,6:063,+'"%+')-,'6,(*7)('04)"$%,+'$%
H,/)$0%' W8N8W' "<<7;' +$6,/)7;' -,6,8' A' (*4()"%)$"7' <06)$0%' 0:' )-,' "%"7;($(' $(' "7(0' (-02%' $%
I$&8 W8W[8
5.8 Discrete-Circuit MOS Amplifiers
VDD (0 V)
RD
CC2
vd
CC1
Rsig
!
#
1
vi & g ! R s '
%
0
RL
m
!
!
vsig
vo
RG
vi
#
1.gm
vi
1
vi & g ! Rs'
%
m
Ro " R D
Rs
#
Rin " RG
0V
0
CS
I
#VSS
(a)
1
id " i " vi$ & gm ! Rs'
vd
D
RD
i
0
Rsig
vsig
!
#
!
vi
vgs
RG
i
Ro " R D
1
gm
#
S
Rin " RG
RL
G
!
#
vo
1
i " v i$ & g ! R s '
m
Rs
(b)
Figure 5.58 1(2'?0330%5(0*6/,'"3<7$:$,6'2$)-'"'6,($()"%/,'F)'$%')-,'(0*6/,'7,"+8'1/2'H3"775($&%"7',O*$#5
"7,%)'/$6/*$)'2$)-'6$'%,&7,/),+8
'
319
320 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
VDD (0 V)
RD
CC2
vd
vo
RL
ii " gmvi
1
" vsig$& g ! Rsig'
m
ii
Rsig
CC1
!
#
ii
I
vi
1
Rin " g
m
Ro " RD
0
!
vsig
1
gm
#
#VSS
(a)
D
i
id " i
vd
RD
vo
RL
G
i
Rsig
ii
1
gm
Ro " RD
S
!
vsig
vi
!
#
1
Rin " g
m
#
(b)
Figure 5.59 1(2'A'/0330%5&"),'"3<7$:$,6'4"(,+'0%')-,'/$6/*$)'0:'I$&8'W8WN8''1/2'A'(3"775($&%"7',O*$#"7,%)'
/$6/*$)'0:')-,'"3<7$:$,6'$%'E"K8
EXERCISE
5.40' ?0%($+,6'"'?]'"3<7$:$,6'+,($&%,+'*($%&')-,'/$6/*$)'0:'I$&8'W8WN1'2-$/-'$('"%"7;>,+'$%'JB,6/$(,'W8Cf
2$)-')-,'"%"7;($('6,(*7)('+$(<7";,+'$%'I$&8'JW8Cf8'`0),')-")' 7 @ = @'3AcS "%+'F('='@W'PΩ8'I$%+
F$%1'F$1'Gv$1'Gv1'"%+'*v':06'F&'='@W'PΩ'"%+'F($&'='WZ'Ω8'U-")'2$77')-,'0#,6"77'#07)"&,'&"$%'4,/03,
:06'F($&'='@'PΩg'@Z'PΩg'@ZZ'PΩg
Ans. @'PΩ1'@W'PΩ1' +@W'ScS 1' +f8W'ScS1' +f8@'ScS a' +C8fW'ScS a' Z8Nd'ScS a' Z8Zf'ScS
5.8 Discrete-Circuit MOS Amplifiers
5.8.5 The Source Follower
I$&*6,'W8NZE"K'(-02('"'/0330%5+6"$%'"3<7$:$,6'4"(,+'0%')-,'/$6/*$)'0:'I$&8'W8WN8'H$%/,')-,
+6"$%'$(')0':*%/)$0%'"('"'($&%"7'&60*%+1')-,6,'$('%0'%,,+':06'6,($()06'F(1'"%+'$)'-"(')-,6,:06,
4,,%',7$3$%"),+8'9-,'$%<*)'($&%"7'$('/0*<7,+'#$"'/"<"/$)06'<<@')0')-,'FGHIJ9'&"),1'"%+')-,
0*)<*)'($&%"7'")')-,'FGHIJ9'(0*6/,'$('/0*<7,+'#$"'/"<"/$)06'<<Q')0'"'70"+'6,($()060F&H'
i,<7"/$%&')-,'FGHIJ9'2$)-'$)('9'30+,7'6,(*7)('$%')-,',O*$#"7,%)'/$6/*$)'$%'I$&8'W8NZE4K8
U,'%0),')-")')-,'0%7;'+$::,6,%/,'4,)2,,%')-$('/$6/*$)'"%+')-")'$%'I$&8'W8WZE4K'$(')-,'4$"('6,($(5
)"%/,' F * ')-")'"<<,"6('"/60((')-,'$%<*)'),63$%"7(8'9-*(1'-,6,')001')-,'$%<*)'6,($()"%/,'2$77'%0
70%&,6'4,'$%:$%$),'"%+')-,'0#,6"77'#07)"&,'&"$%'2$77'4,/03,'
F*
( F & || 6 $ )
555555555555555555555555555555555555555
5'
* v & 555555555555555555555
F * ( F ($& ( F & || 6 $ ) ( @ ⁄ 7 @
EW8@ZCK
VDD
CC1
Rsig
CC2
!
vsig
!
#
vi
vo
RG
#
RL
I
Rin
Ro
#VSS
(a)
D
i
0
Rsig
G
i
!
vsig
!
#
vi
RG
ro
1
gm
#
Rin " RG
S
Ro = g1m 11 ro
vo
RL
(b)
Figure 5.60 1(2''A''(0*6/,5:07702,6'"3<7$:$,68'1/2'H3"775($&%"71',O*$#"7,%)5/$6/*$)'30+,78
321
322 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
EXERCISE
5.41%I32$1.+(% '% $3#(9+% &3883*+(% $#9"% '$% /"'/% 12% ?10<% @<ARN'P% .+$102+.% 32% /"+% ='$1$% 3&% /"+% 91(9#1/% 3&
?10< @<@A)% /"+% (+$#8/$% 3&% *"3$+% '2'8;$1$% '(+% .1$78';+.% 12% ?10<% F@<JT<% 67+91&19'88;)% 23/+% /"'/
/ 0 = B%-EZY %'2.%*+ =%B@R%CΩ<%U+/%,$10%=%B%4Ω%'2.%,&%=%B@%CΩ<%N'P%?12.%,12)%-v+)%-v)%'2.%,+%*1/"3#/
'2.%*1/"%*+%/'C+2%12/3%'993#2/<%N=P%?12.%/"+%3,+('88%$-'88>$102'8%,38/'0+%0'12%.v%*1/"%*+%/'C+2%12/3
'993#2/<
Ans. N'P% ,12% =% S<T% 4ΩV% - v+ = B%YZY % N*1/"3#/% *+P)% R<LLJ%YZY N*1/"% *+PV% -v% =% R<LJW% N*1/"3#/% *+P)
R<LJX%Y%N*1/"%*+PV%,+%=%B%CΩ%N*1/"3#/%*+P)%R<LLJ%CΩ%N*1/"%*+PV%N=P%R<TAW%YZY
5.8.6 The Amplifier Frequency Response
!"#$%&'()%*+%"',+%'$$#-+.%/"'/%/"+%0'12%3&%456%'-781&1+($%1$%932$/'2/)%12.+7+2.+2/%3&%/"+
&(+:#+29;%3&%/"+%127#/%$102'8<%!"1$%*3#8.%1-78;%/"'/%456%'-781&1+($%"',+%12&121/+%='2.>
*1./")%*"19"%3&%93#($+%1$%23/%/(#+<%!3%188#$/('/+)%*+%$"3*%12%?10<%@<AB%'%$C+/9"%3&%/"+%-'0>
21/#.+%3&%/"+%0'12%3&%'%93--32>$3#(9+%'-781&1+(%,+($#$%&(+:#+29;<%5=$+(,+%/"'/%/"+(+%1$
12.++.%'%*1.+%&(+:#+29;%('20+%3,+(%*"19"%/"+%0'12%(+-'12$%'8-3$/%932$/'2/<%!"1$%3=,1>
3#$8;%1$%/"+%#$+&#8%&(+:#+29;%('20+%3&%37+('/132%&3(%/"+%7'(/19#8'(%'-781&1+(<%!"#$%&'()%*+
"',+%=++2%'$$#-120%/"'/%3#(%'-781&1+($%'(+%37+('/120%12%/"1$%&(+:#+29;%='2.)%9'88+.%!"#
$%&'()&<
?10#(+%@<AB%12.19'/+$%/"'/%'/%83*+(%&(+:#+291+$)%/"+%-'021/#.+%3&%'-781&1+(%0'12%&'88$%3&&<
!"1$%1$%=+9'#$+%/"+%93#78120%'2.%=;7'$$%9'7'91/3($%23%8320+(%"',+%83*%1-7+.'29+$<%D+9'88
/"'/%*+%'$$#-+.%/"'/%/"+1(%1-7+.'29+$%*+(+%$-'88%+23#0"%/3%'9/%'$%$"3(/%91(9#1/$<%E8/"3#0"
/"1$%9'2%=+%/(#+%'/%-1.='2.%&(+:#+291+$)%'$%/"+%&(+:#+29;%3&%/"+%127#/%$102'8%1$%83*+(+.)%/"+
(+'9/'29+%B ⁄ #ω$%3&%+'9"%3&%/"+$+%9'7'91/3($%=+93-+$%$1021&19'2/)%'2.%1/%9'2%=+%$"3*2%/"'/
/"1$%(+$#8/$%12%/"+%3,+('88%,38/'0+%0'12%3&%/"+%'-781&1+(%.+9(+'$120<
?10#(+%@<AB%12.19'/+$%'8$3%/"'/%/"+%0'12%3&%/"+%'-781&1+(%&'88$%3&&%'/%/"+%"10">&(+:#+29;
+2.<%!"1$%1$%.#+%/3%/"+%12/+(2'8%9'7'91/1,+%+&&+9/$%12%/"+%456?F!<%G+%"',+%"'.%'%=(1+&%12/(3>
.#9/132%/3%$#9"%9'7'91/1,+%+&&+9/$%12%3#(%$/#.;%3&%/"+%!"%H#29/132%12%I"'7/+(%J<%K2%I"'7/+(%L)
*+%$"'88%$/#.;%/"+%12/+(2'8%9'7'91/1,+%+&&+9/$%3&%/"+%456?F!%'2.%*188%'#0-+2/%/"+%";=(1.>π
-3.+8%*1/"%9'7'91/'29+$%/"'/%-3.+8%/"+$+%+&&+9/$<
G+% *188% #2.+(/'C+% '% .+/'18+.% $/#.;% 3&% /"+% &(+:#+29;% (+$732$+% 3&% 456% '-781&1+($% 12
I"'7/+(%L<%?3(%/"+%/1-+%=+120)%"3*+,+()%1/%1$%1-73(/'2/%&3(%/"+%(+'.+(%/3%(+'81M+%/"'/%&3(%+,+(;
456%'-781&1+(%/"+(+%1$%'%&121/+%='2.%3,+(%*"19"%/"+%0'12%1$%'8-3$/%932$/'2/<%!"+%=3#2.'(1+$
3&%/"1$%#$+&#8%&(+:#+29;%='2.%3(%-1.='2.)%'(+%/"+%/*3%&(+:#+291+$% % &%'2.% % ' )%'/%*"19"%/"+
0'12%.(37$%=;%'%9+(/'12%2#-=+(%3&%.+91=+8$%N#$#'88;%J%.OP%=+83*%1/$%,'8#+%'/%-1.='2.<%E$
12.19'/+.%12%?10<%@<AB)%/"+%($*+%,%#-%'()&.%&!")%3(%J>.O%='2.*1./")%1$%.+&12+.%'$%/"+%.1&&+(>
+29+%=+/*++2%/"+%83*+(%N % &P%'2.%/"+%#77+(%3(%"10"+(%N % ' P%J>.O%&(+:#+291+$Q
()% " % ' ! % &
N@<BRSP
() ! % '
N@<BR@P
'2.%$129+%#$#'88;% % & ! % ' )
5.9 The Body Effect and Other Topics
Vo
(dB)
Vsig
Low-frequency
band
High-frequency band
Midband
• All capacitances can be neglected
• Gain falls off
due to the effect
of CC1, CS,
and CC2
• Gain falls off due
to the internal
capacitive effects
of the MOSFET
3 dB
20 log |AM| (dB)
fH
fL
f (Hz)
Figure 5.61 !"0P(+6,")#"+,("#'(Q&(16B"'(0.)10(")#"-"@E"-*./$#$('"4(/$1(-+$1%"+,("+,'(("#'(Q&(16B"3-140")#
$1+('(0+:
!"#$%&'(")#"*('$+"#)'"+,("-*./$#$('"$0"$+0"%-$123-145$4+,".')4&6+7"4(#$1(4"-0"
&%" ! ' ( %)
89:;<=>
5,('(" ' ( "$0"+,("*-%1$+&4(")#"+,("-*./$#$('"%-$1"$1"+,("*$43-14:"?+"5$//"3("0((1"$1"@,-.+('"A
+,-+"$1"-*./$#$('"4(0$%1"$+"$0"&0&-//B".)00$3/("+)"+'-4(")##"%-$1"#)'"3-145$4+,:"C1("5-B"+)"-66)*D
./$0,"+,$07"#)'"$10+-16(7"$0"3B"$16/&4$1%"'(0$0+-16(" * +"$1"+,("0)&'6(")#"+,("@E"-*./$#$(':
5.9 The Body Effect and Other Topics11
?1"+,$0"0(6+$)1"5("3'$(#/B"6)10$4('"-"1&*3('")#"$*.)'+-1+"+,)&%,"0(6)14-'B"$00&(0:
5.9.1 The Role of the Substrate—The Body Effect
?1"*-1B"-../$6-+$)10"+,("0)&'6("+('*$1-/"$0"6)11(6+(4"+)"+,("0&30+'-+("8)'"3)4B>"+('*$1-/"F7
5,$6,"'(0&/+0"$1"+,("!""G&16+$)1"3(+5((1"+,("0&30+'-+("-14"+,("$14&6(4"6,-11(/"8'(H$(5"I$%:
9:9>",-H$1%"-"6)10+-1+"J(')"86&+)##>"3$-0:"?1"0&6,"-"6-0("+,("0&30+'-+("4)(0"1)+"./-B"-1B"')/(
$1"6$'6&$+").('-+$)1"-14"$+0"(K$0+(16("6-1"3("$%1)'(4"-/+)%(+,(':
?1"$1+(%'-+(4"6$'6&$+07",)5(H('7"+,("0&30+'-+("$0"&0&-//B"6)**)1"+)"*-1B"LCE"+'-10$0D
+)'0:"?1")'4('"+)"*-$1+-$1"+,("6&+)##"6)14$+$)1"#)'"-//"+,("0&30+'-+(D+)D6,-11(/"G&16+$)107"+,(
0&30+'-+("$0"&0&-//B"6)11(6+(4"+)"+,("*)0+"1(%-+$H(".)5('"0&../B"$1"-1"MLCE"6$'6&$+"8+,(
*)0+" .)0$+$H(" $1" -" NLCE" 6$'6&$+>:" O,(" '(0&/+$1%" '(H('0(D3$-0" H)/+-%(" 3(+5((1" 0)&'6(" -14
3)4B"8#$%"$1"-1""D6,-11(/"4(H$6(>"5$//",-H("-1"(##(6+")1"4(H$6(").('-+$)1:"O)"-..'(6$-+("+,$0
#-6+7" 6)10$4('" -1" MLCE" +'-10$0+)'" -14" /(+" $+0" 0&30+'-+(" 3(" *-4(" 1(%-+$H(" '(/-+$H(" +)" +,(
;;
O,$0"0(6+$)1"6-1"3(")*$++(4"$1"-"#$'0+"'(-4$1%"5$+,"/$++/(")'"1)"/)00")#"6)1+$1&$+B:"E)*(")#"+,$0"*-+('$-/7
,)5(H('7"5$//"3("'(Q&$'(4"#)'"+,("0+&4B")#"4$%$+-/"6$'6&$+0"$1"@,-.+('";R:
323
324 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
(0*6/,8'9-,'6,#,6(,54$"('#07)"&,'2$77'2$+,%')-,'+,<7,)$0%'6,&$0%'E6,:,6')0'I$&8'W8QK8'9-$('$%
)*6%' 6,+*/,(' )-,' /-"%%,7' +,<)-8' 90' 6,)*6%' )-,' /-"%%,7' )0' $)(' :063,6' ()"),1' v*)' -"(' )0' 4,
$%/6,"(,+8
9-,',::,/)'0:'8)A'0%')-,'/-"%%,7'/"%'4,'30()'/0%#,%$,%)7;'6,<6,(,%),+'"('"'/-"%&,'$%')-,
)-6,(-07+'#07)"&,'8#8'H<,/$:$/"77;1'$)'-"('4,,%'(-02%')-")'$%/6,"($%&')-,'6,#,6(,'(*4()6"),'4$"(
#07)"&,'8)A'6,(*7)('$%'"%'$%/6,"(,'$%'8#'"//06+$%&')0')-,'6,7")$0%(-$<
8 # = 8 #Z + γ [ Q φ M + 8)A ' ' ' Q φ M ]
EW8@ZfK
2-,6,'8# Z'$(')-,')-6,(-07+'#07)"&,':06'8)A'='Za'φM'$('"'<-;($/"7'<"6"3,),6'2$)-'EQφMK');<$/"77;
Z8N'Sa'γ' $('"':"46$/")$0%5<60/,(('<"6"3,),6'&$#,%'4;
QOI G ε 1
5
γ = 555555555555555555555
< $%
EW8@ZdK
2-,6,'O'$(')-,',7,/)60%'/-"6&,'E@8N'×'@Z−@['?K1'IG'$(')-,'+0<$%&'/0%/,%)6")$0%'0:')-,'"5);<,'(*45
()6"),1'"%+' ε1'$(')-,'<,63$))$#$);'0:'($7$/0%'E@@8fεZ'='@@8f'×'d8dWb'× @Z−@b'= @8Zb'× @Z−@Q'Ic/3K8
9-,' <"6"3,),6' γ' -"(' )-,' +$3,%($0%' 0:' S ' "%+' $(' );<$/"77;' Z8b' S@cQ8' I$%"77;1' %0),' )-")
JO8 EW8@ZfK'"<<7$,(',O*"77;'2,77':06'"5/-"%%,7'+,#$/,('2$)-'8)A'6,<7"/,+'4;')-,'6,#,6(,'4$"(
0:')-,'(*4()6"),1'8A)'E061'"7),6%")$#,7;1'6,<7"/,'8)A'4;' 8)A K'"%+'%0),')-")'γ'$('%,&")$#,8'A7(01
$%',#"7*")$%&' γ1'IG'3*()'4,'6,<7"/,+'2$)-'I(1')-,'+0<$%&'/0%/,%)6")$0%'0:')-,'!'2,77'$%
2-$/-')-,'_FGH'$(':063,+8'I06'"5/-"%%,7'+,#$/,(1'QφM'$(');<$/"77;'Z8fW'S1'"%+'γ'$(');<$/"77;
−Z8W'S@cQ8
EXERCISE
5.42' A%'`FGH')6"%($()06'-"('8# Z'='Z8d'S1'QφM'='Z8f'S1'"%+'γ'='Z8b'S@cQ8'I$%+'8#'2-,%'8)A'='C'S8
Ans. @8QC'S
JO*")$0%'EW8@ZfK'$%+$/"),(')-")'"%'$%/6,3,%)"7'/-"%&,'$%'8)A'&$#,('6$(,')0'"%'$%/6,3,%)"7
/-"%&,'$%'8# 1'2-$/-'$%')*6%'6,(*7)('$%'"%'$%/6,3,%)"7'/-"%&,'$%'+(',#,%')-0*&-'v*)'3$&-)'-"#,
4,,%'P,<)'/0%()"%)8'=)':07702(')-")')-,'40+;'#07)"&,'/0%)607('+(a')-*(')-,'40+;'"/)('"('"%0)-,6
&"),' :06' )-,' FGHIJ91' "' <-,%03,%0%' P%02%' "(' )-,' /"'0+ &??&%-8' !,6,' 2,' %0),' )-")' )-,
<"6"3,),6'γ'$('P%02%'"(')-,'/"'03&??&%-+A($(B&-&$8
5.9.2 Modeling the Body Effect
A('3,%)$0%,+'"40#,')-,'40+;',::,/)'0//*6('$%'"'FGHIJ9'2-,%')-,'(0*6/,'$('%0)')$,+')0')-,
(*4()6"),'E2-$/-'$('"72";('/0%%,/),+')0')-,'30()'%,&")$#,'<02,6'(*<<7;'$%')-,'$%),&6"),+
/$6/*$)':06'!5/-"%%,7'+,#$/,('"%+')0')-,'30()'<0($)$#,':06'"5/-"%%,7'+,#$/,(K8'9-*(')-,'(*45
()6"),'E40+;K'2$77'4,'")'($&%"7'&60*%+1'4*)'($%/,')-,'(0*6/,'$('%0)1'"'($&%"7'#07)"&,' vK1'+,#,75
0<('4,)2,,%')-,'40+;'ELK'"%+')-,'(0*6/,'EHK8'9-,'(*4()6"),')-,%'"/)('"('"'X(,/0%+'&"),Y'06'"
/(%H,(-&':06')-,'FGHIJ98'9-*(')-,'($&%"7'vK1'&$#,('6$(,')0'"'+6"$%5/*66,%)'/03<0%,%)1'2-$/2,'(-"77'26$),'"('7@KvK11'2-,6,'7@K'$(')-,'/"'0+-$(*!%"*'#%-(*%&1'+,:$%,+'"('
''''''''
∂ +(
5 v*) = /0%()"%)
7 @K ≡ 5555555555
∂ v A) v() = /0%()"%)
EW8@Z[K
i,/"77$%&')-")'+('+,<,%+('0%'vA)')-60*&-')-,'+,<,%+,%/,'0:'8#'0%'8A)1'2,'/"%'(-02')-")
5.9 The Body Effect and Other Topics
D
D
B
G
S
(a)
(b)
Figure 5.62 H3"775($&%"71',O*$#"7,%)5/$6/*$)'30+,7'0:'"'FGHIJ9'$%'2-$/-')-,'(0*6/,'$('%0)'/0%%,/),+')0
)-,'40+;8
7@K'='χ 7@
EW8@@ZK
∂8
γ
χ ≡ 5555555555#5 = 55555555555555555555555555555
∂ 8)A
Q Q φ M + 8 )A
EW8@@@K
2-,6,
9;<$/"77;')-,'#"7*,'0:'χ'7$,('$%')-,'6"%&,'Z8@')0'Z8C8
I$&*6,'W8NQ'(-02(')-,'FGHIJ9'30+,7'"*&3,%),+')0'$%/7*+,')-,'/0%)6077,+'(0*6/,
7@KvK1')-")'30+,7(')-,'40+;',::,/)8'=+,"77;1')-$('$(')-,'30+,7')0'4,'*(,+'2-,%,#,6')-,'(0*6/,'$(
%0)'/0%%,/),+')0')-,'(*4()6"),8'=)'-"('4,,%':0*%+1'-02,#,61')-")',B/,<)'$%'(03,'#,6;'<"6)$/*7"6
($)*")$0%(1')-,'40+;',::,/)'/"%'&,%,6"77;'4,'$&%06,+'$%')-,'$%$)$"71'<,%/$75"%+5<"<,6'+,($&%'0:
FGHIJ9'"3<7$:$,6(8
I$%"77;1'"7)-0*&-')-,'"%"7;($('"40#,'2"('<,6:063,+'0%'"'`FGH')6"%($()061')-,'6,(*7)('"%+
)-,',O*$#"7,%)'/$6/*$)'0:'I$&8'W8NQ'"<<7;',O*"77;'2,77')0'_FGH')6"%($()06(1',B/,<)':06'*($%&
|8*)|1'|8#|1'|8:8|1'|8G|1'|8)A|1'|γ |1'"%+'|λ |'"%+'6,<7"/$%&' > !′ 2$)-' > "′ '$%')-,'"<<60<6$"),':063*7"8
5.9.3 Temperature Effects
L0)-'8#'"%+' >′ '"6,'),3<,6")*6,'(,%($)$#,8'9-,'3"&%$)*+,'0:'8#'+,/6,"(,('4;'"40*)'Q'3S':06
,#,6;'@°?'6$(,'$%'),3<,6")*6,8'9-$('+,/6,"(,'$%' 8 # &$#,('6$(,')0'"'/066,(<0%+$%&'$%/6,"(,'$%
+6"$%'/*66,%)'"('),3<,6")*6,'$('$%/6,"(,+8'!02,#,61'4,/"*(,' >′ +,/6,"(,('2$)-'),3<,6")*6,
"%+'$)(',::,/)'$('"'+03$%"%)'0%,1')-,'0#,6"77'04(,6#,+',::,/)'0:'"'),3<,6")*6,'$%/6,"(,'$('"
,/.6/21/'$%'+6"$%'/*66,%)8'9-$('#,6;'$%),6,()$%&'6,(*7)'$('<*)')0'*(,'$%'"<<7;$%&')-,'FGHIJ9
$%'<02,6'/$6/*$)('E?-"<),6'@@K8
5.9.4 Breakdown and Input Protection
A(')-,'#07)"&,'0%')-,'+6"$%'$('$%/6,"(,+1'"'#"7*,'$('6,"/-,+'")'2-$/-')-,'"!'.*%/)$0%'4,)2,,%
)-,'+6"$%'6,&$0%'"%+'(*4()6"),'(*::,6('"#"7"%/-,'46,"P+02%'E(,,'H,/)$0%'C8W8CK8'9-$('46,"P5
+02%'*(*"77;'0//*6('")'#07)"&,('0:'QZ'S')0'@WZ'S'"%+'6,(*7)('$%'"'(03,2-")'6"<$+'$%/6,"(,
$%'/*66,%)'EP%02%'"('"'D&(H+(>(.(*%9&K8
325
326 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
A%0)-,6'46,"P+02%',::,/)')-")'0//*6('")'702,6'#07)"&,('E"40*)'QZ'SK'$%'30+,6%'+,#$/,(
$('/"77,+'A#*%93-9$"#,98'=)'0//*6('$%'+,#$/,('2$)-'6,7")$#,7;'(-06)'/-"%%,7('2-,%')-,'+6"$%
#07)"&,'$('$%/6,"(,+')0')-,'<0$%)')-")')-,'+,<7,)$0%'6,&$0%'(*660*%+$%&')-,'+6"$%'6,&$0%',B),%+(
)-60*&-')-,'/-"%%,7')0')-,'(0*6/,8'9-,'+6"$%'/*66,%)')-,%'$%/6,"(,('6"<$+7;8'`063"77;1'<*%/-5
)-60*&-'+0,('%0)'6,(*7)'$%'<,63"%,%)'+"3"&,')0')-,'+,#$/,8'
u,)'"%0)-,6'P$%+'0:'46,"P+02%'0//*6('2-,%')-,'&"),5)05(0*6/,'#07)"&,',B/,,+('"40*)
CZ S8' 9-$(' $(' )-,' 46,"P+02%' 0:' )-,' &"),' 0B$+,' "%+' 6,(*7)(' $%' <,63"%,%)' +"3"&,' )0' )-,
+,#$/,8'A7)-0*&-'CZ'S'3";'(,,3'-$&-1'$)'3*()'4,'6,3,34,6,+')-")')-,'FGHIJ9'-"('"
#,6;'-$&-'$%<*)'6,($()"%/,1'"%+'"'#,6;'(3"77'$%<*)'/"<"/$)"%/,1'"%+')-*('(3"77'"30*%)('0:
()")$/' /-"6&,' "//*3*7")$%&' 0%' )-,' &"),' /"<"/$)06' /"%' /"*(,' $)(' 46,"P+02%' #07)"&,' )0' 4,
,B/,,+,+8
90'<6,#,%)')-,'"//*3*7")$0%'0:'()")$/'/-"6&,'0%')-,'&"),'/"<"/$)06'0:'"'FGHIJ91'&"),5
<60),/)$0%'+,#$/,('"6,'*(*"77;'$%/7*+,+'")')-,'$%<*)'),63$%"7('0:'FGH'$%),&6"),+'/$6/*$)(8'9-,
<60),/)$0%'3,/-"%$(3'$%#"6$"47;'3"P,('*(,'0:'/7"3<$%&'+$0+,(8
5.9.5 Velocity Saturation
A)' -$&-' 70%&$)*+$%"7' ,7,/)6$/' :$,7+(1' )-,' +6$:)' #,70/$);' 0:' /-"6&,' /"66$,6(' $%' )-,' /-"%%,7
6,"/-,(' "%' *<<,6' 7$3$)' E"<<60B$3"),7;' @Zf' /3c(' :06' ,7,/)60%(' "%+' -07,(' $%' ($7$/0%K8' 9-$(
,::,/)1' 2-$/-' $%' 30+,6%' #,6;5(-06)5/-"%%,7' +,#$/,(' /"%' 0//*6' :06' v()' 702,6' )-"%' @' S1' $(
/"77,+'#,70/$);'(")*6")$0%8'=)'/"%'4,'(-02%'4,')-")'2-,%'#,70/$);'(")*6")$0%'0//*6(1')-,'/*65
6,%)'+('2$77'%0'70%&,6'4,'6,7"),+')0'v*)04;')-,'(O*"6,57"2'6,7")$0%(-$<8'i")-,61'+(04,/03,('7$%5
,"67;'+,<,%+,%)'0%' v*)'"%+')-,')6"%(/0%+*/)"%/,'7@'4,/03,('/0%()"%)'"%+'$%+,<,%+,%)'0:
v*)8'=%'?-"<),6'@C1'2,'(-"77'/0%($+,6'#,70/$);'(")*6")$0%'$%'0*6'()*+;'0:'+,,<'(*43$/60%'E$8,81
&'x'Z8QW'µ3K'?FGH'+$&$)"7'/$6/*$)(8
5.9.6 The Depletion-Type MOSFET
U,'/0%/7*+,')-$('(,/)$0%'2$)-'"'46$,:'+$(/*(($0%'0:'"%0)-,6');<,'0:'FGHIJ91')-,'+,<7,5
)$0%5);<,' FGHIJ98' =)(' ()6*/)*6,' $(' ($3$7"6' )0' )-")' 0:' )-,' ,%-"%/,3,%)5);<,' FGHIJ9
2$)-' 0%,' $3<06)"%)' +$::,6,%/,D' 9-,' +,<7,)$0%' FGHIJ9' -"(' "' <-;($/"77;' $3<7"%),+
/-"%%,78'9-*('"%'!5/-"%%,7'+,<7,)$0%5);<,'FGHIJ9'-"('"%'!5);<,'($7$/0%'6,&$0%'/0%5
%,/)$%&')-,'!+'(0*6/,'"%+')-,'!+'+6"$%'6,&$0%('")')-,')0<'0:')-,'"5);<,'(*4()6"),8'9-*('$:'"
#07)"&,' v()'$('"<<7$,+'4,)2,,%'+6"$%'"%+'(0*6/,1'"'/*66,%)'+(':702(':06' v*)'='Z8'=%'0)-,6
206+(1' )-,6,' $(' %0' %,,+' )0' $%+*/,' "' /-"%%,71' *%7$P,' )-,' /"(,' 0:' )-,' ,%-"%/,3,%)
FGHIJ98
9-,' /-"%%,7' +,<)-' "%+' -,%/,' $)(' /0%+*/)$#$);' /"%' 4,' /0%)6077,+' 4;' v*)' $%' ,B"/)7;' )-,
("3,'3"%%,6'"('$%')-,',%-"%/,3,%)5);<,'+,#$/,8'A<<7;$%&'"'<0($)$#,'v*)',%-"%/,(')-,'/-"%5
%,7' 4;' "))6"/)$%&' 306,' ,7,/)60%(' $%)0' $)8' !,6,1' -02,#,61' 2,' "7(0' /"%' "<<7;' "' %,&")$#,' v*)1
2-$/-'/"*(,(',7,/)60%(')0'4,'6,<,77,+':603')-,'/-"%%,71'"%+')-*(')-,'/-"%%,7'4,/03,('(-"75
702,6'"%+'$)('/0%+*/)$#$);'+,/6,"(,(8'9-,'%,&")$#,' v*)'$('("$+')0''&A.&-&')-,'/-"%%,7'0:'$)(
/-"6&,'/"66$,6(1'"%+')-$('30+,'0:'0<,6")$0%'E%,&")$#,' v*)K'$('/"77,+''&A.&-)"*+B"'&8'A(')-,
3"&%$)*+,'0:'v*)'$('$%/6,"(,+'$%')-,'%,&")$#,'+$6,/)$0%1'"'#"7*,'$('6,"/-,+'")'2-$/-')-,'/-"%5
%,7'$('/03<7,),7;'+,<7,),+'0:'/-"6&,'/"66$,6('"%+'+('$('6,+*/,+')0'>,60',#,%')-0*&-'v()'3"; 4,
()$77'"<<7$,+8'9-$('%,&")$#,'#"7*,'0:' v*)'$(')-,')-6,(-07+'#07)"&,'0:')-,'!5/-"%%,7'+,<7,)$0%5
);<,'FGHIJ98
9-,'+,(/6$<)$0%'"40#,'(*&&,()('E/066,/)7;K')-")'"'+,<7,)$0%5);<,'FGHIJ9'/"%'4,'0<,65
"),+' $%' )-,' ,%-"%/,3,%)' 30+,' 4;' "<<7;$%&' "' <0($)$#,' v*)' "%+' $%' )-,' +,<7,)$0%' 30+,' 4;
5.9 The Body Effect and Other Topics
"<<7;$%&'"'%,&")$#,' v*)8'9-$('$('$77*()6"),+'$%'I$&8'W8NC1'2-$/-'(-02('40)-')-,'/$6/*$)'(;3407
:06')-,'+,<7,)$0%'`FGH')6"%($()06'EI$&8'W8NC"K'"%+'$)('+( V v*)'/-"6"/),6$()$/8'G4(,6#,')-")'-,6,
)-,' )-6,(-07+' #07)"&,' 8#!' $(' %,&")$#,8' 9-,' +( V v()' /-"6"/),6$()$/(' E%0)' (-02%K' "6,' ($3$7"6' )0
)-0(,':06')-,',%-"%/,3,%)5);<,'FGHIJ9',B/,<)':06')-,'%,&")$#,'8#!8'I$%"77;1'%0),')-")')-,
+,#$/,'(;3407'+,%0),(')-,',B$()$%&'/-"%%,7'#$"')-,'(-"+,+'"6,"'%,B)')0')-,'#,6)$/"7'7$%,8'
^,<7,)$0%5);<,'FGHIJ9('/"%'4,':"46$/"),+'0%')-,'("3,'=?'/-$<'"(',%-"%/,3,%)5);<,
+,#$/,(1' 6,(*7)$%&' $%' /$6/*$)(' 2$)-' $3<60#,+' /-"6"/),6$()$/(1' "(' 2$77' 4,' (-02%' $%' "' 7"),6
/-"<),68
iD
Depletion
mode
Enhancement
mode
vDS & vGS # Vt
D
iG " 0
iD
IDSS
!
vDS
G
!
vGS
S
#
0
#
vGS
Vt
(a)
(b)
Figure 5.63 9-,' /$6/*$)' (;3407' E(K' "%+' )-,' +(Vv*)' /-"6"/),6$()$/' $%' (")*6")$0%a' E/K' :06' "%' !5/-"%%,7
+,<7,)$0%5);<,'FGHIJ98
EXERCISE
Q
5.43' I06'"'+,<7,)$0%5);<,'`FGH')6"%($()06'2$)-'8#'='−Q'S'"%+' > !′ ( ' ⁄ & ) = Q'3AcS 1':$%+')-,'3$%$3*3
v() 6,O*$6,+')0'0<,6"),'$%')-,'(")*6")$0%'6,&$0%'2-,%'v*)'='+@'S8'U-")'$(')-,'/066,(<0%+$%&'#"7*,
0:'+(g
Ans. C'Sa'['3A
327
328 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Summary
9-,' ,%-"%/,3,%)5);<,' FGHIJ9' $(' /*66,%)7;' )-,' 30()
2$+,7;' *(,+' (,3$/0%+*/)06' +,#$/,8' =)' $(' )-,' 4"($(' 0:
?FGH'),/-%070&;1'2-$/-'$(')-,'30()'<0<*7"6'=?':"46$5
/")$0%'),/-%070&;'")')-$(')$3,8'?FGH'<60#$+,('40)-'!5
/-"%%,7' E`FGHK' "%+' "5/-"%%,7' E_FGHK' )6"%($()06(1
2-$/-'$%/6,"(,('+,($&%':7,B$4$7$);8'9-,'3$%$3*3'FGH5
IJ9'/-"%%,7'7,%&)-'"/-$,#"47,'2$)-'"'&$#,%'?FGH'<605
/,(('$('*(,+')0'/-"6"/),6$>,')-,'<60/,((8'9-$(':$&*6,'-"(
4,,%'/0%)$%*"77;'6,+*/,+'"%+'$('/*66,%)7;'bW'%38
9-,' 0#,6+6$#,' #07)"&,1' v :8 ≡ v *) ' 8 # 1' $(' )-,' P,;
O*"%)$);')-")'&0#,6%(')-,'0<,6")$0%'0:')-,'FGHIJ98'I06
)-,'FGHIJ9')0'0<,6"),'$%')-,'(")*6")$0%'6,&$0%1'2-$/-'$(
)-,'6,&$0%':06'"3<7$:$,6'"<<7$/")$0%1' v () ≥ v :8 1'"%+')-,
Q
@
6,(*7)$%&' + ( ' & 55Q5 µ ! < $% ( 'c& ) v :8 'E:06'`FGHa'6,<7"/,
µ ! '2$)-' µ " ':06'_FGHK8'=:' v () < v :8 1')-,'FGHIJ9
0<,6"),('$%')-,')6$0+,'6,&$0%1'2-$/-')0&,)-,6'2$)-'/*)0::
$('*(,+':06'0<,6")$%&')-,'FGHIJ9'"('"'(2$)/-8
9"47,('W8@'"%+'W8Q'<60#$+,'(*33"6$,('0:')-,'/0%+$)$0%(
"%+' 6,7")$0%(-$<(' )-")' +,(/6$4,' )-,' 0<,6")$0%' 0:' `FGH
"%+'_FGH')6"%($()06(1'6,(<,/)$#,7;8
=%'(")*6")$0%1'+ ( '(-02('(03,'7$%,"6'+,<,%+,%/,'0%'v () '"(
"' 6,(*7)' 0:' )-,' /-"%&,' $%' /-"%%,7' 7,%&)-8' 9-$(' /-"%%,75
7,%&)-' 30+*7")$0%' <-,%03,%0%' 4,/03,(' 306,' <605
%0*%/,+'"('&'+,/6,"(,(8'=)'$('30+,7,+'4;'"(/6$4$%&'"%'0*)5
<*)' 6,($()"%/,' 6 $ ' & 8 G ⁄ ? ( ' )0' )-,' FGHIJ9' 30+,78
A7)-0*&-')-,',::,/)'0:'6 $'0%')-,'0<,6")$0%'0:'+$(/6,),5/$65
/*$)'FGH'"3<7$:$,6('$('(3"771')-")'$('%0)')-,'/"(,'$%'=?
"3<7$:$,6('E?-"<),6'fK8
9-,',((,%/,'0:')-,'*(,'0:')-,'FGHIJ9'"('"%'"3<7$:$,6
$(')-")'$%'(")*6")$0%' v *) '/0%)607(' + ('$%')-,'3"%%,6'0:'"
#07)"&,5/0%)6077,+' /*66,%)' (0*6/,8' U-,%' )-,' +,#$/,' $(
+/'4$"(,+'$%')-,'(")*6")$0%'6,&$0%'"%+')-,'($&%"7' v 71 '$(
P,<)'(3"771')-,'0<,6")$0%'0:')-,'FGHIJ9'4,/03,('"75
30()'7$%,"68
A'(;(),3")$/'<60/,+*6,')0'"%"7;>,'"'FGH'"3<7$:$,6'/$65
/*$)' /0%($()(' 0:' 6,<7"/$%&' )-,' FGHIJ9' 2$)-' 0%,' 0:' $)(
(3"775($&%"71' ,O*$#"7,%)5/$6/*$)' 30+,7(' Ei,:,6' )0' 9"47,
W8CK8'^?'#07)"&,'(0*6/,('"6,'6,<7"/,+'4;'(-06)'/$6/*$)(1
"%+'+/'/*66,%)'(0*6/,('4;'0<,%'/$6/*$)(8'9-,'"%"7;($('$(
)-,%'<,6:063,+'0%')-,'6,(*7)$%&',O*$#"7,%)'/$6/*$)8
=%'/"(,('2-,6,'"'6,($()"%/,'$('/0%%,/),+'$%'(,6$,('2$)-')-,
(0*6/,'7,"+'0:')-,'FGHIJ91')-,'9'30+,7'$(')-,'30()'/0%5
#,%$,%)')0'*(,8
9-,' )-6,,' 4"($/' /0%:$&*6")$0%(' 0:' FGH' "3<7$:$,6(' "6,
(-02%' $%' I$&8' W8bC' E2$)-0*)' )-,' 4$"(' "66"%&,3,%)(K8
9-,$6' /-"6"/),6$()$/' <"6"3,),6' #"7*,(' "6,' <60#$+,+' $%
9"47,'W8b8
9-,' ?H' "3<7$:$,6' -"(' E$+,"77;K' $%:$%$),' $%<*)' 6,($()"%/,
"%+'"'6,"(0%"47;'-$&-'&"$%'4*)'"'6")-,6'-$&-'0*)<*)'6,($(5
)"%/,'"%+'"'7$3$),+'-$&-5:6,O*,%/;'6,(<0%(,8'=)'$('*(,+')0
04)"$%'30()'0:')-,'&"$%'$%'"'/"(/"+,'"3<7$:$,68
A++$%&'"'6,($()"%/,' F 1'$%')-,'(0*6/,'7,"+'0:')-,'?H'"35
<7$:$,6'/"%'7,"+')0'4,%,:$/$"7'6,(*7)(8
9-,'?]'"3<7$:$,6'-"('"'702'$%<*)'6,($()"%/,'"%+')-*('$)
"70%,'-"('7$3$),+'"%+'(<,/$"7$>,+'"<<7$/")$0%(8'!02,#5
,61' $)(' ,B/,77,%)' -$&-5:6,O*,%/;' 6,(<0%(,' 3"P,(' $)' ")5
)6"/)$#,'$%'/034$%")$0%'2$)-')-,'?H'"3<7$:$,6'E?-"<),6(
f'"%+'[K8
9-,' (0*6/,' :07702,6' -"(' E$+,"77;K' $%:$%$),' $%<*)' 6,($(5
)"%/,1'"'#07)"&,'&"$%'702,6')-"%'4*)'/70(,')0'*%$);1'"%+'"
702'0*)<*)'6,($()"%/,8'=)'$(',3<70;,+'"('"'#07)"&,'4*::,6
"%+'"(')-,'0*)<*)'()"&,'0:'"'3*7)$()"&,'"3<7$:$,68
A'P,;'(),<'$%')-,'+,($&%'0:')6"%($()06'"3<7$:$,6('$(')0'4$"(
)-,')6"%($()06')0'0<,6"),'")'"%'"<<60<6$"),'<0$%)'$%')-,'(")5
*6")$0%'6,&$0%8'A'&00+'4$"('+,($&%',%(*6,(')-")')-,'<"6"35
,),6('0:')-,'4$"('<0$%)1'?( 1'8:8 1'"%+'8() 1'"6,'<6,+$/)"47,'"%+
()"47,1'"%+'+0'%0)'#"6;'4;'"'7"6&,'"30*%)'2-,%')-,')6"%5
($()06'$('6,<7"/,+'4;'"%0)-,6'0:')-,'("3,');<,8
A(' ,#$+,%/,+' 4;' )-,' ,B"3<7,' /$6/*$)(' &$#,%' $%' H,/)$0%
W8d1' +$(/6,),5/$6/*$)' FGH' "3<7$:$,6(' *)$7$>,' 7"6&,' /0*5
<7$%&'"%+'4;<"(('/"<"/$)06(8'A('2$77'4,'(,,%'$%'?-"<),6'f1
)-$('$('!$#')-,'/"(,'$%'=?'"3<7$:$,6(8
9-,'+,<7,)$0%5);<,'FGHIJ9'-"('"%'$3<7"%),+'/-"%5
%,7'"%+')-*('/"%'4,'0<,6"),+'$%',$)-,6')-,'+,<7,)$0%'06
,%-"%/,3,%)' 30+,(8' =)' $(' /-"6"/),6$>,+' 4;' )-,' ("3,
,O*")$0%('*(,+':06')-,',%-"%/,3,%)'+,#$/,',B/,<)':06
-"#$%&'"'%,&")$#,'8#'E<0($)$#,'8#':06'+,<7,)$0%'_FGH
)6"%($()06(K8
PROBLEMS
Computer Simulation Problems
!"#$%&'()*+&,-*.*&+)$/)-0*()*1#,)2"&)*,-&,+&+)-#)+&'3
#,(-"2-&)-0&)42%5&)#.)5(*,6)7!89:)(*'5%2-*#,)-#)4&"*./)02,+
2,2%/(*()2,+)+&(*6,;)2,+)-#)*,4&(-*62-&)*'<#"-2,-)*((5&()(510
2()2%%#=2$%&)(*6,2%)(=*,6)2,+)2'<%*.*&"),#,%*,&2")+*(-#"-*#,>
8,(-"51-*#,()-#)2((*(-)*,)(&--*,6)5<)!7<*1&)2,+)?5%-*(*')(*'3
5%2-*#,().#")2%%) -0&) *,+*12-&+)<"#$%&'() 12,)$&).#5,+)*,) -0&
1#""&(<#,+*,6) .*%&() #,) -0&) +*(1>) @#-&) -02-) *.) 2) <2"-*15%2"
<2"2'&-&") 42%5&) *() ,#-) (<&1*.*&+) *,) -0&) <"#$%&') (-2-&'&,-;
/#5)2"&)-#)'2A&)2)"&2(#,2$%&)2((5'<-*#,>
B)+*..*15%-)<"#$%&'C)BB)'#"&)+*..*15%-C)BBB)4&"/)102%%&,6*,6
2,+D#")-*'&31#,(5'*,6C)EF)+&(*6,)<"#$%&'>
Section 5.1: Device Structure and
Physical Operation
5.1 ?G7)-&10,#%#6/)*()5(&+)-#).2$"*12-&)2)12<21*-#";)5-*%*H3
*,6)-0&)62-&)'&-2%%*H2-*#,)2,+)-0&)(5$(-"2-&)2()-0&)12<21*-#"
&%&1-"#+&(>)I*,+)-0&)2"&2)"&J5*"&+)<&")K3<I)12<21*-2,1&).#"
#L*+&)-0*1A,&(()"2,6*,6)."#')M),')-#)KN),'>)I#")2)(J52"&
<%2-&)12<21*-#")#.)KN)<I;)=02-)+*'&,(*#,()2"&),&&+&+O
5.2) 92%15%2-&) -0&) -#-2%) 102"6&) (-#"&+) *,) -0&) 102,,&%) #.) 2,
@?G7)-"2,(*(-#")024*,6) + )* > ^).IDµ'M;)!)P)N>MQ)µ';)2,+
")P)M>Q)µ';)2,+)#<&"2-&+)2-)% -% > N>Q)R)2,+)% '( > N)R>
5.3)S(&)+*'&,(*#,2%)2,2%/(*()-#)(0#=)-02-)-0&)5,*-()#.)-0&)<"#3
1&(() -"2,(1#,+51-2,1&) <2"2'&-&") #′$ ) 2"&) TDRM>) U02-) 2"&) -0&
+*'&,(*#,()#.)-0&)?G7I:V)-"2,(1#,+51-2,1&)<2"2'&-&")#$O
5.4)T,)@?G7)-"2,(*(-#")-02-)*()#<&"2-&+)=*-0)2)('2%%) v '(
*().#5,+)-#)&L0*$*-)2)"&(*(-2,1&) 1 '( >)W/)=02-).21-#")=*%%) 1 '(
102,6&)*,)&210)#.)-0&).#%%#=*,6)(*-52-*#,(O
X2Y)% -% )*()+#5$%&+>
X$Y) V0&) +&4*1&) *() "&<%21&+) =*-0) 2,#-0&") .2$"*12-&+) *,) -0&
(2'&)-&10,#%#6/)$5-)=*-0)+#5$%&)-0&)=*+-0>
X1Y)V0&)+&4*1&)*()"&<%21&+)=*-0)2,#-0&").2$"*12-&+)*,)-0&)(2'&
-&10,#%#6/)$5-)=*-0)$#-0)-0&)=*+-0)2,+)%&,6-0)+#5$%&+>
X+Y) V0&) +&4*1&) *() "&<%21&+) =*-0) 2,#-0&") .2$"*12-&+) *,) 2) '#"&
2+42,1&+)-&10,#%#6/) .#")=0*10) -0&) #L*+&)-0*1A,&(() *()02%4&+
2,+)(*'*%2"%/).#")")2,+)!)X2((5'&)µ$)"&'2*,()5,102,6&+Y>
D 5.5) T,) @?G7) -"2,(*(-#") .2$"*12-&+) *,) 2) -&10,#%#6/) .#"
=0*10) #′$ > [NN )µTDRM)2,+)% & > N>[)R)*()"&J5*"&+)-#)#<&"3
2-&)=*-0)2)('2%%)v '( )2()2)42"*2$%&)"&(*(-#")"2,6*,6)*,)42%5&)."#'
MNN)Ω)-#)K)AΩ>)7<&1*./)-0&)"2,6&)"&J5*"&+).#")-0&)1#,-"#%)4#%-3
26&)% .( )2,+)-0&)"&J5*"&+)-"2,(*(-#")=*+-0)">)8-)*()"&J5*"&+)-#
5(&) -0&) ('2%%&(-) <#((*$%&) +&4*1&;) 2() %*'*-&+) $/) -0&) '*,*'5'
102,,&%)%&,6-0)#.)-0*()-&10,#%#6/)X ! '*, > N>KZ)µ'Y)2,+)-0&
'2L*'5')2%%#=&+)4#%-26&)#.)K>Z)R>
5.6) 7A&-10) 2) (&-) #.) 2 ' ? v '( ) 102"21-&"*(-*1) 15"4&() .#") 2,
@?G7)-"2,(*(-#")#<&"2-*,6)=*-0)2)('2%%) v '()X*,)-0&)'2,,&"
(0#=,) *,) I*6>) Q>[Y>) \&-) -0&) ?G7I:V) 024&) # $ > Q) 'TDRM
2,+) % & > N>Q) R>) 7A&-10) 2,+) 1%&2"%/) %2$&%) -0&) 6"2<0() .#"
% .( > N>Q;)K>N;)K>Q;)M>N;)2,+)M>Q)R>)\&-)% '()$&)*,)-0&)"2,6&)N
-#)QN)'R>)]*4&)-0&)42%5&)#.) 1 '()#$-2*,&+).#")&210)#.)-0&).*4&
42%5&()#.)% .( >)T%-0#560)#,%/)2)(A&-10;)/#5")+*26"2')(0#5%+
$&)+"2=,)-#)(12%&)2()'510)2()<#((*$%&>
D 5.7 T,)$3102,,&%)?G7)+&4*1&)*,)2)-&10,#%#6/).#")=0*10
#L*+&)-0*1A,&(()*()MN),';)'*,*'5')102,,&%)%&,6-0)*()K)µ';
M
# $′ = KNN)µTDR ; ) 2,+) %&) =) N>Z) R) #<&"2-&() *,) -0&) -"*#+&
"&6*#,;) =*-0) ('2%%) v'() 2,+) =*-0) -0&) 62-&−(#5"1&) 4#%-26&) *,
-0&) "2,6&) N) R) -#) +Q) R>) U02-) +&4*1&) =*+-0) *() ,&&+&+) -#
&,(5"&)-02-)-0&)'*,*'5')242*%2$%&)"&(*(-2,1&)*()K)AΩO
5.8) 9#,(*+&") 2,) @?G7) -"2,(*(-#") #<&"2-*,6) *,) -0&) -"*#+&
"&6*#,) =*-0) 2,) #4&"+"*4&) 4#%-26&) % -% >) I*,+) 2,) &L<"&((*#,
.#")-0&)*,1"&'&,-2%)"&(*(-2,1&
∂2 '
3
1 34 ≡ K ⁄ 3333333333
∂ v '(
v '( >% '(
]*4&)-0&)42%5&()#.) 1 34)*,)-&"'()#.) # $)2,+)% -% ).#") % '( > N;
N>Q)% -% ;)N>Z)% -% ;)2,+)% -% >
5.9)T,)@?G7)-"2,(*(-#")=*-0)# $ > K)'TDRM)2,+)% & > K)R
*()#<&"2-&+)=*-0) % .( > M>Q)R>)T-)=02-)42%5&) #.)% '() +#&(
-0&)-"2,(*(-#")&,-&")-0&)(2-5"2-*#,)"&6*#,O)U02-)42%5&)#.) / '
*()#$-2*,&+)*,)(2-5"2-*#,O)
5.10 9#,(*+&")2)9?G7)<"#1&(().#")=0*10)!'*,)=)N>MQ)µ';
&)* =)^),';)µ$)=)[^N)1'MDR⋅ (;)2,+)%&)=)N>Q)R>
X2Y I*,+)+)*)2,+) #′$>
X$Y I#")2,)@?G7)-"2,(*(-#")=*-0)",!)=)KQ)µ'DN>MQ)µ';
12%15%2-&)-0&)42%5&()#.)%-% ;)%.( ;)2,+)%'('*,),&&+&+)-#)#<&"2-&
-0&)-"2,(*(-#")*,)-0&)(2-5"2-*#,)"&6*#,)=*-0)2)+1)15""&,-)/')=)N>Z
'T>
!"# $%&' ()*' +*,-"*' -.' !/#0' 1-.+' ()*' ,234*' %1' %-%' 2.+' %.(
&*54-&*+'(%'"246*'()*'+*,-"*'(%'%7*&2(*'26'2'899:Ω'&*6-6(%&
1%&',*&;'6<233'v'(=
5.11) T) 03102,,&%) ?G7I:V) =*-0) 2) -0"&(0#%+) 4#%-26&
% &0 > ? N>_)R)02()*-()(#5"1&)1#,,&1-&+)-#)6"#5,+>
X2Y)U02-)(0#5%+)-0&)62-&)4#%-26&)$&).#")-0&)+&4*1&)-#)#<&"2-&
=*-0)2,)#4&"+"*4&)4#%-26&)#.) %-% > N>Q )RO)
X$Y)U*-0)-0&)62-&)4#%-26&)2()*,)X$Y;)=02-)*()-0&)0*60&(-)4#%-3
26&)2%%#=&+)2-)-0&)+"2*,)=0*%&)-0&)+&4*1&)#<&"2-&()*,)-0&)(2-3
5"2-*#,)"&6*#,O
X1Y)8.)-0&)+"2*,)15""&,-)#$-2*,&+)*,)X$Y)*()K)'T;)=02-)=#5%+
-0&)15""&,-)$&).#") % ' > ? KN )'R)2,+).#") % ' > ? MRO
5.12 U*-0)-0&)A,#=%&+6&)-02-) µ0)!)N>[µ$;)=02-)'5(-)$&
-0&) "&%2-*4&) =*+-0) #.) $3102,,&%) 2,+) 03102,,&%) +&4*1&() *.
-0&/)2"&)-#)024&)&J52%)+"2*,)15""&,-()=0&,)#<&"2-&+)*,)-0&
(2-5"2-*#,) '#+&) =*-0) #4&"+"*4&) 4#%-26&() #.) -0&) (2'&
'26,*-5+&O
CHAPTER 5
PROBLEMS
330 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Q
5.13 A%' !5/-"%%,7' +,#$/,' -"(' > !′ = WZ'µAcS 1' 8#0 = Z8d' S1
"%+''P&'='QZ8'9-,'+,#$/,'$(')0'0<,6"),'"('"'(2$)/-':06'(3"77
v()1'*)$7$>$%&'"'/0%)607'#07)"&,'v*)'$%')-,'6"%&,'Z'S')0'W'S8
I$%+')-,'(2$)/-'/70(*6,'6,($()"%/,1'6()1'"%+'/70(*6,'#07)"&,1
8()1'04)"$%,+'2-,%'v*)'='W'S'"%+'+('='@'3A8'i,/"77$%&')-")
µ"'"'Z8b µ!1'2-")'3*()''P&'4,':06'"'"5/-"%%,7'+,#$/,')-")
<60#$+,(')-,'("3,'<,6:063"%/,'"(')-,'!5/-"%%,7'+,#$/,'$%
)-$('"<<7$/")$0%g
5.14 ?0%($+,6'"%'!5/-"%%,7'FGHIJ9'2$)-'#$%'='['%31'µ!'=
WZZ'/3QcS⋅ (1'8#'='Z8f'S1'"%+''P&'='@Z8'I$%+')-,'+6"$%'/*65
6,%)'$%')-,':07702$%&'/"(,(D
E"K v*)'='W'S'"%+'v()'='@'S
E4K v*)'='Q'S'"%+'v()'='@8C'S
E/K v*)'='W'S'"%+'v()'='Z8Q'S
E+K v*)'='v()'='W'S
*5.15'9-$('<6047,3'$77*()6"),(')-,'/,%)6"7'<0$%)'$%')-,',7,/5
)60%$/(' 6,#07*)$0%' )-")' -"(' 4,,%' $%' ,::,/)' :06' )-,' <"()' :0*6
+,/"+,(D'L;'/0%)$%*"77;'6,+*/$%&')-,'FGHIJ9'($>,1'2,'"6,
"47,')0'<"/P'306,' +,#$/,('0%' "%' =?' /-$<8' ]06+0%' F006,1'
/05:0*%+,6' 0:' =%),7' ?06<06")$0%1' <6,+$/),+' )-$(' ,B<0%,%)$"7
&602)-'0:'/-$<5<"/P$%&'+,%($);'#,6;',"67;'$%')-,'-$()06;'0:
)-,'+,#,70<3,%)'0:')-,'$%),&6"),+'/$6/*$)'$%')-,':063*7")$0%
)-")'-"('4,/03,'P%02%'"(':""$&I!+.(D8
9-,' )"47,' 4,702' (-02(' :0*6' ),/-%070&;' &,%,6")$0%(1
,"/-' /-"6"/),6$>,+' 4;' )-,' 3$%$3*3' <0(($47,' FGHIJ9
/-"%%,7' 7,%&)-' E602' @K8' =%' &0$%&' :603' 0%,' &,%,6")$0%' )0
"%0)-,61' 40)-'&' "%+' # $% ' "6,' (/"7,+' 4;' )-,' ("3,' :"/)068' 9-,
<02,6'(*<<7;'*)$7$>,+'8 (('$('"7(0'(/"7,+'4;')-,'("3,':"/)061
)0' P,,<' )-,' 3"&%$)*+,(' 0:' "77' ,7,/)6$/"7' :$,7+(' 2$)-$%' )-,
+,#$/,' *%/-"%&,+8' n%:06)*%"),7;1' 4*)' :06' &00+' 6,"(0%(1'8 #
/"%%0)'4,'(/"7,+'($3$7"67;8
?03<7,),')-,' )"47,',%)6$,(1' %0)$%&')-")'602' W' "(P(':06
)-,')6"%(/0%+*/)"%/,'<"6"3,),6'0:'"%'`FGH')6"%($()06'2$)'c&' e' @Za' 602' [' "(P(' :06' )-,' #"7*,' 0:' ? (' 04)"$%,+' 2$)8 *) & 8 () & 8 ((a' 602' @Z' "(P(' :06' )-,' <02,6
J & 8 (( ? ('+$(($<"),+'$%')-,'/$6/*$)8'A%'$3<06)"%)'O*"%)$);
$(')-,'<02,6'+,%($);1'JcG1'"(P,+':06'$%'602'@@8'I$%"77;1';0*
"6,'"(P,+')0':$%+')-,'%*34,6'0:')6"%($()06(')-")'/"%'4,'<7"/,+
0%'"%'=?'/-$<':"46$/"),+'$%',"/-'0:')-,'),/-%070&$,('$%'),63(
0:')-,'%*34,6'04)"$%,+'2$)-')-,'Z8W5µ3'),/-%070&; E!K8
@
&'Eµ3K
Z8W
Q
# $% 'E%3K
@Z
C
< $% 'E:Icµ3QK
b
>′!'EµAcSQK
W
Z8QW
Z8@d
Z8@C
Z8W
Z8b
Z8b
Eµ%'e'WZZ'/3Qc S ⋅ ( K
> ! 'E3AcSQK
:06''c&'e'@Z
N
^,#$/,'"6,"1'G'Eµ3QK
f
8 (( 'ESK
W
d
8 # 'ESK
Z8f
[
? ( 'E3AK
I06' 8 *) & 8 () & 8 ((
@Z
J'E3UK
@@
JcG'E3Uc'µ3QK
@Q
^,#$/,('<,6'/-$<
!
Problems 331
=%')-,':07702$%&'<6047,3(1'2-,%' λ $('%0)'(<,/$:$,+1'"((*3,
$)'$('>,608
5.24 U-,%')-,'+6"$%'"%+'&"),'0:'"'FGHIJ9'"6,'/0%%,/),+
)0&,)-,61' "' )205),63$%"7' +,#$/,' P%02%' "(' "' X+$0+,5/0%%,/),+
)6"%($()06Y'6,(*7)(8'I$&*6,'_W8Qb'(-02('(*/-'+,#$/,('04)"$%,+
:603'FGH')6"%($()06('0:'40)-'<07"6$)$,(8'H-02')-")
E"K )-,'+Vv'6,7")$0%(-$<'$('&$#,%'4;
@ '
Q
+ = 555 >′ 55555 ( v ' 8 # )
Q &
E4K )-,'$%/6,3,%)"7'6,($()"%/,'6':06'"'+,#$/,'4$"(,+')0'0<,65
"),'")' v = 8 # + 8 :8 '$('&$#,%'4;
∂+
'
6 ≡ @'' 555555 = @'' >′ 55555 8 :8
&
∂v
5.17 A%'`FGH')6"%($()06'-"#$%&'8#'='@'S'$('0<,6"),+'$%')-,
)6$0+,'6,&$0%'2$)-'v()'(3"778'U$)-'8*)'='@8W'S1'$)'$(':0*%+')0
-"#,'"'6,($()"%/,'6()'0:'@'PΩ8'U-")'#"7*,'0:'8*)'$('6,O*$6,+')0
04)"$%'6()'='QZZ'Ωg'I$%+')-,'/066,(<0%+$%&'6,($()"%/,'#"7*,(
04)"$%,+'2$)-'"'+,#$/,'-"#$%&')2$/,')-,'#"7*,'0:''8
i
5.18 A' <"6)$/*7"6' ,%-"%/,3,%)' FGHIJ9' :06' 2-$/8# = Z8W''S'"%+' > !′ E'P&K'='Z8@'3AcSQ'$(')0'4,'0<,6"),+'$%')-,
(")*6")$0%'6,&$0%8'=:'+('$(')0'4,'@Q8W'µA1':$%+')-,'6,O*$6,+'v*)
"%+')-,'3$%$3*3'6,O*$6,+'v()8'i,<,")':06'+('='WZ'µA8
5.19 A' <"6)$/*7"6' !5/-"%%,7' ,%-"%/,3,%)' FGHIJ9' $(
3,"(*6,+')0'-"#,'"'+6"$%'/*66,%)'0:'Z8b'3A'")'8*)'='8()'='Q'S
"%+'0:'Z8@'3A'")'8*)'='8()'='@8W'S8'U-")'"6,')-,'#"7*,('0:' > !
"%+'8#':06')-$('+,#$/,g
D 5.20 I06' "' <"6)$/*7"6' =?5:"46$/")$0%' <60/,((1' )-,' )6"%(5
/0%+*/)"%/,'<"6"3,),6' > !′ = bZZ'µAcSQ1'"%+'8# = Z8b S8'=%
"%'"<<7$/")$0%'$%'2-$/-'v*) = v() '='8(*<<7;'='@8d'S1'"'+6"$%'/*65
6,%)' 0:' Q' 3A' $(' 6,O*$6,+' 0:' "' +,#$/,' 0:' 3$%$3*3' 7,%&)-' 0:
Z8@d µ38'U-")'#"7*,'0:'/-"%%,7'2$+)-'3*()')-,'+,($&%'*(,g
5.21 A%'`FGH')6"%($()061'0<,6")$%&'$%')-,'7$%,"656,($()"%/,
6,&$0%' 2$)-' v()' =' Z8@' S1' $(' :0*%+' )0' /0%+*/)' NZ' µA' :06
v*) = Q S' "%+' @NZ' µA' :06' v*)' =' b' S8' U-")' $(' )-,' "<<"6,%)
#"7*,' 0:' )-6,(-07+' #07)"&,' 8#g' =:' > !′ = WZ µAcSQ1' 2-")' $(
)-,' +,#$/,' 'P&' 6")$0g' U-")' /*66,%)' 20*7+' ;0*' ,B<,/)' )0
:702'2$)-'v*) = C'S'"%+'v()'='Z8@W'Sg'=:')-,'+,#$/,'$('0<,65
"),+'")'v*)'='C'S1'")'2-")'#"7*,'0:'v()'2$77')-,'+6"$%',%+'0:
)-,'FGHIJ9'/-"%%,7'.*()'6,"/-'<$%/-50::1'"%+'2-")'$(')-,
/066,(<0%+$%&'+6"$%'/*66,%)g
5.22 I06'"%'`FGH')6"%($()061':06'2-$/-'8#'='Z8W'S1'0<,6")5
$%&'2$)-'v*)'$%')-,'6"%&,'0:'Z8d'S')0'@8d'S1'2-")'$(')-,'7"6&5
,()'#"7*,'0:'v()':06'2-$/-')-,'/-"%%,7'6,3"$%('/0%)$%*0*(g
5.23 A%'`FGH')6"%($()061':"46$/"),+'2$)-'''='@ZZ'µ3'"%+
& = W' µ3' $%' "' ),/-%070&;' :06' 2-$/-' > !′ =' WZ' µAcSQ' "%+
8# = @'S1'$(')0'4,'0<,6"),+'")'#,6;'702'#"7*,('0:'v()'"('"'7$%,"6
6,($()068'I06'v*)'#"6;$%&':603'@8@'S')0'@@'S1'2-")'6"%&,'0:
6,($()06'#"7*,('/"%'4,'04)"$%,+g'U-")'$(')-,'"#"$7"47,'6"%&,'$:
i
!
!
v
v
#
#
(b)
(a)
Figure P5.24
5.25'I06')-,'/$6/*$)'$%'I$&8'_W8QW1'(P,)/-'+ ( '#,6(*('v ) ':06'v )
#"6;$%&':603'Z')0'8 ((8'?7,"67;'7"4,7';0*6'(P,)/-8
VDD
iD
vS
!
#
Figure P5.25
5.26' I06' )-,' /$6/*$)' $%' I$&8' _W8QN1' :$%+' "%' ,B<6,(($0%' :06
v () '$%'),63('0:' + ( 8'HP,)/-'"%+'/7,"67;'7"4,7'"'&6"<-':06' v ()
#,6(*(' + ( 8
PROBLEMS
5.16'H-02')-")'2-,%'/-"%%,757,%&)-'30+*7")$0%'$('%,&7,/),+
E$8,81'λ & ZK1'<70))$%&' + ( ⁄ > !'#,6(*('v () ':06'#"6$0*('#"7*,('0:
v :8 1'"%+'<70))$%&' + ( ⁄ > !'#,6(*(' v :8 ':06' v () ≥ v :8 1'6,(*7)(
$%'*%$#,6("7'6,<6,(,%)")$0%'0:')-,' + ( ' v () '"%+'+ ( ' v *) '/-"65
"/),6$()$/(' 0:' )-,' `FGH' )6"%($()068' 9-")' $(1' )-,' 6,(*7)$%&
&6"<-('"6,'40)-'),/-%070&;'"%+'+,#$/,'$%+,<,%+,%)8'I*6)-,65
306,1')-,(,'&6"<-('"<<7;',O*"77;'2,77')0')-,'_FGH')6"%($()06
4;'"'($3<7,'6,7"4,7$%&'0:'#"6$"47,(8'E!02gK'U-")'$(')-,'(70<,
")' v () & Z'0:',"/-'0:')-,' + ( ⁄ > !'#,6(*(' v () '&6"<-(g'I06')-,
+ ( ⁄ > !'#,6(*('v *)'&6"<-1':$%+')-,'(70<,'")'"'<0$%)'v:8 e 8:8 8
E"K )-,'+,#$/,'2$+)-'$('-"7#,+g
E4K )-,'+,#$/,'7,%&)-'$('-"7#,+g
E/K 40)-')-,'2$+)-'"%+'7,%&)-'"6,'-"7#,+g
CHAPTER 5
Section 5.2: Current–Voltage Characteristics
332 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
CHAPTER 5
PROBLEMS
(0*6/,'4,:06,'(07#$%&')-,'<6047,38'u0*'/"%'+0')-$('4,/"*(,
)-,'FGHIJ9'$('"'(;33,)6$/'+,#$/,8
5.28' 9-,' `FGH' )6"%($()06' $%' I$&8' _W8Qd' -"(' 8 # & Z8b' S
"%+' > !′ ( ' ⁄ & ) & @ 3A ⁄ S Q 8' HP,)/-' "%+' /7,"67;' 7"4,7' + (
#,6(*(' v *' 2$)-' v * ' #"6;$%&' $%' )-,' 6"%&,' Z' )0' k@8d' S8' ]$#,
,O*")$0%(':06')-,'#"6$0*('<06)$0%('0:')-,'6,(*7)$%&'&6"<-8
iD
!
5.29'I$&8'_W8Q['(-02(')20'`FGH')6"%($()06('0<,6")$%&'$%
(")*6")$0%'")',O*"7'8 *)'"%+'8 ()8
vDS
E"K' =:' )-,' )20' +,#$/,(' "6,' 3")/-,+' ,B/,<)' :06' "' 3"B$3*3
<0(($47,' 3$(3")/-' $%' )-,$6' 'c&' 6")$0(' 0:' Qo1' 2-")' $(' )-,
3"B$3*3'6,(*7)$%&'3$(3")/-'$%')-,'+6"$%'/*66,%)(g
#
Figure P5.26
E4K' =:' )-,' )20' +,#$/,(' "6,' 3")/-,+' ,B/,<)' :06' "' 3"B$3*3
<0(($47,'3$(3")/-'$%')-,$6'8 # '#"7*,('0:'@Z'3S1'2-")'$(')-,
3"B$3*3'6,(*7)$%&'3$(3")/-'$%')-,'+6"$%'/*66,%)(g'A((*3,
)-")')-,'%03$%"7'#"7*,'0:'8 # '$('@'S8
!1V
iD
!5V
vG !
#
ID1
Q1
!2V
ID2
Q2
Figure P5.28
*5.27 9-,')"47,'4,702'7$()('@Z'+$::,6,%)'/"(,('7"4,7,+'E"K')0
E.K':06'0<,6")$%&'"%'`FGH')6"%($()06'2$)-'8 # & @'S8'=%',"//"(,' )-,'#07)"&,('")')-,' (0*6/,1' &"),1' "%+' +6"$%' E6,7")$#,')0
)-,'/$6/*$)'&60*%+K'"6,'(<,/$:$,+8'u0*'"6,'6,O*$6,+')0'/035
<7,),')-,')"47,',%)6$,(8'`0),')-")'$:';0*',%/0*%),6'"'/"(,':06
2-$/-' v () '$('%,&")$#,1';0*'(-0*7+',B/-"%&,')-,'+6"$%'"%+
Figure P5.29
5.30 I06'"'<"6)$/*7"6'FGHIJ9'0<,6")$%&'$%')-,'(")*6"5
)$0%' 6,&$0%' ")' "' /0%()"%)' v*) 1' +(' $(' :0*%+' )0' 4,' @' 3A' :06
Voltage (V)
Case
VS
VG
VD
"
k@8Z
k@8Z
kQ8Z
4
k@8Z
kQ8W
kQ8Z
/
k@8Z
kQ8W
k@8W
+
k@8Z
k@8W
Z
,
Z
kQ8W
''' @8Z
:
k@8Z
k@8Z
k@8Z
&
' @8Z
Z
Z
-
' @8W
Z
Z
$
' @8Z
Z
k@8Z
.
kZ8W
kQ8Z
kZ8W
VGS
VOV
VDS
Region of operation
Problems 333
5.31 A'<"6)$/*7"6'FGHIJ9'-"('8G'='WZ'S8'I06'0<,6")$0%'")
Z8@'3A'"%+'@'3A1'2-")'"6,')-,',B<,/),+'0*)<*)'6,($()"%/,(g
=%' ,"/-' /"(,1' :06' "' /-"%&,' $%' v()' 0:' @' S1' 2-")' <,6/,%)"&,
/-"%&,'$%'+6"$%'/*66,%)'20*7+';0*',B<,/)g
D 5.33 I06' "' <"6)$/*7"6' !5/-"%%,7' FGH' ),/-%070&;1' $%
2-$/-')-,'3$%$3*3'/-"%%,7'7,%&)-'$('@'µ31')-,'"((0/$"),+
#"7*,'0:' λ'$('Z8ZQ'S−@8'=:'"'<"6)$/*7"6'+,#$/,':06'2-$/-'&'$(
C µ3' 0<,6"),(' ")' v()' =' @' S' 2$)-' "' +6"$%' /*66,%)' 0:' dZ' µA1
2-")'+0,(')-,'+6"$%'/*66,%)'4,/03,'$:'v()'$('6"$(,+')0'W'Sg
U-")' <,6/,%)"&,' /-"%&,' +0,(' )-$(' 6,<6,(,%)g' U-")' /"%' 4,
+0%,')0'6,+*/,')-,'<,6/,%)"&,'4;'"':"/)06'0:'Qg
5.34 A%' `FGH' )6"%($()06' $(' :"46$/"),+' $%' "' Z8d5µ3' <605
/,(('-"#$%&' > !′ ='@CZ'µAcSQ'"%+' 8 G′ '='QZ'Scµ3'0:'/-"%%,7
7,%&)-8'=:'&'='@8N'µ3'"%+'''='@N'µ31':$%+'8G'"%+'λ8'I$%+')-,
#"7*,'0:'?(')-")'6,(*7)('2-,%')-,'+,#$/,'$('0<,6"),+'2$)-'"%
0#,6+6$#,' #07)"&,' 0:' Z8W' S' "%+' 8()' =' Q' S8' A7(01' :$%+
)-, #"7*,'0:'6$'")')-$('0<,6")$%&'<0$%)8'=:'8()'$('$%/6,"(,+'4;
@ S1'2-")'$(')-,'/066,(<0%+$%&'/-"%&,'$%'?(g
5.35'=:'$%'"%'`FGH')6"%($()061'40)-'''"%+0&'"6,'O*"+6*5
<7,+'"%+'8 :8 '$('-"7#,+1'4;'2-")':"/)06'+0,(' 6 $'/-"%&,g
VS
VG
VD
"
kQ
kQ
Z
4
kQ
k@
Z
/
kQ
Z
Z
+
kQ
Z
k@
,
kQ
Z
k@8W
:
kQ
Z
kQ
VSG
5.37 ?03<7,),')-,'3$(($%&',%)6$,('$%')-,':07702$%&')"47,1
2-$/-' +,(/6$4,(' /-"6"/),6$()$/(' 0:' (*$)"47;' 4$"(,+' `FGH
)6"%($()06(D
MOS
1
λES−@K
8G00ESK
?(00E3AK
6$00EPΩK
@Z
''@
2
Z8Z@
'CZ
3
'''''''
'Z8@
@ZZ
4
+QZZ
@ZZZ
5.38 A%' ,%-"%/,3,%)' _FGH' )6"%($()06' -"( > "′ ( 'c& ) =
Q
dZ'µAcS 1 8#'='−@8W'S1'"%+'λ'='−Z8ZQ'S−@8'9-,'&"),'$('/0%5
%,/),+')0'&60*%+'"%+')-,'(0*6/,')0'+W'S8'I$%+')-,'+6"$%'/*65
6,%)':06'v('='+b'S1'+@8W'S1'Z'S1'"%+'−W'S8
5.39 A'"5/-"%%,7')6"%($()06':06'2-$/-' 8 # = @'S'"%+' 8 G =
WZ' S' 0<,6"),(' $%' (")*6")$0%' 2$)-' v *) = C'S1' v () = ' b' S1
"%+' +(' =' C' 3A8' I$%+' /066,(<0%+$%&' ($&%,+' #"7*,(' :06' v*) 1
v)* 1'v() 1'v)( 1'8# 1'8G1'λ1'"%+' > "′ E'P&K8
5.40'9-,')"47,'4,702'7$()(')-,'),63$%"7'#07)"&,('0:'"'_FGH
)6"%($()06'$%'($B'/"(,(1'7"4,7,+'"1'41'/1'+1',1'"%+':8'9-,')6"%($(5
)06'-"('8 #" & ' @'S8'?03<7,),')-,')"47,',%)6$,(8
|VOV |
VSD
Region of
operation
PROBLEMS
D 5.32 =%'"'<"6)$/*7"6'=?'+,($&%'$%'2-$/-')-,'()"%+"6+'/-"%5
%,7'7,%&)-'$('Q'µ31'"%'`FGH'+,#$/,'2$)-''P&'0:'W'0<,6")5
$%&' ")' @ZZ' µA' $(' :0*%+' )0' -"#,' "%' 0*)<*)' 6,($()"%/,' 0:
Z8W FΩ1'"40*) 55@b5 0:')-")'%,,+,+8'U-")'+$3,%($0%"7'/-"%&,
/"%'4,'3"+,')0'(07#,')-,'<6047,3g'U-")'$(')-,'%,2'+,#$/,
7,%&)-g'9-,'%,2'+,#$/,'2$+)-g'9-,'%,2''P&'6")$0g'U-")'$(
8G':06')-,'()"%+"6+'+,#$/,'$%')-$('=?g'9-,'%,2'+,#$/,g
D 5.36'?0%($+,6')-,'/$6/*$)'$%'I$&8'_W8Q['2$)-'40)-')6"%($()06(
<,6:,/)7;' 3")/-,+' 4*)' 2$)-')-,' +/'#07)"&,' ")')-,'+6"$%'0:' ; @
702,6,+')0' kQ'S8'=:')-,')20'+6"$%'/*66,%)('"6,')0'4,'3")/-,+
2$)-$%'@o'E$8,81')-,'3"B$3*3'+$::,6,%/,'"7702,+'4,)2,,%')-,
)20' /*66,%)(' $(' @oK1' 2-")' $(' )-,' 3$%$3*3' 6,O*$6,+' #"7*,' 0:
8 Gg' =:' )-,' ),/-%070&;' $(' (<,/$:$,+' )0' -"#,' 8′G & @ZZ' Scµ31
2-")'$(')-,'3$%$3*3'/-"%%,7'7,%&)-')-,'+,($&%,6'3*()'*(,g
CHAPTER 5
v() = @'S'"%+'@8ZW'3A':06'v()'='Q'S8'U-")'#"7*,('0:'6$1
8G1'"%+'λ'/066,(<0%+g
CHAPTER 5
PROBLEMS
334 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.41'9-,'_FGH')6"%($()06'$%'I$&8'_W8b@'-"('8 #" & ' Z8W'S8
A(' )-,' &"),' #07)"&,' v *' $(' #"6$,+' :603' kQ8W' S' )0' Z' S1' )-,
)6"%($()06' 30#,(' )-60*&-' "77' 0:' $)(' )-6,,' <0(($47,' 30+,(' 0:
0<,6")$0%8' H<,/$:;' )-,' #"7*,' 0:' v *' ")' 2-$/-' )-,' +,#$/,
/-"%&,('30+,('0:'0<,6")$0%8
<60<,67;1' 2-")' $(' )-,' 7"6&,()' 6,($()06' )-")' /"%' 4,' <7"/,+' $%
(,6$,('2$)-',"/-'FGHIJ9'(0*6/,'2-$7,',%(*6$%&'(")*6"),+5
30+,'0<,6")$0%'0:',"/-')6"%($()06'")'?('='?g'=%')-,'7")),6'7$35
$)$%&'($)*")$0%1'2-")'+0'8@1'8Q1'8C1'"%+'8b'4,/03,g
!1 V
!2.5 V
!2.5 V
!1 V
Q2
I
vG !
#
!1 V
*5.42 E"K n($%&' )-,' ,B<6,(($0%' :06' +(' $%' (")*6")$0%' "%+
%,&7,/)$%&' )-,' /-"%%,757,%&)-' 30+*7")$0%' ,::,/)' E$8,81' 7,)
λ = ZK1'+,6$#,'"%',B<6,(($0%':06')-,'<,6'*%$)'/-"%&,'$%'+('<,6
°?'' [ ( ∂ + ( ⁄ + ( ) ⁄ ∂ 9 ] $%'),63('0:')-,'<,6'*%$)'/-"%&,'$%' > !′ <,6
°?' [ ( ∂ > !′ / > !′ )P ∂ 9 ]1')-,'),3<,6")*6,'/0,::$/$,%)'0:'8#'$%'Sc°?
( ∂ 8 # ⁄ ∂ 9 )1 '"%+'8*)'"%+'8# 8
E4K =:'8#'+,/6,"(,('4;'Q'3S':06',#,6;'°?'6$(,'$%'),3<,6")*6,1
:$%+' )-,' ),3<,6")*6,' /0,::$/$,%)' 0:' > !′ ' )-")' 6,(*7)(' $%' +(
+,/6,"($%&'4;'Z8Qoc°?'2-,%')-,'`FGH')6"%($()06'2$)-'8#'e'@
S'$('0<,6"),+'")'8*)'='W'S8
#1.5 V
(a)
'''0
'''2
!1.25 V
Q4
I
V4
V3
I
Q3
*5.44 A77')-,')6"%($()06('$%')-,'/$6/*$)('(-02%'$%'I$&8'_W8bb
-"#,')-,'("3,'#"7*,('0:' 8 # 1 ' >′10'P&1'"%+'λ8'F06,0#,61'λ''$(
%,&7$&$47;' (3"778' A77' 0<,6"),' $%' (")*6")$0%' ")' ?(' =' ?' "%+
8 *) = 8 () = @'S8'I$%+')-,'#07)"&,('8@1'8Q1'8C1'"%+'8b8'=:
8 # = Z8W'S' "%+' ?' =' Z8@' 3A1' -02' 7"6&,' "' 6,($()06' /"%' 4,
$%(,6),+' $%' (,6$,(' 2$)-' ,"/-' +6"$%' /0%%,/)$0%' 2-$7,' 3"$%5
)"$%$%&' (")*6")$0%g' U-")' $(' )-,' 7"6&,()' 6,($()06' )-")' /"%' 4,
<7"/,+' $%' (,6$,(' 2$)-' ,"/-' &"),g' =:' )-,' /*66,%)' (0*6/,' ?
6,O*$6,(' ")' 7,"()' Z8W' S' 4,)2,,%' $)(' ),63$%"7(' )0' 0<,6"),
'''/
(b)
!2.5 V
*5.43 S"6$0*('`FGH'"%+'_FGH')6"%($()06(1'%*34,6,+'@
)0'b1'"6,'3,"(*6,+'$%'0<,6")$0%1'"('(-02%'$%')-,')"47,'")')-,
40))03' 0:' )-,' <"&,8' I06' ,"/-' )6"%($()061' :$%+' )-,' #"7*,' 0:
µ<$%'P&'"%+'8#')-")'"<<7;'"%+'/03<7,),')-,')"47,1'2$)-'8'$%
#07)(1'?'$%'µA1'"%+'µ<$%'P&'$%'µAcSQ8
'''*
I
Q1
Figure P5.41
Case
V2
V1
#1.25 V
(c)
(d)
Figure P5.44
Transistor
VS
VG
VD
ID
))) $
)))$
))),
))),
))))))))).
))).
)))+
)))+
)))"
)))"
)))"
)))"
−,
−.
,
,
,
+
+
)))))"
)))))"
−.#"
−+#"
))))).
)))))+
)))))+
)))−-
$++
.++
))"+
."+
,++
1++
))3,
,3+
Type
Mode
µ CoxW/L
Vt
Problems 335
2.5 V
I$#/D'=:'λ'$('%0)'(<,/$:$,+1'"((*3,'$)'$('>,608
D 5.46'I06')-,'/$6/*$)'$%'I$&8'JW8@Z1'"((*3,')-")' ; @'"%+' ; Q
"6,' 3")/-,+' ,B/,<)' :06' -"#$%&' +$::,6,%)' 2$+)-(1' ' @' "%+' ' Q8
T,)' 8 # & Z8W ' S1' >′! & Z8b' 3AcSQ1' & @ & & Q & Z8CN ' µ31
' @ & @8d'µ31'"%+' λ & Z8
E"K'I$%+')-,'#"7*,'0:'F'6,O*$6,+')0',()"47$(-'"'/*66,%)'0:'[Z'µA
$%'; @8
E4K'I$%+'' Q'"%+' F Q'(0')-")' ; Q'0<,6"),('")')-,',+&,'0:'(")*6"5
)$0%'2$)-'"'/*66,%)'0:'Z8['3A8
PROBLEMS
D 5.45 ^,($&%')-,'/$6/*$)'0:'I$&8'W8Q@')0',()"47$(-'"'+6"$%
/*66,%)' 0:' Z8QW' 3A' "%+' "' +6"$%' #07)"&,' 0:' Z' S8' 9-,
FGHIJ9'-"(' 8#' ='@' S1' µ!<$%' =' NZ'µAcSQ1'&' ='C' µ31' "%+
' = @ZZ'µ38
Figure P5.49
8
!2.5 V
5.47' 9-,' )6"%($()06' $%' )-,' /$6/*$)' 0:' I$&8' _W8bf' -"(
> !′ & Z8b'3AcSQ1' 8 # & Z8W'S1'"%+'λ & Z8'H-02')-")'0<,65
")$0%'")')-,',+&,'0:'(")*6")$0%'$('04)"$%,+'2-,%')-,':077025
$%&'/0%+$)$0%'$('(")$(:$,+D
0.25 mA
!1.8 V
'
55555 & F ( & @8W'PΩ
!1.0 V
!1.8 V
RD
Figure P5.50
D 5.51 9-,' `FGH' )6"%($()06(' $%' )-,' /$6/*$)' 0:' I$&8' _W8W@
-"#,'8#'='@'S1' µ!<$%'='@QZ'µAcSQ1' λ'='Z1'"%+'&@'='&Q'='&C'=
@ µ38'I$%+')-,'6,O*$6,+'#"7*,('0:'&"),'2$+)-':06',"/-'0:';@1
;Q1 "%+' ;C' )0' 04)"$%' )-,' #07)"&,' "%+' /*66,%)' #"7*,(
$%+$/"),+8
Figure P5.47
!5 V
5.48'=)'$('6,O*$6,+')0'0<,6"),')-,')6"%($()06'$%')-,'/$6/*$)'0:
I$&8' _W8bf' ")' )-,' ,+&,' 0:' (")*6")$0%' 2$)-' ? ( & @' 3A8' =:
8 # & Z8W'S1':$%+')-,'6,O*$6,+'#"7*,'0:' F (8
120 "A
!3.5 V
D 5.49 9-,' _FGH' )6"%($()06' $%' )-,' /$6/*$)' 0:' I$&8' _W8b[
-"('8#'='−Z8N'S1'µ"<$%'='@ZZ'µAcSQ1'&'='Z8QW'µ31'"%+'λ'='Z8
I$%+')-,'#"7*,('6,O*$6,+':06'''"%+'F'$%'06+,6')0',()"47$(-'"
+6"$%'/*66,%)'0:'Z8d'3A'"%+'"'#07)"&,'8('0:'@8W'S8
D 5.50 9-,'`FGH')6"%($()06('$%')-,'/$6/*$)'0:'I$&8'_W8WZ
-"#,'8#'='Z8W'S1' µ!<$%'='QWZ'µAcSQ1' λ'='Z1'"%+'&@'='&Q'=
Z8QW'µ38'I$%+')-,'6,O*$6,+'#"7*,('0:'&"),'2$+)-':06',"/-'0:
;@' "%+' ;Q1' "%+' )-,' #"7*,' 0:' F1' )0' 04)"$%' )-,' #07)"&,' "%+
/*66,%)'#"7*,('$%+$/"),+8
!1.5 V
Figure P5.51
CHAPTER 5
Section 5.3: MOSFET Circuits at DC
CHAPTER 5
PROBLEMS
336 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
5.52 ?0%($+,6')-,'/$6/*$)'0:'I$&8'W8QbE"K8'=%'JB"3<7,'W8W
$)'2"(':0*%+')-")'2-,%'8#'='@'S'"%+' > !′ E'P&K'='@'3AcSQ1
)-,'+6"$%'/*66,%)'$('Z8W'3A'"%+')-,'+6"$%'#07)"&,'$('+f'S8'=:
)-,')6"%($()06'$('6,<7"/,+'2$)-'"%0)-,6'-"#$%&'8#'='Q'S'"%+
> !′ E'P&K' =' Q 3AcSQ1' :$%+' )-,' %,2' #"7*,(' 0:' ?(' "%+' 8(8
?033,%)' 0%' -02' )07,6"%)' E06' $%)07,6"%)K' )-,' /$6/*$)' $(' )0
/-"%&,('$%'+,#$/,'<"6"3,),6(8
!10 V
4 k$
!10 V
V2
D 5.53 n($%&' "%' ,%-"%/,3,%)5);<,' _FGH' )6"%($()06' 2$)8# = −@8W'S1' > "′ E'P&K'='@'3AcSQ1'"%+'λ'='Z1'+,($&%'"'/$6/*$)
)-")' 6,(,347,(' )-")' $%' I$&8' W8QbE"K8' n($%&' "' @Z5S' (*<<7;1
+,($&%':06'"'&"),'#07)"&,'0:'+N'S1'"'+6"$%'/*66,%)'0:'Z8W'3A1
"%+'"'+6"$%'#07)"&,'0:'+W'S8'I$%+')-,'#"7*,('0:'F)'"%+'F(8
1 mA
V1
5.54 9-,' FGHIJ9' $%' I$&8' _W8Wb' -"(' 8#' =' Z8W' S1' > !′ =
bZZ µAcSQ1'"%+' λ'='Z8'I$%+')-,'6,O*$6,+'#"7*,('0:''P&'"%+
0:'F'(0')-")'2-,%' v?'='8((' ='+@8d'S1'6()'='WZ'Ω1'"%+' v:'=
WZ 3S8
V3
2 mA
#10 V
VDD
(b)
(a)
!10 V
!10 V
R
2 mA
vO
vI
V4
V6
Figure P5.54
V5
V7
2.5 k$
2 mA
5.55 =%' )-,' /$6/*$)(' (-02%' $%' I$&8' _W8WW1' )6"%($()06(' "6,
/-"6"/),6$>,+'4;' 8 # ='Q'S1' >′'c&'='@'3AcSQ1'"%+'λ'='Z8
E"K I$%+')-,'7"4,7,+'#07)"&,('8@')-60*&-'8f8
E4K =%',"/-'0:')-,'/$6/*$)(1'6,<7"/,')-,'/*66,%)'(0*6/,'2$)-'"
6,($()068'H,7,/)')-,'6,($()06'#"7*,')0';$,7+'"'/*66,%)'"('/70(,')0
)-")'0:')-,'/*66,%)'(0*6/,'"('<0(($47,1'2-$7,'*($%&'6,($()06(
(<,/$:$,+'$%')-,'@o')"47,'<60#$+,+'$%'A<<,%+$B']8'I$%+')-,
%,2'#"7*,('0:'8@')0'8f8
5.56 I06',"/-'0:')-,'/$6/*$)('$%'I$&8'_W8WN1':$%+')-,'7"4,7,+
%0+,' #07)"&,(8' I06' "77' )6"%($()06(1' > !′ E'P&K' =' Z8W' 3AcSQ1
8# = Z8d'S1'"%+'λ'='Z8
#10 V
(c)
Figure P5.55
(d)
Problems 337
5.57 I06',"/-'0:')-,'/$6/*$)('(-02%'$%'I$&8'_W8Wf1':$%+')-,
7"4,7,+'%0+,'#07)"&,(8'9-,'`FGH')6"%($()06('-"#,'8#'='@'S
"%+' > !′ 'P&'='W'3AcSQ8
!5 V
V2
10 "A
100 "A
(a)
!5 V
!2.5 V
!5 V
1 k$
V3
Q1
(b)
Q1
V1
!5 V
V4
Q2
10 "A
V3
Q2
V2
V5
V4
1 k$
1 k$
1 mA
#2.5 V
Figure P5.57
!5 V
1 mA
(b)
(a)
(d)
(c)
*5.58 I06' )-,' _FGH' )6"%($()06' $%' )-,' /$6/*$)' (-02%' $%
Q
I$&8' _W8Wd1' > "′ = d'µAcS 1 'c&' =' QW1' "%+' 8 #" = @'S8
I06'? ='@ZZ'µA1':$%+')-,'#07)"&,('8)('"%+'8)*':06' F'='Z1
@Z PΩ1'CZ PΩ1'"%+'@ZZ'PΩ8'I06'2-")'#"7*,'0:'i'$('8)('=
8)*g'8)('='8)* c Qg'8)('='8)* c@Zg'
100 k$
V6
V5
!10 V
!
VSG
(f)
(e)
#
!5 V
!5 V
!
VSD
#
R
1 k$
V8
V7
100 k$
I
#5 V
(g)
Figure P5.56
(h)
Figure P5.58
PROBLEMS
V1
CHAPTER 5
!5 V
5.59 I06' )-,' /$6/*$)(' $%' I$&8' _W8W[1' µ!<$%' =' Q8W' µ"<$%' =
QZ µAcSQ1' 8 # = @'S1 ' λ'='Z1''&'='@Z'µ31'"%+'''='CZ µ31
*%7,((' 0)-,62$(,' (<,/$:$,+8' I$%+' )-,' 7"4,7,+' /*66,%)(' "%+
#07)"&,(8
!3 V
!5 V
!3 V
Q4
Q2
I2
V2
CHAPTER 5
PROBLEMS
338 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
I1
Q3
I3
Q1
V4
V2
Figure P5.60
!5 V
(a)
(b)
!3 V
40 k$
40 k$
V2
V1
W
Q1
Q2
I6
V5
V3
200 "A
(c)
Figure P5.59
*5.60 I06' )-,' +,#$/,(' $%' )-,' /$6/*$)(' 0:' I$&8' _W8NZ1
8 # = ' @ S1' λ' =' Z1' µ!<$%' =' WZ' µAcSQ1' &' =' @' µ31' "%+' '' =
@Z µ38'I$%+'8Q'"%+'?Q8'!02'+0')-,(,'#"7*,('/-"%&,'$:';C'"%+
;b'"6,'3"+,')0'-"#,'''='@ZZ'µ3g
5.61 =%')-,'/$6/*$)'0:'I$&8'_W8N@1')6"%($()06(';@'"%+';Q'-"#,'8# =
@' S1' "%+' )-,' <60/,((' )6"%(/0%+*/)"%/,' <"6"3,),6' > !′ =
Q
@ZZ'µAcS 8 'I$%+'8@1'8Q1'"%+'8C':06',"/-'0:')-,':07702$%&'/"(,(D
E"K ( 'c& ) @ = ( 'c& ) Q = QZ
E4K ( 'c& ) @ = @8W ( 'c& ) Q = QZ
Section 5.4: Applying the MOSFET in
Amplifier Design
5.62' ?0%($+,6' )-,' "3<7$:$,6' 0:' I$&8' W8QfE"K' 2$)-
8 (( & Q8W' S' "%+' 2$)-' )-,' FGHIJ9' -"#$%&' 8 # & Z8W' S1
>′! & Z8QW '3AcSQ'"%+''c&'e'bZ8
Figure P5.61
E"K'I$%+')-,'#"7*,'0:' F ( ')-")'2$77'6,(*7)'$%')-,'(,&3,%)'AL
0:')-,'S9?',B),%+$%&'0#,6')-,'6"%&,'v () & Z8W')0'Q8W'S8'
E4K'U-")'"6,')-,'/066,(<0%+$%&'#"7*,('0:'v *) g
E/K'I$%+' v () l < '2-$/-'/066,(<0%+(')0' v *) & 8 (( 8'U-")'$(
)-,'FGHIJ9m('6,($()"%/,' 6 ()'")'0<,6")$%&'<0$%)'?g
E+K'=:')-,'"3<7$:$,6'$('4$"(,+')0'0<,6"),'")'8 *) & Z8d'S1':$%+
8 ()'"%+')-,'#07)"&,'&"$%8
5.63'I06')-,'"3<7$:$,6'0:'I$&8'W8Q[E"K':$%+'"%',B<6,(($0%':06
)-,'4$"('#07)"&,'8 *)'")'2-$/-')-,'3"&%$)*+,'0:'#07)"&,'&"$%
$('")'$)('7"6&,()'#"7*,8'U-")'$(')-,'#"7*,'0:')-,'&"$%g'U-")'$(
)-,' 3"B$3*3' "7702"47,' ($&%"7' (2$%&' ")' )-$(' 4$"(' <0$%)g
?033,%)'0%')-,'<6"/)$/"7'(*$)"4$7$);'0:')-$('4$"('<0$%)8
5.64 ?0%($+,6' )-,' "3<7$:$,6' 0:' I$&8' W8Q[E"K' :06' )-,' /"(,
8(('='W'S1'F('='Qb'PΩ1' > !′ E'P&K'='@'3AcSQ1'"%+'8#'='@'S8
E"K I$%+')-,'/006+$%"),('0:')-,')20',%+'<0$%)('0:')-,'(")*6"5
)$0%56,&$0%'(,&3,%)'0:')-,'"3<7$:$,6')6"%(:,6'/-"6"/),6$()$/1
)-")'$(1'<0$%)('A'"%+'L'0%')-,'(P,)/-'0:'I$&8'W8Q[E4K8
Problems 339
*D 5.66 S)%)/&'2&'()&)T,/)00.24&%2/&'()&.4</)+)4'*-&52-'I
*6)&6*.4&.4&EH8&!98UV#8&:*/.2?0&1)0.64&<240.1)/*'.240&,-*<)&*
-23)/& -.+.'& 24& '()& 5*-?)& 2%& '()& 25)/1/.5)& 52-'*6)& !"! 8& @2/
2?/& ,?/,20)0& ()/);& -)'& '(.0& -23)/& -.+.'& ")& 78N& :8& >-02;
*00?+)&'(*'&!$$&=&9&:8
!*# K.'(2?'& *--23.46& *4A& /22+& %2/& 2?',?'& 52-'*6)& 03.46;
3(*'&.0&'()&+*T.+?+&52-'*6)&6*.4&*<(.)5*"-)J
!"# $%&3)&*/)&/)H?./)1&'2&*--23&%2/&*4&2?',?'&52-'*6)&03.46
2%&±789&:;&3(*'&1<&".*0&52-'*6)&0(2?-1&")&)0'*"-.0()1&*'&'()
1/*.4&'2&2"'*.4&+*T.+?+&6*.4J&K(*'&6*.4&5*-?)&.0&*<(.)5I
*"-)J&K(*'&.4,?'&0.64*-&/)0?-'0&.4&*&±789I:&2?',?'&03.46J
!<# @2/& '()& 0.'?*'.24& .4& !"#;& %.41& ()*& 2%& '()& '/*40.0'2/& '2
)0'*"-.0(&*&1<&1/*.4&<?//)4'&2%&P77&µ>8&@2/&'()&6.5)4&,/2<)00
')<(42-26A;& / 0′ =&P77&µ>R:N8
!1# @.41&'()&/)H?./)1&5*-?)&2%&&$8
@2/&!$$&=&9&:&*41&!"!&=&789&:;&,/25.1)&*&'*"-)&2%&5*-?)0&%2/
%v ;& v[ 1;&*41&'()&<2//)0,241.46& v[ . &%2/&!$+&=&P&:;&P89&:;&N&:;
*41&N89&:8&$%& / 0′ ()*&=&P&+>R:N;&%.41&#$&*41&&$&%2/&'()&1)0.64
%2/&3(.<(&!$+&=&P&:8
*5.68 @.6?/)& W98XV& 0(230& *4& *+,-.%.)/& .4& 3(.<(& '()& -2*1
/)0.0'2/&&$&(*0&"))4&/),-*<)1&3.'(&*42'()/&MBCD&'/*40.0'2/
,N&<244)<')1&*0&*&'32I')/+.4*-&1)5.<)8&M2')&'(*'&")<*?0)&v$2%& ,N& .0& Y)/2;& .'& 3.--& ")& 2,)/*'.46& .4& 0*'?/*'.24& *'& *--& '.+)0;
)5)4&3()4&v#&=&7&*41&.$N&=&.$P&=&78&M2')&*-02&'(*'&'()&'32&'/*4I
0.0'2/0&<241?<'&)H?*-&1/*.4&<?//)4'08&Z0.46&.$P&=&.$N;&0(23&'(*'
%2/& '()& /*46)& 2%& v#&25)/& 3(.<(& ,P& .0&2,)/*'.46& .4&0*'?/*'.24;
'(*'&.0;&%2/
! 'P ≤ v # ≤ v " + ! 'P
'()&2?',?'&52-'*6)&3.--&")&6.5)4&"A
v " = ! $$ ! ! ' +
( ( ⁄ * )P
(( ⁄ *)
IIIIIIIIIIIIIIIIIII&! ! IIIIIIIIIIIIIIIIIIPI v #
( ( ⁄ * )N '
( ( ⁄ * )N
3()/)&3)&(*5)&*00?+)1&!'P&=&!'N&=&!' 8&F(?0&'()&<./<?.'&%?4<I
'.240& *0& *& -.4)*/& *+,-.%.)/;& )5)4& %2/& -*/6)& .4,?'& 0.64*-08& @2/
( ( ⁄ * )P&=&!97&µ+ ⁄ 789&µ+#&*41&( ( ⁄ * ) N&=&!9&µ+ ⁄ 789&µ+#;
%.41&'()&52-'*6)&6*.48
VDD
iD2
Q2
5.67 F()& )T,/)00.24& %2/& '()& .4</)+)4'*-& 52-'*6)& 6*.4& %v
6.5)4&.4&EH8&!98UV#&<*4&")&3/.'')4&.4&*0
vO
iD1
N ( ! $$ ! ! $+ )
I
% v = ! IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
! "!
3()/)&!$+&.0&'()&".*0&52-'*6)&*'&'()&1/*.48&&F(.0&)T,/)00.24
.41.<*')0&'(*'&%2/&6.5)4&5*-?)0&2%&!$$&*41&!"! ;&'()&6*.4&+*6I
4.'?1)&<*4&")&.4</)*0)1&"A&".*0.46&'()&'/*40.0'2/&*'&*&-23)/
!$+ 8& F(.0;& (23)5)/;& /)1?<)0& '()& *--23*"-)& 2?',?'& 0.64*-
P
%v
v[ 1 = ( ! $+ ! ! "! )&& P + IIIIIIII vI
Figure P5.68
Q1
PROBLEMS
5.65 :*/.2?0&+)*0?/)+)4'0&*/)&+*1)&24&*4&MBCD&*+,-.I
%.)/&%2/&3(.<(&'()&1/*.4&/)0.0'2/& &$&.0&N7&OΩ8&@./0';&1<&+)*I
0?/)+)4'0&0(23&'()&52-'*6)&*</200&'()&1/*.4&/)0.0'2/;&!&$ ;&'2
")& P89 :& *41& '()& 6*')I'2I02?/<)& ".*0& 52-'*6)& '2& ")& 78Q& :8
F()4;&*<&+)*0?/)+)4'0&3.'(&0+*--&0.64*-0&0(23&'()&52-'*6)
6*.4&'2&")&−P7&:R:8&K(*'&.0&'()&5*-?)&2%&!'&%2/&'(.0&'/*40.0'2/J
$%& '()& ,/2<)00& '/*40<241?<'*4<)& ,*/*+)')/& / 0′ .0& N77& µ>R:N;
3(*'&.0&'()&BCD@EFG0&()*J
03.46&.4&'()&4)6*'.5)&1./)<'.248&>00?+.46&-.4)*/&2,)/*'.24
*/2?41&'()&".*0&,2.4';&0(23&'(*'&'()&-*/6)0'&,200."-)&4)6*'.5)
2?',?'&0.64*-&,)*O v[ 1 '(*'&.0&*<(.)5*"-)&3(.-)&'()&'/*40.0'2/
/)+*.40&0*'?/*')1&.0
CHAPTER 5
!"# $%& '()& *+,-.%.)/& .0& ".*0)1& '2& 2,)/*')& 3.'(& *4& 25)/1/.5)
52-'*6)&!"!&2%&789&:;&%.41&'()&<22/1.4*')0&2%&'()&".*0&,2.4'&=
24&'()&'/*40%)/&<(*/*<')/.0'.<8&>-02;&%.41&'()&5*-?)&2%&#$&*41
2%&'()&.4</)+)4'*-&6*.4&%v&*'&'()&".*0&,2.4'8
!<# @2/&'()&0.'?*'.24&.4&!"#;&*41&1.0/)6*/1.46&'()&1.0'2/'.24
<*?0)1&"A&'()&BCD@EFG0&0H?*/)I-*3&<(*/*<')/.0'.<;&3(*'&.0
'()&-*/6)0'&*+,-.'?1)&2%&*&0.4)I3*5)&52-'*6)&0.64*-&'(*'&<*4
")&*,,-.)1&*'&'()&.4,?'&3(.-)&'()&'/*40.0'2/&/)+*.40&.4&0*'?/*I
'.24J&K(*'&.0&'()&*+,-.'?1)&2%&'()&2?',?'&52-'*6)&0.64*-&'(*'
/)0?-'0J& K(*'& 6*.4& 5*-?)& 12)0& '()& <2+".4*'.24& 2%& '()0)
*+,-.'?1)0&.+,-AJ&LA&3(*'&,)/<)4'*6)&.0&'(.0&6*.4&5*-?)&1.%I
%)/)4'& %/2+& '()& .4</)+)4'*-& 6*.4& 5*-?)& <*-<?-*')1& *"25)J
K(A&.0&'()/)&*&1.%%)/)4<)J
CHAPTER 5
PROBLEMS
340 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Section 5.5: Small-Signal Operation and
Models
2-")'7@'$('6,O*$6,+g'n($%&'"'+/'(*<<7;'0:'@8d'S1'2-")'#"7*,('0:
?(' "%+' 8:8' 20*7+' ;0*' /-00(,g' U-")' 'P&' 6")$0' $(' 6,O*$6,+' $:
µ!<$%'='QZZ'µAcSQg'=:'8#'='Z8b'S1':$%+'8*)8
*5.69 9-$(' <6047,3' $%#,()$&"),(' )-,' %0%7$%,"6' +$()06)$0%
$%)60+*/,+'4;'"'FGHIJ9'"3<7$:$,68'T,)')-,'($&%"7'v71'4,'"'($%,
2"#,'2$)-'"3<7$)*+,'8711'"%+'(*4()$)*),'v71'='871'($%'ω #'$%'JO8
EW8bCK8' n($%&')-,')6$&0%03,)6$/'$+,%)$);' ($% Q θ = 55@Q5 ' 55@Q5 /0( Q θ 1
(-02' )-")' )-,' 6")$0' 0:' )-,' ($&%"7' ")' :6,O*,%/;' Qω' )0' )-")
") :6,O*,%/;' ω 1' ,B<6,((,+' "(' "' <,6/,%)"&,' EP%02%' "(' )-,
(,/0%+5-"630%$/'+$()06)$0%K'$(
@ 8 715
'H,/0%+5-"630%$/'+$()06)$0% = 555 55555555
× @ZZ
b 8 :8
=:' $%' "' <"6)$/*7"6' "<<7$/")$0%' 871' $(' @Z' 3S1' :$%+' )-,' 3$%$5
3*3' 0#,6+6$#,' #07)"&,' ")' 2-$/-' )-,' )6"%($()06' (-0*7+' 4,
0<,6"),+'(0')-")')-,'(,/0%+5-"630%$/'+$()06)$0%'$('P,<)')0
7,((')-"%'@o8
D *5.73 =%')-$('<6047,3'2,'$%#,()$&"),'"%'0<)$3*3'+,($&%
0:')-,'?H'"3<7$:$,6'/$6/*$)'0:'I$&8'W8Cb8'I$6()1'*(,')-,'#07)"&,
&"$%' ,B<6,(($0%' G v = ' 7 @ F ( ' )0&,)-,6' 2$)-' JO8' EW8WfK' :06
7@')0'(-02')-")
Q? ( F (
Q ( 8 (( ' 8 ( )
G v = ' 55555555555555
5 = ' 555555555555555555555555555555
5
8 :8
8 :8
`,B)1'7,)')-,'3"B$3*3'<0($)$#,'$%<*)'($&%"7'4,' vt + 8'90'P,,<
)-,' (,/0%+5-"630%$/' +$()06)$0%' )0' "%' "//,<)"47,' 7,#,71' 2,
4$"(')-,'FGHIJ9')0'0<,6"),'")'"%'0#,6+6$#,'#07)"&,'8:8' /
vt+ 8'T,)'8 :8 = @ vt 8'`021')0'3"B$3$>,')-,'#07)"&,'&"$%' G v 1
+
2,' +,($&%' :06' )-,' 702,()' <0(($47,' 8(8' H-02' )-")' )-,' 3$%$5
3*3' 8(' )-")' $(' /0%($(),%)' 2$)-' "7702$%&' "' %,&")$#,' ($&%"7
#07)"&,'(2$%&'")')-,'+6"$%'0:' G v vt+ '2-$7,'3"$%)"$%$%&'(")*6"5
)$0%530+,'0<,6")$0%'$('&$#,%'4;
8 :8 + vt + + Q8 (( ( vt+ ⁄ 8 :8 )
5
8 ( = 5555555555555555555555555555555555555555555555555555555555555
@ + Q ( vt+ ⁄ 8 :8 )
5.70 ?0%($+,6'"%'`FGH')6"%($()06'-"#$%&' > ! '='@Z'3AcSQ8
T,)' )-,' )6"%($()06' 4,' 4$"(,+' ")' 8:8' =' Z8W' S8' I06' 0<,6")$0%' $%
(")*6")$0%1'2-")'+/'4$"('/*66,%)'?('6,(*7)(g'=:'"'08ZW5S'($&%"7'$(
(*<,6$3<0(,+'0%'8*)1':$%+')-,'/066,(<0%+$%&'$%/6,3,%)'$%'/075
7,/)06' /*66,%)' 4;' ,#"7*")$%&' )-,' )0)"7' /077,/)06' /*66,%)' +(' "%+
(*4)6"/)$%&')-,'+/'4$"('/*66,%)'?(8'i,<,")':06'"'−Z8ZW5S'($&%"78
n(,')-,(,'6,(*7)(')0',()$3"),'7@'0:')-,'IJ9'")')-$('4$"('<0$%)8
?03<"6,'2$)-')-,'#"7*,'0:'7@'04)"$%,+'*($%&'JO8'EW8bdK8
`021' :$%+' 8:8 1' 8(1' Gv 1' "%+' vt$' :06' )-,' /"(,' 8((' =' Q8W' S1
vt+ = QZ'3S1'"%+'@'='@W8'=:'$)'$('+,($6,+')0'0<,6"),')-$(')6"%($(5
)06'")'?('='@ZZ'µA1':$%+')-,'#"7*,('0:'F('"%+''P&1'"((*3$%&
Q
)-")':06')-$('<60/,(('),/-%070&;' > !′ = @ZZ'µAcS 8
5.71 ?0%($+,6')-,'IJ9'"3<7$:$,6'0:'I$&8'W8Cb':06')-,'/"(,
8#'='Z8b'S1' > ! '='b'3AcSQ10 8*)'='Z8NW'S1'8(('='@8d'S1'"%+
F( ='d'PΩ8
5.74 =%')-,')"47,'4,7021':06',%-"%/,3,%)'FGH')6"%($()06(
0<,6")$%&' *%+,6' "' #"6$,);' 0:' /0%+$)$0%(1' /03<7,),' "(' 3"%;
,%)6$,('"('<0(($47,8'A7)-0*&-'(03,'+")"'$('%0)'"#"$7"47,1'$)'$(
"72";(' <0(($47,' )0' /"7/*7"),' 7@' *($%&' 0%,' 0:' JO(8' EW8WWK1
EW8WNK'06'EW8WfK8'A((*3,'µ!'='WZZ'/3QcSh(1'µ"'='QWZ /3QcSh(1
"%+'<$%'='Z8b':Icµ3Q8
E"K I$%+')-,'+/'O*"%)$)$,('?('"%+'8(8
E4K ?"7/*7"),')-,'#"7*,'0:'7@'")')-,'4$"('<0$%)8
E/K ?"7/*7"),')-,'#"7*,'0:')-,'#07)"&,'&"$%8
E+K =:')-,'FGHIJ9'-"('λ'='Z8@'S−@1':$%+'6$'")')-,'4$"('<0$%)
"%+'/"7/*7"),')-,'#07)"&,'&"$%8
5.75 A%' `FGH' ),/-%070&;' -"(' µ!<$%' =' QWZ' µAcSQ' "%+
8# ='Z8W'S8'I06'"')6"%($()06'2$)-'&'='Z8W'µ31':$%+')-,'#"7*,'0:
'')-")' 6,(*7)('$%'7@'='@'3AcS'")'?('='Z8QW'3A8'A7(01':$%+')-,
6,O*$6,+'8*)8
D *5.72 A%'`FGH'"3<7$:$,6'$(')0'4,'+,($&%,+')0'<60#$+,'"
Z8WZ5S'<,"P'0*)<*)'($&%"7'"/60(('"'WZ5PΩ'70"+')-")'/"%'4,'*(,+
"(' "' +6"$%' 6,($()068' =:' "' &"$%' 0:' ")' 7,"()' W' ScS' $(' %,,+,+1
Voltages (V)
Case
Type
ID (mA)
V GS
Vt
*
/
0
2
5
6
7
9
:
;
<
=
4
4
4
4
4
4
8
8
8
8
8
8
$
$
))$+
+#"
+#$
-
,
+#3
+#"
))$+
))$+
+#$
$#1
-
+#1
))))$
Dimensions (µm)
VOV
W
+#"
,
+#"
"+
,
.
$
"
L
W/L
k′(W/L)
$
$
$+
.+
,
.
.+++
,
-+
-
,"
+#"
+#++1
gm(mA/V)
Problems 341
vo
Figure P5.76
5.77 =%')-,'/$6/*$)'0:'I$&8'_W8ff1')-,'`FGH')6"%($(5
)06'-"(' 8 # '='Z8W'S'"%+'8G'='WZ'S'"%+'0<,6"),('2$)-'8('='@
S8'U-")'$(')-,'#07)"&,'&"$%' v $ ⁄ v + g'U-")'+0'8('"%+')-,'&"$%
4,/03,':06'?'$%/6,"(,+')0'@'3Ag
5.78 I06' "' Z8d5µ3' ?FGH' :"46$/")$0%' <60/,((D' 8#!' =
Z8d S1'8#"'='−Z8['S1' µ!<$%'='[Z'µAcSQ1' µ"<$%'='CZ'µAcSQ1
<$%'='@8[ :Icµ3Q1'8G'E!5/-"%%,7'+,#$/,(K'='d&'Eµ3K1'"%+
8 G 'E"5/-"%%,7'+,#$/,(K'='@Q&'Eµ3K8'I$%+')-, (3"775($&5
%"7'30+,7'<"6"3,),6('E7@'"%+'6$K':06'40)- "%'`FGH'"%+'"
_FGH' )6"%($()06' -"#$%&' 'P&' =' QZ' µ3cQ' µ3' "%+
0<,6")$%&'")'?('='@ZZ'µA8'A7(01':$%+')-,'0#,6+6$#,'#07)"&,
")'2-$/-',"/-'+,#$/,'3*()'4,'0<,6")$%&8
*5.79 I$&*6,'_W8f['(-02('"'+$(/6,),5/$6/*$)'"3<7$:$,68'9-,
$%<*)'($&%"7'v($&'$('/0*<7,+')0')-,'&"),')-60*&-'"'#,6;'7"6&,
/"<"/$)06' E(-02%' "(' $%:$%$),K8' 9-,' )6"%($()06' (0*6/,' $(' /0%5
%,/),+' )0' &60*%+' ")' ($&%"7' :6,O*,%/$,(' #$"' "' #,6;' 7"6&,
/"<"/$)06'E(-02%'"('$%:$%$),K8'9-,'0*)<*)'#07)"&,'($&%"7')-")
+,#,70<(' ")' )-,' +6"$%' $(' /0*<7,+' )0' "' 70"+' 6,($()"%/,' #$"' "
#,6;'7"6&,'/"<"/$)06'E(-02%'"('$%:$%$),K8
E"K =:')-,')6"%($()06'-"('8#'='@'S1'"%+' > !'='Q'3AcSQ1'#,6$:;
)-")' )-,'4$"(' /$6/*$)',()"47$(-,(' 8*)'='Q' S1' ?(' ='@' 3A1'"%+
8( = +f8W' S8' 9-")' $(1' "((*3,' )-,(,' #"7*,(1' "%+' #,6$:;' )-")
)-,;'"6,'/0%($(),%)'2$)-')-,'#"7*,('0:')-,'/$6/*$)'/03<0%,%)(
"%+')-,'+,#$/,'<"6"3,),6(8
E4K I$%+'7@'"%+'6$'$:'8G'='@ZZ'S8
E/K ^6"2'"'/03<7,),'(3"775($&%"7',O*$#"7,%)'/$6/*$)':06')-,
"3<7$:$,61'"((*3$%&'"77'/"<"/$)06('4,-"#,'"('(-06)'/$6/*$)('")
($&%"7':6,O*,%/$,(8
E+K I$%+'F$%1' v 71 ⁄ v ($& 1' v $ ⁄ v 711'"%+'v $ ⁄ v ($&8
8
!15 V
10 M$
Rsig % 100 k$
7.5 k$
&
vo
&
vgs
10 k$
&
vsig !
#
5 M$
Rin
Figure P5.79
3 k$
PROBLEMS
Figure P5.77
CHAPTER 5
5.76 I06' )-,' `FGH' "3<7$:$,6' $%' I$&8' _W8fN1' 6,<7"/,' )-,
)6"%($()06' 2$)-' $)(' 9' ,O*$#"7,%)' /$6/*$)1' "((*3$%&' λ & Z8
^,6$#,',B<6,(($0%(':06')-,'#07)"&,'&"$%(' v 1 ⁄ v + '"%+' v , ⁄ v + 8
CHAPTER 5
PROBLEMS
342 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
0:' )-,'"3<7$:$,6'<60<,6' G v ' $(' &$#,%' 4;' G v & * @ ( F $ || F & )
"%+')-,'0#,6"77'#07)"&,'&"$%' * v '$('&$#,%'4;
Section 5.6: Basic MOSFET Amplifier
Configurations*
5.80'A%'"3<7$:$,6'2$)-'"%'$%<*)'6,($()"%/,'0:'@ZZ'PΩ1'"%
0<,%5/$6/*$)' #07)"&,' &"$%' 0:' @ZZ' ScS' "%+' "%' 0*)<*)' 6,($(5
)"%/,'0:'@ZZ'Ω'$('/0%%,/),+'4,)2,,%'"'@Z5PΩ'($&%"7'(0*6/,
"%+'"'@5PΩ'70"+8'I$%+')-,'0#,6"77'#07)"&,'&"$%'* v8'A7(0':$%+
)-,'/*66,%)' &"$%1'+,:$%,+'"(')-,'6")$0'0:')-,'70"+'/*66,%)' )0
)-,'/*66,%)'+6"2%':603')-,'($&%"7'(0*6/,8
D 5.81'H<,/$:;')-,'<"6"3,),6(' F $%1' G v$'"%+' F $'0:'"%'"3<7$5
:$,6')-")'$(')0'4,'/0%%,/),+'4,)2,,%'"'@ZZ5PΩ'(0*6/,'"%+'"
Q5PΩ'70"+'"%+'$('6,O*$6,+')0'3,,)')-,':07702$%&'(<,/$:$/"5
)$0%(D
E"K' `0' 306,' )-"%' @Zo' 0:' )-,' ($&%"7' ()6,%&)-' $(' 70()' $%' )-,
/0%%,/)$0%')0')-,'"3<7$:$,6'$%<*)a
E4K'=:')-,'70"+'6,($()"%/,'/-"%&,(':603')-,'%03$%"7'#"7*,'0:
Q'PΩ')0'"'702'#"7*,'0:'@'PΩ1')-,'/-"%&,'$%'0*)<*)'#07)"&,'$(
7$3$),+')0'@Zo'0:'%03$%"7'#"7*,a'"%+
E/K'9-,'%03$%"7'0#,6"77'#07)"&,'&"$%'$('@Z'ScS8
5.82' I$&*6,' _W8dQ' (-02(' "%' "7),6%")$#,' ,O*$#"7,%)' /$6/*$)
6,<6,(,%)")$0%'0:'"%'"3<7$:$,68'=:')-$('/$6/*$)'$(')0'4,',O*$#"5
7,%)' )0' )-")' $%' I$&8' W8bbE4K' (-02' )-")' * @ & G v$ ⁄ F $8' A7(0
/0%#$%/,';0*6(,7:')-")')-,')6"%(/0%+*/)"%/,'* @'$('+,:$%,+'"(
+
* @ & 555$5
v+
F& & Z
"%+' -,%/,' $(' P%02%' "(' )-,' (-06)5/$6/*$)' )6"%(/0%+*/)"%/,8
`021'$:')-,'"3<7$:$,6'$(':,+'2$)-'"'($&%"7'(0*6/,'( v ($& 1 F ($& )
"%+'$('/0%%,/),+')0'"'70"+'6,($()"%/,' F &'(-02')-")')-,'&"$%
F $%
5 * ( F || F & )
* v & 555555555555555555555
F $% ( F ($& @ $
5.83' A%' "7),6%")$#,' ,O*$#"7,%)' /$6/*$)' 0:' "%' "3<7$:$,6' :,+
2$)-'"'($&%"7'(0*6/,' ( v ($& 1 F ($& )'"%+'/0%%,/),+')0'"'70"+'F &
$('(-02%'$%'I$&8'_W8dC8'!,6,' * v $ '$(')-,'0<,%5/$6/*$)'0#,6"77
#07)"&,'&"$%1
v
* v $ & 555555$5
v ($&
"%+' F 0*)'$(')-,'0*)<*)'6,($()"%/,'2$)-' v ($& '(,)')0'>,608'9-$('$(
+$::,6,%)')-"%' F $8'H-02')-")
F+
5 G
* v $ & 5555555555555555555
F + ( F ($& v $
2-,6,' F + & F $%
Rin
vi
G m vi
Ro
#
F&
5
* v & * v$ 55555555555555555555
F & ( F 0*)
**5.84' ' F0()' <6"/)$/"7' "3<7$:$,6(' -"#,' $%),6%"7' :,,+4"/P
)-")'3"P,')-,3'%0%5*%$7"),6"78'=%'(*/-'"'/"(,1' F $%'+,<,%+(
0%' F &8' 90' $77*()6"),' )-$(' <0$%)' 2,' (-02' $%' I$&8' _W8db' )-,
,O*$#"7,%)' /$6/*$)' 0:' "%' "3<7$:$,6' 2-,6,' "' :,,+4"/P' 6,($(5
)"%/,' F M ' 30+,7(' )-,' $%),6%"7' :,,+4"/P' 3,/-"%$(3' )-")' $(
<6,(,%)' $%' )-$(' "3<7$:$,68' =)' $(' F M ' )-")' 3"P,(' )-,' "3<7$:$,6
%0%5*%$7"),6"78'H-02')-")
F M ( ( F Q || F & )
5
F $% & F @ || 5555555555555555555555555555555555555
@ ( 7 @ ( F Q || F & )
!
@ ' @ ⁄ ( 7@ FM )
5
G v$ & ' 7 @ F Q 5555555555555555555555555555555
@ ( ( FQ ⁄ FM )
vo
F $ & F Q 'll'F M
#
Figure P5.82
Rsig
Rout
vsig
vi
io
#
!
Rin
'
J#"7*"),' F $%1' G v$'"%+' F $':06')-,'/"(,' F @ & @ZZ'PΩ1' F M & @
FΩ1' 7 @ & @ZZ' 3AcS1' F Q & @ZZ' Ω' "%+' F & & @' PΩ8
U-$/-' 0:' )-,' "3<7$:$,6' /-"6"/),6$()$/' <"6"3,),6(' $(' 30()
"::,/),+'4;' F M 'E)-")'$(1'6,7")$#,')0')-,'/"(,'2$)-' F M & ∞ Kg
!
!
#
8
F& & ∞
A7(0'(-02')-")')-,'0#,6"77'#07)"&,'&"$%'$(
Io
!
F& & ∞
!
Gvovsig #
Figure P5.83
y'_6047,3('W8dZ')0'W8db'"6,'$+,%)$/"7')0'_6047,3('N8@Zf')0'N8@@@8
R L vo
#
Problems 343
5.85' ?"7/*7"),' )-,' 0#,6"77' #07)"&,' &"$%' 0:' "' ?H' "3<7$:$,6
:,+'2$)-'"'@5FΩ'(0*6/,'"%+'/0%%,/),+')0'"'QZ5PΩ'70"+8'9-,
FGHIJ9'-"(' 7 @ & Q'3AcS'"%+' 6 $ & WZ'P Ω1'"%+'"'+6"$%
6,($()"%/,' F ( & @Z 'P Ω'$('*)$7$>,+8
5.90'A'FGHIJ9'/0%%,/),+'$%')-,'?H'/0%:$&*6")$0%'-"('"
)6"%(/0%+*/)"%/,' 7 @ & W ' 3AcS8' U-,%' "' 6,($()"%/,' F 1' $(
/0%%,/),+'$%')-,'(0*6/,'7,"+1')-,',::,/)$#,')6"%(/0%+*/)"%/,
$('6,+*/,+')0'@'3AcS8'U-")'+0';0*',()$3"),')-,'#"7*,'0:' F 1
)0'4,g
5.86' A' ?H' "3<7$:$,6' *)$7$>,(' "' FGHIJ9' 2$)µ ! < $% & bZZ' µAcSQ10 'c&' e' @Z1' "%+' 8 G & @Z' S8' =)' $(
4$"(,+' ")' ? ( & Z8Q' 3A' "%+' *(,(' F ( & N' P Ω8' I$%+' F $%1
G v$1'"%+' F $8'A7(01'$:'"'70"+'6,($()"%/,'0:'@Z'PΩ'$('/0%%,/),+
)0')-,'0*)<*)1'2-")'0#,6"77'#07)"&,'&"$%'* v'$('6,"7$>,+g'`021
$:' "' Z8Q5S' <,"P' ($%,52"#,' ($&%"7' $(' 6,O*$6,+' ")' )-,' 0*)<*)1
2-")'3*()')-,'<,"P'"3<7$)*+,'0:' v ($&'4,g
5.87' A' /0330%5(0*6/,' "3<7$:$,6' *)$7$>,(' "' FGHIJ9' :06
2-$/-' 8 G & @Q8W' S' "%+' $(' 0<,6"),+' ")' 8 :8 & Z8QW' S8
U-")'$(')-,'#"7*,'0:'$)(' ( 7 @ 6 $ )g'9-,'"3<7$:$,6':,,+('"'70"+
6,($()"%/,' F & & @W'P Ω8'9-,'+,($&%,6'(,7,/)(' F ( & QF & 8'=:
$)'$('6,O*$6,+')0'6,"7$>,'"%'0#,6"77'#07)"&,'&"$%'* v'0:'' @Z'Sc
S'2-")' 7 @'$('%,,+,+g'A7(0'(<,/$:;')-,'4$"('/*66,%)' ? (8'=:1')0
$%/6,"(,' )-,' 0*)<*)' ($&%"7' (2$%&1' F (' $(' 6,+*/,+' )0
F ( & F & 1'2-")'+0,('* v'4,/03,g
5.88'920'$+,%)$/"7'?H'"3<7$:$,6('"6,'/0%%,/),+'$('/"(/"+,8
9-,':$6()'()"&,'$(':,+'2$)-'"'(0*6/,' v ($&'-"#$%&'"'6,($()"%/,
F ($& & @ZZ' PΩ 8' A' 70"+' 6,($()"%/,' F & & @Z' P Ω ' $(' /0%5
%,/),+' )0' )-,' +6"$%' 0:' )-,' (,/0%+' ()"&,8' J"/-' FGHIJ9' $(
4$"(,+'")' ? ( & Z8QW '3A'"%+'0<,6"),('2$)-' 8 :8 & Z8QW 'S8
A((*3,' 8 G' $('#,6;'7"6&,8' J"/-' ()"&,' *)$7$>,(' "'+6"$%' 6,($(5
)"%/,' F ( & @Z'PΩ 8'
E"K'HP,)/-')-,',O*$#"7,%)'/$6/*$)'0:')-,')205()"&,'"3<7$:$,68
E4K'?"7/*7"),')-,'0#,6"77'#07)"&,'&"$%' * v 8
5.89' =%' +$(/6,),5/$6/*$)' "3<7$:$,6(1' ( F ( || F & )' $(' *(*"77;
3*/-'(3"77,6')-"%' 6 $1'"%+')-*(' 6 $'/"%'4,'%,&7,/),+'$%'+,),65
3$%$%&')-,'#07)"&,'&"$%'0:')-,'?H'"3<7$:$,68'`,#,6)-,7,((1'$)
$('*(,:*7')0'%0),')-")' 6 $'<0(,('"%'"4(07*),'*<<,6'7$3$)'0%')-,
#07)"&,'&"$%'0:'"'?H'"3<7$:$,68'I$%+')-$('*<<,6'7$3$)'4;'7,)5
Rsig
ii
5.91' A' ?H' "3<7$:$,6' *($%&' "%' `FGH' )6"%($()06' 2$)-' 7 @ &
b 3AcS'$(':0*%+')0'-"#,'"%'0#,6"77'#07)"&,'&"$%'0:' ' @N'ScS8
U-")'#"7*,'(-0*7+'"'6,($()"%/,' F 1 '$%(,6),+'$%')-,'(0*6/,'7,"+
-"#,')0'6,+*/,')-,'0#,6"77'#07)"&,'&"$%')0' ' d'ScSg
5.92' 9-,' 0#,6"77' #07)"&,' &"$%' 0:' "' ?H' "3<7$:$,6' 2$)-' "
6,($()"%/,' F 1 & @'PΩ '$%')-,'(0*6/,'7,"+'2"('3,"(*6,+'"%+
:0*%+' )0' 4,' ' @W' ScS8' U-,%' F 1 ' $(' (-06),+1' 4*)' )-,' /$6/*$)
0<,6")$0%'6,3"$%,+'7$%,"61')-,'&"$%'+0*47,+8'U-")'3*()' 7 @
4,g'U-")'#"7*,'0:' F 1 '$('%,,+,+')0'04)"$%'"%'0#,6"77'#07)"&,
&"$%'0:' ' @Z'ScSg
5.93'A'?]'"3<7$:$,6'*($%&'"%'`FGH')6"%($()06':06'2-$/7 @ & b'3AcS'-"('"'W5PΩ'+6"$%'6,($()"%/,' F ('"%+'"'W5PΩ
70"+' 6,($()"%/,' F &8' 9-,' "3<7$:$,6' $(' +6$#,%' 4;' "' #07)"&,
(0*6/,' -"#$%&' "' WZZ' Ω' 6,($()"%/,8' U-")' $(' )-,' $%<*)' 6,($(5
)"%/,'0:')-,'"3<7$:$,6g'U-")'$(')-,'0#,6"77'#07)"&,'&"$%'* vg
L;'2-")':"/)06'3*()')-,'4$"('/*66,%)' ? ('0:')-,'FGHIJ9'4,
/-"%&,+'(0')-")' F $%'3")/-,(' F ($& g
5.94' A' ?]' "3<7$:$,6' 2-,%' :,+' 2$)-' "' ($&%"7' (0*6/,' -"#$%&
F ($& & QZZ ' Ω'$(':0*%+')0'-"#,'"%'0#,6"77'#07)"&,'&"$%'0:'@Z
ScS8'U-,%'"'QZZ5Ω'6,($()"%/,'$('"++,+'$%'(,6$,('2$)-')-,'($&5
%"7'&,%,6")06')-,'0#,6"77'#07)"&,'&"$%'+,/6,"(,+')0'd'ScS8'U-")
3*()' 7 @' 0:' )-,' FGHIJ9' 4,g' =:' )-,' FGHIJ9' $(' 4$"(,+' ")
? ( & Z8Q '3A1'")'2-")'0#,6+6$#,'#07)"&,'$)'3*()'4,'0<,6")$%&g
D 5.95' A' (0*6/,' :07702,6' $(' 6,O*$6,+' )0' /0%%,/)' "' -$&-5
6,($()"%/,'(0*6/,')0'"'70"+'2-0(,'6,($()"%/,'$('%03$%"77;'Q
PΩ'4*)'/"%'4,'"('702'"('@'P Ω'"%+'"('-$&-'"('C'PΩ8'U-")'$(
)-,' 3"B$3*3' 0*)<*)' 6,($()"%/,' )-")' )-,' (0*6/,' :07702,6
3*()'-"#,'$:')-,'0*)<*)'#07)"&,'$(')0'6,3"$%'2$)-$%'± QZo'0:
%03$%"7' #"7*,g' =:' )-,' FGHIJ9' -"(' > ! & @N' 3AcSQ1' ")
Rf
!
vsig !
#
vi
#
Rin
Figure P5.84
!
R1
g mvi
R2
RL
vo
#
PROBLEMS
)$%&' F ( || F & & ∞ 8'JB<6,((')-,'3"B$3*3'"/-$,#"47,'&"$%
$%'),63('0:'8 G'"%+'8 :8 8
CHAPTER 5
I06' F ($& & @ZZ'PΩ'+,),63$%,')-,' 0#,6"77'#07)"&,'&"$%1' * v1
2$)-'"%+'2$)-0*)' F M '<6,(,%)8
CHAPTER 5
PROBLEMS
344 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
2-")'/*66,%)' ? ('3*()'$)'4,'4$"(,+g'A)'2-")'0#,6+6$#,'#07)5
"&,'$(')-,'FGHIJ9'0<,6")$%&g
/*66,%)'6,(*7)(g'=:'"')6"%($()06':06'2-$/-' > ! '$('WZo'-$&-,6'$(
*(,+1'2-")'$(')-,'6,(*7)$%&'<,6/,%)"&,'$%/6,"(,'$%'?(g
*5.96' i,:,6' )0' )-,' (0*6/,5:07702,6' ,O*$#"7,%)' /$6/*$)
(-02%'$%'I$&8'W8WZE4K8'H-02')-")
5.102 9-,' 4$"(' /$6/*$)' 0:' I$&8' W8WQE/K' $(' *(,+' $%' "
+,($&%'2$)-'8*'='W'S'"%+'F)'='Q'PΩ8'I06'"%',%-"%/,3,%)
FGHIJ9'2$)-' > ! '='Q'3AcSQ1')-,'(0*6/,'#07)"&,'2"('3,"5
(*6,+'"%+':0*%+')0'4,'Q'S8'U-")'3*()'8#'4,':06')-$('+,#$/,g
=:'"'+,#$/,':06'2-$/-'8#'$('Z8W'S'7,(('$('*(,+1'2-")'+0,('8)
4,/03,g'U-")'4$"('/*66,%)'6,(*7)(g
v
F & || 6 $
* v ≡ 555555$5 & 555555555555555555555555555555555
v ($&
@
( F & || 6 $ ) ( 555555
7@
`021'2$)-' F &' 6,30#,+1' )-,' #07)"&,'&"$%' $(' /"6,:*77;' 3,"5
(*6,+'"%+':0*%+')0'4,'Z8[d8'9-,%1'2-,%' F &'$('/0%%,/),+'"%+
$)(' #"7*,' $(' #"6$,+1' $)' $(' :0*%+' )-")' )-,' &"$%' $(' -"7#,+' ")
F & & WZZ ' Ω8' =:' )-,' "3<7$:$,6' 6,3"$%,+' 7$%,"6' )-60*&-0*)
)-$('3,"(*6,3,%)1'2-")'3*()')-,'#"7*,('0:' 7 @'"%+' 6 $ '4,g
D 5.97' A' (0*6/,' :07702,6' $(' 6,O*$6,+' )0' +,7$#,6' "' Z8W5S
<,"P'($%*(0$+')0'Q5PΩ'70"+8'=:')-,'<,"P'"3<7$)*+,'0:'v 71'$(')0
4,'7$3$),+')0'WZ'3S1'2-")'$(')-,'702,()'#"7*,'0:' ? ('")'2-$/)-,'FGHIJ9'/"%'4,'4$"(,+g'A)')-$('4$"('/*66,%)1'2-")'"6,
)-,'3"B$3*3'"%+'3$%$3*3'/*66,%)(')-")')-,'FGHIJ9'2$77
4,'/0%+*/)$%&'E")')-,'<0($)$#,'"%+'%,&")$#,'<,"P('0:')-,'0*)5
<*)'($%,'2"#,Kg'U-")'3*()')-,'<,"P'"3<7$)*+,'0:' v ($&'4,g
Section 5.7: Biasing in MOS Amplifier Circuits
D 5.98 ?0%($+,6')-,'/7"(($/"7'4$"($%&'(/-,3,'(-02%'$%
I$&8 W8WQE/K1'*($%&'"'[5S'(*<<7;8'I06')-,'FGHIJ91'8#'='@'S1
λ = Z1''"%+' > ! & Q'3AcS Q8'A66"%&,')-")')-,'+6"$%'/*66,%)'$(
@'3A1'2$)-'"40*)'0%,5)-$6+'0:')-,'(*<<7;'#07)"&,'"/60((',"/0:'F)'"%+'F(8'n(,'QQ'FΩ':06')-,'7"6&,6'0:'F*@'"%+'F*Q8'U-")
"6,' )-,' #"7*,(' 0:'F*@1'F*Q1' F)1' "%+'F(' )-")' ;0*' -"#,' /-0(,%g
H<,/$:;')-,3')0')20'($&%$:$/"%)'+$&$)(8'I06';0*6'+,($&%1'-02':"6
$(')-,'+6"$%'#07)"&,':603')-,',+&,'0:'(")*6")$0%g
D 5.99 n($%&' )-,' /$6/*$)' )0<070&;' +$(<7";,+' $%' I$&8
W8WQE,K1'"66"%&,')0'4$"(')-,'`FGH')6"%($()06'")'?('='@'3A
2$)-' 8(' 3$+2";' 4,)2,,%' /*)0::' "%+' )-,' 4,&$%%$%&' 0:' )6$5
0+,' 0<,6")$0%8' 9-,' "#"$7"47,' (*<<7$,(' "6,' ±W' S8' I06' )-,
Q
`FGH')6"%($()061'8# ='@8Z'S1' λ'='Z1'"%+' > ! & Q'3AcS 8
n(,' "' &"),54$"(' 6,($()06' 0:' @Z' FΩ8' H<,/$:;' F)' "%+' F(' )0
)20'($&%$:$/"%)'+$&$)(8
D *5.100 =%' "%' ,7,/)60%$/' $%()6*3,%)' *($%&' )-,' 4$"($%&
(/-,3,' (-02%' $%' I$&8' W8WQE/K1' "' 3"%*:"/)*6$%&' ,6606
6,+*/,('F)')0'>,608'T,)'8(('='@Q'S1'F*@'='W8N'FΩ1'"%+'F*Q'=
Q8Q'FΩ8'U-")'$(')-,'#"7*,'0:'8*'/6,"),+g'=:'(*<<7$,6'(<,/$:$5
/")$0%(' "7702' > ! ' )0' #"6;' :603' Z8Q' )0' Z8C' 3AcSQ' "%+' 8#' )0
#"6;':603'@8Z'S')0'@8W'S1'2-")'"6,')-,',B)6,3,'#"7*,('0:'?(
)-")'3";'6,(*7)g'U-")'#"7*,'0:'F)'(-0*7+'-"#,'4,,%'$%()"77,+
)0' 7$3$)' )-,' 3"B$3*3' #"7*,' 0:' ?(' )0' Z8W' 3Ag' ?-00(,' "%
"<<60<6$"),'()"%+"6+'Wo'6,($()06'#"7*,'E6,:,6')0'A<<,%+$B']K8
U-")',B)6,3,'#"7*,('0:'/*66,%)'%02'6,(*7)g
5.101 A%' ,%-"%/,3,%)' `FGH' )6"%($()06' $(' /0%%,/),+' $%
)-,'4$"('/$6/*$)'0:'I$&8'W8WQE/K1'2$)-'8*'='b'S'"%+'F)'='Q'PΩ8
9-,' )6"%($()06' -"(' 8#' =' @' S' "%+' > ! ' =' Q' 3AcSQ8' U-")' 4$"(
D 5.103 ^,($&%')-,'/$6/*$)'0:'I$&8'W8WQE,K':06'"%',%-"%/,5
3,%)'FGHIJ9'-"#$%&'8#'='@'S'"%+' > !'='Q'3AcSQ8'T,)'8(('=
8))'='W'S8'^,($&%':06'"'+/'4$"('/*66,%)'0:'@'3A'"%+':06')-,
7"6&,()' <0(($47,' #07)"&,' &"$%' E"%+' )-*(' )-,' 7"6&,()' <0(($47,
F(K' /0%($(),%)' 2$)-' "7702$%&' "' Q5S' <,"P5)05<,"P' #07)"&,
(2$%&' ")' )-,' +6"$%8' A((*3,' )-")' )-,' ($&%"7' #07)"&,' 0%' )-,
(0*6/,'),63$%"7'0:')-,'IJ9'$('>,608
D 5.104 ^,($&%')-,'/$6/*$)'$%'I$&8'_W8@Zb'(0')-")')-,
)6"%($()06'0<,6"),('$%'(")*6")$0%'2$)-'8('4$"(,+'@'S':603')-,
,+&,'0:')-,')6$0+,'6,&$0%1'2$)-'?('='@'3A'"%+'8('='C'S1':06
,"/-' 0:')-,' :07702$%&' )20' +,#$/,('E*(,'"'@Z5µA' /*66,%)' $%
)-,'#07)"&,'+$#$+,6KD
E"K 8 # = @'S '"%+' > "′ 'P&'='Z8W'3AcSQ
E4K 8 # = Q'S '"%+' > "′ 'P&'= @8QW'3AcSQ
I06' ,"/-' /"(,1' (<,/$:;' )-,' #"7*,(' 0:' 8*1'8(1' 8)1'F@1' FQ1' F)1
"%+ F(8
!10 V
R1
RS
VS
VG
VD
R2
RD
Figure P5.104
**D 5.105 A'#,6;'*(,:*7'2";')0'/-"6"/),6$>,')-,'()"4$7$);
0:')-,'4$"('/*66,%)'?('$(')0',#"7*"),')-,'(,%($)$#$);'0:'?('6,7"5
)$#,' )0' "' <"6)$/*7"6' )6"%($()06' <"6"3,),6' 2-0(,' #"6$"4$7$);
3$&-)'4,'7"6&,8'9-,'(,%($)$#$);'0:'?('6,7")$#,')0')-,'FGHIJ9
<"6"3,),6'' Q ≡ @55Q5 >′ ( ' ⁄ & )'$('+,:$%,+'"(
∂? ( ⁄ ? ( ∂? ( Q
?
5 = 555555555 55555
) Q( ≡ 5555555555555555
∂Q ⁄ Q
∂Q ? (
Problems 345
VDD
RD
RG1
E"K H-02')-")':06'8#'/0%()"%)1
E4K I06'"'FGHIJ9'-"#$%&'Q'='@ZZ'µAcSQ'2$)-'"'#"6$"4$7$);
0:''±@Zo'"%+'8#'='@'S1':$%+')-,'#"7*,'0:'F)')-")'20*7+'6,(*7)
$%'?('='@ZZ'µA'2$)-'"'#"6$"4$7$);'0:''±@o8'A7(01':$%+'8*)'"%+
)-,'6,O*$6,+'#"7*,'0:'8))8
E/K =:')-,'"#"$7"47,'(*<<7;'8))'='W'S1':$%+')-,'#"7*,'0:'F)':06
?('='@ZZ'µA8'J#"7*"),')-,'(,%($)$#$);':*%/)$0%1'"%+'&$#,')-,
,B<,/),+'#"6$"4$7$);'0:'?('$%')-$('/"(,8
Figure P5.109
5.106 I06')-,'/$6/*$)'$%'I$&8'W8WWE"K'2$)-'?'='Z8Q'3A1'F*'='Z1
F('='@Z'PΩ1'"%+'8(('='Q8W'S1'/0%($+,6')-,'4,-"#$06'$%',"/-'0:
)-,' :07702$%&' )20' /"(,(8' =%' ,"/-' /"(,1' :$%+' )-,' #07)"&,(' 8) 1
8( 1'"%+'8()')-")'6,(*7)8
D 5.111 9-$('<6047,3'$%#,()$&"),('"'6,+,($&%'0:')-,'/0330%5
(0*6/,'"3<7$:$,6'0:'JB,6/$(,'W8Cd'2-0(,'4$"('+,($&%'2"('+0%,
$%'JB,6/$(,'W8Cf'"%+'(-02%'$%'I$&8'JW8Cf8'_7,"(,'6,:,6')0')-,(,
)20',B,6/$(,(8
E"K 8#'='@'S'"%+' > ! '='@8N'3AcSQ
E4K 8#'='Z8d'S'"%+' > !'='@8QW'3AcSQ
E"K 9-,'0<,%5/$6/*$)'#07)"&,'&"$%'0:')-,'?H'"3<7$:$,6'/"%'4,
26$)),%'"(
Q ( 8 (( ' 8 ( )
5
G v$ = ' 555555555555555555555555555555
8 :8
S,6$:;')-")')-$(',B<6,(($0%';$,7+(')-,'6,(*7)('$%'JB,6/$(,'W8Cd
E$8,81'Gv$'='−@W'ScSK8
E4K Gv$' /"%' 4,' +0*47,+' 4;' 6,+*/$%&' 8:8' 4;' "' :"/)06' 0:' Q1
E$8,81':603'@'S')0'Z8W'SK'2-$7,'8('$('P,<)'*%/-"%&,+8'U-")
/066,(<0%+$%&'#"7*,(':06'?(1'F(1'7@1'"%+'6$'"<<7;g
E/K I$%+'Gv$'"%+'F$'2$)-'6$')"P,%'$%)0'"//0*%)8
E+K I06')-,'("3,'#"7*,'0:'($&%"75&,%,6")06'6,($()"%/,'F($&'=
@ZZ' PΩ1' )-,' ("3,' #"7*,' 0:' &"),54$"(' 6,($()"%/,' F*' =' b8d
FΩ1'"%+')-,'("3,'#"7*,'0:'70"+'6,($()"%/,'F&'='@W'PΩ1',#"75
*"),' )-,' %,2' #"7*,' 0:' 0#,6"77' #07)"&,' &"$%' *v' 2$)-' 6$' )"P,%
$%)0'"//0*%)8
E,K ?03<"6,' ;0*6' 6,(*7)(' )0' )-0(,' 04)"$%,+' $%' JB,6/$(,(
W8Cf'"%+'W8Cd1'"%+'/033,%)8
5.107 =%')-,'/$6/*$)'0:'I$&8'W8Wb1'7,)'F*'='@Z'FΩ1'F('=
@Z'PΩ1'"%+'8(('='@Z'S8'I06',"/-'0:')-,':07702$%&')20')6"%($(5
)06(1':$%+')-,'#07)"&,('8('"%+'8*8
E"K 8#'='@'S'"%+0 > !'='Z8W'3AcSQ
E4K 8#'='Q'S'"%+0 > !'='@8QW'3AcSQ
D 5.108 n($%&')-,':,,+4"/P'4$"('"66"%&,3,%)'(-02%'$%
I$&8'W8Wb'2$)-'"'W5S'(*<<7;'"%+'"%'`FGH'+,#$/,':06'2-$/8#' =' @ S' "%+' > ! ' =' Z8N' 3AcSQ1' :$%+' F(' )0' ,()"47$(-' "' +6"$%
/*66,%)'0:'Z8Q'3A8'=:'6,($()06'#"7*,('"6,'7$3$),+')0')-0(,'0%
)-,'Wo' 6,($()06'(/"7,'E(,,' A<<,%+$B']K1'2-")' #"7*,' 20*7+
;0*'/-00(,g'U-")'#"7*,('0:'/*66,%)'"%+'8('6,(*7)g
D 5.109 I$&*6,'_W8@Z['(-02('"'#"6$")$0%'0:')-,':,,+4"/P5
4$"('/$6/*$)'0:'I$&8'W8Wb8'n($%&'"'W5S'(*<<7;'2$)-'"%'`FGH
)6"%($()06' :06'2-$/-' 8#' ='@' S1' > ! = N8QW' 3AcSQ'"%+' λ' =' Z1
<60#$+,'"'+,($&%')-")'4$"(,(')-,')6"%($()06'")'?('='Q'3A1'2$)8()' 7"6&,' ,%0*&-' )0' "7702' (")*6")$0%' 0<,6")$0%' :06' "' Q5S
%,&")$#,'($&%"7'(2$%&'")')-,'+6"$%8'n(,'QQ'FΩ'"(')-,'7"6&,()
6,($()06' $%' )-,' :,,+4"/P54$"(' %,)206P8' U-")' #"7*,(' 0:' F(1
F*@1' "%+' F*Q'-"#,' ;0*'/-0(,%g'H<,/$:;'"77' 6,($()06(')0' )20
($&%$:$/"%)'+$&$)(8
Section 5.8: Discrete-Circuit MOS Amplifiers
5.110 ?"7/*7"),')-,'0#,6"77'#07)"&,'&"$%'*v'0:'"'/0330%5
(0*6/,'"3<7$:$,6':06'2-$/-'7@'='Q'3AcS1'6$'='WZ'PΩ1'F('=
@Z PΩ1'"%+'F*'='@Z'FΩ8'9-,'"3<7$:$,6'$(':,+':603'"'($&%"7
(0*6/,'2$)-'"'9-w#,%$%'6,($()"%/,'0:'Z8W'FΩ1'"%+')-,'"3<7$5
:$,6'0*)<*)'$('/0*<7,+')0'"'70"+'6,($()"%/,'0:'QZ'PΩ8
RG2
5.112' ' 9-,' `FGH' )6"%($()06' $%' )-,' ?H' "3<7$:$,6
(-02%'$%'I$&8'_W8@@Q'-"('8 # & Z8f'S'"%+'8 G & WZ 'S8
E"K'`,&7,/)$%&')-,'J"67;',::,/)1'#,6$:;')-")')-,'FGHIJ9'$(
0<,6")$%&' $%' (")*6")$0%'2$)-' ? ( & Z8W' 3A' "%+' 8 :8 & Z8C
S8'U-")'3*()')-,'FGHIJ9m(' > !'4,g'U-")'$(')-,'+/'#07)"&,
")')-,'+6"$%g
E4K'I$%+' F $%'"%+'* v 8
E/K'=:' v ($&'$('"'($%*(0$+'2$)-'"'<,"P'"3<7$)*+,' vt ($& 1':$%+')-,
3"B$3*3' "7702"47,' #"7*,' 0:' vt ($&' :06' 2-$/-' )-,' )6"%($()06
6,3"$%('$%'(")*6")$0%8'U-")'$(')-,'/066,(<0%+$%&'"3<7$)*+,
0:')-,'0*)<*)'#07)"&,g
E+K' U-")' $(' )-,' #"7*,' 0:' 6,($()"%/,' F 1' )-")' %,,+(' )0' 4,
$%(,6),+'$%'(,6$,('2$)-'/"<"/$)06' < )'$%'06+,6')0'"7702'*(')0
PROBLEMS
?
) Q( = @ ⁄ ( @ + Q Q? ( F ) )
CHAPTER 5
"%+' $)(' #"7*,1' 2-,%' 3*7)$<7$,+' 4;' )-,' #"6$"4$7$);' E06' )07,65
"%/,K'0:'Q1'<60#$+,(')-,'/066,(<0%+$%&',B<,/),+'#"6$"4$7$);
0:'?(8'9-,'<*6<0(,'0:')-$('<6047,3'$(')0'$%#,()$&"),')-,'*(,'0:
)-, (,%($)$#$);' :*%/)$0%' $%' )-,' +,($&%' 0:' )-,' 4$"(' /$6/*$)' 0:
I$&8 W8WQE,K8
CHAPTER 5
PROBLEMS
346 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
+0*47,' )-,' $%<*)' ($&%"7' vt ($& g' U-")' 0*)<*)' #07)"&,' %02
6,(*7)(g
D *5.113'9-,'_FGH')6"%($()06'$%')-,'?H'"3<7$:$,6'0:
I$&8'_W8@@C'-"(' 8 #" & ' Z8f 'S'"%+'"'#,6;'7"6&,' 8 G 8
E"K'H,7,/)'"'#"7*,':06' F ) ')0'4$"(')-,')6"%($()06'")'?('e'Z8C 3A
"%+' 8 :8 & Z8C'S8'A((*3,' v ($& ')0'-"#,'"'>,60'+/'/03<05
%,%)8
E4K'H,7,/)'"'#"7*,':06' F (')-")'6,(*7)('$%'* v & ' @Z'ScS8
E/K'I$%+')-,'7"6&,()'($%*(0$+' vt ($&')-")')-,'"3<7$:$,6'/"%'-"%5
+7,' 2-$7,' 6,3"$%$%&' $%' )-,' (")*6")$0%' 6,&$0%8' U-")' $(' )-,
/066,(<0%+$%&'($&%"7'")')-,'0*)<*)g
E+K'=:')0'04)"$%'6,"(0%"47;'7$%,"6'0<,6")$0%1' vt ($& '$('7$3$),+')0
WZ'3S1'2-")'#"7*,'/"%' F ('4,'$%/6,"(,+')0'2-$7,'3"$%)"$%$%&
(")*6")$0%56,&$0%'0<,6")$0%g'U-")'$(')-,'%,2'#"7*,'0:'* vg
5.114 I$&*6,' _W8@@b' (-02(' "' (/-,3,' :06' /0*<7$%&' "%+
"3<7$:;$%&' "' -$&-5:6,O*,%/;' <*7(,' ($&%"78' 9-,' /$6/*$)
*)$7$>,(')20'FGHIJ9('2-0(,'4$"('+,)"$7('"6,'%0)'(-02%'"%+
"'WZ5Ω'/0"B$"7'/"47,8'96"%($()06';@'0<,6"),('"('"'?H'"3<7$5
:$,6'"%+';Q'"('"'?]'"3<7$:$,68'I06'<60<,6'0<,6")$0%1')6"%($(5
)06';Q'$('6,O*$6,+')0'<6,(,%)'"'WZ5Ω'6,($()"%/,')0')-,'/"47,8
9-$('($)*")$0%'$('P%02%'"('X<60<,6'),63$%")$0%Y'0:')-,'/"47,
"%+' ,%(*6,(' )-")' )-,6,' 2$77' 4,' %0' ($&%"7' 6,:7,/)$0%' /03$%&
4"/P'0%')-,'/"47,8'U-,%')-,'/"47,'$('<60<,67;'),63$%"),+1'$)(
$%<*)'6,($()"%/,'$('WZ'Ω8'U-")'3*()'7@Q'4,g'=:';@'$('4$"(,+'")
)-,' ("3,' <0$%)' "(' ;Q1' 2-")' $(' )-,' "3<7$)*+,' 0:' )-,' /*66,%)
<*7(,('$%')-,'+6"$%'0:';@g'U-")'$(')-,'"3<7$)*+,'0:')-,'#07)5
"&,'<*7(,('")')-, +6"$%'0:';@g'U-")'#"7*,'0:'F('$('6,O*$6,+')0
<60#$+,'@5S'<*7(,('")')-,'+6"$%'0:';Qg
VDD
!2.5 V
RD
RS
vo
CS
50-$ Coaxial cable Q2
Rsig
vd1
CC
vsig !
#
id
vo
vi
RD
5 mV
#2.5 V
Figure P5.113
Figure P5.114
!5 V
300 k$
5 k$
CC2
120 k$
vo
CC1
5 k$
CS
vsig !
#
Figure P5.112
200 k$
Rin
2 k$
Q1
Ri2 % 50 $
Problems 347
vi
&
vo1
PROBLEMS
E"K I$%+')-,'#"7*,('0:'F)1'F(1'"%+'F*'(0')-")'?('='Z8@'3A1')-,
7"6&,()'<0(($47,'#"7*,':06'F('$('*(,+'2-$7,'"'3"B$3*3'($&5
%"7' (2$%&' ")' )-,' +6"$%' 0:' ±@' S' $(' <0(($47,1' "%+' )-,' $%<*)
6,($()"%/,'")')-,'&"),'$('@Z'FΩ8'`,&7,/)')-,'J"67;',::,/)8
E4K I$%+')-,'#"7*,('0:'7@'"%+'6$'")')-,'4$"('<0$%)8
E/K =:'),63$%"7'z'$('&60*%+,+1'),63$%"7'v'$('/0%%,/),+')0'"
($&%"7'(0*6/,'-"#$%&'"'6,($()"%/,'0:'@'FΩ1'"%+'),63$%"7'u
$('/0%%,/),+')0'"'70"+'6,($()"%/,'0:'bZ'PΩ1':$%+')-,'#07)"&,
&"$%':603'($&%"7'(0*6/,')0'70"+8
E+K =:'),63$%"7'u'$('&60*%+,+1':$%+')-,'#07)"&,'&"$%':603'v
)0'z'2$)-'z'0<,%5/$6/*$),+8'U-")'$(')-,'0*)<*)'6,($()"%/,'0:
)-,'(0*6/,':07702,6g
E,K =:'),63$%"7'v'$('&60*%+,+'"%+'),63$%"7'z'$('/0%%,/),+')0
"' /*66,%)' (0*6/,' +,7$#,6$%&' "' ($&%"7' /*66,%)' 0:' @Z' µA' "%+
-"#$%&'"'6,($()"%/,'0:'@ZZ'PΩ1':$%+')-,'#07)"&,'($&%"7')-")
/"%'4,'3,"(*6,+'")'u8'I06'($3<7$/$);1'%,&7,/)')-,',::,/)'0:'6$8
CHAPTER 5
D *5.115 9-,'FGHIJ9'$%')-,' /$6/*$)'0:'I$&8' _W8@@W'-"(
8# ='@ S1' > ! '='Z8d'3AcSQ1'"%+'8G'='bZ'S8
10 k$
(a)
5 k$
&
vo
!5 V
2 k$
vi2
RD
!
Y
10 k$
!
X
!
(b)
Z
RG
Figure P5.116
RS
#5 V
Figure P5.115
*5.116 E"K 9-,' `FGH' )6"%($()06' $%' )-,' (0*6/,5:07702,6
/$6/*$)' 0:' I$&8' _W8@@NE"K' -"(' 7@' =' W' 3AcS' "%+' "' 7"6&,' 6$8
I$%+')-,'0<,%5/$6/*$)'#07)"&,'&"$%'"%+')-,'0*)<*)'6,($()"%/,8
E4K 9-,'`FGH')6"%($()06'$%')-,'/0330%5&"),'"3<7$:$,6'0:
I$&8' _W8@@NE4K' -"(' 7@' =' W' 3AcS' "%+' "' 7"6&,' 6$8' I$%+' )-,
$%<*)'6,($()"%/,'"%+')-,'#07)"&,'&"$%8
E/K =:')-,'0*)<*)'0:')-,'(0*6/,':07702,6'$%'E"K'$('/0%%,/),+')0
)-,'$%<*)'0:')-,'/0330%5&"),'"3<7$:$,6'$%'E4K1'*(,')-,'6,(*7)(
0:'E"K'"%+'E4K')0'04)"$%')-,'0#,6"77'#07)"&,'&"$%' v $ ⁄ v + 8
*5.117 =%')-$('<6047,3'2,'$%#,()$&"),')-,'7"6&,5($&%"7'0<,65
")$0%'0:')-,'(0*6/,':07702,6'0:'I$&8'W8NZE"K8'H<,/$:$/"77;1'/0%5
($+,6' )-,' ($)*")$0%' 2-,%' %,&")$#,' $%<*)' ($&%"7(' "6,' "<<7$,+8
T,)')-,'%,&")$#,'($&%"7'#07)"&,'")')-,'0*)<*)'4,'−88'9-,'/*65
6,%)'$%'F&'2$77':702'"2";':603'&60*%+'"%+'2$77'-"#,'"'#"7*,
0:' 8PF&8' 9-$(' /*66,%)' 2$77' (*4)6"/)' :603' )-,' 4$"(' /*66,%)' ?1
6,(*7)$%&'$%'"')6"%($()06'/*66,%)'0:'E?'−'8PF&K8'G%,'/"%'*(,')-$(
/*66,%)'#"7*,')0'+,),63$%,'v*)8'`021')-,'($&%"7'")')-,')6"%($(5
)06'(0*6/,'),63$%"7'2$77'4,'−81'(*<,6$3<0(,+'0%')-,'+/'#07)5
"&,1'2-$/-'$('−8*)'E/066,(<0%+$%&')0'"'+6"$%'/*66,%)'0:'?K8'U,
/"%')-*(':$%+')-,'($&%"7'#07)"&,'")')-,'&"),' v+8'I06')-,'/$6/*$)
"%"7;>,+'$%'JB,6/$(,'W8b@1':$%+'v+':06'v$'='−@'S1'''−W'S1'−N'S1
"%+' −f' S8' A)' ,"/-' <0$%)1' :$%+' )-,' #07)"&,' &"$%' v$ Pv+' "%+
/03<"6,' )0' )-,' (3"775($&%"7' #"7*,' :0*%+' $%' JB,6/$(,' W8b@8
U-")'$(')-,'7"6&,()'<0(($47,'%,&")$#,50*)<*)'($&%"7g
CHAPTER 5
PROBLEMS
348 Chapter 5 MOS Field-Effect Transistors (MOSFETs)
Section 5.9: The Body Effect and Other Topics
General Problems
5.118' =%' "' <"6)$/*7"6' "<<7$/")$0%1' "%' !5/-"%%,7' FGHIJ9
0<,6"),('2$)-'8 )A'$%')-,'6"%&,'Z'S')0'b'S8'=:'8 #Z'$('%03$%"77;
@⁄Q
@8Z'S1':$%+')-,'6"%&,'0:'8 # ')-")'6,(*7)('$:' γ & Z8W'S '"%+
Qφ M & Z8N 'S8'=:')-,'&"),'0B$+,')-$/P%,(('$('$%/6,"(,+'4;'"
:"/)06'0:'b1'2-")'+0,(')-,')-6,(-07+'#07)"&,'4,/03,g
**5.124 9-,'/$6/*$)('(-02%'$%'I$&8'_W8@Qb',3<70;'%,&")$#,
:,,+4"/P1' "' (*4.,/)' 2,' (-"77' ()*+;' $%' +,)"$7' $%' ?-"<),6' @Z8
A((*3,' )-")' ,"/-' )6"%($()06' $(' ($>,+' "%+' 4$"(,+' (0' )-")
7@ = @ 3AcS'"%+'6$'='@ZZ'PΩ8'G)-,62$(,1'$&%06,'"77'+/'4$"(5
$%&'+,)"$7'"%+'/0%/,%)6"),'0%'(3"775($&%"7'0<,6")$0%'6,(*7)5
$%&' $%' 6,(<0%(,' )0' )-,' $%<*)' ($&%"7' v($&8' I06' F&' =' @Z' PΩ1
F@ = WZZ'PΩ1'"%+'FQ'='@'FΩ1':$%+')-,'0#,6"77'#07)"&,'&"$%
v$ Pv($&'"%+')-,'$%<*)' 6,($()"%/,'F$%' :06' ,"/-' /$6/*$)8' `,&7,/)
)-,' 40+;' ,::,/)8' ^0' )-,(,' /$6/*$)(' 6,3$%+' ;0*' 0:' 0<5"3<
/$6/*$)(g'?033,%)8
5.119' A'"5/-"%%,7' )6"%($()06' 0<,6"),(' $%' (")*6")$0%'2$)-' $)(
(0*6/,' #07)"&,' C' S' 702,6' )-"%' $)(' (*4()6"),8' I06
@⁄Q
γ & Z8W'S 1 ' Qφ M & Z8fW 'S1'"%+'8 #Z & ' Z8f 'S1':$%+'8 # 8
5.120' I06' "%' `FGH' )6"%($()06' 2$)-' Qφ M & Z8N ' S1
@⁄Q
γ & Z8W'S 1 1' "%+' 8 )A & b ' S1' :$%+' χ & 7 @K ⁄ 7 @ 8 ' =:
)-,' )6"%($()06' $(' 4$"(,+' ")' ? ( & Z8W ' 3A' 2$)-' 8 :8 & Z8QW
S1':$%+' 7 @'"%+' 7 @K 8
VDD
5.121' A' +,<7,)$0%5);<,' !5/-"%%,7' FGHIJ9' 2$)>′! ' ⁄ & & Q '3AcSQ'"%+'8 # & ' C'S'-"('$)('(0*6/,'"%+'&"),
&60*%+,+8'I$%+')-,'6,&$0%'0:'0<,6")$0%'"%+')-,'+6"$%'/*66,%)
:06' v ( & Z8@' S1' @' S1' C' S1' "%+' W' S8' `,&7,/)' )-,' /-"%%,75
7,%&)-530+*7")$0%',::,/)8
RL
R2
R1
5.122' I06' "' <"6)$/*7"6' +,<7,)$0%530+,' `FGH' +,#$/,1
'@
8 # & ' Q ' S1' >′! ' ⁄ & & QZZ' µAcSQ1' "%+' λ & Z8ZQ'S 8
U-,%' 0<,6"),+' ")' v *) & Z1' 2-")' $(' )-,' +6"$%' /*66,%)' )-")
:702(':06' v () & @ 'S1'Q'S1'C'S1'"%+'@Z'Sg'U-")'+0,(',"/-
vsig !
#
0:')-,(,'/*66,%)('4,/03,'$:')-,'+,#$/,'2$+)-'$('+0*47,+'2$)&')-,'("3,g'U$)-'&'"7(0'+0*47,+g'
5.123' `,&7,/)$%&' )-,' /-"%%,757,%&)-530+*7")$0%' ,::,/)
(-02' )-")' :06' )-,' +,<7,)$0%5);<,' `FGH' )6"%($()06' 0:' I$&8
_W8@QC1')-,' + ' v'6,7")$0%(-$<'$('&$#,%'4;
Rin
(a)
@
Q
+ & 555 >′! ( ' ⁄ & ) ( v ' Q8 # v ) 1 :06' v ≥ 8 #
Q
Q
+ & '@
:06' v ≤ 8 #
555 >′! ( ' ⁄ & )8 #
Q
VDD
Ei,/"77')-")'8 # '$('%,&")$#,K8'HP,)/-')-,' + ' v'6,7")$0%(-$<':06
)-,'/"(,D' 8 # & ' Q 'S'"%+' >′! ( ' ⁄ & ) & Q'3AcSQ8'
RL
R2
vo
i !
R1
v
! vsig
#
#
Rin
Figure P5.123
(b)
Figure P5.124
vo
Problems 349
VDD
I1
Q2
Q1
R1
R2
vo
vi
vsig
!
#
RL
Rin
Figure P5.126
5.127 ?0%($+,6')-,'4$"('+,($&%'0:')-,'/$6/*$)'0:'_6047,3'W8@QN
E(-02%' $%' I$&8' _W8@QNK8' I06' > !′ =' QZZ' µAcSQ' "%+' 8((' =
C8C S1':$%+' ( 'c& ) @'"%+' ( 'c& ) Q')0'04)"$%')-,'0<,6")$%&'/0%5
+$)$0%('(<,/$:$,+'$%'_6047,3'W8@QN8
PROBLEMS
**5.126 =%')-,'"3<7$:$,6'(-02%'$%'I$&8'_W8@QN1')6"%($()06(
-"#$%&'8#'='Z8N'S'"%+'8G'='QZ'S'"6,'0<,6"),+'")'8*)'='Z8d'S
*($%&' )-,' "<<60<6$"),' /-0$/,' 0:' 'P&' 6")$08' =%' "' <"6)$/*7"6
"<<7$/")$0%1';@'$(')0'4,'($>,+')0'0<,6"),'")'@Z'µA1'2-$7,';Q'$(
$%),%+,+')0'0<,6"),'")'@'3A8'I06'F&'='Q'PΩ1')-,'EF@1'FQK'%,)5
206P' ($>,+' )0' /0%(*3,' 0%7;' @o' 0:' )-,' /*66,%)' $%' F&1' v($&1
-"#$%&'>,60'+/'/03<0%,%)1'"%+'?@'='@Z'µA1':$%+')-,'#"7*,(
0:'F@'"%+'FQ')-")'(")$(:;'"77')-,'6,O*$6,3,%)(8'ER+!#D'8:'3*()
4,'+Q S8K'U-")'$(')-,'#07)"&,'&"$%'v$ Pv+g'n($%&'"'6,(*7)':603
"')-,06,3'P%02%'"('F$77,6m(')-,06,3'E?-"<),6'[K1':$%+')-,
$%<*)'6,($()"%/,'F$%'"(' F Q ⁄ ( @ ' v $ ⁄ v + )8 '`021'/"7/*7"),')-,
#"7*,' 0:' )-,' 0#,6"77' #07)"&,' &"$%' v$ Pv($&8' ^0,(' )-$(' 6,(*7)
6,3$%+' ;0*' 0:' )-,' $%#,6)$%&' /0%:$&*6")$0%' 0:' )-,' 0<' "3<g
?033,%)8'!02'20*7+';0*'30+$:;')-,'/$6/*$)'")')-,'$%<*)'4;
*($%&' "%' "++$)$0%"7' 6,($()06' "%+' "' #,6;' 7"6&,' /"<"/$)06' )0
6"$(,')-,'&"$%'v$ Pv($&')0'−W'ScSg'`,&7,/)')-,'40+;',::,/)8
CHAPTER 5
5.125 I06' )-,' )20' /$6/*$)(' $%' _6047,3' W8@Qb' E(-02%' $%
I$&8 _W8@QbK1'2,'2$(-')0'/0%($+,6')-,$6'+/'4$"('+,($&%8'H$%/,
v($&'-"('"'>,60'+/'/03<0%,%)1'2,'(-06)5/$6/*$)'$)('&,%,6")068
I06'`FGH')6"%($()06('2$)-'8#'='Z8N'S1':$%+'8:8 1' > !′ ( ' ⁄ & )1
"%+'8G')0'4$"(',"/-'+,#$/,'")'?('='Z8@'3A'"%+')0'04)"$%')-,
#"7*,(' 0:' 7@' "%+' 6$' (<,/$:$,+' $%' _6047,3' W8@QbD' %"3,7;1
7@ = @ 3AcS'"%+'6$'='@ZZ'PΩ8'I06'F@'='Z8W'FΩ1'FQ'='@'FΩ1
"%+'F&'='@Z'PΩ1':$%+')-,'6,O*$6,+'#"7*,'0:'8((8
CHAPTER 6
Bipolar Junction
Transistors (BJTs)
Introduction
6.1
351
Device Structure and
Physical Operation 352
6.2 Current–Voltage Characteristics 365
6.3 BJT Circuits at DC
378
6.4 Applying the BJT in Amplifier
Design 396
6.5 Small-Signal Operation and
Models 403
6.6 Basic BJT Amplifier
Configurations 422
6.7 Biasing in BJT Amplifier
Circuits 446
6.8 Discrete-Circuit BJT Amplifiers
453
6.9 Transistor Breakdown and Temperature
Effects 463
Summary
465
Problems
466
IN THIS CHAPTER YOU WILL LEARN
1. The physical structure of the bipolar transistor and how it works.
2. How the voltage between two terminals of the transistor controls the
current that flows through the third terminal, and the equations that
describe these current–voltage characteristics.
3. How to analyze and design circuits that contain bipolar transistors, resistors, and dc sources.
4. How the transistor can be used to make an amplifier.
5. How to obtain linear amplification from the fundamentally nonlinear BJT.
6. The three basic ways for connecting a BJT to be able to construct amplifiers with different properties.
7. Practical circuits for bipolar-transistor amplifiers that can be constructed by using discrete components.
Introduction
!"#$%&'#(%)*$+,-#.+#'$/01#$%+#2$%+,#3)42,#$%,++5$+,3&")6#0+7&(+8#$%+#9&*26),#4/"($&2"#$,)"'&'$2,
:;<=>?#=%+#*,+'+"$)$&2"#2@#$%+#3)$+,&)6#&"#$%&'#(%)*$+,#*),)66+6'#9/$#02+'#"2$#,+61#2"#$%)$#@2,
$%+#ABCDE=#&"#F%)*$+,#GH#$%/'-#&@#0+'&,+0-#$%+#;<=#()"#9+#'$/0&+0#9+@2,+#$%+#ABCDE=?
!"#$$%&$#'()*+,-$.(/$0,*#$,1*#,'2#$,30$13+,&"*),&42%&$#'()*+,2)$05,03/",*0,&"$,-(2-$0
0&3-($-,(),6"*7&$#,85,9$/*30$,&"$:,/*),9$,30$-,(),*,'3+&(&3-$,21,*77+(/*&(2)05,#*);();,1#2'
0(;)*+,*'7+(1(/*&(2),&2,&"$,-$0(;),21,-(;(&*+,+2;(/,*)-,'$'2#:,/(#/3(&0<,!"$,9*0(/,7#()/(7+$
().2+.$-,(0,&"$,30$,21,&"$,.2+&*;$,9$&4$$),&42,&$#'()*+0,&2,/2)&#2+,&"$,/3##$)&,1+24();,()
&"$ &"(#-,&$#'()*+<,=),&"(0,4*:5,*,&"#$$%&$#'()*+,-$.(/$,/*),9$,30$-,&2,#$*+(>$,*,/2)&#2++$023#/$5, 4"(/", *0, 4$, +$*#)$-, (), 6"*7&$#, ?, (0, &"$, 9*0(0, 12#, *'7+(1($#, -$0(;)<, @+025, (), &"$
$A&#$'$5,&"$,/2)&#2+,0(;)*+,/*),9$,30$-,&2,/*30$,&"$,/3##$)&,(),&"$,&"(#-,&$#'()*+,&2,/"*);$
1#2',>$#2,&2,* +*#;$,.*+3$5,&"30,*++24();,&"$,-$.(/$,&2,*/&,*0,*,04(&/"<,!"$,04(&/",(0,&"$,9*0(0
12#,&"$,#$*+(>*&(2),21,&"$,+2;(/,().$#&$#5,&"$,9*0(/,$+$'$)&,21,-(;(&*+,/(#/3(&0<
!"$,().$)&(2),21,&"$,BC!,(),?D8E,*&,&"$,B$++,!$+$7"2)$,F*92#*&2#($0,30"$#$-,(),&"$,$#*
21,02+(-%0&*&$,/(#/3(&05,4"(/",+$-,&2,$+$/&#2)(/0,/"*);();,&"$,4*:,4$,42#G5,7+*:5,*)-,()-$$-5
+(.$<,!"$,().$)&(2),21,&"$,BC!,*+02,$.$)&3*++:,+$-,&2,&"$,-2'()*)/$,21,()12#'*&(2),&$/")2+2;:
*)-,&"$,$'$#;$)/$,21,&"$,G)24+$-;$%9*0$-,$/2)2':<
!"$, 9(72+*#, &#*)0(0&2#, $)H2:$-, )$*#+:, &"#$$, -$/*-$0, *0, &"$, -$.(/$, 21, /"2(/$, (), &"$
-$0(;), 21, 92&", -(0/#$&$, *)-, ()&$;#*&$-, /(#/3(&0<, @+&"23;", &"$, IJKLM!, "*-, 9$$), G)24)
351
352 Chapter 6 Bipolar Junction Transistors (BJTs)
.$#:,$*#+:,2)5,(&,4*0,)2&,3)&(+,&"$,?DNO0,*)-,?DEO0,&"*&,(&,9$/*'$,*,0$#(230,/2'7$&(&2#,&2
&"$,BC!<,B:,POOD5,&"$,IJKLM!,4*0,3)-239&$-+:,&"$,'20&,4(-$+:,30$-,$+$/&#2)(/,-$.(/$5
*)-,6IJK,&$/")2+2;:,&"$,&$/")2+2;:,21,/"2(/$,(),&"$,-$0(;),21,()&$;#*&$-,/(#/3(&0<,Q$.%
$#&"$+$005, &"$, BC!, #$'*()0, *, 0(;)(1(/*)&, -$.(/$, &"*&, $A/$+0, (), /$#&*(), *77+(/*&(2)0<, L2#
()0&*)/$5,&"$,#$+(*9(+(&:,21,BC!,/(#/3(&0,3)-$#,0$.$#$,$).(#2)'$)&*+,/2)-(&(2)0,'*G$0,&"$'
&"$,-2'()*)&,-$.(/$,(),/$#&*(),*3&2'2&(.$,*77+(/*&(2)0<,
!"$,BC!,#$'*()0,7273+*#,(),-(0/#$&$%/(#/3(&,-$0(;)5,(),4"(/",*,.$#:,4(-$,0$+$/&(2),21
BC!,&:7$0,*#$,*.*(+*9+$,&2,&"$,-$0(;)$#<,R$#$,4$,0"23+-,'$)&(2),&"*&,&"$,/"*#*/&$#(0&(/0,21
&"$,9(72+*#,&#*)0(0&2#,*#$,02,4$++,3)-$#0&22-,&"*&,2)$,(0,*9+$,&2,-$0(;),&#*)0(0&2#,/(#/3(&0
4"20$,7$#12#'*)/$,(0,#$'*#G*9+:,7#$-(/&*9+$,*)-,S3(&$,()0$)0(&(.$,&2,.*#(*&(2)0,(),-$.(/$
7*#*'$&$#0<
!"$,BC!,(0,0&(++,&"$,7#$1$##$-,-$.(/$,(),.$#:,-$'*)-();,*)*+2;,/(#/3(&,*77+(/*&(2)05,92&"
()&$;#*&$-,*)-,-(0/#$&$<,!"(0,(0,$07$/(*++:,&#3$,(),.$#:%"(;"%1#$S3$)/:,*77+(/*&(2)05,03/",*0
#*-(2%1#$S3$)/:,TULV,/(#/3(&0,12#,4(#$+$00,0:0&$'0<,@,.$#:%"(;"%07$$-,-(;(&*+,+2;(/%/(#/3(&
1*'(+:, 9*0$-, 2), 9(72+*#, &#*)0(0&2#05, )*'$+:5, $'(&&$#%/237+$-, +2;(/5, (0, 0&(++, (), 30$<, L()*++:5
9(72+*#,&#*)0(0&2#0,/*),9$,/2'9()$-,4(&",IJKLM!0,&2,/#$*&$,())2.*&(.$,/(#/3(&0,&"*&,&*G$
*-.*)&*;$, 21, &"$, "(;"%()73&%('7$-*)/$, *)-, +24%724$#, 27$#*&(2), 21, IJKLM!0, *)-, &"$
.$#:%"(;"%1#$S3$)/:, 27$#*&(2), *)-, "(;"%/3##$)&%-#(.();, /*7*9(+(&:, 21, 9(72+*#, &#*)0(0&2#0<
!"$,#$03+&();,&$/")2+2;:,(0,G)24),*0,B(6IJK5,*)-,(&,(0,1()-();,()/#$*0();+:,+*#;$#,*#$*0,21
*77+(/*&(2),T0$$,6"*7&$#0,N5,E5,?P5,*)-,?8V<
=), &"(0, /"*7&$#5, 4$, 0"*++, 0&*#&, 4(&", *, -$0/#(7&(2), 21, &"$, 7":0(/*+, 27$#*&(2), 21, &"$, BC!<
!"23;",0('7+$5,&"(0,7":0(/*+,-$0/#(7&(2),7#2.(-$0,/2)0(-$#*9+$,()0(;"&,#$;*#-();,&"$,7$#12#%
'*)/$,21,&"$,&#*)0(0&2#,*0,*,/(#/3(&,$+$'$)&<,W$,&"$),S3(/G+:,'2.$,1#2',-$0/#(9();,/3##$)&
1+24,(),&$#'0,21,$+$/&#2)0,*)-,"2+$0,&2,*,0&3-:,21,&"$,&#*)0(0&2#,&$#'()*+,/"*#*/&$#(0&(/0<
6(#/3(&,'2-$+0,12#,&#*)0(0&2#,27$#*&(2),(),-(11$#$)&,'2-$0,4(++,9$,-$.$+27$-,*)-,3&(+(>$-,()
&"$,*)*+:0(0,*)-,-$0(;),21,&#*)0(0&2#,/(#/3(&0<,!"$,'*(),29H$/&(.$,21,&"(0,/"*7&$#,(0,&2,-$.$+27
(),&"$,#$*-$#,*,"(;",-$;#$$,21,1*'(+(*#(&:,4(&",&"$,BC!<,!"305,9:,&"$,$)-,21,&"$,/"*7&$#5,&"$
#$*-$#,0"23+-,9$,*9+$,&2,7$#12#',#*7(-,1(#0&%2#-$#,*)*+:0(0,21,&#*)0(0&2#,/(#/3(&0,*)-,&2,-$0(;)
0();+$%0&*;$,&#*)0(0&2#,*'7+(1($#0<
6.1 Device Structure and Physical Operation
6.1.1 Simplified Structure and Modes of Operation
L(;3#$,X<?,0"240,*,0('7+(1($-,0&#3/&3#$,12#,&"$,BC!<,@,7#*/&(/*+,&#*)0(0&2#,0&#3/&3#$,4(++,9$
0"24),+*&$#,T0$$,*+02,@77$)-(A,@5,4"(/",-$*+0,4(&",1*9#(/*&(2),&$/")2+2;:V<
@0,0"24),(),L(;<,X<?5,&"$,BC!,/2)0(0&0,21,&"#$$,0$'(/2)-3/&2#,#$;(2)0Y,&"$,$'(&&$#,#$;(2)
T!,&:7$V5,&"$,9*0$,#$;(2),T",&:7$V5,*)-,&"$,/2++$/&2#,#$;(2),T!,&:7$V<,K3/",*,&#*)0(0&2#,(0,/*++$*), !"!,&#*)0(0&2#<, @)2&"$#, &#*)0(0&2#5,*, -3*+,21, &"$,!"!, *0,0"24), (), L(;<,X<P5,"*0, *, "%&:7$
$'(&&$#5,*),!%&:7$,9*0$5,*)-,*,"%&:7$,/2++$/&2#5,*)-,(0,*77#27#(*&$+:,/*++$-,*,"!",&#*)0(0&2#<
@,&$#'()*+,(0,/2))$/&$-,&2,$*/",21,&"$,&"#$$,0$'(/2)-3/&2#,#$;(2)0,21,&"$,&#*)0(0&2#5,4(&"
&"$,&$#'()*+0,+*9$+$-,!"#$$!%,TMV5,&'(!,TBV5,*)-,)*++!)$*%,T6V<
!"$, &#*)0(0&2#, /2)0(0&0, 21, &42, "!, H3)/&(2)05, &"$, !"#$$!%,&'(!- ./0)$#*0, TMBCV, *)-, &"$
)*++!)$*%,&'(!- ./0)$#*0, T6BCV<, Z$7$)-();, 2), &"$, 9(*0, /2)-(&(2), T12#4*#-, 2#, #$.$#0$V, 21
$*/" 21, &"$0$, H3)/&(2)05, -(11$#$)&, '2-$0, 21, 27$#*&(2), 21, &"$, BC!, *#$, 29&*()$-5, *0, 0"24), ()
!*9+$, X<?<, !"$, ')$#1!- "*2!, (0, &"$, 2)$, 30$-, (1, &"$, &#*)0(0&2#, (0, &2, 27$#*&$, *0, *), *'7+(1($#<
K4(&/"();,*77+(/*&(2)0,T$<;<5,+2;(/,/(#/3(&0V,3&(+(>$,92&",&"$,)/$*33,"*2!,*)-,&"$,('$/%'$#*0
"*2!<,@0,&"$,)*'$,('7+($05,(),&"$,/3&211,'2-$,)2,/3##$)&,1+240,9$/*30$,92&",H3)/&(2)0,*#$
#$.$#0$,9(*0$-<
6.1 Device Structure and Physical Operation
Emitter
(E)
n-type
p-type
n-type
Emitter
region
Base
region
Collector
region
Emitter–base
junction
(EBJ)
Base
(B)
Metal
contact
Collector
(C)
Collector–base
junction
(CBJ)
Figure 6.1 I#'&3*6&@&+0#'$,/($/,+#2@#$%+#!"!#$,)"'&'$2,?
Metal
contact
E
p
n
p
Emitter
region
Base
region
Collector
region
C
B
Figure 6.2 I#'&3*6&@&+0#'$,/($/,+#2@#$%+#"!"#$,)"'&'$2,?
Table 6.1 BJT Modes of Operation
A20+
E;<
F;<
F/$2@@
I($&7+
C)$/,)$&2"
J+7+,'+
D2,.),0
D2,.),0
J+7+,'+
J+7+,'+
D2,.),0
@0,4$,4(++,0$$,0"2#&+:5,/"*#;$,/*##($#0,21,92&",72+*#(&($0[&"*&,(05,$+$/&#2)0,*)-,"2+$0[
7*#&(/(7*&$,(),&"$,/3##$)&%/2)-3/&(2),7#2/$00,(),*,9(72+*#,&#*)0(0&2#5,4"(/",(0,&"$,#$*02),12#
&"$,)*'$,#$"%&'(<?,,
6.1.2 Operation of the npn Transistor in the Active Mode
J1,&"$,&"#$$,'2-$0,21,27$#*&(2),21,&"$,BC!5,&"$,*/&(.$,'2-$,(0,&"$,'20&,('72#&*)&<,!"$#$12#$5
4$,9$;(),23#,0&3-:,21,&"$,BC!,9:,/2)0(-$#();,(&0,7":0(/*+,27$#*&(2),(),&"$,*/&(.$,'2-$<P,!"(0
0(&3*&(2),(0,(++30&#*&$-,(),L(;<,X<\,12#,&"$,!"!,&#*)0(0&2#<,!42,$A&$#)*+,.2+&*;$,023#/$0,T0"24),*0
9*&&$#($0V,*#$,30$-,&2,$0&*9+(0",&"$,#$S3(#$-,9(*0,/2)-(&(2)0,12#,*/&(.$%'2-$,27$#*&(2)<,!"$,.2+&*;$
K
=%&'#'%2/60#9+#(2"$,)'$+0#.&$%#$%+#'&$/)$&2"#&"#$%+#ABCDE=-#.%+,+#(/,,+"$#&'#(2"0/($+0#91#(%),L+
(),,&+,'#2@#2"+#$1*+#2"61H#+6+($,2"'#&"#!5(%)""+6#0+7&(+'#2,#%26+'#&"#"5(%)""+6#0+7&(+'?#!"#+),6&+,#0)1''23+#,+@+,,+0#$2#DE='#)'#/"&*26),#0+7&(+'?
M
=%+#3)$+,&)6#&"#$%&'#'+($&2"#)''/3+'#$%)$#$%+#,+)0+,#&'#@)3&6&),#.&$%#$%+#2*+,)$&2"#2@#$%+#"!#4/"($&2"
/"0+,#@2,.),059&)'#(2"0&$&2"'#:C+($&2"#N?G>?
353
354 Chapter 6 Bipolar Junction Transistors (BJTs)
Reverse-biased
Forward-biased
n
Diffusing
electrons
Injected
electrons
E
Collected
electrons
iC
C
iB2
iE
iE
n
p
Injected holes (iB1)
iC
Recombined
electrons (iB2)
iB
–
v BE
iB
+
iE
iE
VBE
B
–
v CB
+
iC
iC
VCB
Figure 6.3 73''#./$ %5&($ ,.$ ).$ %$%$ /').-,-/&'$ +,)-#*$ /&$ &8#')/#$ ,.$ /"#$ )4/,>#$ 0&*#6$ ?J#>#'-#$ 43''#./
4&08&.#./-$*3#$/&$*',%/$&%$/"#'0)55<$=#.#')/#*$0,.&',/<$4)'',#'-$)'#$.&/$-"&(.6@
!"#!"#$%&%!'(&!$)'*+&!,#%&!'-!,&!(./(&0!.1!+-'&1'.#2!'(#1!'(&!%)'*+&!&3.''&04!'($%!5-06#07),.#%.1/
'(&!&3.''&08,#%&!9$1"'.-1:!;(&!"-22&"'-08,#%&!<-2'#/&!!&"!"#$%&%!'(&!%)'*+&!"-22&"'-0!'-!,&!#'!#
(./(&0!+-'&1'.#2!'(#1!'(&!$)'*+&!,#%&4!'($%!0&<&0%&),.#%.1/!'(&!"-22&"'-08,#%&!9$1"'.-1:
Current Flow !"#$%&'()'*$+,)-$&.$/"#$#0,//#'1+)-#$23.4/,&.$(,55$4)3-#$43''#./$/&$%5&($)4'&-/",-$23.4/,&.6$73''#./$(,55$4&.-,-/$&%$/(&$4&08&.#./-9$#5#4/'&.-$,.2#4/#*$%'&0$/"#$#0,//#'$,./&$/"#
+)-#:$).*$"&5#-$,.2#4/#*$%'&0$/"#$+)-#$,./&$/"#$#0,//#'6$;-$(,55$+#4&0#$)88)'#./$-"&'/5<:$,/$,-$",="5<
*#-,')+5#$/&$")>#$/"#$%,'-/$4&08&.#./$?#5#4/'&.-$%'&0$#0,//#'$/&$+)-#@$)/$)$034"$",="#'$5#>#5$/").
/"#$-#4&.*$4&08&.#./$?"&5#-$%'&0$+)-#$/&$#0,//#'@6$!",-$4).$+#$)44&085,-"#*$+<$%)+',4)/,.=$/"#
*#>,4#$(,/"$)$"#)>,5<$*&8#*$#0,//#'$).*$)$5,="/5<$*&8#*$+)-#A$/")/$,-:$/"#$*#>,4#$,-$*#-,=.#*$/&$")>#
)$",="$*#.-,/<$&%$#5#4/'&.-$,.$/"#$#0,//#'$).*$)$5&($*#.-,/<$&%$"&5#-$,.$/"#$+)-#6
!"#$43''#./$/")/$%5&(-$)4'&--$/"#$#0,//#'1+)-#$23.4/,&.$(,55$4&.-/,/3/#$/"#$#0,//#'$43''#./$'#:$),.*,4)/#*$,.$B,=6$C6D6$!"#$*,'#4/,&.$&%$'#$,-$E&3/$&%F$/"#$#0,//#'$5#)*:$(",4":$%&55&(,.=$/"#$3-3)5
4&.>#./,&.-:$ ,-$ ,.$ /"#$ *,'#4/,&.$ &%$ /"#$ 8&-,/,>#G4")'=#$ %5&($ ?"&5#$ 43''#./@$ ).*$ &88&-,/#$ /&$ /"#
*,'#4/,&.$&%$/"#$.#=)/,>#G4")'=#$%5&($?#5#4/'&.$43''#./@:$(,/"$/"#$#0,//#'$43''#./$'#$+#,.=$#H3)5$/&
/"#$-30$&%$/"#-#$/(&$4&08&.#./-6$I&(#>#':$-,.4#$/"#$#5#4/'&.$4&08&.#./$,-$034"$5)'=#'$/").
/"#$"&5#$4&08&.#./:$/"#$#0,//#'$43''#./$(,55$+#$*&0,.)/#*$+<$/"#$#5#4/'&.$4&08&.#./6
=&'!$%!1-6!"-1%.7&0!'(&!&2&"'0-1%!.19&"'&7!50-3!'(&!&3.''&0!.1'-!'(&!,#%&:!;(&%&!&2&"'0-1%
6.22!,&!!"#$%"&'()*%%"+%,!.1!'(&!$)'*+&!,#%&!0&/.-1:!>&"#$%&!'(&!,#%&!.%!$%$#22*!<&0*!'(.14
.1 '(&!%'&#7*!%'#'&!'(&!&?"&%%!3.1-0.'*!"#00.&0!@&2&"'0-1A!"-1"&1'0#'.-1!.1!'(&!,#%&!6.22!(#<&
#1!#23-%')%'0#./(')2.1&!+0-5.2&4!#%!.17."#'&7!,*!'(&!%-2.7!%'0#./('!2.1&!.1!B./:!C:D:!;(&!&2&"'0-1
"-1"&1'0#'.-1!6.22!,&!(./(&%'!E7&1-'&7!,*!%$@FAG!#'!'(&!&3.''&0!%.7&!#17!2-6&%'!@H&0-A!#'!'(&
"-22&"'-0! %.7&:I! J%! .1! '(&! "#%&! -5! #1*! 5-06#07),.#%&7! $%! 9$1"'.-1! @K&"'.-1! I:LA4! '(&
v ⁄!
"-1"&1'0#'.-1! % $ ( O ) 6.22!,&!+0-+-0'.-1#2!'-! ( "# ) :
D
!",-$ 0,.&',/<$ 4)'',#'$ *,-/',+3/,&.$ ,.$ /"#$ +)-#$ '#-35/-$ %'&0$ /"#$ +&3.*)'<$ 4&.*,/,&.-$ ,08&-#*$ +<$ /"#
/(& 23.4/,&.-6$K/$,-$.&/$).$#L8&.#./,)55<$*#4)<,.=$*,-/',+3/,&.:$(",4"$(&35*$'#-35/$,%$/"#$+)-#$'#=,&.
(#'#$,.%,.,/#5<$/",4M6$J)/"#':$/"#$/",.$+)-#$4)3-#-$/"#$*,-/',+3/,&.$/&$*#4)<$5,.#)'5<6$B3'/"#'0&'#:$/"#
'#>#'-#$+,)-$&.$/"#$4&55#4/&'1+)-#$23.4/,&.$4)3-#-$/"#$#5#4/'&.$4&.4#./')/,&.$)/$/"#$4&55#4/&'$-,*#$&%$/"#
+)-#$/&$+#$N#'&6
6.1 Device Structure and Physical Operation
Carrier concentration
Emitter
(n)
EBJ
depletion
region
Base
(p)
CBJ
depletion
region
Collector
(n)
Electron
concentration
np (ideal)
Hole
concentration
pn0
np (0)
pn (0)
Distance (x)
np (with
recombination)
Effective base
width W
Figure 6.4 O,2@&6+'#2@#3&"2,&$15(),,&+,#(2"(+"$,)$&2"'#&"#$%+#9)'+#)"0#&"#$%+#+3&$$+,#2@#)"#!"!#$,)"'&'$2,
2*+,)$&"L#&"#$%+#)($&7+#320+8# v )* > P #)"0# v -) ≥ P ?
v
! " ( P ) = ! "P 4 )*
⁄ +,
TX<?V
4"$#$, ! "P (0,&"$,&"$#'*+%$S3(+(9#(3',.*+3$,21,&"$,'()2#(&:,/*##($#,T$+$/&#2)V,/2)/$)&#*&(2)
(),&"$,9*0$,#$;(2)5,v)*,(0,&"$,12#4*#-,9*0$]$'(&&$#,9(*0,.2+&*;$5,*)-,+,,(0,&"$,&"$#'*+,.2+&*;$5
4"(/",(0,$S3*+,&2,*77#2A('*&$+:,P^,'_,*&,#22',&$'7$#*&3#$<,!"$,#$*02),12#,&"$,>$#2,/2)%
/$)&#*&(2),*&,&"$,/2++$/&2#,0(-$,21,&"$,9*0$,(0,&"*&,&"$,720(&(.$,/2++$/&2#,.2+&*;$,v-),/*30$0,&"$
$+$/&#2)0,*&,&"*&,$)-,&2,9$,04$7&,*/#200,&"$,6BC,-$7+$&(2),#$;(2)<
!"$,&*7$#$-,'()2#(&:%/*##($#,/2)/$)&#*&(2),7#21(+$,TL(;<,X<8V,/*30$0,&"$,$+$/&#2)0,()H$/&$()&2,&"$,9*0$,&2,-(1130$,&"#23;",&"$,9*0$,#$;(2),&24*#-,&"$,/2++$/&2#<,!"(0,$+$/&#2),-(1130(2)
/3##$)&,.!,(0,-(#$/&+:,7#272#&(2)*+,&2,&"$,0+27$,21,&"$,0&#*(;"&%+()$,/2)/$)&#*&(2),7#21(+$5
5! " ( 3 )
.! = / * 01 ! 5555555555555555
53
!" ( P )
= / * 01 ! ] 55555555555555
2
TX<PV
4"$#$,/*,(0,&"$,/#200%0$/&(2)*+,*#$*,21,&"$,9*0$]$'(&&$#,H3)/&(2),T(),&"$,-(#$/&(2),7$#7$)-(%
/3+*#,&2,&"$,7*;$V5,0,(0,&"$,'*;)(&3-$,21,&"$,$+$/&#2),/"*#;$5,1!,(0,&"$,$+$/&#2),-(1130(.(&:,()
&"$, 9*0$5,*)-, 2,(0,&"$,$11$/&(.$,4(-&",21,&"$,9*0$<,J90$#.$, &"*&, &"$,)$;*&(.$,0+27$,21,&"$
'()2#(&:,/*##($#,/2)/$)&#*&(2),#$03+&0,(),*,)$;*&(.$,/3##$)&,.!,*/#200,&"$,9*0$`,&"*&,(05,.!,1+240
1#2',#(;"&,&2,+$1&,T(),&"$,)$;*&(.$,-(#$/&(2),21,3V5,4"(/",/2##$072)-0,&2,&"$,303*+,/2).$)&(2)5
)*'$+:5,27720(&$,&2,&"$,-(#$/&(2),21,$+$/&#2),1+24<
K2'$,21,&"$,$+$/&#2)0,&"*&,*#$,-(1130();,&"#23;",&"$,9*0$,#$;(2),4(++,/2'9()$,4(&","2+$05
4"(/",*#$,&"$,'*H2#(&:,/*##($#0,(),&"$,9*0$<,R24$.$#5,0()/$,&"$,9*0$,(0,303*++:,.$#:,&"(),*)+(;"&+:,-27$-5,&"$,7#272#&(2),21,$+$/&#2)0,a+20&b,&"#23;",&"(0,%!)*"&#0'$#*0-4%*)!((,4(++,9$
S3(&$,0'*++<,Q$.$#&"$+$005,&"$,#$/2'9()*&(2),(),&"$,9*0$,#$;(2),/*30$0,&"$,$A/$00,'()2#(&:,/*#%
#($#,/2)/$)&#*&(2),7#21(+$,&2,-$.(*&$,1#2',*,0&#*(;"&,+()$,*)-,&*G$,&"$,0+(;"&+:,/2)/*.$,0"*7$
()-(/*&$-,9:,&"$,9#2G$),+()$,(),L(;<,X<8<,!"$,0+27$,21,&"$,/2)/$)&#*&(2),7#21(+$,*&,&"$,MBC,(0
355
356 Chapter 6 Bipolar Junction Transistors (BJTs)
0+(;"&+:,"(;"$#,&"*),&"*&,*&,&"$,6BC5,4(&",&"$,-(11$#$)/$,*//23)&();,12#,&"$,0'*++,)3'9$#,21
$+$/&#2)0,+20&,(),&"$,9*0$,#$;(2),&"#23;",#$/2'9()*&(2)<
The Collector Current D,23#$%+#0+'(,&*$&2"#)927+#.+#'++#$%)$#32'$#2@#$%+#0&@@/'&"L#+6+(5
$,2"'#.&66#,+)(%#$%+#92/"0),1#2@#$%+#(266+($2,Q9)'+#0+*6+$&2"#,+L&2"?#;+()/'+#$%+#(266+($2,#&'
32,+#*2'&$&7+#$%)"#$%+#9)'+#:91#v-)#726$'>-#$%+'+#'/((+''@/6#+6+($,2"'#.&66#9+#'.+*$#)(,2''#$%+
F;<#0+*6+$&2"#,+L&2"#&"$2#$%+#(266+($2,?#=%+1#.&66#$%/'#L+$#R(266+($+0S#$2#(2"'$&$/$+#$%+#(265
6+($2,#(/,,+"$#$-?#=%/'#$-#=#.!-#.%&(%#.&66#1&+60#)#"+L)$&7+#7)6/+#@2,#$--#&"0&()$&"L#$%)$#$-#@62.'
&"#$%+#"+L)$&7+#0&,+($&2"#2@#$%+#3#)T&'#:&?+?-#@,23#,&L%$#$2#6+@$>?#C&"(+#.+#.&66#$)U+#$%&'#$2 9+#$%+
*2'&$&7+#0&,+($&2"#2@#$- -#.+#()"#0,2*#$%+#"+L)$&7+#'&L"#&"#EV?#:W?M>?#X2&"L#$%&'#)"0#'/9'$&$/$&"L
@2,#!" :P>#@,23#EV?#:W?K>-#.+#()"#$%/'#+T*,+''#$%+#(266+($2,#(/,,+"$#$-#)'#
v
$ - = . 6 4 )*
⁄ +,
TX<\V
4"$#$,&"$,('$/%'$#*0-)/%%!0$,.6,(0,;(.$),9:
. 6 = / * 01 ! ! "P ⁄ 2
K390&(&3&();, ! "P = ! $M ⁄ 7 / - 4"$#$,!$,(0,&"$,()&#()0(/,/*##($#,-$)0(&:,*)-,7/,(0,&"$,-27();,/2)%
/$)&#*&(2),(),&"$,9*0$5,4$,/*),$A7#$00,.6,*0
M
/ * 01 ! ! $
5
. 6 = 55555555555555555555
7/ 2
TX<8V
@),('72#&*)&,290$#.*&(2),&2,'*G$,"$#$,(0,&"*&,&"$,'*;)(&3-$,21,$-,(0,()-$7$)-$)&,21,v-)<
!"*&,(05,*0,+2);,*0,&"$,/2++$/&2#,(0,720(&(.$,4(&",#$07$/&,&2,&"$,9*0$5,&"$,$+$/&#2)0,&"*&,#$*/"
&"$,/2++$/&2#,0(-$,21,&"$,9*0$,#$;(2),4(++,9$,04$7&,()&2,&"$,/2++$/&2#,*)-,#$;(0&$#,*0,/2++$/&2#
/3##$)&<
!"$, 0*&3#*&(2), /3##$)&, .6, (0, ().$#0$+:, 7#272#&(2)*+, &2, &"$, 9*0$, 4(-&", 2, *)-, (0, -(#$/&+:
7#272#&(2)*+,&2,&"$,*#$*,21,&"$,MBC<,!:7(/*++:,.6,(0,(),&"$,#*);$,21,?O−?P,@,&2,?O−?E,@,T-$7$)-%
M
();,2),&"$,0(>$,21,&"$,-$.(/$V<,B$/*30$,.6,(0,7#272#&(2)*+,&2, ! $ - ,(&,(0,*,0&#2);,13)/&(2),21,&$'%
7$#*&3#$5,*77#2A('*&$+:,-239+();,12#,$.$#:,^°6,#(0$,(),&$'7$#*&3#$<,TL2#,&"$,-$7$)-$)/$,21
!M$ ,2),&$'7$#*&3#$5,#$1$#,&2,MS<,\<\N<V
K()/$,.6,(0,-(#$/&+:,7#272#&(2)*+,&2,&"$,H3)/&(2),*#$*,T(<$<5,&"$,-$.(/$,0(>$V5,(&,4(++,*+02,9$
#$1$##$-, &2, *0, &"$, ()'+!- )/%%!0$<, !42, &#*)0(0&2#0, &"*&, *#$, (-$)&(/*+, $A/$7&, &"*&, 2)$, "*0, *)
MBC *#$*5,0*:5,&4(/$,&"*&,21,&"$,2&"$#,4(++,"*.$,0*&3#*&(2),/3##$)&0,4(&",&"*&,0*'$,#*&(2,T(<$<5 PV<
!"30,12#,&"$,0*'$,.*+3$,21,v)*,&"$,+*#;$#,-$.(/$,4(++,"*.$,*,/2++$/&2#,/3##$)&,&4(/$ &"*&,(),&"$
0'*++$#,-$.(/$<,!"(0,/2)/$7&,(0,1#$S3$)&+:,$'7+2:$-,(),()&$;#*&$-%/(#/3(&,-$0(;)<
The Base Current =%+#9)'+#(/,,+"$#$)#&'#(23*2'+0#2@#$.2#(23*2"+"$'?#=%+#@&,'$#(23*25
"+"$#$)K#&'#0/+#$2#$%+#%26+'#&"4+($+0#@,23#$%+#9)'+#,+L&2"#&"$2#$%+#+3&$$+,#,+L&2"?#=%&'#(/,,+"$
v ⁄+
(23*2"+"$#&'#*,2*2,$&2")6#$2# 4 )* , ? #=%+#'+(2"0#(23*2"+"$#2@#9)'+#(/,,+"$-#$)M-#&'#0/+#$2
%26+'#$%)$#%)7+#$2#9+#'/**6&+0#91#$%+#+T$+,")6#(&,(/&$#&"#2,0+,#$2#,+*6)(+#$%+#%26+'#62'$#@,23
$%+#9)'+#$%,2/L%#$%+#,+(239&")$&2"#*,2(+''?#;+()/'+#$)M#&'#*,2*2,$&2")6#$2#$%+#"/39+,#2@#+6+(5
$,2"'#&"4+($+0#&"$2#$%+#9)'+-#&$#)6'2#.&66#9+#*,2*2,$&2")6#$2# 4 v)* ⁄ +, ? #=%/'#$%+#$2$)6#9)'+#(/,,+"$$)898$):8; $)<-#.&66#9+#*,2*2,$&2")6#$2#4 v)* ⁄ +, -#)"0#()"#9+#+T*,+''+0#)'#)#@,)($&2"#2@#$%+#(266+($2,
(/,,+"$#$-#)'#@2662.'8
$
$ ) = 555-5
β
external=
from
battero
from B
TX<^V
e
x
6.1 Device Structure and Physical Operation
!"*&,(05
. v ⁄+
$ ) = 55556 4 )* ,
β
TX<XV
4"$#$,β,(0,*,&#*)0(0&2#,7*#*'$&$#<
D2,#320+,"#!"!#$,)"'&'$2,'-#β#&'#&"#$%+#,)"L+#GP#$2#MPP-#9/$#&$#()"#9+#)'#%&L%#)'#KPPP#@2,
'*+(&)6# 0+7&(+'?# D2,# ,+)'2"'# $%)$# .&66# 9+(23+# (6+),# 6)$+,-# $%+# *),)3+$+,# β# &'# ()66+0# $%+
)*""*05!"#$$!%-)/%%!0$-6'#0?
!"$,*92.$,-$0/#(7&(2),()-(/*&$0,&"*&,&"$,.*+3$,21, β,(0,"(;"+:,()1+3$)/$-,9:,&42,1*/&2#0Y
&"$,4(-&",21,&"$,9*0$,#$;(2)5,25,*)-,&"$,#$+*&(.$,-27();0,21,&"$,9*0$,#$;(2),*)-,&"$,$'(&&$#
#$;(2)5, 7 / ⁄ 7 1 ? , !2, 29&*(), *, "(;", β, T4"(/", (0, "(;"+:, -$0(#*9+$, 0()/$, β, #$7#$0$)&0, *, ;*()
7*#*'$&$#V, &"$, 9*0$, 0"23+-, 9$, &"(), T2, 0'*++V, *)-, +(;"&+:, -27$-, *)-, &"$, $'(&&$#, "$*.(+:
-27$-, ( 3)U&"L#7 / ⁄ 7 1 #'3)66 )? ,L2#,'2-$#),()&$;#*&$-,/(#/3(&,1*9#(/*&(2),&$/")2+2;($05
2,(0,(),&"$,)*)2'$&$#,#*);$<
The Emitter Current C&"(+#$%+#(/,,+"$#$%)$#+"$+,'#)#$,)"'&'$2,#3/'$#6+)7+#&$-#&$#()"#9+#'++"
@,23#D&L?#W?N#$%)$#$%+#+3&$$+,#(/,,+"$#$*#&'#+V/)6#$2#$%+#'/3#2@#$%+#(266+($2,#(/,,+"$#$-#)"0#$%+
9)'+#(/,,+"$#$)H#$%)$#&'-
$* = $- + $)
TX<NV
β+K
$ * = 555555555555 $ -
TX<EV
β + K v ⁄+
$ * = 555555555555 . 6 4 )* ,
TX<DV
c0$,21,MS0<,TX<^V,*)-,TX<NV,;(.$0
β
!"*&,(05
β
@+&$#)*&(.$+:5,4$,/*),$A7#$00,MS<,TX<EV,(),&"$,12#'
$- = α $*
TX<?OV
β
α = 555555555555
β+K
TX<??V
4"$#$,&"$,/2)0&*)&,α,(0,#$+*&$-,&2,β,9:
!"30,&"$,$'(&&$#,/3##$)&,(),MS<,TX<DV,/*),9$,4#(&&$)
v
$ * = ( . 6 ⁄ α )4 )*
⁄ +,
TX<?PV
L()*++:5,4$,/*),30$,MS<,TX<??V,&2,$A7#$00,β,(),&$#'0,21,α 5,&"*&,(05
α
β = 555555555555
K]α
TX<?\V
=&,/*),9$,0$$),1#2',MS<,TX<??V,&"*&,α,(0,*,/2)0&*)&,T12#,*,7*#&(/3+*#,&#*)0(0&2#V,&"*&,(0,+$00
&"*),93&,.$#:,/+20$,&2,3)(&:<,L2#,()0&*)/$5,(1,β,=,?OO5,&"$),α,!,O<DD<,MS3*&(2),TX<?\V,#$.$*+0
*),('72#&*)&,1*/&Y,K'*++,/"*);$0,(),α,/2##$072)-,&2,.$#:,+*#;$,/"*);$0,(),β<,!"(0,'*&"$'*&%
(/*+,290$#.*&(2),'*)(1$0&0,(&0$+1,7":0(/*++:5,4(&",&"$,#$03+&,&"*&,&#*)0(0&2#0,21,&"$,0*'$,&:7$
357
358 Chapter 6 Bipolar Junction Transistors (BJTs)
'*:, "*.$, 4(-$+:, -(11$#$)&, .*+3$0, 21, β<, L2#, #$*02)0, &"*&, 4(++, 9$/2'$, *77*#$)&, +*&$#5, α, (0
/*++$-,&"$,)*""*05&'(!-)/%%!0$-6'#0<
Recapitulation and Equivalent-Circuit Models Y+#%)7+#*,+'+"$+0#)#@&,'$52,0+,#320+6
@2,#$%+#2*+,)$&2"#2@#$%+#!"!#$,)"'&'$2,#&"#$%+#)($&7+#320+?#;)'&()661-#$%+#@2,.),059&)'#726$)L+#v)*
()/'+'#)"#+T*2"+"$&)661#,+6)$+0#(/,,+"$#$-#$2#@62.#&"#$%+#(266+($2,#$+,3&")6?#=%+#(266+($2,#(/,,+"$#$&'#&"0+*+"0+"$#2@#$%+#7)6/+#2@#$%+#(266+($2,#726$)L+#)'#62"L#)'#$%+#(266+($2,Q9)'+#4/"($&2"#,+3)&"'
,+7+,'+#9&)'+0H#$%)$#&'-#v-)#≥#P?#=%/'#&"#$%+#)($&7+#320+#$%+#(266+($2,#$+,3&")6#9+%)7+'#)'#)"#&0+)6
(2"'$)"$5(/,,+"$#'2/,(+#.%+,+#$%+#7)6/+#2@#$%+#(/,,+"$#&'#0+$+,3&"+0#91#v)*?#=%+#9)'+#(/,,+"$#$)#&'
)#@)($2,#KZβ##2@#$%+#(266+($2,#(/,,+"$-#)"0#$%+#+3&$$+,#(/,,+"$#&'#+V/)6#$2#$%+#'/3#2@#$%+#(266+($2,#)"0
9)'+#(/,,+"$'?#C&"(+#$)#&'#3/(%#'3)66+,#$%)"#$-#:&?+?-#β#!#K>-#$*# ! #$-?#A2,+#*,+(&'+61-#$%+#(266+($2,
(/,,+"$#&'#)#@,)($&2"#α 2@#$%+#+3&$$+,#(/,,+"$-#.&$%#α#'3)66+,#$%)"-#9/$#(62'+#$2-#/"&$1?
!"(0,1(#0&%2#-$#,'2-$+,21,&#*)0(0&2#,27$#*&(2),(),&"$,*/&(.$,'2-$,/*),9$,#$7#$0$)&$-,9:
&"$,$S3(.*+$)&,/(#/3(&,0"24),(),L(;<,X<^T*V<,R$#$5,-(2-$,1*,"*0,*,0/*+$,/3##$)&,.6*,$S3*+,&2
( . 6 ⁄ α ) ,*)-,&"30,7#2.(-$0,*,/3##$)&,$*,#$+*&$-,&2,v)*,*//2#-();,&2,MS<,TX<?PV<,!"$,/3##$)&,21
&"$,/2)&#2++$-,023#/$5,4"(/",(0,$S3*+,&2,&"$,/2++$/&2#,/3##$)&5,(0,/2)&#2++$-,9:, v)*,*//2#-%
();,&2,&"$,$A72)$)&(*+,#$+*&(2)0"(7,()-(/*&$-5,*,#$0&*&$'$)&,21,MS<,TX<\V<,!"(0,'2-$+,(0,()
$00$)/$,*,)2)+()$*#,.2+&*;$%/2)&#2++$-,/3##$)&,023#/$<,=&,/*),9$,/2).$#&$-,&2,&"$,/3##$)&%
/2)&#2++$-,/3##$)&%023#/$,'2-$+,0"24),(),L(;<,X<^T9V,9:,$A7#$00();,&"$,/3##$)&,21,&"$,/2)%
&#2++$-, 023#/$, *0, α8 $*<, Q2&$, &"*&, &"(0, '2-$+, (0, *+02, )2)+()$*#, 9$/*30$, 21, &"$, $A72)$)&(*+
C
C
iC
iC
IS ev BE #V T
aiE
iB
iB
B
B
$
vBE
%
DE
(ISE " IS #a)
vBE
iE
iE
%
E
E
(a)
(b)
iB
iC
iB
C
B
iC
C
B
iB
$
vBE
DE
(ISE " IS #a)
iE
$
DB
(ISB " IS"b)
IS evBE "VT
DB
(ISB " IS"b)
$
biB
%
iE
vBE
iE
%
E
E
(c)
(d)
Figure 6.5 [),L+5'&L")6#+V/&7)6+"$5(&,(/&$#320+6'#2@#$%+#!"!#;<=#2*+,)$&"L#&"#$%+#@2,.),0#)($&7+#320+?
6.1 Device Structure and Physical Operation
#$+*&(2)0"(7,21,&"$,/3##$)&,$*,&"#23;",-(2-$, 1*,*)-,&"$,.2+&*;$, v)*<,L#2',&"(0,'2-$+,4$
290$#.$,&"*&,(1,&"$,&#*)0(0&2#,(0,30$-,*0,*,&42%72#&,)$&42#G,4(&",&"$,()73&,72#&,9$&4$$),M
*)-,B,*)-,&"$,23&73&,72#&,9$&4$$),6,*)-,B,T(<$<5,4(&",B,*0,*,/2''2),&$#'()*+V5,&"$),&"$
/3##$)&,;*(),290$#.$-,(0,$S3*+,&2,α<,!"30,α,(0,/*++$-,&"$,/2''2)%9*0$,/3##$)&,;*()<,,
=.2#2$%+,#+V/&7)6+"$#(&,(/&$#320+6'-#'%2."#&"#D&L?#W?G:(>#)"0#:0>-#3)1#9+#/'+0#$2#,+*,+'+"$
$%+# 2*+,)$&2"# 2@# $%+# ;<=?# =%+# 320+6# 2@# D&L?# W?G:(># &'# +''+"$&)661# )# 726$)L+5(2"$,266+0# (/,,+"$
'2/,(+?#\2.+7+,-#%+,+#0&20+#1)#(2"0/($'#$%+#9)'+#(/,,+"$#)"0#$%/'#&$'#(/,,+"$#'()6+#@)($2,#&'#.6 =β,
,+'/6$&"L#&"#$%+#$)#Q v)*#,+6)$&2"'%&*#L&7+"#&"#EV?#:W?W>?#;1#'&3*61#+T*,+''&"L#$%+#(266+($2,#(/,,+"$
)'#β $Β#.+#29$)&"#$%+#(/,,+"$5(2"$,266+0#(/,,+"$5'2/,(+#320+6#'%2."#&"#D&L?#W?G:0>?#D,23#$%&'#6)$5
$+,# 320+6# .+# 29'+,7+# $%)$# &@# $%+# $,)"'&'$2,# &'# /'+0# )'# )# $.25*2,$# "+$.2,U# .&$%# $%+# &"*/$# *2,$
9+$.++"#;#)"0#E#)"0#$%+#2/$*/$#*2,$#9+$.++"#F#)"0#E#:&?+?-#.&$%#E#)'#$%+#(2332"#$+,3&")6>-#$%+"
$%+#(/,,+"$#L)&"#29'+,7+0#&'#+V/)6#$2#β?#=%/'#β#&'#()66+0#$%+#(2332"5+3&$$+,#(/,,+"$#L)&"?
L()*++:5,4$,)2&$,&"*&,&"$,'2-$+0,(),L(;<,X<^,*77+:,12#,*):,720(&(.$,.*+3$,21, v)*<,!"*&,(05
3)+(G$,&"$,'2-$+0,4$,4(++,9$,-(0/300();,(),K$/&(2),X<^5,"$#$,&"$#$,(0,)2,+('(&*&(2),2),&"$,0(>$
21,v)*5,*)-,&"30,&"$0$,'2-$+0,*#$,#$1$##$-,&2,*0,+'%6!5(#60'+-"*2!+(<
Example 6.1
] KG
I"#!"!#$,)"'&'$2,#%)7&"L# . 6 d KP I#)"0# β d KPP #&'#(2""+($+0#)'#@2662.'8#=%+#+3&$$+,#&'#L,2/"0+0$%+#9)'+#&'#@+0#.&$%#)#(2"'$)"$5(/,,+"$#'2/,(+#'/**61&"L#)#0(#(/,,+"$#2@#KP#µI-#)"0#$%+#(266+($2,#&'#(2"5
"+($+0#$2#)#G5]#0(#'/**61#7&)#)#,+'&'$)"(+#>F#2@#N#U Ω?#I''/3&"L#$%)$#$%+#$,)"'&'$2,#&'#2*+,)$&"L#&"#$%+
)($&7+#320+-#@&"0# + )* #)"0# + -* ?#^'+#$%+'+#7)6/+'#$2#7+,&@1#)($&7+5320+#2*+,)$&2"?#J+*6)(+#$%+#(/,,+"$
'2/,(+#.&$%#)#,+'&'$)"(+#(2""+($+0#@,23#$%+#9)'+#$2#$%+#G5]#0(#'/**61?#Y%)$#,+'&'$)"(+#7)6/+#&'#"++0+0#$2
,+'/6$#&"#$%+#')3+#2*+,)$&"L#(2"0&$&2"'_
Solution
!@#$%+#$,)"'&'$2,#&'#2*+,)$&"L#&"#$%+#)($&7+#320+-#&$#()"#9+#,+*,+'+"$+0#91#2"+#2@#$%+#@2/,#*2''&96+#+V/&7)6+"$5
(&,(/&$#320+6'#'%2."#&"#D&L?#W?G?#;+()/'+#$%+#+3&$$+,#&'#L,2/"0+0-#+&$%+,#$%+#320+6#&"#D&L?#W?G:(>#2,#$%)$#&"
D&L? W?G:0>#.2/60#9+#'/&$)96+?#C&"(+#.+#U"2.#$%+#9)'+#(/,,+"$# . ) - #$%+#320+6#2@#D&L?#W?G:0>#&'#$%+#32'$#'/&$)96+?#
VCC " $5V
VCC " $5V
RB
RC " 3 k&
10 'A
IB
B
C
$
$
DB
IB
B
E
(a)
Figure 6.6 F&,(/&$'#@2,#ET)3*6+#W?K?
C
$
VCE
VBE
%
%
IC
$
DB
bIB
VBE
%
IC
RC
bIB
VCE
E
(b)
%
359
360 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.1 continued
D&L/,+# W?W:)># '%2.'# $%+# (&,(/&$# )'# 0+'(,&9+0# .&$%# $%+# $,)"'&'$2,# ,+*,+'+"$+0# 91# $%+# 320+6# 2@# D&L?
W?G:0>?#Y+#()"#0+$+,3&"+# + )* #@,23#$%+#+T*2"+"$&)6#(%),)($+,&'$&(#2@# 1 ) #)'#@2662.'8#
.)
+ )* d + , 6" 5555555555
5
.6 ⁄ β
KP × KP ]W 5
d MG 6" 55555555555555555555555
] Kd
KP
#################`#WaP#3]#`#P?Wa#]
b+T$#.+#0+$+,3&"+#$%+#7)6/+#2@# + -* #@,23
+ -* d + -- ] > - . .%+,+
. - d β . ) d KPP# × KP × KP
]W
]N
d KP ,@,d,?,'@
=%/'-
, + -* d G ] N × K d c#M#]##
C&"(+# + - #)$#cM#]#&'#%&L%+,#$%)"# + ) #)$#P?Wa#]-#$%+#$,)"'&'$2,#&'#&"0++0#2*+,)$&"L#&"#$%+#)($&7+#320+?
b2.-#,+*6)(&"L#$%+#KP5µI#(/,,+"$#'2/,(+#.&$%#)#,+'&'$)"(+# > ) #(2""+($+0#@,23#$%+#9)'+#$2#$%+#G5]#0(
'/**61# + -- -#)'#&"#D&L?#W?W:9>-#$%+#7)6/+#2@# > ) #3/'$#9+
+ -- ] + )*
> ) d 5555555555555555555555555
5
.)
] P?Wa5 d eNK#UΩ
d G
555555555555555555
KP µI
,
EXERCISES
6.1
F2"'&0+,#)"#!"!#$,)"'&'$2,#.&$%#v)*#=#P?d#]#)$#$-#=#K#3I?#D&"0#v)*#)$#$-#=#P?K#3I#)"0#KP#3I?
Ans. P?We#]H#P?dW#]
6.2
=,)"'&'$2,'#2@#)#(+,$)&"#$1*+#),+#'*+(&@&+0#$2#%)7+#β#7)6/+'#&"#$%+#,)"L+#GP#$2#KGP?#D&"0#$%+#,)"L+#2@
$%+&,#α#7)6/+'?
Ans. P?afP#$2#P?aaN
6.3
A+)'/,+3+"$#2@#)"#!"!#;<=#&"#)#*),$&(/6),#(&,(/&$#'%2.'#$%+#9)'+#(/,,+"$#$2#9+#Ke?eW#µI-#$%+#+3&$5
$+,#(/,,+"$#$2#9+#K?eWP#3I-#)"0#$%+#9)'+Q+3&$$+,#726$)L+#$2#9+#P?d#]?#D2,#$%+'+#(2"0&$&2"'-#()6(/6)$+
α-#β-#)"0#.6?
Ans. P?aaH#KPPH#KPQKG#I
6.4
F)6(/6)$+#β#@2,#$.2#$,)"'&'$2,'#@2,#.%&(%#α#=#P?aa#)"0#P?af?#D2,#(266+($2,#(/,,+"$'#2@#KP#3I-#@&"0
$%+#9)'+#(/,,+"$#2@#+)(%#$,)"'&'$2,?
Ans. aaH#eaH#P?K#3IH#P?M#3I
6.1 Device Structure and Physical Operation
6.5
I#$,)"'&'$2,#@2,#.%&(%#.C#`#KPQKW#I#)"0#β# `#KPP##&'#(2"0/($&"L#)#(266+($2,#(/,,+"$#2@#K#3I?#D&"0#v)*?
I6'2-#@&"0#.6*8)"0#.6)8@2,#$%&'#$,)"'&'$2,?
] KW
Ans. ded?G#3]H# K?PK × KP I H#KPQKfI
6.6
D2,#$%+#(&,(/&$#&"#D&L?#W?W:)>#)")61h+0#&"#ET)3*6+#W?K-#@&"0#$%+#3)T&3/3#7)6/+#2@# > - #$%)$#.&66#'$&66
,+'/6$#&"#)($&7+5320+#2*+,)$&2"?
Ans. e?NK#U Ω
6.1.3 Structure of Actual Transistors
L(;3#$,X<N,0"240,*,'2#$,#$*+(0&(/,T93&,0&(++,0('7+(1($-V,/#200,0$/&(2),21,*),!"!,BC!<,Q2&$,&"*&
&"$,/2++$/&2#,.(#&3*++:,03##23)-0,&"$,$'(&&$#,#$;(2)5,&"30,'*G();,(&,-(11(/3+&,12#,&"$,$+$/&#2)0
()H$/&$-,()&2,&"$,&"(),9*0$,&2,$0/*7$,9$();,/2++$/&$-<,=),&"(0,4*:5,&"$,#$03+&();, α,(0,/+20$,&2
3)(&:,*)-, β,(0,+*#;$<,@+025,290$#.$,&"*&,&"$,-$.(/$,(0,!%?,0:''$&#(/*+5,*)-,&"30,&"$,$'(&&$#
*)-, /2++$/&2#, /*))2&, 9$, ()&$#/"*);$-<8, L2#, '2#$, -$&*(+, 2), &"$, 7":0(/*+, 0&#3/&3#$, 21, */&3*+
-$.(/$05,&"$,#$*-$#,(0,#$1$##$-,&2,@77$)-(A,@<
E
p
B
C
n
n
Figure 6.7 F,2''5'+($&2"#2@#)"#!"!#;<=?
!"$,0&#3/&3#$,(),L(;<,X<N,()-(/*&$0,*+02,&"*&,&"$,6BC,"*0,*,'3/",+*#;$#,*#$*,&"*),&"$,MBC<,!"30
&"$,6B,-(2-$,1-,"*0,*,0*&3#*&(2),/3##$)&,.6-8&"*&,(0,'3/",+*#;$#,&"*),&"$,0*&3#*&(2),/3##$)&,21
&"$,MB,-(2-$,1*<,!:7(/*++:5,.6-8(0,?O,&2,?OO,&('$0,+*#;$#,&"*),.6*,T#$/*++,&"*&,.6*,d,.68=α !,,.6 V@,,
EXERCISE
6.7
e
] KG
I#*),$&(/6),#$,)"'&'$2,#%)'# . 6 d KP I #)"0# α ! K?#!@#$%+#F;<#),+)#&'#KPP#$&3+'#$%+#),+)#2@#$%+#E;<@&"0#$%+#(266+($2,#'()6+#(/,,+"$# . 6- ?
] KN
Ans. KP #I
!@#$%+#+3&$$+,#)"0#(266+($2,#),+#,+7+,'+0g$%)$#&'-#$%+#F;<#&'#@2,.),0#9&)'+0#)"0#$%+#E;<#&'#,+7+,'+
9&)'+0g$%+#0+7&(+#2*+,)$+'#&"#)#320+#()66+0#$%+#R,+7+,'+5)($&7+#320+?S#=%+#,+'/6$&"L#7)6/+'#2@#α )"0
β-#0+"2$+0#α> )"0#β>#:.&$%#>#0+"2$&"L#,+7+,'+>-#),+#3/(%#62.+,#$%)"#$%+#7)6/+'#2@#α )"0#β-#,+'*+($&7+6129$)&"+0#&"#$%+#R@2,.),0S#)($&7+#320+#0&'(/''+0#)927+?#\+"(+-#$%+#,+7+,'+5)($&7+#320+#%)'#"2#*,)($&()6
)**6&()$&2"?#=%+#ABCDE=-#2"#$%+#2$%+,#%)"0-#9+&"L#)#*+,@+($61#'133+$,&()6#0+7&(+-#()"#2*+,)$+#+V/)661
.+66#.&$%#&$'#0,)&"#)"0#'2/,(+#$+,3&")6'#&"$+,(%)"L+0?#
361
362 Chapter 6 Bipolar Junction Transistors (BJTs)
6.1.4 Operation in the Saturation Mode5
I'#3+"$&2"+0#)927+-#@2,#$%+#;<=#$2#2*+,)$+#&"#$%+#)($&7+#320+-#$%+#F;<#3/'$#9+#,+7+,'+
9&)'+0?#=%/'#@),-#.+#%)7+#'$)$+0#$%&'#(2"0&$&2"#@2,#$%+#!"!#$,)"'&'$2,#)'# v -) ≥ P?#\2.+7+,.+#U"2.#$%)$#)#"!#4/"($&2"#02+'#"2$#+@@+($&7+61#9+(23+#@2,.),0#9&)'+0#/"$&6#$%+#@2,.),0
726$)L+#)(,2''#&$#+T(++0'#)**,2T&3)$+61#P?e#]?#!$#@2662.'#$%)$#2"+#()"#3)&"$)&"#)($&7+5320+
2*+,)$&2"#2@#)"#!"!#$,)"'&'$2,#@2,#"+L)$&7+# v -) #02."#$2#)**,2T&3)$+61# ] P?e ]?#=%&'#&'#&66/'5
$,)$+0#&"#D&L?#W?f-#.%&(%#&'#)#'U+$(%#2@# $ - #7+,'/'# v -) #@2,#)"#!"!#$,)"'&'$2,#2*+,)$+0#.&$%#)
(2"'$)"$#+3&$$+,#(/,,+"$# . * ?#I'#+T*+($+0-# $ - #&'#&"0+*+"0+"$#2@# v -) #&"#$%+#)($&7+#320+-#)#'&$5
/)$&2"# $%)$# +T$+"0'# @2,# v -) # L2&"L# "+L)$&7+# $2# )**,2T&3)$+61# ] P?e ]?# ;+62.# $%&'# 7)6/+# 2@
v -)-#$%+# F;<#9+L&"'#$2# (2"0/($#'/@@&(&+"$61#$%)$#$%+#$,)"'&'$2,#6+)7+'# $%+#)($&7+#320+# )"0
+"$+,'#$%+#')$/,)$&2"#320+#2@#2*+,)$&2"-#.%+,+# $ - #0+(,+)'+'?
=2#'++#.%1# $ - #0+(,+)'+'#&"#')$/,)$&2"-#.+#()"#(2"'$,/($#)#320+6#@2,#$%+#')$/,)$+0#!"!
$,)"'&'$2,#)'#@2662.'?#Y+#)/L3+"$#$%+#320+6#2@#D&L?#W?G:(>#.&$%#$%+#@2,.),05(2"0/($&"L#F;<
0&20+# 1 - -#)'#'%2."#&"#D&L?#W?a?#B9'+,7+#$%)$#$%+#(/,,+"$# $ )- #.&66#'/9$,)($#@,23#$%+#(2"5
$,266+05'2/,(+#(/,,+"$-#,+'/6$&"L#&"#$%+#,+0/(+0#(266+($2,#(/,,+"$# $ - #L&7+"#91
$- d .6 4
v )* ⁄ + ,
] . 6- 4
v )- ⁄ + ,
TX<?8V
=%+# '+(2"0# $+,3# .&66# *6)1# )"# &"(,+)'&"L# ,26+# )'# v )- # +T(++0'# P?e# ]# 2,# '2-# ()/'&"L# $ - # $2
0+(,+)'+#)"0#+7+"$/)661#,+)(%#h+,2?#
L(;3#$,X<D,*+02,()-(/*&$0,&"*&,(),0*&3#*&(2),&"$,9*0$,/3##$)&,4(++,()/#$*0$,&2,&"$,.*+3$
$ ) d ( . 6 ⁄ β )4
v )* ⁄ + ,
e . 6- 4
v )- ⁄ + ,
TX<?^V
iC
Saturation
mode
Active mode
aIE
%0.4 V
0
iE " IE
vCB
Expanded
scale
Figure 6.8 =%+#$- Qv-)#(%),)($+,&'$&(#2@#)"#!"!#$,)"'&'$2,#@+0#.&$%#)#(2"'$)"$#+3&$$+,#(/,,+"$#.*?#=%+#$,)"'&'5
$2,#+"$+,'#$%+#')$/,)$&2"#320+#2@#2*+,)$&2"#@2,#v-)#i#QP?e#]-#)"0#$%+#(266+($2,#(/,,+"$#0&3&"&'%+'?
G
C)$/,)$&2"#&"#)#;<=#3+)"'#'23+$%&"L#(23*6+$+61#0&@@+,+"$#@,23#$%)$#&"#)#ABCDE=?#=%+#')$/,)$&2"
320+#2@#2*+,)$&2"#2@#$%+#;<=#&'#)")62L2/'#$2#$%+#$,&20+#,+L&2"#2@#2*+,)$&2"#2@#$%+#ABCDE=?#B"#$%+
2$%+,#%)"0-#$%+#')$/,)$&2"#,+L&2"#2@#2*+,)$&2"#2@#$%+#ABCDE=#(2,,+'*2"0'#$2#$%+#)($&7+#320+#2@#;<=
2*+,)$&2"?
6.1 Device Structure and Physical Operation
/
ISC e vBC VT
iB
B
$
iC
C
vBE
DB
DC
/
ISe vBE VT
%
E
Figure 6.9 A20+6&"L#$%+#2*+,)$&2"#2@#)"#!"!#$,)"5
'&'$2,# &"# ')$/,)$&2"# 91# )/L3+"$&"L# $%+# 320+6# 2@
D&L? W?G:(>#.&$%#)#@2,.),0#(2"0/($&"L#0&20+#1- ?#b2$+
$%)$#$%+#(/,,+"$#$%,2/L%#1-#&"(,+)'+'#$)#)"0#,+0/(+'#$-?
EV/)$&2"'#:W?Ke>#)"0#:W?KG>#()"#9+#(239&"+0#$2#29$)&"#$%+#,)$&2# $ - ⁄ $ ) #@2,#)#')$/,)$+0#$,)"'&'$2,?
Y+#29'+,7+#$%)$#$%&'#,)$&2#.&66#9+#&%A4(#$%)"#$%+#7)6/+#2@# β ? #D/,$%+,32,+-#$%+#,)$&2#.&66#0+(,+)'+
)'# v )- #&'#&"(,+)'+0#)"0#$%+#$,)"'&'$2,#&'#0,&7+"#0++*+,#&"$2#')$/,)$&2"?#;+()/'+# $ - ⁄ $ ) #2@#)#')$/5
,)$+0#$,)"'&'$2,#()"#9+#'+$#$2#)"1#0+'&,+0#7)6/+#62.+,#$%)"# β #91#)04/'$&"L# v )- - #$%&'#,)$&2#&'#U"2."
)'#3*%)!2-β )"0#0+"2$+0#β@2,(+0-#
$
$)
β @2,(+0 d 555-5
,≤ β
TX<?XV
')$/,)$&2"
@0,4(++,9$,0"24),+*&$#5,(),*)*+:>();,*,/(#/3(&,4$,/*),-$&$#'()$,4"$&"$#,&"$,BC!,(0,(),&"$
0*&3#*&(2),'2-$,9:,$(&"$#,21,&"$,12++24();,&42,&$0&0Y
1. =0,&"$,6BC,12#4*#-,9(*0$-,9:,'2#$,&"*),O<8,_f,
2. !'#$%+#,)$&2# $ - ⁄ $ ) #62.+,#$%)"# β _
!"$,/2++$/&2#%&2%$'(&&$#,.2+&*;$, v -* ,21,*,0*&3#*&$-,&#*)0(0&2#,/*),9$,123)-,1#2',L(;<,X<D
*0,&"$,-(11$#$)/$,9$&4$$),&"$,12#4*#-%9(*0,.2+&*;$0,21,&"$,MBC,*)-,&"$,6BC5
+ -*')$ d + )* ] + )-
TX<?NV
J+()66&"L#$%)$#$%+#F;<#%)'#)#3/(%#6),L+,#),+)#$%)"#$%+#E;<-# + )- #.&66#9+#'3)66+,#$%)"# + )*
91#P?K#$2#P?N#]?#=%/'+ -*')$ ! P?K ,&2,O<\,_
=1*&()661# .+# .&66# )''/3+# $%)$# )# $,)"'&'$2,# )$# $%+# +0L+# 2@# ')$/,)$&2"# %)'# + -*')$ d P?N # ].%&6+#)#$,)"'&'$2,#0++*#&"#')$/,)$&2"#%)'# + -*')$# d P?M #]?
EXERCISES
6.8
^'+#EV?#:W?Ke>#$2#'%2.#$%)$# $ - #,+)(%+'#h+,2#)$#
+ -* d + , 6" ( . 6- ⁄ . 6 )
F)6(/6)$+# + -* #@2,#)#$,)"'&'$2,#.%2'+#F;<#%)'#KPP#$&3+'#$%+#),+)#2@#$%+#E;<?
Ans. KKG#3]
6.9
^'+#EV'?#:W?Ke>-#:W?KG>-#)"0#:W?KW>#$2#'%2.#$%)$#)#;<=#2*+,)$&"L#&"#')$/,)$&2"#.&$%# +-* d +-*')$
%)'#)#@2,(+0# β #L&7+"#91
+ -*')$ ⁄ + ,
4
] . 6- ⁄ . 6
5
β @2,(+0 d β 555555555555555555555555555555555555555555555
+ -*')$ ⁄ + ,
4
e β . 6- ⁄ . 6
D&"0#β@2,(+0#@2,# β d KPP-# . 6- ⁄ . 6 d KPP-#)"0# + -*')$ d P?M #]?
Ans. MM?M
363
364 Chapter 6 Bipolar Junction Transistors (BJTs)
6.1.5 The pnp Transistor
!"#$!"!$%&'()*)%+&$+,#&'%#)$*($'$-'((#&$)*-*.'&$%+$%"'%$+/$%"#$"!"$0#1*2#$0#)2&*3#0$'3+1#4
5*67&#$849:$)"+;)$'$!"!$%&'()*)%+&$3*')#0$%+$+,#&'%#$*($%"#$'2%*1#$-+0#4$<#&#$%"#$1+.%'6#$#$%
2'7)#)$%"#$!=%>,#$#-*%%#&$%+$3#$"*6"#&$*($,+%#(%*'.$%"'($%"#$"=%>,#$3')#?$%"7)$/+&;'&0=3*')*(6
%"#$#-*%%#&@3')#$A7(2%*+(4$!"#$2+..#2%+&@3')#$A7(2%*+($*)$&#1#&)#$3*')#0$3>$%"#$1+.%'6#$#%&?
;"*2"$B##,)$%"#$!=%>,#$2+..#2%+&$.+;#&$*($,+%#(%*'.$%"'($%"#$"=%>,#$3')#4$$
C(.*B#$ %"#$ "!"$ %&'()*)%+&?$ 27&&#(%$ *($ %"#$ !"!$ 0#1*2#$ *)$ -'*(.>$ 2+(072%#0$ 3>$ "+.#)
*(A#2%#0$/&+-$%"#$#-*%%#&$*(%+$%"#$3')#$')$'$&#)7.%$+/$%"#$/+&;'&0=3*')$1+.%'6#$#$%4$D*(2#$%"#
2+-,+(#(%$+/$#-*%%#&$27&&#(%$2+(%&*37%#0$3>$#.#2%&+()$*(A#2%#0$/&+-$3')#$%+$#-*%%#&$*)$B#,%
)-'..$3>$7)*(6$'$.*6"%.>$0+,#0$3')#?$-+)%$+/$%"#$#-*%%#&$27&&#(%$;*..$3#$07#$%+$"+.#)4$!"#
#.#2%&+()$*(A#2%#0$/&+-$3')#$%+$#-*%%#&$6*1#$&*)#$%+$%"#$/*&)%$2+-,+(#(%$+/$3')#$27&&#(%?$'%94
E.)+?$'$(7-3#&$+/$%"#$"+.#)$*(A#2%#0$*(%+$%"#$3')#$;*..$&#2+-3*(#$;*%"$%"#$-'A+&*%>$2'&&*=
#&)$*($%"#$3')#$F#.#2%&+()G$'(0$;*..$%"7)$3#$.+)%4$!"#$0*)',,#'&*(6$3')#$#.#2%&+()$;*..$"'1#
%+$3#$&#,.'2#0$/&+-$%"#$#H%#&('.$2*&27*%?$6*1*(6$&*)#$%+$%"#$)#2+(0$2+-,+(#(%$+/$3')#$27&=
&#(%?$'%I4$!"#$"+.#)$%"'%$)722##0$*($&#'2"*(6$%"#$3+7(0'&>$+/$%"#$0#,.#%*+($&#6*+($+/$%"#
2+..#2%+&@3')#$ A7(2%*+($ ;*..$ 3#$ '%%&'2%#0$ 3>$ %"#$ (#6'%*1#$ 1+.%'6#$ +($ %"#$ 2+..#2%+&4$ !"7)
%"#)#$"+.#)$;*..$3#$);#,%$'2&+))$%"#$0#,.#%*+($&#6*+($*(%+$%"#$2+..#2%+&$'(0$',,#'&$')$2+.=
.#2%+&$27&&#(%4
J%$2'($#')*.>$3#$)##($/&+-$%"#$'3+1#$0#)2&*,%*+($%"'%$%"#$27&&#(%@1+.%'6#$&#.'%*+()"*,
+/$%"#$!"!$%&'()*)%+&$;*..$3#$*0#(%*2'.$%+$%"'%$+/$%"#$"!"$%&'()*)%+&$#H2#,%$%"'%$ v%$$"')$%+$3#
&#,.'2#0$3>$ v$%4$E.)+?$%"#$.'&6#=)*6('.?$'2%*1#=-+0#$+,#&'%*+($+/$%"#$!"!$%&'()*)%+&$2'($3#
-+0#.#0$3>$'(>$+/$/+7&$#K7*1'.#(%$2*&27*%)$)*-*.'&$%+$%"+)#$/+&$%"#$"!"$%&'()*)%+&$*($5*64
84L4$!;+$+/$%"#)#$/+7&$2*&27*%)$'&#$)"+;($*($5*64$84994$5*('..>?$;#$(+%#$%"'%$%"#$!"!$%&'(=
)*)%+&$2'($+,#&'%#$*($%"#$)'%7&'%*+($-+0#$*($'$-'((#&$'('.+6+7)$%+$%"'%$0#)2&*3#0$/+&$%"#
"!"$0#1*2#4
Reverse-biased
Forward-biased
p
E
Diffusing holes
Injected holes
iE
iE
p
n
iC
Collected holes
iB2
Injected
electrons
iC
C
Recombined
holes
iB1
iB
+
v EB
iB
–
iE
iE
VEB
B
+
v BC
–
iC
VBC
Figure 6.10 !"##$%&'()*+',%'-'!"!'&#-%.,.&*#'/,-.$0'&*'*1$#-&$',%'&2$'-3&,4$'5*0$6
iC
6.2 Current–Voltage Characteristics
iE
iE
D
(IS"aF)
iB
$
vEB
%
IS evEB"VT
iC
E
IS e vEB "VT
DB
(IS "b)
B
C
iB
(a)
iC
(b)
Figure 6.11 =.2#6),L+5'&L")6#320+6'#@2,#$%+#"!"#$,)"'&'$2,#2*+,)$&"L#&"#$%+#)($&7+#320+?
,,
EXERCISES
6.10 F2"'&0+,#$%+#320+6#&"#D&L?#W?KK:)>#)**6&+0#&"#$%+#()'+#2@#)#"!"#$,)"'&'$2,#.%2'+#9)'+#&'#L,2/"0+0$%+#+3&$$+,#&'#@+0#91#)#(2"'$)"$5(/,,+"$#'2/,(+#$%)$#'/**6&+'#)#M53I#(/,,+"$#&"$2#$%+#+3&$$+,#$+,3&")6)"0#$%+#(266+($2,#&'#(2""+($+0#$2#)#Q KP5]#0(#'/**61?#D&"0#$%+#+3&$$+,#726$)L+-#$%+#9)'+#(/,,+"$-#)"0
$%+#(266+($2,#(/,,+"$#&@#@2,#$%&'#$,)"'&'$2,#β#=#GP#)"0#.6#=#KPQKe#I?
Ans. P?WGP#]H#Na?M#µIH#K?aW#3I
6.11
D2,#)#"!"#$,)"'&'$2,#%)7&"L#.6#=#KPQKK#I#)"0#β#=#KPP-#()6(/6)$+#v*)#@2,#$-#=#K?G#I?
Ans. O<X8\,_
6.2 Current–Voltage Characteristics
6.2.1 Circuit Symbols and Conventions
!"$,7":0(/*+,0&#3/&3#$,30$-,&"30,1*#,&2,$A7+*(),&#*)0(0&2#,27$#*&(2),(0,#*&"$#,/3'9$#02'$,&2
$'7+2:,(),-#*4();,&"$,0/"$'*&(/,21,*,'3+&(&#*)0(0&2#,/(#/3(&<,L2#&3)*&$+:5,*,.$#:,-$0/#(7&(.$
*)-,/2).$)($)&,/(#/3(&,0:'92+,$A(0&0,12#,&"$,BC!<,L(;3#$,X<?PT*V,0"240,&"$,0:'92+,12#,&"$
!"!,&#*)0(0&2#`,&"$,"!",0:'92+,(0,;(.$),(),L(;<,X<?PT9V<,=),92&",0:'92+0,&"$,$'(&&$#,(0,-(0&()%
;3(0"$-,9:,*),*##24"$*-<,!"(0,-(0&()/&(2),(0,('72#&*)&,9$/*30$5,*0,4$,"*.$,0$$),(),&"$,+*0&
0$/&(2)5,7#*/&(/*+,BC!0,*#$,)2&,0:''$&#(/,-$.(/$0<,,
!"$,72+*#(&:,21,&"$,-$.(/$[!"!,2#,"!"[(0,()-(/*&$-,9:,&"$,-(#$/&(2),21,&"$,*##24"$*2),&"$,$'(&&$#<,!"(0,*##24"$*-,72()&0,(),&"$,-(#$/&(2),21,)2#'*+,/3##$)&,1+24,(),&"$,$'(&&$#5
4"(/",(0,*+02,&"$,12#4*#-,-(#$/&(2),21,&"$,9*0$]$'(&&$#,H3)/&(2)<,K()/$,4$,"*.$,*-27&$-,*
-#*4();,/2).$)&(2),9:,4"(/",/3##$)&0,1+24,1#2',&27,&2,92&&2'5,4$,4(++,*+4*:0,-#*4,"!"
&#*)0(0&2#0,(),&"$,'*))$#,0"24),(),L(;<,X<?PT9V,T(<$<5,4(&",&"$(#,$'(&&$#0,2),&27V<
L(;3#$,X<?\,0"240,!"!,*)-,"!",&#*)0(0&2#0,9(*0$-,&2,27$#*&$,(),&"$,*/&(.$,'2-$<,=&,0"23+9$,'$)&(2)$-,(),7*00();,&"*&,&"$,9(*0();,*##*);$'$)&,0"24)5,3&(+(>();,&42,-/,.2+&*;$,023#/$05
365
366 Chapter 6 Bipolar Junction Transistors (BJTs)
npn
pnp
(a)
(b)
(a)
Figure 6.12 F&,(/&$#'13926'#@2,#;<='?
(b)
Figure 6.13 ]26$)L+#*26),&$&+'#)"0#(/,,+"$#@62.#&"#$,)"'&'$2,'#9&)'+0#&"#$%+#)($&7+#320+?
(0,)2&,*,303*+,2)$,*)-,(0,30$-,"$#$,'$#$+:,&2,(++30&#*&$,27$#*&(2)<,g#*/&(/*+,9(*0();,0/"$'$0
4(++,9$,7#$0$)&$-,(),K$/&(2),X<N<,L(;3#$,X<?\,*+02,()-(/*&$0,&"$,#$1$#$)/$,*)-,*/&3*+,-(#$/&(2)0
21, /3##$)&, 1+24, &"#23;"23&, &"$, &#*)0(0&2#<, J3#, /2).$)&(2), 4(++, 9$, &2, &*G$, &"$, #$1$#$)/$
-(#$/&(2),&2,/2()/(-$,4(&",&"$,)2#'*+,-(#$/&(2),21,/3##$)&,1+24<,R$)/$5,)2#'*++:5,4$,0"23+)2&,$)/23)&$#,*,)$;*&(.$,.*+3$,12#,$*5,$)5,2#,$-<
!"$, /2).$)($)/$, 21, &"$, /(#/3(&%-#*4();, /2).$)&(2), &"*&, 4$, "*.$, *-27&$-, 0"23+-, 9$
29.(230, 1#2', L(;<, X<?\<, Q2&$, &"*&,/3##$)&0, 1+24, 1#2', &27,&2, 92&&2', *)-, &"*&, .2+&*;$0, *#$
"(;"$#, *&, &"$, &27, *)-, +24$#, *&, &"$, 92&&2'<, !"$, *##24"$*-, 2), &"$, $'(&&$#, *+02, ('7+($0, &"$
72+*#(&:,21 &"$,$'(&&$#]9*0$,.2+&*;$,&"*&,0"23+-,9$,*77+($-,(),2#-$#,&2,12#4*#-,9(*0,&"$,$'(&&$#]
9*0$,H3)/&(2)<,C30&,*,;+*)/$,*&,&"$,/(#/3(&,0:'92+,21,&"$,"!",&#*)0(0&2#5,12#,$A*'7+$5,()-(/*&$0
&"*&,4$,0"23+-,'*G$,&"$,$'(&&$#,"(;"$#,(),.2+&*;$,&"*),&"$,9*0$,T9:, v*)V,(),2#-$#,&2,/*30$
/3##$)&,&2,1+24,()&2,&"$,$'(&&$#,T-24)4*#-V<,Q2&$,&"*&,&"$,0:'92+, v*),'$*)0,&"$,.2+&*;$,9:
4"(/",&"$,$'(&&$#,TMV,(0,"(;"$#,&"*),&"$,9*0$,TBV<,!"30,12#,*,"!",&#*)0(0&2#,27$#*&();,(),&"$
*/&(.$,'2-$,v*),(0,720(&(.$5,4"(+$,(),*),!"!,&#*)0(0&2#,v)*,(0,720(&(.$<
6.2 Current–Voltage Characteristics
L#2',&"$,-(0/300(2),21,K$/&(2),X<?,(&,12++240,&"*&,*),!"!,&#*)0(0&2#,4"20$,MBC,(0,12#4*#9(*0$-,4(++,27$#*&$,(),&"$,*/&(.$,'2-$,'B8&%!C8'B8?D48E%&&4E?%(,F%&?'C485%4B8!%?8G'&&8#4&%A
?D'?8 %G8 ?D48 #'B48 #H8 I%(48 ?D'!8 '""(%3$I'?4&H8 J@K8 +<, J&"$#4(0$5, &"$, &#*)0(0&2#, +$*.$0, &"$
*/&(.$,'2-$,*)-,$)&$#0,&"$,0*&3#*&(2),#$;(2),21,27$#*&(2)<X
Table 6.2 Summary of the BJT Current–Voltage Relationships in the Active Mode
v )* ⁄ + ,
$- = .6 4
$
. v)* ⁄ +,
$ ) = 555-5 = 55565 4
β
β
$
. v)* ⁄ +,
$ * = 555-5 = 55565 4
α
α
7%?4O#D2,#$%+#"!"#$,)"'&'$2,-#,+*6)(+#v)*#.&$%#v*)?
$*
5
$ ) = ( K ] α )$ * = 55555555555
β+K
$- = β $)
$ * = ( β + K )$ )
α
β
β = 555555555555
α = 555555555555
K]α
β+K
P,
+,# =#$%+,3)6#726$)L+# = 555555 ! MG#3] #)$#,223#$+3*+,)$/,+
0
$- = α $*
=),*,7*#*++$+,'*))$#5,&"$,"!",&#*)0(0&2#,4(++,27$#*&$,(),&"$,*/&(.$,'2-$,$G8?D48*)L8$B8G%(M
A'(58#$'B458'!58?D48E%&&4E?%(8F%&?'C48$B8!%?8'&&%A458?%8($B48'#%F48?D'?8%G8?D48#'B48#H8I%(4
?D'!8J@K8+8%(8B%<,J&"$#4(0$5,&"$,6BC,9$/2'$0,12#4*#-,9(*0$-5,*)-,&"$,"!",&#*)0(0&2#,$)&$#0
&"$,0*&3#*&(2),#$;(2),21,27$#*&(2)<
L2#,$*0:,#$1$#$)/$5,4$,7#$0$)&,(),!*9+$,X<P,*,03''*#:,21,&"$,BC!,/3##$)&].2+&*;$,#$+*%
&(2)0"(70,(),&"$,*/&(.$,'2-$,21,27$#*&(2)<
The Collector–Base Reverse Current (ICBO) !"#2/,#0&'(/''&2"#2@#(/,,+"$#@62.#&"#$,)"5
'&'$2,'#.+#&L"2,+0#$%+#'3)66#,+7+,'+#(/,,+"$'#(),,&+0#91#$%+,3)661#L+"+,)$+0#3&"2,&$1#(),,&+,'?
I6$%2/L%# '/(%# (/,,+"$'# ()"# 9+# ')@+61# "+L6+($+0# &"# 320+,"# $,)"'&'$2,'-# $%+# ,+7+,'+# (/,,+"$
)(,2''#$%+#(266+($2,Q9)'+#4/"($&2"#0+'+,7+'#'23+#3+"$&2"?#=%&'#(/,,+"$-#0+"2$+0#.-)N-#&'#$%+
,+7+,'+# (/,,+"$# @62.&"L# @,23# (266+($2,# $2# 9)'+# .&$%# $%+# +3&$$+,# 2*+"5(&,(/&$+0# :%+"(+# $%+
'/9'(,&*$#N>?#=%&'#(/,,+"$#&'#/'/)661#&"#$%+#")"2)3*+,+#,)"L+-#)#7)6/+#$%)$#&'#3)"1#$&3+'#%&L%5
+,#$%)"#&$'#$%+2,+$&()661#*,+0&($+0#7)6/+?#I'#.&$%#$%+#0&20+#,+7+,'+#(/,,+"$-#.-)N#(2"$)&"'#)#'/95
'$)"$&)6# 6+)U)L+# (23*2"+"$-# )"0# &$'# 7)6/+# &'# 0+*+"0+"$# 2"# v-)?# .-)N# 0+*+"0'# '$,2"L61# 2"
$+3*+,)$/,+-#)**,2T&3)$+61#02/96&"L#@2,#+7+,1#KP°F#,&'+?d
W
!$#&'#&"$+,+'$&"L#$2#(2"$,)'$#$%+#)($&7+5320+#2*+,)$&2"#2@#$%+#;<=#.&$%#$%+#(2,,+'*2"0&"L#320+#2@#2*+,5
)$&2"#2@#$%+#ABCDE=8#=%+#;<=#"++0'#)#3&"&3/3#v-*82@#)92/$#P?N#]-#)"0#$%+#ABCDE=#"++0'#)#3&"&5
3/3#v168#+V/)6#$2#VN+-#.%&(%#@2,#320+,"#$+(%"262L&+'#&'#&"#$%+#,)"L+#P?M#]#$2#P?N#]?#=%/'#.+#'++#)#L,+)$
0+)6#2@#'&3&6),&$1j#I6'2#"2$+#$%)$#,+7+,'+#9&)'&"L#$%+#F;<#2@#$%+#;<=#(2,,+'*2"0'#$2#*&"(%&"L#2@@#$%+
(%)""+6#2@#$%+#ABCDE=?#=%&'#(2"0&$&2"#,+'/6$'#&"#$%+#(266+($2,#(/,,+"$#:0,)&"#(/,,+"$#&"#$%+#ABCDE=>
9+&"L#&"0+*+"0+"$#2@#$%+#(266+($2,#726$)L+#:$%+#0,)&"#726$)L+#&"#$%+#ABCDE=>?
d#
=%+#$+3*+,)$/,+#(2+@@&(&+"$#2@#.-)N#&'#0&@@+,+"$#@,23#$%)$#2@#.6#9+()/'+#.-)N#(2"$)&"'#)#'/9'$)"$&)6
6+)U)L+#(23*2"+"$?
367
368 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.2
=%+#$,)"'&'$2,#&"#$%+#(&,(/&$#2@#D&L?#W?Ke:)>#%)'#β#=#KPP#)"0#+T%&9&$'#)#v)*#2@#P?d#]#)$#$-#=#K#3I?#X+'&L"#$%+
(&,(/&$#'2#$%)$#)#(/,,+"$#2@#M#3I#@62.'#$%,2/L%#$%+#(266+($2,#)"0#)#726$)L+#2@#+G#]#)**+),'#)$#$%+#(266+($2,?
$15 V
$15 V
IC " 2 mA
RC
IB "
RC
VC " $5 V
2
" 0.02 mA
(
$
VBE %
RE
VE " %VBE
IE " IC $ IB
" 2.02 mA
RE
%15 V
%15 V
(a)
(b)
Figure 6.14 F&,(/&$#@2,#ET)3*6+#W?M?
Solution
J+@+,#$2#D&L?#W?Ke:9>?#Y+#"2$+#)$#$%+#2/$'+$#$%)$#'&"(+#.+#),+#,+V/&,+0#$2#0+'&L"#@2,#+-#=#+G#]-#$%+#F;<
.&66#9+#,+7+,'+#9&)'+0#)"0#$%+#;<=#.&66#9+#2*+,)$&"L#&"#$%+#)($&7+#320+?#=2#29$)&"#)#726$)L+#+-#=#+G#]$%+# 726$)L+# 0,2*# )(,2''# >-# 3/'$# 9+# KG# Q# G# =# KP# ]?# b2.-# '&"(+# .-# =# M# 3I-# $%+# 7)6/+# 2@# >-# '%2/60# 9+
'+6+($+0#)((2,0&"L#$2#
KP#]
> - = 55555555555555 = G#UΩ
M#3I
C&"(+#v)*#=#P?d#]#)$#$-#=#K#3I-#$%+#7)6/+#2@#v)*#)$#$-#=#M#3I#&'
M
+ )* = P?d + + , 6" 555 = P?dKd#]
K
C&"(+#$%+#9)'+#&'#)$#P#]-#$%+#+3&$$+,#726$)L+#'%2/60#9+
+ * = ] P?dKd #]
D2,#β# =#KPP-# α = KPP ⁄ KPK = P?aa? #=%/'#$%+#+3&$$+,#(/,,+"$#'%2/60#9+
.
M
. * = 5555- = 5555555555 = M?PM#3I
P?aa
α
b2.#$%+#7)6/+#,+V/&,+0#@2,#>*#()"#9+#0+$+,3&"+0#@,23
+ * #− ( ] KG )
5
> * = 55555555555555555555555555
.*
6.2 Current–Voltage Characteristics
369
] P?dKd + KG
= 555555555555555555555555555555 = d?Pd#UΩ
M?PM
=%&'# (23*6+$+'# $%+# 0+'&L"?# Y+# '%2/60# "2$+-# %2.+7+,-# $%)$# $%+# ()6(/6)$&2"'# )927+# .+,+# 3)0+# .&$%# )
0+L,++#2@#*,+(&'&2"#$%)$#&'#/'/)661#"+&$%+,#"+(+''),1#"2,#4/'$&@&+0#&"#*,)($&(+#&"#7&+.-#@2,#&"'$)"(+-#2@#$%+
+T*+($+0#$26+,)"(+'#2@#(23*2"+"$#7)6/+'?#b+7+,$%+6+''-#.+#(%2'+#$2#02#$%+#0+'&L"#*,+(&'+61#&"#2,0+,#$2
&66/'$,)$+#$%+#7),&2/'#'$+*'#&"7267+0?
,
EXERCISES
D6.12 J+*+)$#ET)3*6+#W?M#@2,#)#$,)"'&'$2,#@)9,&()$+0#&"#)#320+,"#&"$+L,)$+05(&,(/&$#*,2(+''?#C/(%#)#*,2(5
+''#1&+60'#0+7&(+'#$%)$#+T%&9&$#6),L+,# v )* #)$#$%+#')3+# $ - #9+()/'+#$%+1#%)7+#3/(%#'3)66+,#4/"($&2"
),+)'?#=%+#0(#*2.+,#'/**6&+'#/$&6&h+0#&"#320+,"#!F#$+(%"262L&+'#@)66#&"#$%+#,)"L+#2@#K#]#$2#N#]?
X+'&L"#)#(&,(/&$#'&3&6),#$2#$%)$#'%2."#&"#D&L?#W?Ke#+T(+*$#$%)$#"2.#$%+#*2.+,#'/**6&+'#),+# ± K?G #]
)"0#$%+#;<=#%)'# β d KPP #)"0#+T%&9&$'# v )* #2@#P?f#]#)$# $ - d K #3I?#X+'&L"#$%+#(&,(/&$#'2#$%)$#)
(/,,+"$#2@#M#3I#@62.'#$%,2/L%#$%+#(266+($2,#)"0#)#726$)L+#2@# cP?G #]#)**+),'#)$#$%+#(266+($2,?
Ans. > - d GPP # Ω H# > * d NNf # Ω
6.13
!"#$%+#(&,(/&$#'%2."#&"#D&L?#EW?KN-#$%+#726$)L+#)$#$%+#+3&$$+,#.)'#3+)'/,+0#)"0#@2/"0#$2#9+
QP?d#]?#!@#β #=#GP-#@&"0#.*-#.)-#.--#)"0#+-?
$10 V
5 k&
IC
VC
IB
VE
IE
10 k&
%10 V
Figure E6.13
Ans. P?aN#3IH#Kf?M#µIH#P?aK#3IH#+G?eG#]
6.14
!"#$%+#(&,(/&$#'%2."#&"#D&L?#EW?Ke-#3+)'/,+3+"$#&"0&()$+'#+)#$2#9+#+K?P#]#)"0#+*#$2#9+#+K?d#]?
Y%)$#),+#α#)"0#β#@2,#$%&'#$,)"'&'$2,_#Y%)$#726$)L+#+-#02#12/#+T*+($#)$#$%+#(266+($2,_
370 Chapter 6 Bipolar Junction Transistors (BJTs)
,
$10 V
5 k&
VE
VB
VC
100 k&
5 k&
%10 V
Figure E6.14
Ans. P?aaeH#KWGH#QK?dG#]
6.2.2 Graphical Representation of Transistor Characteristics
=&,(0,02'$&('$0,30$13+,&2,-$0/#(9$,&"$,&#*)0(0&2#,$]v,/"*#*/&$#(0&(/0,;#*7"(/*++:<,L(;3#$,X<?^
0"240,&"$,$- ]v)*,/"*#*/&$#(0&(/5,4"(/",(0,&"$,$A72)$)&(*+,#$+*&(2)0"(7
v
$ - = . 6 4 )*
⁄ +,
4"(/",(0,(-$)&(/*+,&2,&"$,-(2-$,$]v,#$+*&(2)0"(7<,!"$,$* ]v)*,*)-,$)]v)*,/"*#*/&$#(0&(/0,*#$
*+02,$A72)$)&(*+,93&,4(&",-(11$#$)&,0/*+$,/3##$)&0Y, . 6 ⁄ α ,12#,$*5,*)-, . 6 ⁄ β ,12#,$)<,K()/$,&"$
/2)0&*)&, 21, &"$, $A72)$)&(*+, /"*#*/&$#(0&(/5, K ⁄ + , - , (0, S3(&$, "(;", T! 8OV5, &"$, /3#.$, #(0$0
.$#:,0"*#7+:<,L2#,v)*,0'*++$#,&"*),*923&,O<^,_5,&"$,/3##$)&,(0,)$;+(;(9+:,0'*++<E,@+025,2.$#
'20&,21,&"$,)2#'*+,/3##$)&,#*);$, v)*,+($0,(),&"$,#*);$,21,O<X,_,&2,O<E,_<,=),7$#12#'();
#*7(-, 1(#0&%2#-$#, -/, /*+/3+*&(2)05, 4$, )2#'*++:, 4(++, *003'$, &"*&, +)*, !, O<N, _5, 4"(/", (0
0('(+*#,&2,&"$,*77#2*/",30$-,(),&"$,*)*+:0(0,21,-(2-$,/(#/3(&0,T6"*7&$#,8V<,L2#,*,"!",&#*)%
0(0&2#5,&"$,$- ]v*),/"*#*/&$#(0&(/,4(++,+22G,(-$)&(/*+,&2,&"*&,21,L(;<,X<?^,4(&", v)*,#$7+*/$4(&",v*)<
@0, (), 0(+(/2), -(2-$05, &"$, .2+&*;$, */#200, &"$, $'(&&$#]9*0$, H3)/&(2), -$/#$*0$0, 9:, *923&
P '_,12#,$*/",#(0$,21,?°6,(),&$'7$#*&3#$5,7#2.(-$-,&"$,H3)/&(2),(0,27$#*&();,*&,*,/2)0&*)&,/3#%
#$)&<,L(;3#$,X<?X,(++30&#*&$0,&"(0,&$'7$#*&3#$,-$7$)-$)/$,9:,-$7(/&();,$- ]v)*,/3#.$0,12#,*)
!"!,&#*)0(0&2#,*&,&"#$$,-(11$#$)&,&$'7$#*&3#$0<
f
=%+#$- Qv)*#(%),)($+,&'$&(#&'#$%+#;<=k'#(2/"$+,*),$#2@#$%+#$1QvQ6#(%),)($+,&'$&(#2@#$%+#ABCDE=?#=%+1
'%),+#)"#&3*2,$)"$#)$$,&9/$+8#!"#92$%#()'+'#$%+#726$)L+#%)'#$2#+T(++0#)#R$%,+'%260S#@2,#$%+#0+7&(+#$2#(2"5
0/($#)**,+(&)961?#!"#$%+#()'+#2@#$%+#ABCDE=-#$%+,+#&'#)#@2,3)6#$%,+'%260#726$)L+-#+?-#.%&(%#6&+'#$1*&5
()661#&"#$%+#,)"L+#2@#P?e#]#$2#P?f#]?#D2,#$%+#;<=-#$%+,+#&'#)"#R)**),+"$#$%,+'%260S#2@#)**,2T&3)$+61
P?G#]?#=%+#$1QvQ6#(%),)($+,&'$&(#2@#$%+#ABCDE=#&'#*),)926&(-#)"0#$%/'#&'#6+''#'$++*#$%)"#$%+#$- Qv)*
(%),)($+,&'$&(# 2@# $%+# ;<=?# =%&'# 0&@@+,+"(+# %)'# )# 0&,+($# )"0# '&L"&@&()"$# &3*6&()$&2"# @2,# $%+# 7)6/+# 2@
$,)"'(2"0/($)"(+#CI#,+)6&h+0#.&$%#+)(%#0+7&(+?
6.2 Current–Voltage Characteristics
Figure 6.15 =%+# $- Qv)*# (%),)($+,&'$&(# @2,# )"# !"!
$,)"'&'$2,?
Figure 6.16 E@@+($# 2@# $+3*+,)$/,+# 2"# $%+# $- Qv)*
(%),)($+,&'$&(?# I$# )# (2"'$)"$# +3&$$+,# (/,,+"$# :9,2U+"
6&"+>-#v)*#(%)"L+'#91# ] M#3]Z°F?
,,,
EXERCISE
6.15 F2"'&0+,#)#"!"#$,)"'&'$2,#.&$%#v*)#=#P?d#]#)$#$*#=#K#3I?#[+$#$%+#9)'+#9+#L,2/"0+0-#$%+#+3&$$+,#9+#@+0
91#)#M53I#(2"'$)"$5(/,,+"$#'2/,(+-#)"0#$%+#(266+($2,#9+#(2""+($+0#$2#)#QG5]#'/**61#$%,2/L%#)#K5
UΩ#,+'&'$)"(+?#!@#$%+#$+3*+,)$/,+#&"(,+)'+'#91#NP°F-#@&"0#$%+#(%)"L+'#&"#+3&$$+,#)"0#(266+($2,#726$5
)L+'?#b+L6+($#$%+#+@@+($#2@#.-)N?
Ans. ]XO,'_`,O,_<
6.2.3 Dependence of iC on the Collector Voltage—The Early Effect
W"$),27$#*&$-,(),&"$,*/&(.$,#$;(2)5,7#*/&(/*+,BC!0,0"24,02'$,-$7$)-$)/$,21,&"$,/2++$/&2#
/3##$)&,2),&"$,/2++$/&2#,.2+&*;$5,4(&",&"$,#$03+&,&"*&5,3)+(G$,&"$,;#*7",0"24),(),L(;<,X<E5,&"$(#
$- ]v-),/"*#*/&$#(0&(/0,*#$,)2&,7$#1$/&+:,"2#(>2)&*+,0&#*(;"&,+()$0<,!2,0$$,&"(0,-$7$)-$)/$,'2#$
/+$*#+:5,/2)0(-$#,&"$,/2)/$7&3*+,/(#/3(&,0"24),(),L(;<,X<?NT*V<,!"$,&#*)0(0&2#,(0,/2))$/&$-,()
371
372 Chapter 6 Bipolar Junction Transistors (BJTs)
Figure 6.17 ;'<#F2"(+*$/)6#(&,(/&$#@2,#3+)'/,&"L#$%+#$- Qv-*#(%),)($+,&'$&('#2@#$%+#;<=?
;&<#=%+#$- Rv-*#(%),)($+,&'$&('#2@#)#*,)($&()6#;<=?
&"$,)*""*05!"#$$!%-)*03#6/%'$#*0`,&"*&,(05,"$#$,&"$,$'(&&$#,0$#.$0,*0,*,/2''2),&$#'()*+
9$&4$$),&"$,()73&,*)-,23&73&,72#&0<,!"$,.2+&*;$,+)*,/*),9$,0$&,&2,*):,-$0(#$-,.*+3$,9:,*-H30&%
();,&"$,-/,023#/$,/2))$/&$-,9$&4$$),9*0$,*)-,$'(&&$#<,@&,$*/",.*+3$,21,+)*5,&"$,/2##$072)-%
();, $- ]v-*, /"*#*/&$#(0&(/, /3#.$, /*), 9$, '$*03#$-, 72()&, 9:, 72()&, 9:, .*#:();, &"$, -/, 023#/$
/2))$/&$-,9$&4$$),/2++$/&2#,*)-,$'(&&$#,*)-,'$*03#();,&"$,/2##$072)-();,/2++$/&2#,/3##$)&<
!"$,#$03+&,(0,&"$,1*'(+:,21,$- ]v-*,/"*#*/&$#(0&(/,/3#.$0,0"24),(),L(;<,X<?NT9V,*)-,G)24),*0
)*""*05!"#$$!%-)7'%')$!%#($#)(<
@&,+24,.*+3$0,21,v-*,T+24$#,&"*),*923&,O<\,_V5,*0,&"$,/2++$/&2#,.2+&*;$,;2$0,9$+24,&"*&,21
&"$,9*0$,9:,'2#$,&"*),O<8,_5,&"$,/2++$/&2#]9*0$,H3)/&(2),9$/2'$0,12#4*#-,9(*0$-,*)-,&"$
&#*)0(0&2#,+$*.$0,&"$,*/&(.$,'2-$,*)-,$)&$#0,&"$,0*&3#*&(2),'2-$<,K"2#&+:5,4$,0"*++,,+22G,*&
&"$,-$&*(+0,21,&"$,$- ]v-*,/3#.$0,(),&"$,0*&3#*&(2),#$;(2)<,@&,&"(0,&('$5,"24$.$#5,4$,4(0",&2
$A*'()$,&"$,/"*#*/&$#(0&(/,/3#.$0,(),&"$,*/&(.$,#$;(2),(),-$&*(+<,W$,290$#.$,&"*&,&"$,/"*#*/%
&$#(0&(/,/3#.$05,&"23;",0&(++,0&#*(;"&,+()$05,"*.$,1()(&$,0+27$<,=),1*/&5,4"$),$A&#*72+*&$-5,&"$
/"*#*/&$#(0&(/,+()$0,'$$&,*&,*,72()&,2),&"$,)$;*&(.$, v-*,*A(05,*&, v-*,=,]+/<,!"$,.2+&*;$,+/5,*
720(&(.$,)3'9$#5,(0,*,7*#*'$&$#,12#,&"$,7*#&(/3+*#,BC!5,4(&",&:7(/*+,.*+3$0,(),&"$,#*);$,21
?O _,&2,?OO _<,=&,(0,/*++$-,&"$,8'%+9-1*+$'6!5,*1&$#,C<,I<,M*#+:5,&"$,$);()$$#();,0/($)&(0&,4"2
1(#0&,0&3-($-,&"(0,7"$)2'$)2)<
@&,*,;(.$),.*+3$,21,v)*5,()/#$*0();,v-*,()/#$*0$0,&"$,#$.$#0$%9(*0,.2+&*;$,2),&"$,/2++$/&2#]
9*0$,H3)/&(2)5,*)-,&"30,()/#$*0$0,&"$,4(-&",21,&"$,-$7+$&(2),#$;(2),21,&"(0,H3)/&(2),T#$1$#,&2
L(;<,X<\V<,!"(0,(),&3#),#$03+&0,(),*,-$/#$*0$,(),&"$,!33!)$#1!-&'(!-:#2$7,2<,U$/*++();,&"*&,.6,(0
().$#0$+:,7#272#&(2)*+,&2,2,TMS<,X<8V5,4$,0$$,&"*&,.6,4(++,()/#$*0$,*)-,&"*&,$-,()/#$*0$0,7#2%
72#&(2)*++:<,!"(0,(0,&"$,M*#+:,$11$/&<,L2#,29.(230,#$*02)05,(&,(0,*+02,G)24),*0,&"$,&'(!5:#2$7
"*2/'$#*0-!33!)$<D
a
#J+()66#$%)$#$%+#ABCDE=k'#(2/"$+,*),$#&'#$%+#(%)""+656+"L$%#320/6)$&2"#+@@+($?#=%+'+#$.2#+@@+($'#),+
,+3),U)961#'&3&6),#)"0#%)7+#9++"#)''&L"+0#$%+#')3+#")3+-#E),61#+@@+($?
6.2 Current–Voltage Characteristics
!"$,+()$*#,-$7$)-$)/$,21,$-,2), v-*,/*),9$,$A7+(/(&+:,*//23)&$-,12#,9:,*003'();,&"*&,.6
#$'*()0,/2)0&*)&,*)-,()/+3-();,&"$,1*/&2#, ( K + v -* ⁄ + / ) (),&"$,$S3*&(2),12#,$-,*0,12++240Y
v
$ - = . 6 4 )*
⁄ +,
-*
K + v555555
5
+/
TX<?EV
!"$,)2)>$#2,0+27$,21,&"$,$-− v-*,0&#*(;"&,+()$0,()-(/*&$0,&"*&,&"$,*/$4/$-%!(#($'0)!,+22G();
()&2,&"$,/2++$/&2#,(0,)2&,()1()(&$<,U*&"$#5,(&,(0,1()(&$,*)-,-$1()$-,9:
]K
∂ $( % ≡ 5555555555
,
∂ v -* v
TX<?DV
)* = (2"'$)"$
c0();,MS<,TX<?EV,4$,/*),0"24,&"*&
+ / + + -*
5
( % = 55555555555555555555
.-
TX<POV
4"$#$,.-,*)-,+-*,*#$,&"$,/22#-()*&$0,21,&"$,72()&,*&,4"(/",&"$,BC!,(0,27$#*&();,2),&"$,7*#&(/%
3+*#, $- ] v-*, /3#.$, T(<$<5, &"$, /3#.$, 29&*()$-, 12#, v)* $S3*+, &2, /2)0&*)&, .*+3$ + )* , *&, 4"(/"
MS< TX<?DV,(0,$.*+3*&$-V<,@+&$#)*&(.$+:5,4$,/*),4#(&$
+
( % = 55555/5
.′-
TX<P?V
4"$#$, .′- (0,&"$,.*+3$,21,&"$,/2++$/&2#,/3##$)&,4(&",&"$,M*#+:,$11$/&,)$;+$/&$-`,&"*&,(05
+
.′- = . 6 4 )*
⁄ +,
TX<PPV
=&,(0,#*#$+:,)$/$00*#:,&2,()/+3-$,&"$,-$7$)-$)/$,21,$-,2),v-*,(),-/,9(*0,-$0(;),*)-,*)*+:0(0
&"*&, (0,7$#12#'$-, 9:, "*)-<, K3/", *), $11$/&5, "24$.$#5, /*), 9$, $*0(+:,()/+3-$-, (),&"$, Kg=6M
0('3+*&(2), 21, /(#/3(&, 27$#*&(2)5, 4"(/", (0, 1#$S3$)&+:, 30$-, &2, a1()$%&3)$b, 7$)/(+%*)-%7*7$#
*)*+:0(0,2#,-$0(;)<
!"$, 1()(&$, 23&73&, #$0(0&*)/$, (%, /*), "*.$, *, 0(;)(1(/*)&, $11$/&, 2), &"$, ;*(), 21, &#*)0(0&2#
*'7+(1($#0<,!"(0,(0,7*#&(/3+*#+:,&"$,/*0$,(),()&$;#*&$-]/(#/3(&,*'7+(1($#05,*0,4(++,9$,0"24),()
/"*7&$#,N<,L2#&3)*&$+:5,&"$#$,*#$,'*):,0(&3*&(2)0,(),4"(/",(%8/*),9$,()/+3-$-,#$+*&(.$+:,$*0(+:
(),7$)/(+%*)-%7*7$#,*)*+:0(0<
!"$,23&73&,#$0(0&*)/$,(%,/*),9$,()/+3-$-,(),&"$,/(#/3(&,'2-$+,21,&"$,&#*)0(0&2#<,!"(0,(0,(++30%
&#*&$-,(),L(;<,X<?E5,4"$#$,4$,0"24,&"$,&42,+*#;$%0(;)*+,/(#/3(&,'2-$+0,21,*,/2''2)%$'(&&$#
!"!,&#*)0(0&2#,27$#*&();,(),&"$,*/&(.$,'2-$5,&"20$,(),L(;,X<^T/V,*)-,T-V5,4(&",&"$,#$0(0&*)/$,(%
/2))$/&$-,9$&4$$),&"$,/2++$/&2#,*)-,&"$,$'(&&$#,&$#'()*+0=,
EXERCISES
v )* ⁄ + ,
6.16 c0$,&"$,/(#/3(&,'2-$+,(),L(;<,X<?ET*V,&2,$A7#$00,.-8,(),&$#'0,21, 4
,*)-,v-*,*)-,&"30,0"24,&"*&
&"(0,/(#/3(&,(0,*,-(#$/&,#$7#$0$)&*&(2),21,MS<,TX<?EV<
6.17 D&"0#$%+#2/$*/$#,+'&'$)"(+#2@#)#;<=#@2,#.%&(%#+/#=#KPP#]#)$#.-#=#P?K-#K-#)"0#KP#3I?
Ans. K#AΩH#KPP#UΩH#KP#UΩ
6.18
F2"'&0+,#$%+#(&,(/&$#&"#D&L?#W?Kd:)>?#I$#+-*#=#K#]-#+)*#&'#)04/'$+0#$2#1&+60#)#(266+($2,#(/,,+"$#2@#K#3I?
=%+"-#.%&6+#+)*#&'#U+*$#(2"'$)"$-#+-*#&'#,)&'+0#$2#KK#]?#D&"0#$%+#"+.#7)6/+#2@#.-?#D2,#$%&'#$,)"'&'$2,+/ = KPP#]?
Ans. ?<?,'@
373
374 Chapter 6 Bipolar Junction Transistors (BJTs)
iC
iB
iC
C
B
B
$
$
DB
(IS "b)
vBE
IS evBE "VT
ro
C
iB
vBE
DB
(IS "b)
biB
ro
%
%
iE
E
iE
E
(a)
(b)
Figure 6.18 [),L+5'&L")6#+V/&7)6+"$5(&,(/&$#320+6'#2@#)"#!"!#;<=#2*+,)$&"L#&"#$%+#)($&7+#320+#&"#$%+#
(2332"5+3&$$+,#(2"@&L/,)$&2"#.&$%#$%+#2/$*/$#,+'&'$)"(+#(%#&"(6/0+0?
6.2.4 An Alternative Form of the Common-Emitter Characteristics
@),*+&$#)*&(.$,4*:,21,$A7#$00();,&"$,&#*)0(0&2#,/2''2)%$'(&&$#,/"*#*/&$#(0&(/0,(0,(++30&#*&$-,()
L(;<,X<?D<,R$#$,&"$,9*0$,/3##$)&,$),#*&"$#,&"*),&"$,9*0$−$'(&&$#,.2+&*;$,v)*,(0,30$-,*0,*,7*#*'$%
&$#<,!"*&,(05,$*/",$-− v-*,/3#.$,(0,'$*03#$-,4(&",&"$,9*0$,1$-,4(&",*,/2)0&*)&,/3##$)&,.)<,!"$
#$03+&();, /"*#*/&$#(0&(/05, 0"24), (), L(;<, X<?DT9V5, +22G, 0('(+*#, &2, &"20$, (), L(;<, X<?N<, L(;3#$
X<?DT/V,0"240,*),$A7*)-$-,.($4,21,&"$,/"*#*/&$#(0&(/0,(),&"$,0*&3#*&(2),#$;(2)<
The Common-Emitter Current Gain β !"#$%+#)($&7+#,+L&2"#2@#$%+#(%),)($+,&'$&('#'%2."#&"
D&L?#W?Ka:9>#.+#%)7+#&0+"$&@&+0#)#*),$&(/6),#*2&"$#l?#b2$+#$%)$#$%&'#2*+,)$&"L#*2&"$#@2,#$%+#$,)"'&'$2,
&'#(%),)($+,&h+0#91#)#9)'+#(/,,+"$# . ) - #)#(266+($2,#(/,,+"$# .- - #)"0#)#(266+($2,Q+3&$$+,#726$)L+#+-* ?
=%+#,)$&2# . - ⁄ . ) #&'#$%+#$,)"'&'$2,#β?#\2.+7+,-#$%+,+#&'#)"2$%+,#.)1#$2#3+)'/,+#β 8#(%)"L+#$%+#9)'+
(/,,+"$#91#)"#&"(,+3+"$# ∆$ ) #)"0#3+)'/,+#$%+#,+'/6$&"L#&"(,+3+"$# ∆$ - - #.%&6+#U++*&"L# +-* #(2"5
'$)"$?#=%&'#&'#&66/'$,)$+0#&"#D&L?#W?Ka:9>?#=%+#,)$&2# ∆$ - ⁄ ∆$ ) #'%2/60-#)((2,0&"L#$2#2/,#'$/01#$%/'#@),1&+60#)"#&0+"$&()6#7)6/+#@2,#β?#!$#$/,"'#2/$-#%2.+7+,-#$%)$#$%+#6)$$+,#7)6/+#2@#β#:()66+0#$!E(4I4!?'&2,#)(-#β >#&'#)#6&$$6+#0&@@+,+"$#@,23#$%+#0(#β :&?+?-# . - ⁄ . ) >?#C/(%#)#0&'$&"($&2"-#%2.+7+,-#&'#$22#'/9$6+
@2,#2/,#"++0'#&"#$%&'#922U?#Y+#'%)66#/'+#β $2#0+"2$+#92$%#0(#)"0#&"(,+3+"$)6#7)6/+'?KP
The Saturation Voltage VCEsat and Saturation Resistance RCEsat J+@+,# "+T$# $2# $%+
+T*)"0+0#7&+.#2@#$%+#(2332"5+3&$$+,#(%),)($+,&'$&('#&"#$%+#')$/,)$&2"#,+L&2"#'%2."#&"#D&L?
W?Ka:(>?#=%+#R9/"(%&"L#$2L+$%+,S#2@##$%+#(/,7+'##&"#$%+#')$/,)$&2"#,+L&2"#&3*6&+'#$%)$#$%+#&"5
(,+3+"$)6#β#&'#62.+,#$%+,+#$%)"#&"#$%+#)($&7+#,+L&2"?#I#*2''&96+#2*+,)$&"L#*2&"$#&"#$%+#')$/5
,)$&2"#,+L&2"#&'#$%)$#6)9+6+0#m?#!$#&'#(%),)($+,&h+0#91#)#9)'+#(/,,+"$#.)-#)#(266+($2,#(/,,+"$
.-')$-#)"0#)#(266+($2,Q+3&$$+,#726$)L+#+-*')$?##D,23#2/,#*,+7&2/'#0&'(/''&2"#2@#')$/,)$&2"-#,+()66
$%)$#.-')$#`#β @2,(+0#.)-#.%+,+#β @2,(+0#i#β?
!"$,$-− v-*,/3#.$0,(),0*&3#*&(2),*#$,#*&"$#,0&$$75,()-(/*&();,&"*&,&"$,0*&3#*&$-,&#*)0(0&2#
$A"(9(&0,*,+24,/2++$/&2#%&2%$'(&&$#,#$0(0&*)/$,>-*0*&5
∂v
-*
> -*')$ ≡ 5555555555
)
∂ $ - $$)- == ..-')$
TX<P\V
=1*&()661-#>-*')$#,)"L+'#@,23#)#@+.#2%3'#$2#)#@+.#$+"'#2@#2%3'?
A)"/@)($/,+,'#2@#9&*26),#$,)"'&'$2,'#/'+#DS*#$2#0+"2$+#$%+#0(#7)6/+#2@#β )"0#DG4#$2#0+"2$+#$%+#&"(,+3+"5
$)6# β?#=%+'+#'13926'#(23+#@,23#$%+#D5*),)3+$+,#0+'(,&*$&2"#2@#$.25*2,$#"+$.2,U'#:'++#I**+"0&T#F>.&$%#$%+#'/9'(,&*$#S:GT#0+"2$&"L#@2,.),0#)"0#*:4>#0+"2$&"L#(2332"#+3&$$+,?
KP
6.2 Current–Voltage Characteristics
iC
Saturation
region
iC
Active region iB = IB1 . . .
iB = IB2 . . .
∆iC
iB = IB + ∆iB
IB
vCE
IC
iB = IB
Q
iB
iB = . . .
0
VCE iB = 0
(a)
vCE
(b)
iB " IB
bIB
Slope "
ICsat
1
RCEsat
X
VCEsat
(c)
Figure 6.19 F2332"5+3&$$+,#(%),)($+,&'$&('?#:'>#;)'&(#FE#(&,(/&$H#"2$+#$%)$#&"#:&>##$%+#%2,&h2"$)6#'()6+#&'
+T*)"0+0#),2/"0#$%+#2,&L&"#$2#'%2.#$%+#')$/,)$&2"#,+L&2"#&"#'23+#0+$)&6?#I#3/(%#L,+)$+,#+T*)"'&2"#2@#$%+
')$/,)$&2"#,+L&2"#&'#'%2."#&"#:)>?
!"*&, &"$, /2++$/&2#%&2%$'(&&$#, #$0(0&*)/$, 21, *, 0*&3#*&$-, BC!, (0, 0'*++, 0"23+-, "*.$, 9$$)
*)&(/(7*&$-,1#2',&"$,1*/&,&"*&,9$&4$$),6,*)-,M,4$,)24,"*.$,&42,12#4*#-%/2)-3/&();,-(2-$0
(),0$#($0??,T0$$,*+02,L(;<,X<DV<
KK
!"#$%+#(2,,+'*2"0&"L#320+#2@#2*+,)$&2"#@2,#$%+#ABCDE=-#$%+#$,&20+#,+L&2"-#$%+#,+'&'$)"(+#9+$.++"
0,)&"#)"0#'2/,(+#&'#'3)66#9+()/'+#&$#&'#$%+#,+'&'$)"(+#2@#$%+#(2"$&"/2/'#:"2"5*&"(%+052@@>#(%)""+6?
375
376 Chapter 6 Bipolar Junction Transistors (BJTs)
I#'&3*6+#320+6#@2,#$%+#')$/,)$+0#;<=#&'#'%2."#&"#D&L?#W?MP?#\+,+# + )* #&'#)''/3+0#(2"5
'$)"$#:)**,2T&3)$+61#P?d#]>#)"0# + -* #)6'2#&'#)''/3+0#(2"'$)"$-# + -*')$ ! P?M #]?#=%)$#&'-#.+
%)7+#"+L6+($+0#$%+#'3)66#')$/,)$&2"#,+'&'$)"(+# > -*')$ #@2,#$%+#')U+#2@#3)U&"L#$%+#320+6#'&35
*6+#@2,#%)"0#()6(/6)$&2"'?#########
ICsat
IB
B
$
$
VBE
0.7 V
%
0.2 V
VCEsat
%
Figure 6.20 I#'&3*6&@&+0#+V/&7)6+"$5(&,(/&$#
320+6#2@#$%+#')$/,)$+0#$,)"'&'$2,?
E
Example 6.3
D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#&$#&'#,+V/&,+0#$2#0+$+,3&"+#$%+#7)6/+#2@#$%+#726$)L+# +)) #$%)$#,+'/6$'#&"#$%+#$,)"5
'&'$2,#2*+,)$&"L
:)>#&"#$%+#)($&7+#320+#.&$%# + -* d G #]#
:9>#)$#$%+#+0L+#2@#')$/,)$&2"
:(>#0++*#&"#')$/,)$&2"#.&$%# β @2,(+0 d KP #
D2,#'&3*6&(&$1-#)''/3+#$%)$# + )* #,+3)&"'#(2"'$)"$#)$#P?d#]?#=%+#$,)"'&'$2,#β#&'#'*+(&@&+0#$2#9+#GP?
VCC " 10V
VBB
IC
RB
" 10 k&
RC " 1 k&
IB
$
$
VCE
VBE
%
%
Figure 6.21 F&,(/&$#@2,#ET)3*6+#W?N?
Solution
:)>#=2#2*+,)$+#&"#$%+#)($&7+#320+#.&$%# + -* d G #]+ -- ] + -*
5
. - d 5555555555555555555555555
>KP ] G
d 555555555555555 d G #3I
K#UΩ
6.2 Current–Voltage Characteristics
.
G
. ) d 5555- d 555555 d P?K #3I
β GP
b2.#$%+#,+V/&,+0#7)6/+#2@# + )) #()"#9+#@2/"0#)'#@2662.'8
+ )) d . ) > ) e + )*
d P?K × KP e P?d d K?d#]
:9>#B*+,)$&2"#)$#$%+#+0L+#2@#')$/,)$&2"#&'#29$)&"+0#.&$%# + -* d P?N #]?#=%/'
KP ] P?N
. - d 5555555555555555555 d a?d ,'@
K
C&"(+-#)$#$%+#+0L+#2@#')$/,)$&2"-# . - #)"0# . ) #),+#'$&66#,+6)$+0#91#βa?d
. ) d 5555555 d P?Kae ,'@
GP
=%+#,+V/&,+0#7)6/+#2@# +)) #()"#9+#0+$+,3&"+0#)'
+)) d P?Kae × KP e P?d d M?We,_
:(>#=2#2*+,)$+#0++*#&"#')$/,)$&2"-#
+ -* d + -*')$ ! P?M ,_
=%/'KP ] P?M
, . - d 5555555555555555555 d a?f ,'@
K
Y+#$%+"#/'+#$%+#7)6/+#2@#@2,(+0 β#$2#0+$+,3&"+#$%+#,+V/&,+0#7)6/+#2@# . ) #)'
.5 d a?f
5555555 d P?af ,'@
. ) d 5555555555555
β @2,(+0 KP
)"0#$%+#,+V/&,+0# +)) #()"#"2.#9+#@2/"0#)'
+)) d P?af × KP e P?d d KP?G ,_
B9'+,7+#$%)$#2"(+#$%+#$,)"'&'$2,#&'#&"#')$/,)$&2"-#&"(,+)'&"L#+)) #)"0#$%/'# . ) #,+'/6$'#&"#"+L6&L&96+#(%)"L+#&"
. - #'&"(+# + -*')$ #.&66#(%)"L+#2"61#'6&L%$61?#=%/'# . - #&'#')&0#$28B'?U('?4-#.%&(%#&'#$%+#2,&L&"#2@#$%+#")3+
R')$/,)$&2"#320+#2@#2*+,)$&2"?S
EXERCISES
6.19 J+*+)$#ET)3*6+#W?N#@2,# > - d KP#U Ω?
Ans. P?f#]H#P?fae#]H#K?Wf#]
6.20 D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#@&"0# + -* #@2,# +)) d P ]?
Ans. c#KP#]
6.21 D2,#$%+#(&,(/&$#&"#D&L?#W?MK-#6+$# +)) #9+#'+$#$2#$%+#7)6/+#29$)&"+0#&"#ET)3*6+#W?N-#*),$#:)>-#")3+61+)) d K?d #]?#]+,&@1#$%)$#$%+#$,)"'&'$2,#&'#&"0++0#2*+,)$&"L#&"#$%+#)($&7+#320+?#b2.-#.%&6+#U++*&"L
+)) #(2"'$)"$-#@&"0#$%)$#7)6/+#$2#.%&(%# > - #'%2/60#9+#&"(,+)'+0#&"#2,0+,#$2#29$)&"#:)>#2*+,)$&2"#)$
$%+#+0L+#2@#')$/,)$&2"-#)"0#:9>#2*+,)$&2"#0++*#&"#')$/,)$&2"#.&$%# β @2,(+0 d KP?
Ans. :)>#K?ae#U ΩH #:9>#a?f#U Ω
377
378 Chapter 6 Bipolar Junction Transistors (BJTs)
6.3 BJT Circuits at DC
W$, *#$, )24, #$*-:, &2, /2)0(-$#, &"$, *)*+:0(0, 21, BC!, /(#/3(&0, &2, 4"(/", 2)+:, -/, .2+&*;$0, *#$
*77+($-<,=),&"$,12++24();,$A*'7+$0,4$,4(++,30$,&"$,0('7+$,'2-$+,(),4"(/", + )* 21,*,/2)%
-3/&();,&#*)0(0&2#,(0,O<N,_,*)-, + -* ,21,*,0*&3#*&$-,&#*)0(0&2#,(0,O<P,_5,*)-,4$,4(++,)$;+$/&
&"$,M*#+:,$11$/&<,B$&&$#,'2-$+0,/*)5,21,/23#0$5,9$,30$-,&2,29&*(),'2#$,*//3#*&$,#$03+&0<,!"(05
"24$.$#5,(0,303*++:,*/"($.$-,*&,&"$,$A7$)0$,21,07$$-,21,*)*+:0(05,*)-,'2#$,('72#&*)&+:5,(&
/23+-,('7$-$,&"$,/(#/3(&,-$0(;)$#h0,*9(+(&:,&2,;*(),()0(;"&,#$;*#-();,/(#/3(&,9$"*.(2#<,@//3%
#*&$, #$03+&0, 30();, $+*92#*&$, '2-$+0, /*), 9$, 29&*()$-, 30();, /(#/3(&, 0('3+*&(2), 4(&", Kg=6M<
!"(0,(0,*+'20&,*+4*:0,-2)$,(),&"$,1()*+,0&*;$0,21,*,-$0(;),*)-,/$#&*()+:,9$12#$,/(#/3(&,1*9#(/*%
&(2)<, 62'73&$#, 0('3+*&(2)5, "24$.$#5, (0, )2&, *, 0390&(&3&$, 12#, S3(/G, 7$)/(+%*)-%7*7$#, /(#/3(&
*)*+:0(05,*),$00$)&(*+,*9(+(&:,&"*&,*07(#();,/(#/3(&,-$0(;)$#0,'30&,'30&$#<,!"$,12++24();,0$#($0
21,$A*'7+$0,(0,*,0&$7,(),&"*&,-(#$/&(2)<
@0, 4(++, 9$, 0$$)5, (), *)*+:>();, *, /(#/3(&, &"$, 1(#0&, S3$0&(2), &"*&, 2)$, '30&, *)04$#, (0Y, .!
AD$ED8 I%548 $B8 ?D48 ?('!B$B?%(8 %"4('?$!Cf, =), 02'$, /*0$05, &"$, *)04$#, 4(++, 9$, 29.(230<, L2#
()0&*)/$5,*,S3(/G,/"$/G,21,&"$,&$#'()*+,.2+&*;$0,4(++,()-(/*&$,4"$&"$#,&"$,&#*)0(0&2#,(0,/3&
211,2#,/2)-3/&();<,=1,(&,(0,/2)-3/&();5,4$,"*.$,&2,-$&$#'()$,4"$&"$#,(&,(0,27$#*&();,(),&"$
*/&(.$,'2-$,2#,(),0*&3#*&(2)<,=),02'$,/*0$05,"24$.$#5,&"(0,'*:,)2&,9$,29.(230<,Q$$-+$00,&2
0*:5,*0,&"$,#$*-$#,;*()0,7#*/&(/$,*)-,$A7$#($)/$,(),&#*)0(0&2#,/(#/3(&,*)*+:0(0,*)-,-$0(;)5,&"$
*)04$#,4(++,9$,*77*#$)&,(),*,'3/",+*#;$#,7#272#&(2),21,7#29+$'0<,!"$,*)04$#5,"24$.$#5,/*)
*+4*:0,9$,-$&$#'()$-,9:,3&(+(>();,&"$,12++24();,7#2/$-3#$Y
@003'$,&"*&,&"$,&#*)0(0&2#,(0,27$#*&();,(),&"$,*/&(.$,'2-$5,*)-,7#2/$$-,&2,-$&$#'()$,&"$
.*#(230,.2+&*;$0,*)-,/3##$)&0,&"*&,/2##$072)-<,!"$),/"$/G,12#,/2)0(0&$)/:,21,&"$,#$03+&0,4(&"
&"$, *003'7&(2), 21, */&(.$%'2-$, 27$#*&(2)`, &"*&, (05, (0, v-), 21, *), !"!, &#*)0(0&2#, ;#$*&$#, &"*)
−O<8 _,T2#,v-),21,*,"!",&#*)0(0&2#,+24$#,&"*),O<8,_Vf,=1,&"$,*)04$#,(0,:$05,&"$),23#,&*0G,(0
/2'7+$&$<,=1,&"$,*)04$#,(0,)25,*003'$,0*&3#*&(2)%'2-$,27$#*&(2)5,*)-,7#2/$$-,&2,-$&$#'()$
/3##$)&0,*)-,.2+&*;$0,*)-,&"$),&2,/"$/G,12#,/2)0(0&$)/:,21,&"$,#$03+&0,4(&",&"$,*003'7&(2),21
0*&3#*&(2)%'2-$,27$#*&(2)<,R$#$,&"$,&$0&,(0,303*++:,&2,/2'73&$,&"$,#*&(2, . - ⁄ . ) ,*)-,&2,.$#(1:
&"*&,(&,(0,+24$#,&"*),&"$,&#*)0(0&2#,β,T(<$<5,β12#/$-,i,β V<,K()/$,β,12#,*,;(.$),&#*)0(0&2#,&:7$,.*#($0
2.$#,*,4(-$,#*);$5?P,2)$,'30&,30$,&"$,+24$0&,07$/(1($-, β,12#,&"(0,&$0&<,L()*++:5,)2&$,&"*&,&"$
2#-$#,21,&"$0$,&42,*003'7&(2)0,/*),9$,#$.$#0$-<,@0,*,13#&"$#,*(-,&2,&"$,#$*-$#5,4$,7#2.(-$,()
!*9+$,X<\,*,03''*#:,21,&"$,/2)-(&(2)0,*)-,'2-$+0,12#,&"$,27$#*&(2),21,&"$,BC!,(),(&0,&"#$$
7200(9+$,'2-$0<
KM
=%)$#&'-#&@#2"+#9/1'#;<='#2@#)#(+,$)&"#*),$#"/39+,-#$%+#3)"/@)($/,+,#L/),)"$++'#2"61#$%)$#$%+&,#7)6/+'
2@#β @)66#.&$%&"#)#(+,$)&"#,)"L+-#')1#GP#$2#KGP?
+,#"-,#($.
!#"$%/0)1,)-%#+,*'.#"$%/0)1,)-%#+,*'-
&'#()*
!#"$%/0)1,)-%#+,*'.#"$%&'(')*'%#+,*'-
!"#$%%
!"#$%&'(')*'%#+,*'.#"$%&'(')*'%#+,*'-
!
IC # O
C
C
"
IB > 0 "
! IC = bforcedIB
C
"
B
"
C
"
!
! IC # bIB
"
VEC > 0.3 V
!
IC # O
"
VCB ! 0.5 V
E
VCB < 0.4 V
bIB
!
C
VECsat ! 0.2 V
IB > 0 "
E
VCB < 0.4 V
E
"
VEB ! 0.7 V
!
B
VEB ! 0.7 V
"
!
IC
VEC
!
VCEsat ! 0.2 V
C
forced IB
IB # O
"
!
B
VEB < 0.5 V
!
"
"
VCB
!
VBE ! 0.7 V
C
" I #b
"
VCE > 0.3 V
!
" I # bI
C
B
"
"
VCE
IB
VEB
!
E
VBC ! 0.5 V
E
bIB
VBC < 0.4 V
E
VBC < 0.4 V
"
!
!
VBE
IC !
"!"
!
B
IB > 0
"
!
IB > 0 !
VBE ! 0.7 V
B
"
VBE < 0.5 V
B
!
IB # O !
IB
"
VBC
!"!
Table 6.3 Conditions and Models for the Operation of the BJT in Various Modes
6.3 BJT Circuits at DC
379
380 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.4
62)0(-$#,&"$,/(#/3(&,0"24),(),L(;<,X<PPT*V5,4"(/",(0,#$-#*4),(),L(;<,X<PPT9V,&2,#$'()-,&"$,#$*-$#,21,&"$
/2).$)&(2),$'7+2:$-,&"#23;"23&,&"(0,922G,12#,()-(/*&();,/2))$/&(2)0,&2,-/,023#/$0<,W$,4(0",&2,*)*+:>$
&"(0, /(#/3(&, &2, -$&$#'()$, *++, )2-$, .2+&*;$0, *)-, 9#*)/", /3##$)&0<, W$, 4(++, *003'$, &"*&, β, (0, 07$/(1($-, &2
9$ ?OO<
$10 V
IC
RC " 4.7 k&
RC " 4.7 k&
$4 V
VC
IB
10 V
VE
4V
IE
RE " 3.3 k&
RE "
3.3 k&
(b)
(a)
$10 V
3
0.99 ) 1 " 0.99 mA
4.7 k&
$4 V
5
10 % 0.99 ) 4.7
5.3 V
4 % 0.7 " 3.3 V
1
4
1.00 % 0.99 " 0.01 mA
3.3 k&
3.3
" 1 mA
3.3
2
(c)
Figure 6.22 I")61'&'#2@#$%+#(&,(/&$#@2,#ET)3*6+#W?e8#;'<#(&,(/&$H#;&<#(&,(/&$#,+0,)."#$2#,+3&"0#$%+#,+)0+,#2@#$%+#(2"5
7+"$&2"#/'+0#&"#$%&'#922U#$2#'%2.#(2""+($&2"'#$2#$%+#*2.+,#'/**61H#;)<#)")61'&'#.&$%#$%+#'$+*'#"/39+,+0?
Solution
n6)"(&"L#)$#$%+#(&,(/&$#&"#D&L?#W?MM:)>-#.+#"2$+#$%)$#$%+#9)'+#&'#(2""+($+0#$2#+e#]#)"0#$%+#+3&$$+,#&'#(2"5
"+($+0#$2#L,2/"0#$%,2/L%#)#,+'&'$)"(+#>*?#=%+,+@2,+-#&$#&'#')@+#$2#(2"(6/0+#$%)$#$%+#9)'+Q+3&$$+,#4/"($&2"
6.3 BJT Circuits at DC
.&66#9+#@2,.),0#9&)'+0?#I''/3&"L#$%)$#$%&'#&'#$%+#()'+#)"0#)''/3&"L#$%)$#+)*#&'#)**,2T&3)$+61#P?d#]-#&$#@265
62.'#$%)$#$%+#+3&$$+,#726$)L+#.&66#9+#
+ * = e ] + )* #! e ] P?d = N?N#]
Y+#),+#"2.#&"#)"#2**2,$/"+#*2'&$&2"H#.+#U"2.#$%+#726$)L+'#)$#$%+#$.2#+"0'#2@#>*#)"0#$%/'#()"#0+$+,3&"+
$%+#(/,,+"$#.*#$%,2/L%#&$+* ] P
N?N
5 = 5555555 = K#3I
. * = 55555555555555
>*
N?N
C&"(+#$%+#(266+($2,#&'#(2""+($+0#$%,2/L%#>-#$2#$%+#+KP5]#*2.+,#'/**61-#&$#)**+),'#*2''&96+#$%)$#$%+#(266+(5
$2,#726$)L+#.&66#9+#%&L%+,#$%)"#$%+#9)'+#726$)L+-#.%&(%#&3*6&+'#)($&7+5320+#2*+,)$&2"?#I''/3&"L#$%)$#$%&'
&'#$%+#()'+-#.+#()"#+7)6/)$+#$%+#(266+($2,#(/,,+"$#@,23
.- = α .*
=%+#7)6/+#2@#α#&'#29$)&"+0#@,23
β
KPP
α = 555555555555 = 555555555 #!#P?aa
β+K
KPK
=%/'#.-#.&66#9+#L&7+"#91
. - = P?aa × K = P?aa#3I
Y+#),+#"2.#&"#)#*2'&$&2"#$2#/'+#B%3k'#6).#$2#0+$+,3&"+#$%+#(266+($2,#726$)L+#+- -#
+ - = KP ] . - > - = KP ] P?aa × e?d#! +G?N#]
C&"(+# $%+# 9)'+# &'# )$# +e# ]-# $%+# (266+($2,Q9)'+# 4/"($&2"# &'# ,+7+,'+# 9&)'+0# 91# K?N# ]-# )"0# $%+# $,)"'&'$2,# &'
&"0++0#&"#$%+#)($&7+#320+#)'#)''/3+0?
!$#,+3)&"'#2"61#$2#0+$+,3&"+#$%+#9)'+#(/,,+"$#.)-#)'#@2662.'8
.*
K5
5 = 55555555
. ) = 55555555555
#!#P?PK#3I
β+K
KPK
;+@2,+#6+)7&"L#$%&'#+T)3*6+#.+#.&'%#$2#+3*%)'&h+#'$,2"L61#$%+#7)6/+#2@#(),,1&"L#2/$#$%+#)")61'&'
0&,+($61#2"#$%+#(&,(/&$#0&)L,)3?#B"61#&"#$%&'#.)1#.&66#2"+#9+#)96+#$2#)")61h+#(23*6+T#(&,(/&$'#&"#)#,+)'2"5
)96+#6+"L$%#2@#$&3+?#D&L/,+#W?MM:(>#&66/'$,)$+'#$%+#)927+#)")61'&'#2"#$%+#(&,(/&$#0&)L,)3-#.&$%#$%+#2,0+,#2@
$%+#)")61'&'#'$+*'#&"0&()$+0#91#$%+#(&,(6+0#"/39+,'?#
381
382 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.5
Y+#.&'%#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?MN:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'
$%,2/L%#)66#9,)"(%+'?#b2$+#$%)$#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#2@#D&L?#W?MM#+T(+*$#$%)$#$%+#726$)L+#)$
$%+#9)'+#&'#"2.#+W#]?#I''/3+#$%)$#$%+#$,)"'&'$2,# β#&'#'*+(&@&+0#$2#9+#'?8&4'B?#GP?
$10 V
$10 V
3
1.6 mA
4.7 k&
4.7 k&
10 % 1.6 ) 4.7 " 2.48
Impossible, not in
active mode
$6 V
$6 V
6 % 0.7 " $5.3 V
3.3 k&
3.3 k&
5.3
" 1.6 mA
3.3
4
1
2
(b)
(a)
(c)
Figure 6.23 I")61'&'#2@#$%+#(&,(/&$#@2,#ET)3*6+#W?G?#b2$+#$%)$#$%+#(&,(6+0#"/39+,'#&"0&()$+#$%+#2,0+,#2@ $%+#)")615
'&'#'$+*'?
6.3 BJT Circuits at DC
Solution
Y&$%#cW#]#)$#$%+#9)'+-#$%+#9)'+Q+3&$$+,#4/"($&2"#.&66#9+#@2,.),0#9&)'+0H#$%/'+ * = + W ] + )* #!#W ] P?d = G?N#]
)"0
G?N
. * = 5555555 = K?W#3I
N?N
b2.-#)''/3&"L#)($&7+5320+#2*+,)$&2"-#.-#`#α.*8!#.*H#$%/'+ - = +KP ] e?d × . - #!#KP ] d?GM = M?ef#]
=%+#0+$)&6'#2@#$%+#)")61'&'#*+,@2,3+0#)927+#),+#&66/'$,)$+0#&"#D&L?#W?MN:9>?
C&"(+#$%+#(266+($2,#726$)L+#()6(/6)$+0#)**+),'#$2#9+#6+''#$%)"#$%+#9)'+#726$)L+#91#N?GM#]-#&$#@2662.'
$%)$#2/,#2,&L&")6#)''/3*$&2"#2@#)($&7+5320+#2*+,)$&2"#&'#&"(2,,+($?#!"#@)($-#$%+#$,)"'&'$2,#%)'#$2#9+#&"#$%+
B'?U('?$%!#320+?#I''/3&"L#$%&'#$2#9+#$%+#()'+-#$%+#7)6/+'#2@#+*#)"0#.*#.&66#,+3)&"#/"(%)"L+0?#=%+#(266+(5
$2,#726$)L+-#%2.+7+,-#9+(23+'##
+ - = + * + + -*')$ #!#+G?N + P?M = +G?G#]
@,23#.%&(%#.+#()"#0+$+,3&"+#.-8#)'
+KP ] G?G
. - = 55555555555555555555555 = P?aW#3I
e?d
*)-,.),/*),)24,9$,123)-,*0
. ) = . * ] . - = K?W ] P?aW = P?We#3I
!"30,&"$,&#*)0(0&2#,(0,27$#*&();,*&,*,12#/$-,β,21
.
.)
P?aW
P?We
β @2,(+0 = 5555- = 5555555555 = K?G
K()/$,β12#/$-,(0,+$00,&"*),&"$,I$!$IUI,07$/(1($-,.*+3$,21,β5,&"$,&#*)0(0&2#,(0,()-$$-,0*&3#*&$-<,W$,0"23+$'7"*0(>$, "$#$, &"*&, (), &$0&();, 12#, 0*&3#*&(2), &"$, '()('3', .*+3$, 21, β, 0"23+-, 9$, 30$-<, B:, &"$, 0*'$
&2G$)5,(1,4$,*#$,-$0(;)();,*,/(#/3(&,(),4"(/",*,&#*)0(0&2#,(0,&2,9$,0*&3#*&$-5,&"$,-$0(;),0"23+-,9$,9*0$2),&"$,'()('3',07$/(1($-,β<,J9.(230+:5,(1,*,&#*)0(0&2#,4(&",&"(0,'()('3',β,(0,0*&3#*&$-5,&"$),&#*)0(0&2#0
4(&","(;"$#,.*+3$0,21,β,4(++,*+02,9$,0*&3#*&$-<,!"$,-$&*(+0,21,&"$,*)*+:0(0,*#$,0"24),(),L(;<,X<P\T/V5,4"$#$
&"$,2#-$#,21,&"$,0&$70,30$-,(0,()-(/*&$-,9:,&"$,/(#/+$-,)3'9$#0<
383
384 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.6
Y+# .&'%# $2# )")61h+# $%+# (&,(/&$# &"# D&L?# W?Me:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$'
$%,2/L%#)66#9,)"(%+'?#b2$+#$%)$#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#(2"'&0+,+0#&"#ET)3*6+'#W?e#)"0#W?G#+T(+*$
$%)$#"2.#$%+#9)'+#726$)L+#&'#h+,2?
2
1
(a)
(b)
Figure 6.24 ET)3*6+#W?W8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#2,0+,#2@#$%+#)")61'&'#'$+*'#&"0&()$+0#91#(&,(6+0#"/39+,'?
Solution
C&"(+#$%+#9)'+#&'#)$#h+,2#726$'#)"0#$%+#+3&$$+,#&'#(2""+($+0#$2#L,2/"0#$%,2/L%#>*-#$%+#9)'+Q+3&$$+,#4/"($&2"#()"5
"2$#(2"0/($#)"0#$%+#+3&$$+,#(/,,+"$#&'#h+,2?#b2$+#$%)$#$%&'#'&$/)$&2"#.&66#29$)&"#)'#62"L#)'#$%+#726$)L+#)$#$%+#9)'+#&'
6+''#$%)"#P?G#]#2,#'2?#I6'2-#$%+#(266+($2,Q9)'+#4/"($&2"#()""2$#(2"0/($-#'&"(+#$%+#!5$1*+#(266+($2,#&'#(2""+($+0
$%,2/L%#>-#$2#$%+#*2'&$&7+#*2.+,#'/**61#.%&6+#$%+#"5$1*+#9)'+#&'#)$#L,2/"0?#!$#@2662.'#$%)$#$%+#(266+($2,#(/,,+"$
.&66#9+#h+,2?#=%+#9)'+#(/,,+"$#.&66#)6'2#%)7+#$2#9+#h+,2-#)"0#$%+#$,)"'&'$2,#&'#&"#$%+#EU?%GG#320+#2@#2*+,)$&2"?
=%+#+3&$$+,#726$)L+#.&66#9+#h+,2-#.%&6+#$%+#(266+($2,#726$)L+#.&66#9+#+V/)6#$2#+KP ]-#'&"(+#$%+#726$)L+
0,2*'#)(,2''#>*#)"0#>-#),+#h+,2?#D&L/,+#W?Me:9>#'%2.'#$%+#)")61'&'#0+$)&6'?
,,,,,,,,,,
EXERCISES
D6.22 D2,#$%+#(&,(/&$#&"#D&L?#W?MM:)>-#@&"0#$%+#%&L%+'$#726$)L+#$2#.%&(%#$%+#9)'+#()"#9+#,)&'+0#.%&6+#$%+
$,)"'&'$2,#,+3)&"'#&"#$%+#)($&7+#320+?#I''/3+#α#!#K?
Ans. +e?d#]
D6.23 J+0+'&L"#$%+#(&,(/&$#2@#D&L?#W?MM:)>#:&?+?-#@&"0#"+.#7)6/+'#@2,#>*#)"0#>->#$2#+'$)96&'%#)#(266+($2,
(/,,+"$#2@#P?G#3I#)"0#)#,+7+,'+59&)'#726$)L+#2"#$%+#(266+($2,Q9)'+#4/"($&2"#2@#M#]?#I''/3+#α#!#K?
Ans. >*#=#W?W#UΩH#>-#=#f#UΩ
6.24 D2,#$%+#(&,(/&$#&"#D&L?#W?MN:)>-#@&"0#$%+#7)6/+#$2#.%&(%#$%+#9)'+#726$)L+#'%2/60#9+#(%)"L+0#'2#$%)$
$%+#$,)"'&'$2,#2*+,)$+'#&"#')$/,)$&2"#.&$%#)#@2,(+0#β#2@#G?
Ans. +^<?E,_
6.3 BJT Circuits at DC
385
Example 6.7
Y+# .)"$# $2# )")61h+# $%+# (&,(/&$# 2@# D&L?# W?MG:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$'
$%,2/L%#)66#9,)"(%+'?
V $ " $10 V
$10 V
10 % 0.7
" 4.65 mA
2
2 k&
RE " 2 k&
$0.7 V
5
2
1
0.05 mA
%10 $ 4.6 ) 1 " %5.4 V
RC " 1 k&
4
1 k&
3
0.99 ) 4.65
V % " %10 V
4.6 mA
%10 V
(a)
(b)
Figure 6.25 ET)3*6+#W?d8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#'$+*'#&"0&()$+0#91#(&,(6+0#"/39+,'?
Solution
=%+#9)'+#2@#$%&'#"!"#$,)"'&'$2,#&'#L,2/"0+0-#.%&6+#$%+#+3&$$+,#&'#(2""+($+0#$2#)#*2'&$&7+#'/**61#:+ +#=#+KP#]>
$%,2/L%#>*?#!$#@2662.'#$%)$#$%+#+3&$$+,Q9)'+#4/"($&2"#.&66#9+#@2,.),0#9&)'+0#.&$%
+ * = + *) #!#P?d#]
=%/'#$%+#+3&$$+,#(/,,+"$#.&66#9+#L&7+"#91#
+
+ ]+
KP ] P?d
. * = 55555555555555555*5 = 5555555555555555555 = e?WG#3I
M
>*
K()/$,&"$,/2++$/&2#,(0,/2))$/&$-,&2,*,)$;*&(.$,0377+:,T'2#$,)$;*&(.$,&"*),&"$,9*0$,.2+&*;$V,&"#23;",>-5,(&
(0,"%BB$#&4,&"*&,&"(0,&#*)0(0&2#,(0,27$#*&();,(),&"$,*/&(.$,'2-$<,@003'();,&"(0,&2,9$,&"$,/*0$5,4$,29&*()
.- = α .*
K()/$,)2,.*+3$,12#,β "*0,9$$),;(.$)5,4$,0"*++,*003'$,β,=,?OO5,4"(/",#$03+&0,(),α,=,O<DD<,K()/$,+*#;$,.*#(%
*&(2)0,(), β,#$03+&,(),0'*++,-(11$#$)/$0,(), α5,&"(0,*003'7&(2),4(++,)2&,9$,/#(&(/*+,*0,1*#,*0,-$&$#'()();,&"$
.*+3$,21,.-,(0,/2)/$#)$-<,!"305
. - = P?aa × e?WG = e?W#3I
!"$,/2++$/&2#,.2+&*;$,4(++,9$
−
+- = + + .- >= # −KP + e?W × K = ] G?e#]
386 Chapter 6 Bipolar Junction Transistors (BJTs)
,,,
=%/'# $%+# (266+($2,Q9)'+# 4/"($&2"# &'# ,+7+,'+# 9&)'+0# 91# G?e# ]-# )"0# $%+# $,)"'&'$2,# &'# &"0++0# &"# $%+# )($&7+
320+-#.%&(%#'/**2,$'#2/,#2,&L&")6#)''/3*$&2"?
!$#,+3)&"'#2"61#$2#()6(/6)$+#$%+#9)'+#(/,,+"$.*
5 = e?WG
5555555555 #!#P?PG#3I
. ) = 55555555555
β+K
KPK
B97&2/'61-#$%+#7)6/+#2@#β#(,&$&()661#)@@+($'#$%+#9)'+#(/,,+"$?#b2$+-#%2.+7+,-#$%)$#&"#$%&'#(&,(/&$#$%+#7)6/+#2@#β
.&66#%)7+#"2#+@@+($#2"#$%+#320+#2@#2*+,)$&2"#2@#$%+#$,)"'&'$2,?#C&"(+#β#&'#L+"+,)661#)"#&665'*+(&@&+0#*),)3+$+,$%&'#(&,(/&$#,+*,+'+"$'#)#L220#0+'&L"?#I'#)#,/6+-#2"+#'%2/60#'$,&7+#$2#54B$C!8?D48E$(EU$?8BUED8?D'?8$?B8"4(G%(M
I'!E48$B8'B8$!B4!B$?$F48?%8?D48F'&U48%G8β8'B8"%BB$#&4@#=%+#)")61'&'#0+$)&6'#),+#&66/'$,)$+0#&"#D&L?#W?MG:9>?
EmIAO[E#G?d
EXERCISES
D6.25#D2,#$%+#(&,(/&$#&"#D&L?#W?MG:)>-#@&"0#$%+#6),L+'$#7)6/+#$2#.%&(%#>-#()"#9+#,)&'+0#.%&6+#$%+#$,)"'&'$2,
,+3)&"'#&"#$%+#)($&7+#320+?
Ans. M?MW#UΩ
D6.26 J+0+'&L"#$%+#(&,(/&$#2@#D&L?#W?MG:)>#:&?+?-#@&"0#"+.#7)6/+'#@2,#>*#)"0#>->#$2#+'$)96&'%#)#(266+($2,
(/,,+"$#2@#K#3I#)"0#)#,+7+,'+#9&)'#2"#$%+#(266+($2,Q9)'+#4/"($&2"#2@#e#]?#I''/3+#α#!#K?
Ans. >*#=#a?N#UΩH#>-#=#W#UΩ
Example 6.8
Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#&"#D&L?#W?MW:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#&"#)66
9,)"(%+'?#I''/3+#β# =#KPP?
(a)
(b)
Figure 6.26 ET)3*6+#W?f8#;'<#(&,(/&$H#;&<#)")61'&'-#.&$%#$%+#'$+*'#&"0&()$+0#91#$%+#(&,(6+0#"/39+,'?
6.3 BJT Circuits at DC
387
Solution
=%+#9)'+Q+3&$$+,#4/"($&2"#&'#(6+),61#@2,.),0#9&)'+0?#=%/'+G ] + )*
G ] P?d
#!# 5555555555555555 = P?PeN#3I
. ) = 555555555555555555555
>)
KPP
I''/3+#$%)$#$%+#$,)"'&'$2,#&'#2*+,)$&"L#&"#$%+#)($&7+#320+?#Y+#"2.#()"#.,&$+
. - = β . ) = KPP × P?PeN = e?N#3I
=%+#(266+($2,#726$)L+#()"#"2.#9+#0+$+,3&"+0#)'
+ - = +KP ] . - > - = KP ] e?N × M = +K?e#]
C&"(+#$%+#9)'+#726$)L+#+)#&'#
+ ) = + )* #!#+ P?d#]
&$#@2662.'#$%)$#$%+#(266+($2,Q9)'+#4/"($&2"#&'#,+7+,'+59&)'+0#91#P?d#]#)"0#$%+#$,)"'&'$2,#&'#&"0++0#&"#$%+#)($&7+
320+?#=%+#+3&$$+,#(/,,+"$#.&66#9+#L&7+"#91
. * = ( β + K ). ) = KPK × P?PeN#!#e?N#3I
Y+#"2$+#@,23#$%&'#+T)3*6+#$%)$#$%+#(266+($2,#)"0#+3&$$+,#(/,,+"$'#0+*+"0#(,&$&()661#2"#$%+ 7)6/+#2@# β?#!"
@)($-#&@#β#.+,+#KPo#%&L%+,-#$%+#$,)"'&'$2,#.2/60#6+)7+#$%+#)($&7+#320+#)"0#+"$+,#')$/,)$&2"?#=%+,+@2,+#$%&'
(6+),61#&'#)##'5#0+'&L"?#=%+#)")61'&'#0+$)&6'#),+#&66/'$,)$+0#&"#D&L?#W?MW:9>?
EXERCISE
D6.27 =%+#(&,(/&$#2@#D&L?#W?MW:)>#&'#$2#9+#@)9,&()$+0#/'&"L#)#$,)"'&'$2,#$1*+#.%2'+#β#&'#'*+(&@&+0#$2#9+
&"#$%+#,)"L+#2@#GP#$2#KGP?#=%)$#&'-#&"0&7&0/)6#/"&$'#2@#$%&'#')3+#$,)"'&'$2,#$1*+#()"#%)7+#β#7)6/+'
)"1.%+,+# &"# $%&'# ,)"L+?# J+0+'&L"# $%+# (&,(/&$# 91# '+6+($&"L# )# "+.# 7)6/+# @2,# >-# '2# $%)$# )66
@)9,&()$+0# (&,(/&$'# ),+# L/),)"$++0# $2# 9+# &"# $%+# )($&7+# 320+?# Y%)$# &'# $%+# ,)"L+# 2@# (266+($2,
726$)L+'#$%)$#$%+#@)9,&()$+0#(&,(/&$'#3)1#+T%&9&$_
Ans. >-,=,?<^,GΩ`,+-,=,O<\,_,&2,X<E,_
388 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.9
Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?Md#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#$%,2/L%
)66#9,)"(%+'?#=%+#3&"&3/3#7)6/+#2@#β#&'#'*+(&@&+0#$2#9+#NP?
$5 V
$5 V
4
1 k&
IE "
5 % ( VB $ 0.7)
1
2 IB " VB /10
10 k&
7 IC "
$
10 k&
1
10 k&
1 k&
VEC sat " 0.2 V
%
VB
VB $ 0.5 % (%5)
10
%5 V
(a)
VE " VB $ 0.7
3
5
VC " VB $ 0.5
6
10 k&
%5 V
(b)
Figure 6.27 ET)3*6+#W?a8#;'<#(&,(/&$H#;&<#)")61'&'#.&$%#'$+*'#"/39+,+0?
Solution
I#V/&(U#L6)"(+#)$#$%&'#(&,(/&$#,+7+)6'#$%)$#$%+#$,)"'&'$2,#.&66#9+#+&$%+,#)($&7+#2,#')$/,)$+0?#I''/3&"L#)($&7+5
320+#2*+,)$&2"#)"0#"+L6+($&"L#$%+#9)'+#(/,,+"$-#.+#'++#$%)$#$%+#9)'+#726$)L+#.&66#9+#)**,2T&3)$+61#h+,2
726$'-#$%+#+3&$$+,#726$)L+#.&66#9+#)**,2T&3)$+61#+P?d#]-#)"0#$%+#+3&$$+,#(/,,+"$#.&66#9+#)**,2T&3)$+61#e?N
3I?#C&"(+#$%+#3)T&3/3#(/,,+"$#$%)$#$%+#(266+($2,#()"#'/**2,$#.%&6+#$%+#$,)"'&'$2,#,+3)&"'#&"#$%+#)($&7+
320+#&'#)**,2T&3)$+61#P?G#3I-#&$#@2662.'#$%)$#$%+#$,)"'&'$2,#&'#0+@&"&$+61#')$/,)$+0?
I''/3&"L# $%)$# $%+# $,)"'&'$2,# &'# ')$/,)$+0# )"0# 0+"2$&"L# $%+# 726$)L+# )$# $%+# 9)'+# 91# +)# :,+@+,# $2# D&L?
W?Md9>-#&$#@2662.'#$%)$
+ * = + ) + + *) #!#+ ) + P?d
+ - = + * ] + *-')$ #!#+ ) + P?d ] P?M = + ) + P?G
+G ] +
G ] + ) ] P?d
. * = 555555555555555555*5 = 5555555555555555555555555555
= e?N ] + ) # 3I
K
K
+
. ) = 55555)5 = P?K+ ) # 3I
KP
+- Q ( ]G )
+ ) + P?G + G
5 = 5555555555555555555555555555
5 = P?K+ ) + P?GG# 3I
. - = 5555555555555555555555
KP
KP
6.3 BJT Circuits at DC
c0();,&"$,#$+*&(2)0"(7,.*, =, .),+,.- 5,4$,29&*()
e?N ] + ) = P?K+ ) + P?K+ ) + P?GG
4"(/",#$03+&0,()
N?dG
+ ) = 5555555555 #!#N?KN#]
K?M
K390&(&3&();,(),&"$,$S3*&(2)0,*92.$5,4$,29&*()
+ * = N?fN#]
+ - = N?WN#]
. * = K?Kd#3I
. - = P?fW#3I
. ) = P?NK#3I
1#2',4"(/",4$,0$$,&"*&,&"$,&#*)0(0&2#,(0,0*&3#*&$-5,0()/$,&"$,.*+3$,21,12#/$-,β,(0
P?fW
P?NK
β @2,(+0 = 5555555555 #!#M?f
.%&(%#&'#3/(%#'3)66+,#$%)"#$%+#'*+(&@&+0#3&"&3/3#β?
,,,,,,,,,,,
389
390 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.10
Y+#.)"$#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?Mf:)>#$2#0+$+,3&"+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#$%,2/L%
)66#9,)"(%+'?#I''/3+#β #=#KPP?
$15 V
$15 V
RC "
5 k&
RB 1 "
100 k&
RC "
5 k&
VBB " $5 V
RBB "
33.3 k&
IE
IB
RB 2 "
50 k&
RE "
3 k&
RE "
3 k&
L
(b)
(a)
$15 V
$15 V
1.28 mA
0.103 mA
5 k&
$8.6 V
$5 V
100 k&
0.013 mA
33.3 k&
$4.57 V
0.013 mA
$3.87 V
$4.57 V
1.29 mA
50 k&
3 k&
(c)
0.09 mA
(d)
Figure 6.28 F&,(/&$'#@2,#ET)3*6+#W?KP?
Solution
=%+#@&,'$#'$+*#&"#$%+#)")61'&'#(2"'&'$'#2@#'&3*6&@1&"L#$%+#9)'+#(&,(/&$#/'&"L#=%p7+"&"k'#$%+2,+3?#=%+#,+'/6$
&'#'%2."#&"#D&L?#W?Mf:9>-#.%+,+
> )M
GP
= KG 555555555555555555555 = +G#]
+ )) = +KG 55555555555555555555555
> )K + > )M
KPP + GP
6.3 BJT Circuits at DC
> )) = > )K #qq#> )M = KPP#qq#GP = NN?N#UΩ
=2#+7)6/)$+#$%+#9)'+#2,#$%+#+3&$$+,#(/,,+"$-#.+#%)7+#$2#.,&$+#)#622*#+V/)$&2"#),2/"0#$%+#622*#6)9+6+0#[#&"
D&L?#W?Mf:9>?#b2$+-#%2.+7+,-#$%)$#$%+#(/,,+"$#$%,2/L%# >))#&'#0&@@+,+"$#@,23#$%+#(/,,+"$#$%,2/L%#>*?#=%+
622*#+V/)$&2"#.&66#9+
+ )) = . ) > )) + + )* + . * > *
b2.-#)''/3&"L#)($&7+5320+#2*+,)$&2"-#.+#,+*6)(+#.)#.&$%#
.*
5
. ) = 55555555555
β+K
)"0#,+),,)"L+#$%+#+V/)$&2"#$2#29$)&"
+ )) ] + )*
5
. * = 55555555555555555555555555555555555555555555555
> * + [ > )) ⁄ ( β + K ) ]
D2,#$%+#"/3+,&()6#7)6/+'#L&7+"#.+#%)7+
G ] P?d
. * = 5555555555555555555555555555555555555 = K?Ma#3I
N + ( NN?N ⁄ KPK )
=%+#9)'+#(/,,+"$#.&66#9+
K?Ma
. ) = 5555555555 = P?PKMf#3I
KPK
=%+#9)'+#726$)L+#&'#L&7+"#91
+ ) = + )* + . * > *
= P?d + K?Ma × N = e?Gd#]
W$,/*),$.*+3*&$,&"$,/2++$/&2#,/3##$)&,*0,
. - = α . * = P?aa × K?Ma = K?Mf#3I
=%+#(266+($2,#726$)L+#()"#"2.#9+#+7)6/)$+0#)'#
+ - = +KG ] . - > - = KG ] K?Mf × G = f?W#]
!$#@2662.'#$%)$#$%+#(266+($2,#&'#%&L%+,#&"#*2$+"$&)6#$%)"#$%+#9)'+#91#e?PN#]-#.%&(%#3+)"'#$%)$#$%+ $,)"'&'$2,
&'#&"#$%+#)($&7+#320+-#)'#%)0#9++"#)''/3+0?#=%+#,+'/6$'#2@#$%+#)")61'&'#),+#L&7+"#&"#D&L?#W?Mf:(-#0>?
EXERCISE
6.28 !@#$%+#$,)"'&'$2,#&"#$%+#(&,(/&$#2@#D&L?#W?Mf:)>#&'#,+*6)(+0#.&$%#)"2$%+,#%)7&"L#%)6@#$%+#7)6/+#2@#β
:&?+?- β =#GP>-#@&"0#$%+#"+.#7)6/+#2@#.--#)"0#+T*,+''#$%+#(%)"L+#&"#.-#)'#)#*+,(+"$)L+?
Ans. .-,=,?<?^,'@`,−?Oj
391
392 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.11
Y+# .)"$# $2# )")61h+# $%+# (&,(/&$# &"# D&L?# W?Ma:)># $2# 0+$+,3&"+# $%+# 726$)L+'# )$# )66# "20+'# )"0# $%+# (/,,+"$'
$%,2/L%#)66#9,)"(%+'?
$15 V
RE2 " 2 k&
RC1 " 5 k&
RB 1 " 100 k&
IE2
Q2
IC1
IB2
Q1
IC2
RC2 " 2.7 k&
RB 2 " 50 k&
RE " 3 k&
(a)
$15 V
2.78 mA
1.252 mA
0.103 mA
100 k&
$9.44 V
$8.74 V
Q1
$4.57 V
2 k&
5 k&
Q2
0.0275 mA
1.28 mA
$7.43 V
0.013 mA
$3.87 V
50 k&
0.09 mA
2.7 k&
3 k&
1.29 mA
2.75 mA
(b)
Figure 6.29 F&,(/&$'#@2,#ET)3*6+#W?KK?
Solution
Y+#@&,'$#,+(2L"&h+#$%)$#*),$#2@#$%&'#(&,(/&$#&'#&0+"$&()6#$2#$%+#(&,(/&$#.+#)")61h+0#&"#ET)3*6+#W?KP g")3+61$%+# (&,(/&$# 2@# D&L?# W?Mf:)>?# =%+# 0&@@+,+"(+-# 2@# (2/,'+-# &'# $%)$# &"# $%+# "+.# (&,(/&$# .+# %)7+# )" )00&$&2")6
6.3 BJT Circuits at DC
$,)"'&'$2,#VM#$2L+$%+,#.&$%#&$'#)''2(&)$+0#,+'&'$2,'#>*M#)"0#>-M?#I''/3+#$%)$#VK#&'#'$&66#&"#$%+#)($&7+#320+?
=%+#@2662.&"L#7)6/+'#.&66#9+#&0+"$&()6#$2#$%2'+#29$)&"+0#&"#$%+#*,+7&2/'#+T)3*6+8
+)?,=,+8<^N,_
,.*?,=,?<PD,'@
.)?,=,O<O?PE,'@
.-?,=,?<PE,'@
\2.+7+,-#$%+#(266+($2,#726$)L+#.&66#9+#0&@@+,+"$#$%)"#*,+7&2/'61#()6(/6)$+0-#'&"(+#*),$#2@#$%+#(266+($2,#(/,5
,+"$#.-K#.&66#@62.#&"#$%+#9)'+#6+)0#2@#VM#:.)M>?#I'#)#@&,'$#)**,2T&3)$&2"#.+#3)1#)''/3+#$%)$#.)M#&'#3/(%
'3)66+,# $%)"# .-KH# $%)$# &'-# .+# 3)1# )''/3+# $%)$# $%+# (/,,+"$# $%,2/L%# >-K# &'# )632'$# +V/)6# $2# .-K?# =%&'# .&66
+")96+#/'#$2#()6(/6)$+#+-K8
+ -K #!#+KG ] . -K > -K
= KG ] K?Mf × G = +f?W#]
=%/'#VK#&'#&"#$%+#)($&7+#320+-#)'#%)0#9++"#)''/3+0?
I'#@),#)'#VM#&'#(2"(+,"+0-#.+#"2$+#$%)$#&$'#+3&$$+,#&'#(2""+($+0#$2#+KG#]#$%,2/L%#>*M?#!$#&'#$%+,+@2,+
')@+#$2#)''/3+#$%)$#$%+#+3&$$+,Q9)'+#4/"($&2"#2@#VM#.&66#9+#@2,.),0#9&)'+0?#=%/'#$%+#+3&$$+,#2@#VM#.&66#9+
)$#)#726$)L+#+*M#L&7+"#91#
+ *M = + -K + + *) V #!#f?W + P?d = +a?N#]
M
=%+#+3&$$+,#(/,,+"$#2@#VM#3)1#"2.#9+#()6(/6)$+0#)'#
+KG ] + *M
KG ] a?N
5 = 5555555555555555555 = M?fG#3I
. *M = 55555555555555555555555
M
> *M
K()/$, &"$, /2++$/&2#, 21, VP, (0, #$&3#)$-, &2, ;#23)-, .(*, >-P5,(&, (0, 7200(9+$, &"*&,VP, (0, 27$#*&();,(),&"$, */&(.$
'2-$<,@003'$,&"(0,&2,9$,&"$,/*0$<,W$,)24,1()-,.-P,*0,
. -M = α M . *M
= P?aa × M?fG = M?fM#3I
( )''/3&"L# β M = KPP )
=%+#(266+($2,#726$)L+#2@#VM#.&66#9+#
+ -M = . -M > -M = M?fM × M?d = d?WM#]
.%&(%#&'#62.+,#$%)"#+)M#91#P?af#]?#=%/'#VM#&'#&"#$%+#)($&7+#320+-#)'#)''/3+0?
!$# &'# &3*2,$)"$# )$# $%&'# '$)L+# $2# @&"0# $%+# 3)L"&$/0+# 2@# $%+# +,,2,# &"(/,,+0# &"# 2/,# ()6(/6)$&2"'# 91# $%+
)''/3*$&2"#$%)$#.)M#&'#"+L6&L&96+?#=%+#7)6/+#2@#.)M#&'#L&7+"#91
. *M
M?fG
= 5555555555 = P?PMf#3I
. )M = 55555555555555
βM + K
KPK
4"(/",(0,()-$$-,'3/",0'*++$#,&"*),.-?,T?<PE,'@V<,=1,-$0(#$-5,4$,/*),29&*(),'2#$,*//3#*&$,#$03+&0,9:,(&$#%
*&();,2)$,'2#$,&('$5,*003'();,.)P,&2,9$,O<OPE,'@<,!"$,)$4,.*+3$0,4(++,9$
F/,,+"$#&"#> -K = . -K ] . )M = K?Mf ] P?PMf = K?MGM#3I
+ -K = KG ] G × K?MGM = f?de#]
+ *M = f?de + P?d = a?ee#]
KG ] a?ee
. *M = 5555555555555555555555 = M?df#3I
M
393
394 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.11 continued
. -M = P?aa × M?df = M?dG#3I
+ -M = M?dG × M?d = d?eN#]
M?df
. )M = 5555555555 = P?PMdG#3I
KPK
b2$+#$%)$#$%+#"+.#7)6/+#2@#.)M#&'#7+,1#(62'+#$2#$%+#7)6/+#/'+0#&"#2/,#&$+,)$&2"-#)"0#"2#@/,$%+,#&$+,)$&2"'
),+#.),,)"$+0?#=%+#@&")6#,+'/6$'#),+#&"0&()$+0#&"#D&L?#W?Ma:9>?
=%+#,+)0+,#4/'$&@&)961#3&L%$#9+#.2"0+,&"L#)92/$#$%+#"+(+''&$1#@2,#/'&"L#)"#&$+,)$&7+#'(%+3+#&"#'2675
&"L#)#6&"+),#:2,#6&"+),&h+0>#*,296+3?#!"0++0-#.+#()"#29$)&"#$%+#+T)($#'26/$&2"#:&@#.+#()"#()66#)"1$%&"L#.+
),+#02&"L#.&$%#)#@&,'$52,0+,#320+6#+T)($j>#91#.,&$&"L#)**,2*,&)$+#+V/)$&2"'?#=%+#,+)0+,#&'#+"(2/,)L+0#$2
@&"0#$%&'#'26/$&2"#)"0#$%+"#(23*),+#$%+#,+'/6$'#.&$%#$%2'+#29$)&"+0#)927+?#!$#&'#&3*2,$)"$#$2#+3*%)'&h+%2.+7+,-#$%)$#&"#32'$#'/(%#*,296+3'#&$#&'#V/&$+#'/@@&(&+"$#$2#29$)&"#)"#)**,2T&3)$+#'26/$&2"-#*,27&0+0#.+
()"#29$)&"#&$#V/&(U61#)"0-#2@#(2/,'+-#(2,,+($61?
!"#$%+#)927+#+T)3*6+'-#.+#@,+V/+"$61#/'+0#)#*,+(&'+#7)6/+#2@# α $2#()6(/6)$+#$%+#(266+($2,
(/,,+"$?#C&"(+# α#!#K-#$%+#+,,2,#&"#'/(%#()6(/6)$&2"'#.&66#9+#7+,1#'3)66#&@#2"+#)''/3+'# α#=#K#)"0
.- = .*?#=%+,+@2,+-#+T(+*$#&"#()6(/6)$&2"'#$%)$#0+*+"0#(,&$&()661#2"#$%+#7)6/+#2@#α#:+?L?-#$%+#()6(/6)5
$&2"#2@#9)'+#(/,,+"$>-#2"+#/'/)661#)''/3+'#α ! K?
EXERCISES
6.29 D2,#$%+#(&,(/&$#&"#D&L?#W?Ma-#@&"0#$%+#$2$)6#(/,,+"$#0,)."#@,23#$%+#*2.+,#'/**61?#\+"(+#@&"0#$%+
*2.+,#0&''&*)$+0#&"#$%+#(&,(/&$?
Ans. 8<?\^,'@`,XP,'W
6.30 !"$,/(#/3(&,(),L(;<,MX<\O,(0,&2,9$,/2))$/&$-,&2,&"$,/(#/3(&,(),L(;<,X<PDT*V,*0,()-(/*&$-`,07$/(1(/*++:5
&"$,9*0$,21,V\,(0,&2,9$,/2))$/&$-,&2,&"$,/2++$/&2#,21,VP<,=1,V\,"*0,β, =,?OO5,1()-,&"$,)$4,.*+3$,21,+-P
*)-,&"$,.*+3$0,21,+*\,*)-,.-\<
6.29
Figure E6.30
Ans. +N<OX,_`,+X<\X,_`,?\<8,'@
6.3 BJT Circuits at DC
395
,
Example 6.12
Y+#0+'&,+#$2#+7)6/)$+#$%+#726$)L+'#)$#)66#"20+'#)"0#$%+#(/,,+"$'#$%,2/L%#)66#9,)"(%+'#&"#$%+#(&,(/&$#2@#D&L?
W?NP:)>?#I''/3+#β# =#KPP?
On
0 3.9 mA
5 – 0.7
=
10 + 101 × 1
0.039 mA
Off
0
–5V
(a)
(b)
Figure 6.30 ET)3*6+#W?KM8#;'<#(&,(/&$H#;&<#)")61'&'#.&$%#$%+#'$+*'#"/39+,+0?
Solution
;1#+T)3&"&"L#$%+#(&,(/&$-#.+#(2"(6/0+#$%)$#$%+#$.2#$,)"'&'$2,'#VK#)"0#VM#()""2$#9+#'&3/6$)"+2/'61#(2"0/($&"L?
=%/'#&@#VK#&'#2"-#VM#.&66#9+#2@@-#)"0#7&(+#7+,')?#I''/3+#$%)$#VM#&'#2"?#!$#@2662.'#$%)$#(/,,+"$#.&66#@62.#@,23
L,2/"0#$%,2/L%#$%+#K5UΩ#,+'&'$2,#&"$2#$%+#+3&$$+,#2@#VM?#=%/'#$%+#9)'+#2@#VM#.&66#9+#)$#)#"+L)$&7+#726$)L+-#)"0
9)'+#(/,,+"$#.&66#9+#@62.&"L#2/$#2@#$%+#9)'+#$%,2/L%#$%+#KP5UΩ#,+'&'$2,#)"0#&"$2#$%+#+G5]#'/**61?#=%&'#&'#&3*2'5
'&96+-#'&"(+#&@#$%+#9)'+#&'#"+L)$&7+-#(/,,+"$#&"#$%+#KP5UΩ#,+'&'$2,#.&66#%)7+#$2#@62.#&"$2#$%+#9)'+?#=%/'#.+#(2"5
(6/0+#$%)$#2/,#2,&L&")6#)''/3*$&2"g$%)$#VM#&'#2"g&'#&"(2,,+($?#!$#@2662.'#$%)$#VM#.&66#9+#2@@#)"0#VK#.&66#9+#2"?
=%+#V/+'$&2"#"2.#&'#.%+$%+,#VK#&'#)($&7+#2,#')$/,)$+0?#=%+#)"'.+,#&"#$%&'#()'+#&'#297&2/'8#C&"(+
$%+#9)'+#&'#@+0#.&$%#)#+G5]#'/**61#)"0#'&"(+#9)'+#(/,,+"$#@62.'#&"$2#$%+#9)'+#2@#VK-#&$#@2662.'#$%)$#$%+
9)'+# 2@# VK# .&66# 9+# )$# )# 726$)L+# 62.+,# $%)"# +G# ]?# =%/'# $%+# (266+($2,Q9)'+# 4/"($&2"# 2@# VK# &'# ,+7+,'+
9&)'+0#)"0#VK#&'#&"#$%+#)($&7+#320+?#!$#,+3)&"'#2"61#$2#0+$+,3&"+#$%+#(/,,+"$'#)"0#726$)L+'#/'&"L#$+(%5
"&V/+'#)6,+)01#0+'(,&9+0#&"#0+$)&6?#=%+#,+'/6$'#),+#L&7+"#&"#D&L?#W?NP:9>?#
##########
EXERCISES
6.31 K2+.$,&"$,7#29+$',(),MA*'7+$,X<?P,12#,&"$,/*0$,21,*,.2+&*;$,21,]^,_,1$$-();,&"$,9*0$0<,W"*&,.2+&*;$
*77$*#0,*&,&"$,$'(&&$#0f
Ans. QN?a#]
6.32 C267+#$%+#*,296+3#&"#ET)3*6+#W?KM#.&$%#$%+#726$)L+#@++0&"L#$%+#9)'+'#(%)"L+0#$2#+KP#]?#I''/3+
$%)$#β3&"#=#NP-#)"0#@&"0#+*-#+)-#.-K-#)"0#.-M?
Ans. +e?f#]H#+G?G#]H#e?NG#3IH#P
396 Chapter 6 Bipolar Junction Transistors (BJTs)
6.4 Applying the BJT in Amplifier Design
W$,)24,9$;(),23#,0&3-:,21,&"$,3&(+(>*&(2),21,&"$,BC!,(),&"$,-$0(;),21,*'7+(1($#0<?\,,!"$,9*0(0
12#,&"(0,('72#&*)&,*77+(/*&(2),(0,&"*&,4"$),27$#*&$-,(),&"$,*/&(.$,'2-$5,&"$,BC!,13)/&(2)0,*0,*
.2+&*;$%/2)&#2++$-,/3##$)&,023#/$Y,&"$,9*0$]$'(&&$#,.2+&*;$, v )* ,/2)&#2+0,&"$,/2++$/&2#,/3##$)&
$ - <, @+&"23;", &"$, /2)&#2+, #$+*&(2)0"(7, (0, )2)+()$*#, T$A72)$)&(*+V5, 4$, 4(++, 0"2#&+:, -$.(0$, *
'$&"2-,12#,29&*()();,*+'20&%+()$*#,*'7+(1(/*&(2),1#2',&"(0,13)-*'$)&*++:,)2)+()$*#,-$.(/$<
6.4.1 Obtaining a Voltage Amplifier
=),&"$,()&#2-3/&(2),&2,*'7+(1($#0,(),K$/&(2),?<^5,4$,+$*#)$-,&"*&,*,.2+&*;$%/2)&#2++$-,/3##$)&
023#/$,/*),0$#.$,*0,*,&#*)0/2)-3/&*)/$,*'7+(1($#5,&"*&,(05,*),*'7+(1($#,4"20$,()73&,0(;)*+,(0,*
.2+&*;$,*)-,4"20$,23&73&,0(;)*+,(0,*,/3##$)&<,I2#$,/2''2)+:5,"24$.$#5,2)$,(0,()&$#$0&$-,()
.2+&*;$,*'7+(1($#0<,@,0('7+$,4*:,&2,/2).$#&,*,&#*)0/2)-3/&*)/$,*'7+(1($#,&2,*,.2+&*;$,*'7+(%
1($#,(0,&2,7*00,&"$,23&73&,/3##$)&,&"#23;",*,#$0(0&2#,*)-,&*G$,&"$,.2+&*;$,*/#200,&"$,#$0(0&2#,*0,&"$
23&73&<,Z2();,&"(0,12#,*,BC!,#$03+&0,(),&"$,0('7+$,*'7+(1($#,/(#/3(&,0"24),(),L(;<,X<\?T*V<,R$#$
v )* ,(0,&"$,()73&,.2+&*;$5, > - ,TG)24),*0,*,+*'2-%!(#($'0)!V,/2).$#&0,&"$,/2++$/&2#,/3##$)&, $ - ,&2
*,.2+&*;$,T $ - > - V5,*)-, + -- ,(0,&"$,0377+:,.2+&*;$,&"*&,724$#0,37,&"$,*'7+(1($#,*)-5,&2;$&"$#
4(&", > - 5,$0&*9+(0"$0,27$#*&(2),(),&"$,*/&(.$,'2-$5,*0,4(++,9$,0"24),0"2#&+:<
VCC
Active
mode
Cut off
iC
X
RC
Saturation
Y
$
vBE $
%
vO " vCE
Edge
of Saturation
Z
! 0.3 V
%
0
0.5 V
vBE
Figure 6.31 ;'<-C&3*6+#;<=#)3*6&@&+,#.&$%#&"*/$#v)*#)"0#2/$*/$#v-*?#;&<#=%+#726$)L+#$,)"'@+,#(%),)($+,&'$&(
:]=F>#2@#$%+#)3*6&@&+,#&"#;'<?#=%+#$%,++#'+L3+"$'#2@#$%+#]=F#(2,,+'*2"0#$2#$%+#$%,++#320+'#2@#2*+,)$&2"#2@
$%+#;<=?
!"#$%+#)3*6&@&+,#(&,(/&$#2@#D&L?#W?NK:)>-#$%+#2/$*/$#726$)L+#&'#$)U+"#9+$.++"#$%+#(266+($2,
)"0#L,2/"0-#,)$%+,#$%)"#'&3*61#)(,2''# > - ?#=%&'#&'#02"+#9+()/'+#2@#$%+#"++0#$2#3)&"$)&"#)
L,2/"0#,+@+,+"(+#$%,2/L%2/$#$%+#(&,(/&$?#=%+#2/$*/$#726$)L+# v -* #&'#L&7+"#91
v -* d + -- ] $ - > -
TX<P8V
=%/'#&$#&'#)"#&"7+,$+0#7+,'&2"#:"2$+#$%+#3&"/'#'&L">#2@# $ - > - #$%)$#&'#'%&@$+0#91#$%+#(2"'$)"$
7)6/+#2@#$%+#'/**61#726$)L+#+ -- ?
KN
I"#&"$,20/($&2"#$2#)3*6&@&+,'#@,23#)"#+T$+,")6#$+,3&")6'#*+,'*+($&7+#&'#*,+'+"$+0#&"#C+($&2"'#K?e#)"0
K?G?#!$#.2/60#9+#%+6*@/6#@2,#,+)0+,'#/"@)3&6&),#.&$%#9)'&(#)3*6&@&+,#(2"(+*$'#$2#,+7&+.#$%&'#3)$+,&)6#9+5
@2,+#*,2(++0&"L#.&$%#$%+#'$/01#2@#;<=#)3*6&@&+,'?
6.4 Applying the BJT in Amplifier Design
6.4.2 The Voltage Transfer Characteristic (VTC)
I#7+,1#/'+@/6#$226#$%)$#1&+60'#L,+)$#&"'&L%$#&"$2#$%+#2*+,)$&2"#2@#)"#)3*6&@&+,#(&,(/&$#&'#&$'
726$)L+#$,)"'@+,#(%),)($+,&'$&(#:]=F>?#=%&'#&'#'&3*61#)#*62$#:2,#)#(6+),61#6)9+6+0#'U+$(%>#2@
$%+#2/$*/$#726$)L+#7+,'/'#$%+#&"*/$#726$)L+?#D2,#$%+#;<=#)3*6&@&+,#&"#D&L?#W?NK:)>-#$%&'#&'#$%+
*62$#2@# v-* #7+,'/'# v)* #'%2."#&"#D&L?#W?NK:9>?
B9'+,7+#$%)$#@2,# v)* #62.+,#$%)"#)92/$#P?G#]-#$%+#$,)"'&'$2,#&'#(/$#2@@-# $ - d P-#)"0-#@,23
EV?#:W?Me>-# v-* d + -- ? #I'# v)* #,&'+'-#$%+#$,)"'&'$2,#$/,"'#2"#)"0# v-* #0+(,+)'+'?#\2.+7+,'&"(+#&"&$&)661# v-* #.&66#'$&66#9+#%&L%-#$%+#;<=#.&66#9+#2*+,)$&"L#&"#$%+#)($&7+#320+?#=%&'#(2"5
$&"/+'#)'# v)* #&'#&"(,+)'+0#/"$&6#&$#,+)(%+'#)#7)6/+#$%)$#,+'/6$'#&"# v-* #9+(23&"L#62.+,#$%)"
v)* #91#P?e#726$#2,#'2#:*2&"$#r#2"#$%+#]=F#&"#D&L?#W?NK9>?#D2,# v)* #L,+)$+,#$%)"#$%)$#)$#*2&"$#r$%+#$,)"'&'$2,#2*+,)$+'#&"#$%+#')$/,)$&2"#,+L&2"#)"0# v-* #0+(,+)'+'#7+,1#'62.61?#
=%+#]=F#&"#D&L?#W?NK:9>#&"0&()$+'#$%)$#$%+#'+L3+"$#2@#L,+)$+'$#'62*+#:)"0#%+"(+#*2$+"5
$&)661#$%+#6),L+'$#)3*6&@&+,#L)&">#&'#$%)$#6)9+6+0#sr-#.%&(%#(2,,+'*2"0'#$2#2*+,)$&2"#&"#$%+
)($&7+#320+?#I"#+T*,+''&2"#@2,#$%+#'+L3+"$#sr#()"#9+#29$)&"+0#91#'/9'$&$/$&"L#@2,# $ - #&"#EV?
:W?Me>#91#&$'#)($&7+5320+#7)6/+
$- d .6 4
v)* ⁄ +,
TX<P^V
.%+,+#.+#%)7+#@2,#'&3*6&(&$1#"+L6+($+0#9)'+5.&0$%#320/6)$&2"#:$%+#E),61#+@@+($>?#=%+#,+'/6$#&'
v -* d + -- ] > - . 6 4
v )* ⁄ + ,
TX<PXV
=%&'#&'#297&2/'61#)#"2"6&"+),#,+6)$&2"'%&*?#b+7+,$%+6+''-#6&"+),#:2,#)632'$56&"+),>#)3*6&@&()5
$&2"#()"#9+#29$)&"+0#91#/'&"L#$%+#$+(%"&V/+#2@#9&)'&"L#$%+#;<=?#
6.4.3 Biasing the BJT to Obtain Linear Amplification
;&)'&"L# +")96+'# /'# $2# 29$)&"# )632'$56&"+),# )3*6&@&()$&2"# @,23# $%+# ;<=?# =%+# $+(%"&V/+# &'
&66/'$,)$+0#&"#D&L?#W?NM:)>?#I#0(#726$)L+# +)* #&'#'+6+($+0#$2#29$)&"#2*+,)$&2"#)$#)#*2&"$#l#2"
$%+#'+L3+"$#sr#2@#$%+#]=F?#\2.#$2#'+6+($#)"#)**,2*,&)$+#62()$&2"#@2,#$%+#9&)'#*2&"$#l#.&66
9+# 0&'(/''+0# '%2,$61?# D2,# $%+# $&3+# 9+&"L-# 29'+,7+# $%)$# $%+# (22,0&")$+'# 2@# l# ),+# $%+# 0(
VCC
IC
vCE
X
VCC
RC
Y
$
Q
VCE
VBE
VCE
Z
%
0
VBE
vBE
Figure 6.32 ;&)'&"L#$%+#;<=#)3*6&@&+,#)$#)#*2&"$#l#62()$+0#2"#$%+#)($&7+5320+#'+L3+"$#2@#$%+#]=F?
397
398 Chapter 6 Bipolar Junction Transistors (BJTs)
726$)L+'#+)* #)"0#+-* -#.%&(%#),+#,+6)$+0#91
+ -* d + -- ] > - . 6 4
+ )* ⁄ + ,
TX<PNV
g2()&,k,(0,G)24),*0,&"$,&#'(-4*#0$,2#,&"$,2)-*4!%'$#06-4*#0$<,@+025,0()/$,*&,k,)2,0(;)*+
/2'72)$)&,(0, 7#$0$)&5,(&, (0,*+02,G)24),*0, &"$, >/#!()!0$- 4*#0$, T4"(/", (0,&"$, 2#(;(),21, &"$
0:'92+,kV<,Q2&$,&"*&,*,&#*)0(0&2#,27$#*&();,*&,k,4(++,"*.$,*,/2++$/&2#,/3##$)&, . - ,;(.$),9:,
.- d .6 4
+ )* ⁄ + ,
TX<PEV
b+T$-#$%+#'&L")6#$2#9+#)3*6&@&+0# v#4 ? #)#@/"($&2"#2@#$&3+# ?- #&'#'/*+,&3*2'+0#2"#$%+#9&)'
726$)L+#+)* - #)'#'%2."#&"#D&L?#W?NN:)>?#=%/'#$%+#$2$)6#&"'$)"$)"+2/'#7)6/+#2@# v)* #9+(23+'
v )* ( ? ) d + )* e v #4 ( ? ) ,,
!"$,#$03+&();, v -* ( ? ) ,/*),9$,29&*()$-,9:,0390&(&3&();,&"(0,$A7#$00(2),12#, v )* ( ? ) ,()&2,MS<,TX<P^V<
l#*7"(/*++:5,4$,/*),30$,&"$,_!6,&2,29&*(), v -* ( ? )- ,72()&,9:,72()&5,*0,(++30&#*&$-,(),L(;<,X<\\T9V<
vCE
Cutoff
VCC
X
Active
mode
Saturation
Y
Slope " Av
vce
Time
VCE
Q
VCC
Z
iC
0
RC
0.5
vBE
VBE
$
vbe $
%
VBE
vbe
vCE
$
%
vBE
%
Time
(a)
(b)
,Figure 6.33 BC!,*'7+(1($#,9(*0$-,*&,*,72()&,k5,4(&",*,0'*++,.2+&*;$,0(;)*+,v#4,037$#('720$-,2),&"$,-/,9(*0,.2+&*;$,+)*<
!"$,#$03+&();,23&73&,0(;)*+,vE4,*77$*#0,037$#('720$-,2),&"$,-/,/2++$/&2#,.2+&*;$,+-*<,!"$,*'7+(&3-$,21,vE4,(0,+*#;$#,&"*)
&"*&,21,v#4,9:,&"$,.2+&*;$,;*(),/v<
6.4 Applying the BJT in Amplifier Design
R$#$,4$,0"24,&"$,/*0$,4"$), v #4 ,(0,*,0()$,4*.$,21,a0'*++b,*'7+(&3-$<,K7$/(1(/*++:5,&"$,*'7+(&3-$
21, v #4 ,(0,0'*++,$)23;",&2,#$0&#(/&,&"$,$A/3#0(2),21,&"$,()0&*)&*)$230,27$#*&();,72()&,&2,*,0"2#&
*+'20&%+()$*#,0$;'$)&,21,&"$,_!6,*#23)-,&"$,9(*0,72()&,k<,!"$,0"2#&$#,&"$,0$;'$)&5,&"$,;#$*&$#
&"$,+()$*#(&:,*/"($.$-5,*)-,&"$,/+20$#,&2,*),(-$*+,0()$,4*.$,&"$,0(;)*+,/2'72)$)&,*&,&"$,23&73&5
v E4 - ,4(++,9$<,!"(0,(0,&"$,$00$)/$,21,29&*()();,+()$*#,*'7+(1(/*&(2),1#2',&"$,)2)+()$*#,BC!<
6.4.4 The Small-Signal Voltage Gain
=1,&"$,()73&,0(;)*+, v #4 ,(0,G$7&,0'*++5,&"$,/2##$072)-();,0(;)*+,*&,&"$,23&73&, v E4 ,4(++,9$,)$*#+:
7#272#&(2)*+,&2, v #4 ,4(&",&"$,/2)0&*)&,21,7#272#&(2)*+(&:,9$();,&"$,0+27$,21,&"$,*+'20&%+()$*#
0$;'$)&,21,&"$,_!6,*#23)-,k<,!"(0,(0,&"$,.2+&*;$,;*(),21,&"$,*'7+(1($#5,*)-,(&0,.*+3$,/*),9$
-$&$#'()$-,9:,$.*+3*&();,&"$,0+27$,21,&"$,&*);$)&,&2,&"$,_!6,*&,&"$,9(*0,72()&,k5,
5 v -*
5
/ v ≡ 5555555555
5 v )*
TX<PDV
v )* d + )*
^$&6&h&"L#EV?#:W?MW>#$2L+$%+,#.&$%#EV?#:W?Mf>-#.+#29$)&"
.- 5 >
/ v d ] 55555
+, -
TX<\OV
Y+#3)U+#$%+#@2662.&"L#29'+,7)$&2"'#2"#$%&'#+T*,+''&2"#@2,#$%+#726$)L+#L)&"8
1. !"$,;*(),(0,)$;*&(.$5,4"(/",0(;)(1($0,&"*&,&"$,*'7+(1($#,(0,().$#&();`,&"*&,(05,&"$#$,(0,*
?EO °, 7"*0$, 0"(1&, 9$&4$$), &"$, ()73&, *)-, &"$, 23&73&<, !"(0, ().$#0(2), (0, 29.(230, (), L(;<
X<\\T9V,*)-,0"23+-,"*.$,9$$),*)&(/(7*&$-,1#2',MS<,TX<PXV<,
2. =%+#L)&"#&'#*,2*2,$&2")6#$2#$%+#(266+($2,#9&)'#(/,,+"$# . - #)"0#$2#$%+#62)0#,+'&'$)"(+
>- ? #
I00&$&2")6#&"'&L%$#&"$2#$%+#726$)L+#L)&"#/v8()"#9+#29$)&"+0#91#+T*,+''&"L#EV?#:W?NP>#)'
.- >+ >5 = ] 55555555
/ v = ] 5555555555
+,
+,
TX<\?V
4"$#$,+>-,(0,&"$,-/,.2+&*;$,-#27,*/#200,>- 5
+ >- = + -- − + -*
TX<\PV
!"$,0('7+$,$A7#$00(2),(),MS<,TX<\?V,()-(/*&$0,&"*&,&"$,.2+&*;$,;*(),21,&"$,*'7+(1($#,(0,&"$
#*&(2,21,&"$,-/,.2+&*;$,-#27,*/#200,>-,&2,&"$,&"$#'*+,.2+&*;$,+,,T!,P^,'_,*&,#22',&$'7$#*&3#$V<
=&,12++240,&"*&,&2,'*A('(>$,&"$,.2+&*;$,;*(),4$,0"23+-,30$,*0,+*#;$,*,.2+&*;$,-#27,*/#200,>*0,7200(9+$<,L2#,*,;(.$),.*+3$,21,+--5,MS<,TX<\PV,()-(/*&$0,&"*&,&2,()/#$*0$,+>-,4$,"*.$,&2
27$#*&$,*&,*,+24$#,+-*<,R24$.$#5,#$1$#$)/$,&2,L(;< X<\\T9V,0"240,&"*&,*,+24$#,+-*,'$*)0,*
9(*0,72()&,k,/+20$,&2,&"$,$)-,21,&"$,*/&(.$%#$;(2),0$;'$)&5,4"(/",'(;"&,)2&,+$*.$,0311(/($)&
#22', 12#, &"$, )$;*&(.$%23&73&, 0(;)*+, 04();, 4(&"23&, &"$, *'7+(1($#, $)&$#();, &"$, 0*&3#*&(2)
#$;(2)<,=1,&"(0,"*77$)05,&"$,)$;*&(.$,7$*G0,21,&"$,4*.$12#',21,vE4,4(++,9$,1+*&&$)$-<,=)-$$-5,(&
(0,&"$,)$$-,&2,*++24,0311(/($)&,#22',12#,23&73&,0(;)*+,04();,&"*&,-$&$#'()$0,&"$,'20&,$11$/%
&(.$,7+*/$'$)&,21,&"$,9(*0,72()&,k,2),&"$,*/&(.$%#$;(2),0$;'$)&5,mn5,21,&"$,&#*)01$#,/3#.$<
g+*/();,k,&22,"(;",2),&"(0,0$;'$)&,)2&,2)+:,#$03+&0,(),#$-3/$-,;*(),T9$/*30$,+>-,(0,+24$#V
93&,/23+-,7200(9+:,+('(&,&"$,*.*(+*9+$,#*);$,21,720(&(.$,0(;)*+,04();<,@&,&"$,720(&(.$,$)-5,&"$
+('(&*&(2),(0,('720$-,9:,&"$,BC!,/3&&();,2115,(),4"(/",$.$)&,&"$,720(&(.$%23&73&,7$*G0,423+9$, /+(77$-, 211, *&, *, +$.$+, $S3*+, &2, +--<, L()*++:5, (&, (0, 30$13+, &2, )2&$, &"*&, &"$, &"$2#$&(/*+
399
400 Chapter 6 Bipolar Junction Transistors (BJTs)
'*A('3',;*(),/v,(0,29&*()$-,9:,9(*0();,&"$,BC!,*&,&"$,$-;$,21,0*&3#*&(2)5,4"(/",21,/23#0$
423+-,)2&,+$*.$,*):,#22',12#,)$;*&(.$,0(;)*+,04();<,!"$,#$03+&();,;*(),(0,;(.$),9:
+ -- #− + -*')$
5
/ v = ] 5555555555555555555555555555
+,
TX<\\V
+ -5
/ v3)T ! 55555555
+,
TX<\8V
!"305
@+&"23;",&"$,;*(),/*),9$,()/#$*0$-,9:,30();,*,+*#;$#,0377+:,.2+&*;$5,2&"$#,/2)0(-$#*&(2)0
/2'$,()&2,7+*:,4"$),2)$,(0,-$&$#'()();,*),*77#27#(*&$,.*+3$,12#,+--<,=),1*/&5,&"$,&#$)-,"*0
9$$), &24*#-, 30();, +24$#, *)-, +24$#, 0377+:, .2+&*;$05, /3##$)&+:, *77#2*/"();, ?, _, 2#, 02<, @&
03/",+24,0377+:,.2+&*;$05,+*#;$,;*(),.*+3$0,/*),9$,29&*()$-,9:,#$7+*/();,&"$,#$0(0&*)/$,>4(&",*,/2)0&*)&%/3##$)&,023#/$5,*0,4(++,9$,0$$),(),6"*7&$#,N<
Example 6.13
F2"'&0+,#)"#)3*6&@&+,#(&,(/&$#/'&"L#)#;<=#%)7&"L#.6 = KP−KG#I-#)#(266+($2,#,+'&'$)"(+#>-#=#W?f#UΩ-#)"0#)
*2.+,#'/**61#+--# =#KP#]?
:)> X+$+,3&"+#$%+#7)6/+#2@#$%+#9&)'#726$)L+#+)*#,+V/&,+0#$2#2*+,)$+#$%+#$,)"'&'$2,#)$#+-*#=#N?M#]?#Y%)$#&'
$%+#(2,,+'*2"0&"L#7)6/+#2@#.-_
:9> D&"0#$%+#726$)L+#L)&"#/v#)$#$%&'#9&)'#*2&"$?#!@#)"#&"*/$#'&"+5.)7+#'&L")6#2@#G53]#*+)U#)3*6&$/0+#&'
'/*+,&3*2'+0#2"#+)*-#@&"0#$%+#)3*6&$/0+#2@#$%+#2/$*/$#'&"+5.)7+#'&L")6#:)''/3+#6&"+),#2*+,)$&2">?
:(> D&"0# $%+# *2'&$&7+# &"(,+3+"$# &"# v)*# :)927+# +)*># $%)$# 0,&7+'# $%+# $,)"'&'$2,# $2# $%+# +0L+# 2@# ')$/,)$&2".%+,+#v-*#=#P?N#]?
:0> D&"0# $%+# "+L)$&7+# &"(,+3+"$# &"# v)*# $%)$# 0,&7+'# $%+# $,)"'&'$2,# $2# .&$%&"# Ko# 2@# (/$2@@# :&?+?-# $2
v-* = P?aa+-->?
Solution
+ -- ] + -*
5
T*V,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, . - = 555555555555555555555555
>KP ] N?M
# = 5555555555555555555 = K#3I
W?f
=%+#7)6/+#2@#+)*#()"#9+#0+$+,3&"+0#@,23
K × KP
]N
= KP
] KG + )* ⁄ + ,
4
.%&(%#,+'/6$'#&"
+ )* = WaP?f#3]
6.4 Applying the BJT in Amplifier Design
,,
:9>
+ -- ] + -*
5
/ v = ] 555555555555555555555555
+,
KP ] N?M
# = ] 5555555555555555555 = ] MdM#]Z]
P?PMG
+t E4 = MdM × P?PPG = K?NW#]
:(> D2,#v-*#=#P?N#]KP ] P?N
$ - = 5555555555555555555 = K?WKd#3I
W?f
=2#&"(,+)'+#$-#@,23#K#3I#$2#K?WKd#3I-#v)*#3/'$#9+#&"(,+)'+0#91
K?WKd
∆ v )* = + , 6" 5555555555555
K
d,?P,'_
:0> D2,#v-*8 =8 P?aa+--#=#a?a#]KP ] a?a
$ - = 5555555555555555555 = P?PKed#3I
W?f
=2#0+(,+)'+#$-#@,23#K#3I#$2#P?PKed#3I-#v)*#3/'$#(%)"L+#91
P?PKed
∆ v )* = + , 6" 5555555555555555
K
# = ] KPG?G#3]
EXERCISE
6.33# D2,#$%+#'&$/)$&2"#0+'(,&9+0#&"#ET)3*6+#W?KN-#.%&6+#U++*&"L#.-#/"(%)"L+0#)$#K#3I-#@&"0#$%+#7)6/+#2@
>-#$%)$#.&66#,+'/6$#&"#)#726$)L+#L)&"#2@# ] NMP#]Z]? #Y%)$#&'#$%+#6),L+'$#"+L)$&7+#'&L")6#'.&"L#)662.+0
)$#$%+#2/$*/$#:)''/3+#$%)$#v-*#&'#"2$#$2#0+(,+)'+#9+62.#P?N#]>_#Y%)$#:)**,2T&3)$+61>#&'#$%+#(2,,+5
'*2"0&"L#&"*/$#'&L")6#)3*6&$/0+_#:I''/3+#6&"+),#2*+,)$&2"?>
Ans. E,GΩ`,?<N,_`,^<\,'_
6.4.5 Determining the VTC by Graphical Analysis
D&L/,+#W?Ne#'%2.'#)#L,)*%&()6#3+$%20#@2,#0+$+,3&"&"L#$%+#]=F#2@#$%+#)3*6&@&+,#2@#D&L/,+
W?NN:)>?#I6$%2/L%#L,)*%&()6#)")61'&'#2@#$,)"'&'$2,#(&,(/&$'#&'#,),+61#+3*621+0#&"#*,)($&(+-#&$#&'
/'+@/6# @2,# /'# )$# $%&'# '$)L+# &"# L)&"&"L# L,+)$+,# &"'&L%$# &"$2# (&,(/&$# 2*+,)$&2"-# +'*+(&)661# &"
)"'.+,&"L#$%+#V/+'$&2"#2@#.%+,+#$2#62()$+#$%+#9&)'#*2&"$#l?
401
402 Chapter 6 Bipolar Junction Transistors (BJTs)
Load line
iC
1
Slope " %
RC
vBE " . . .
Z
vBE " . . .
IC
Q
vBE
vBE " . . .
Y
0
VCE
VCC
vCE
Figure 6.34 n,)*%&()6#(2"'$,/($&2"#@2,#0+$+,3&"&"L#$%+#]=F#2@#$%+#)3*6&@&+,#(&,(/&$#2@#D&L?#W?NN:)>?
!"$,;#*7"(/*+,*)*+:0(0,(0,9*0$-,2),&"$,290$#.*&(2),&"*&,12#,$*/",.*+3$,21, v )*5,&"$,/(#/3(&,4(++
9$,27$#*&();,*&,&"$,72()&,21,()&$#0$/&(2),21,&"$,/2##$072)-();, $ - ] v-* ,;#*7",*)-,&"$,0&#*(;"&,+()$
#$7#$0$)&();,MS<,TX<P8V5,4"(/",/*),9$,#$4#(&&$),(),&"$,12#'
+ -- K
5 ] 555555 v
$ - d 55555555
> - > - -*
TX<\^V
=%+#'$,)&L%$#6&"+#,+*,+'+"$&"L#$%&'#,+6)$&2"'%&*#&'#'/*+,&3*2'+0#2"#$%+# $ - ] v-* #(%),)($+,&'5
$&('#&"#D&L?#W?Ne?#!$#&"$+,'+($'#$%+#%2,&h2"$)6#)T&'#)$# v-* d +-- #)"0#%)'#)#'62*+#2@# ] K ⁄ > - ?
C&"(+#$%&'#'$,)&L%$#6&"+#,+*,+'+"$'#&"#+@@+($#$%+#62)0#,+'&'$)"(+# > - -#&$#&'#()66+0#$%+#+*'2-+#0!?
=%+# ]=F# &'# $%+"# 0+$+,3&"+0# *2&"$# 91# *2&"$?# b2$+# $%)$# .+# %)7+# 6)9+6+0# $%,++# &3*2,$)"$
*2&"$'8#*2&"$#s#)$#.%&(%# v)* d P?G #]-#*2&"$#l#)$#.%&(%#$%+#;<=#()"#9+#9&)'+0#@2,#)3*6&@&+,
2*+,)$&2"#: v)* d + )* #)"0# v-* d +-* >-#)"0#*2&"$#r#)$#.%&(%#$%+#;<=#6+)7+'#$%+#)($&7+#320+
)"0#+"$+,'#$%+#')$/,)$&2"#,+L&2"?#!@#$%+#;<=#&'#$2#9+#/'+0#)'#)#'.&$(%-#$%+"#2*+,)$&"L#*2&"$'#s
)"0#r#),+#)**6&()96+8#I$#s#$%+#$,)"'&'$2,#&'#2@@#:2*+"#'.&$(%>-#)"0#)$#r#$%+#$,)"'&'$2,#2*+,)$+'
)'#)#62.#7)6/+0#,+'&'$)"(+# > -*')$ #)"0#%)'#)#'3)66#726$)L+#0,2*#:(62'+0#'.&$(%>?#!$#'%2/60#9+
"2$+0-#%2.+7+,-#$%)$#9+()/'+#2@#$%+#62"L#0+6)1#$&3+#"++0+0#$2#$/,"#2@@#)#')$/,)$+0#;<=-#3205
+,"#0&L&$)6#&"$+L,)$+0#(&,(/&$'#"2#62"L+,#/$&6&h+#$%+#')$/,)$+0#320+#2@#2*+,)$&2"?#b2"')$/,)$+0
;<=#0&L&$)6#(&,(/&$'#.&66#9+#'$/0&+0#&"#F%)*$+,#Ke?
6.4.6 Locating the Bias Point Q
!"$,9(*0,72()&,k,(0,-$&$#'()$-,9:,&"$,.*+3$,21, +)* ,*)-,&"*&,21,&"$,+2*-,#$0(0&*)/$, > - ? ,!42
('72#&*)&,/2)0(-$#*&(2)0,(),-$/(-();,2),&"$,+2/*&(2),21,k,*#$,&"$,;*(),*)-,&"$,*++24*9+$,0(;)*+
04();,*&,&"$,23&73&<,!2,(++30&#*&$5,/2)0(-$#,&"$,_!6,0"24),(),L(;<,X<\\T9V<,R$#$,&"$,.*+3$,21, > (0,1(A$-5,*)-,&"$,2)+:,.*#(*9+$,#$'*()();,(0,&"$,.*+3$,21,+)* ? ,K()/$,&"$,0+27$,()/#$*0$0,*0,4$,'2.$
/+20$#,&2,72()&,n5,4$,29&*(),"(;"$#,;*(),9:,+2/*&();,k,*0,/+20$,&2,n,*0,7200(9+$<,R24$.$#5,&"$
/+20$#, k, (0, &2, &"$, 923)-*#:, 72()&, n5, &"$, 0'*++$#, &"$, *++24*9+$, '*;)(&3-$, 21, )$;*&(.$, 0(;)*+
04();<,!"305,*0,303*+,(),$);()$$#();,-$0(;)5,4$,$)/23)&$#,*,0(&3*&(2),#$S3(#();,*,&#*-$%211<
!"#0+(&0&"L#2"#)#7)6/+#@2,# > - #&$#&'#/'+@/6#$2#,+@+,#$2#$%+# $ - ] v-* #*6)"+?#D&L/,+#W?NG#'%2.'
$.2#62)0#6&"+'#,+'/6$&"L#&"#$.2#+T$,+3+#9&)'#*2&"$'8#O2&"$# l / -#&'#$22#(62'+#$2#+-- -#,+'/6$&"L#&"
)# '+7+,+# (2"'$,)&"$# 2"# $%+# *2'&$&7+# '&L")6# '.&"L# 2@# vE4 ? # ET(++0&"L# $%+# )662.)96+# *2'&$&7+
6.5 Small-Signal Operation and Models
iC
Load-line A
vBE " . . .
QA
vBE " VBE
QB
vBE " . . .
VCE
VCE
QB
VCC
QA
vCE
Load-line B
Figure 6.35 M11$/&,21,9(*0%72()&,+2/*&(2),2),*++24*9+$,0(;)*+,04();Y,F2*-,+()$,@,#$03+&0,(),9(*0,72()&,k/
4(&", *, /2##$072)-();, +-*, &"*&, (0, &22, /+20$, &2, +--, *)-, &"30, +('(&0, &"$, 720(&(.$, 04();, 21, v-*<, @&, &"$, 2&"$#
$A&#$'$5,+2*-,+()$,B,#$03+&0,(),*),27$#*&();,72()&5,k)5,&22,/+20$,&2,&"$,0*&3#*&(2),#$;(2)5,&"30,+('(&();,&"$,)$;%
*&(.$,04();,21,v-*<
3)T&3/3#,+'/6$'#&"#$%+#*2'&$&7+#*+)U'#2@#$%+#'&L")6#9+&"L#(6&**+0#2@@-#'&"(+#$%+#;<=#.&66
$/,"#2@@#@2,#$%+#*),$#2@#+)(%#(1(6+#"+),#$%+#*2'&$&7+#*+)U?#Y+#'*+)U#2@#$%&'#'&$/)$&2"#)'#$%+
(&,(/&$#"2$#%)7&"L#'/@@&(&+"$#R%+)0,223?S#C&3&6),61-#*2&"$# l ) #&'#$22#(62'+#$2#$%+#92/"0),1#2@
$%+# ')$/,)$&2"# ,+L&2"-# $%/'# '+7+,+61# 6&3&$&"L# $%+# )662.)96+# "+L)$&7+# '&L")6# '.&"L# 2@# v E4 ?
ET(++0&"L#$%&'#6&3&$#.2/60#,+'/6$#&"#$%+#$,)"'&'$2,#+"$+,&"L#$%+#')$/,)$&2"#,+L&2"#@2,#*),$#2@
+)(%#(1(6+#"+),#$%+#"+L)$&7+#*+)U'-#,+'/6$&"L#&"#)#0&'$2,$+0#2/$*/$#'&L")6?#Y+#'*+)U#2@#$%&'
'&$/)$&2"#)'#$%+#(&,(/&$#"2$#%)7&"L#'/@@&(&+"$#R6+L,223?S#Y+#.&66#%)7+#32,+#$2#')1#2"#9&)'
0+'&L"#&"#C+($&2"#W?d?
6.5 Small-Signal Operation and Models
R*.();,+$*#)$-,&"$,9*0(0,12#,&"$,27$#*&(2),21,&"$,BC!,*0,*),*'7+(1($#5,4$,)24,&*G$,*,/+20$#
+22G,*&,&"$,0'*++%0(;)*+,27$#*&(2),21,&"$,&#*)0(0&2#<,!24*#-,&"*&,$)-5,/2)0(-$#,2)/$,'2#$,&"$
E%!E4"?U'&,*'7+(1($#,/(#/3(&,0"24),(),L(;<,X<\XT*V<,R$#$,&"$,9*0$]$'(&&$#,H3)/&(2),(0,12#4*#9(*0$-,9:,*,-/,.2+&*;$,+)*,T9*&&$#:V<,!"$,#$.$#0$,9(*0,21,&"$,/2++$/&2#]9*0$,H3)/&(2),(0,$0&*9%
+(0"$-,9:,/2))$/&();,&"$,/2++$/&2#,&2,*)2&"$#,724$#,0377+:,21,.2+&*;$,+--,&"#23;",*,#$0(0&2#
>-<,!"$,()73&,0(;)*+,&2,9$,*'7+(1($-,(0,#$7#$0$)&$-,9:,&"$,.2+&*;$,023#/$,v#4,&"*&,(0,037$#('%
720$-,2),+)*<
Y+# (2"'&0+,# @&,'$# $%+# 0(# 9&)'# (2"0&$&2"'# 91# '+$$&"L# $%+# '&L")6# v#4# $2# h+,2?# =%+# (&,(/&$
,+0/(+'#$2#$%)$#&"#D&L?#W?NW:9>-#)"0#.+#()"#.,&$+#$%+#@2662.&"L#,+6)$&2"'%&*'#@2,#$%+#0(#(/,5
,+"$'#)"0#726$)L+'8
+
. - = . 6 4 )*
.* = .- ⁄ α
⁄ +,
TX<\XV
TX<\NV
403
404 Chapter 6 Bipolar Junction Transistors (BJTs)
iC
IC
RC
RC
iB
$
vbe
$
$
% vBE
VBE
%
vCE
%
IB
VCC
$
VCE
VCC
%
VBE
iE
IE
(b)
(a)
Figure 6.36 ;'<#F2"(+*$/)6#(&,(/&$#$2#&66/'$,)$+#$%+#2*+,)$&2"#2@#$%+#$,)"'&'$2,#)'#)"#)3*6&@&+,?#;&<#=%+#(&,5
(/&$#2@#;'<#.&$%#$%+#'&L")6#'2/,(+#v#4#+6&3&")$+0#@2,#0(#:9&)'>#)")61'&'?
.) = .- ⁄ β
TX<\EV
+ -* = + -- ] . - > -
TX<\DV
B97&2/'61-#@2,#)($&7+5320+#2*+,)$&2"-#+-#'%2/60#9+#L,+)$+,#$%)"#:+)#−#P?e>#91#)"#)32/"$
$%)$#)662.'#@2,#$%+#,+V/&,+0#'&L")6#'.&"L#)$#$%+#(266+($2,?
6.5.1 The Collector Current and the Transconductance
=1,*,0(;)*+, v#4,(0,*77+($-,*0,0"24),(),L(;<,X<\XT*V5,&"$,&2&*+,()0&*)&*)$230,9*0$]$'(&&$#,.2+&%
*;$,v)*,9$/2'$0
v )* = + )* + v #4
62##$072)-();+:5,&"$,/2++$/&2#,/3##$)&,9$/2'$0
v
$ - = . 6 4 )*
+
= . 6 4 )*
⁄ +,
(+
= . 6 4 )*
+ v #4 ) ⁄ + ,
⁄ + , v #4 ⁄ + ,
4
c0$,21,MS<,TX<\XV,:($+-0
$- = .- 4
v#4 ⁄ + ,
TX<8OV
Q245,(1,v#4 *,+, 5,4$,'*:,*77#2A('*&$,MS<,TX<8OV,*0
v
#4 5
$ - #! . - K + 55555
+,
TX<8?V
R$#$,4$,"*.$,$A7*)-$-,&"$,$A72)$)&(*+,(),MS<,TX<8OV,(),*,0$#($0,*)-,#$&*()$-,2)+:,&"$,1(#0&
&42,&$#'0<,!"(0,*77#2A('*&(2)5,4"(/",(0,.*+(-,2)+:,12#,v#4,+$00,&"*),*77#2A('*&$+:,?O,'_5,(0
#$1$##$-,&2,*0,&"$,("'++5(#60'+-'44%*?#"'$#*0<,c)-$#,&"(0,*77#2A('*&(2)5,&"$,&2&*+,/2++$/&2#
/3##$)&,(0,;(.$),9:,MS<,TX<8?V,*)-,/*),9$,#$4#(&&$)
.v
$ - = . - + 55555
+ , #4
TX<8PV
6.5 Small-Signal Operation and Models
!"30,&"$,/2++$/&2#,/3##$)&,(0,/2'720$-,21,&"$,-/,9(*0,.*+3$,.-,*)-,*,0(;)*+,/2'72)$)&,$E 5
.$ E = 55555
v
+ , #4
TX<8\V
!"(0, $S3*&(2), #$+*&$0,&"$,0(;)*+, /3##$)&, (), &"$,/2++$/&2#,&2, &"$, /2##$072)-();,9*0$]$'(&&$#
0(;)*+,.2+&*;$<,=&,/*),9$,#$4#(&&$),*0
$ E = C I v #4
TX<88V
4"$#$,CI,(0,/*++$-,&"$,$%'0()*02/)$'0)!5,*)-,1#2',MS<,TX<8\V5,(&,(0,;(.$),9:
.C I = 55555
+,
TX<8^V
W$,290$#.$,&"*&,&"$,&#*)0/2)-3/&*)/$,21,&"$,BC!,(0,-(#$/&+:,7#272#&(2)*+,&2,&"$,/2++$/&2#,9(*0
/3##$)&,.-<,!"30,&2,29&*(),*,/2)0&*)&,7#$-(/&*9+$,.*+3$,12#,CI5,4$,)$$-,*,/2)0&*)&,7#$-(/&*9+$
.-<,L()*++:5,4$,)2&$,&"*&,BC!0,"*.$,#$+*&(.$+:,"(;",&#*)0/2)-3/&*)/$,T*0,/2'7*#$-,&2,IJK%
LM!05,4"(/",4$,0&3-($-,(),6"*7&$#,^V`,12#,()0&*)/$5,*&,.-,=,?,'@5, C I ! eP#3IZ]?
@,;#*7"(/*+,()&$#7#$&*&(2),12#,CI,(0,;(.$),(),L(;<,X<\N5,4"$#$,(&,(0,0"24),&"*&,CI,(0,$S3*+
&2,&"$,0+27$,21,&"$,$- ]v)*,/"*#*/&$#(0&(/,/3#.$,*&,$-,=,.-,T(<$<5,*&,&"$,9(*0,72()&,kV<,!"305
∂ $C I = 55555555555
∂ v )* $- =.-
TX<8XV
Q
Figure 6.37 [&"+),#2*+,)$&2"#2@#$%+#$,)"'&'$2,#/"0+,#$%+#'3)665'&L")6#(2"0&$&2"8#I#'3)66#'&L")6#v#4#.&$%#)
$,&)"L/6),#.)7+@2,3#&'#'/*+,&3*2'+0#2"#$%+#0(#726$)L+#+)*?#!$#L&7+'#,&'+#$2#)#(266+($2,#'&L")6#(/,,+"$#$E-#)6'2
2@ $,&)"L/6),#.)7+@2,3-#'/*+,&3*2'+0#2"#$%+#0(#(/,,+"$#.-?#\+,+-#$E#=#CIv#4-#.%+,+#CI#&'#$%+#'62*+#2@#$%+#$- Qv)*
(/,7+#)$#$%+#9&)'#*2&"$#l?
405
406 Chapter 6 Bipolar Junction Transistors (BJTs)
!"$,0'*++%0(;)*+,*77#2A('*&(2),('7+($0,G$$7();,&"$,0(;)*+,*'7+(&3-$,0311(/($)&+:,0'*++,&"*&
%"4('?$%!8$B8(4B?($E?458?%8'!8'&I%B?M&$!4'(8B4CI4!?8%G8?D48$- Rv)*843"%!4!?$'&8EU(F4@,=)/#$*0%
();,&"$,0(;)*+,*'7+(&3-$,4(++,#$03+&,(),&"$,/2++$/&2#,/3##$)&,"*.();,/2'72)$)&0,)2)+()$*#+:
#$+*&$-,&2,v#4<,!"(05,21,/23#0$5,(0,&"$,0*'$,*77#2A('*&(2),&"*&,4$,-(0/300$-,(),&"$,/2)&$A&,21
&"$,*'7+(1($#,&#*)01$#,/3#.$,(),K$/&(2),X<8<
!"$,*)*+:0(0,*92.$,03;;$0&0,&"*&,12#,0'*++,0(;)*+0,Tv#4,*,+,V5,&"$,&#*)0(0&2#,9$"*.$0,*0,*
.2+&*;$%/2)&#2++$-,/3##$)&,023#/$<,!"$,()73&,72#&,21,&"(0,/2)&#2++$-,023#/$,(0,9$&4$$),9*0$
*)-,$'(&&$#5,*)-,&"$,23&73&,72#&,(0,9$&4$$),/2++$/&2#,*)-,$'(&&$#<,!"$,&#*)0/2)-3/&*)/$,21
&"$,/2)&#2++$-,023#/$,(0,CI5,*)-,&"$,23&73&,#$0(0&*)/$,(0,()1()(&$<,!"$,+*&&$#,(-$*+,7#27$#&:,(0,*
#$03+&,21,23#,1(#0&%2#-$#,'2-$+,21,&#*)0(0&2#,27$#*&(2),(),4"(/",&"$,/2++$/&2#,.2+&*;$,"*0,)2
$11$/&,2),&"$,/2++$/&2#,/3##$)&,(),&"$,*/&(.$,'2-$<,@0,4$,"*.$,0$$),(),K$/&(2),X<P5,7#*/&(/*+
BC!0,"*.$,1()(&$,23&73&,#$0(0&*)/$,9$/*30$,21,&"$,M*#+:,$11$/&<,!"$,$11$/&,21,&"$,23&73&,#$0(0%
&*)/$,2),*'7+(1($#,7$#12#'*)/$,4(++,9$,/2)0(-$#$-,+*&$#<,,
EXERCISES
6.34 ^'+#EV?#:W?eW>#$2#0+,&7+#$%+#+T*,+''&2"#@2,#CI#&"#EV?#:W?eG>?
6.35 6*+/3+*&$,&"$,.*+3$,21,CI,12#,*,BC!,9(*0$-,*&,.-,d,O<^,'@<
Ans. MP#3IZ]
6.5.2 The Base Current and the Input Resistance at the Base
!2, -$&$#'()$, &"$, #$0(0&*)/$, 0$$), 9:, v#45, 4$, 1(#0&, $.*+3*&$, &"$, &2&*+, 9*0$, /3##$)&, $), 30();
MS< TX<8PV5,*0,12++240Y
$
.
K .$ ) = 555-5 = 555-5 + 555 55555
v
β
β β + , #4
!"305
$) = .) + $#
TX<8NV
4"$#$,.),(0,$S3*+,&2, . - ⁄ β *)-,&"$,0(;)*+,/2'72)$)&,$#,(0,;(.$),9:
K .$ # = 555 55555
v
β + , #4
TX<8EV
C
$ # = 55555I v #4
TX<8DV
K390&(&3&();,12#, . - ⁄ + , ,9:,CI,;(.$0
β
!"$,0'*++%0(;)*+,()73&,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#5,&%%P$!C8$!?%8?D48#'B4W,(0,-$)2&$9:,(π,*)-,(0,-$1()$-,*0
v
#4
5
( π ≡ 55555
$#
TX<^OV
6.5 Small-Signal Operation and Models
c0();,MS<,TX<8DV,;(.$0
β
( π = 55555
CI
TX<^?V
!"30,(π,(0,-(#$/&+:,-$7$)-$)&,2),β,*)-,(0,().$#0$+:,7#272#&(2)*+,&2,&"$,9(*0,/3##$)&,.- <,K390&(%
&3&();, 12#, CI, (), MS<, TX<^?V, 1#2', MS<, TX<8^V, *)-, #$7+*/();, .- oβ, 9:, .), ;(.$0, *), *+&$#)*&(.$
$A7#$00(2),12#,(π 5
+
( π = 55555,
.)
TX<^PV
EXERCISE
6.36 I#;<=#)3*6&@&+,#&'#9&)'+0#$2#2*+,)$+#)$#)#(2"'$)"$#(266+($2,#(/,,+"$# . - d P?G #3I#&,,+'*+($&7+#2@
$%+#7)6/+# β ?#!@#$%+#$,)"'&'$2,#3)"/@)($/,+,#'*+(&@&+'# β #$2#,)"L+#@,23#GP#$2#MPP-#L&7+#$%+#+T*+($+0
,)"L+#2@# C I-# . ) - #)"0# ( π ?
Ans. C I ,(0,/2)0&*)&,*&,PO,'@o_`, . ) d KP ,µ@,&2,P<^,µ@`, ( π d M?G,G Ω ,&2,?O,G Ω
6.5.3 The Emitter Current and the Input Resistance at the Emitter
!"$,&2&*+,$'(&&$#,/3##$)&,$*,/*),9$,-$&$#'()$-,1#2'
$
.
$
$ * = 555-5 = 555-5 + 555E
α
α
α
!"305,
$* = .* + $4
TX<^\V
4"$#$,.*,(0,$S3*+,&2,.- oα,*)-,&"$,0(;)*+,/3##$)&,$4,(0,;(.$),9:
$
.
.5 v #4 = 55555* v #4
$ 4 = 555E = 555555555
α
α +,
+,
TX<^8V
=1,4$,-$)2&$,&"$,0'*++%0(;)*+,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#,&%%P$!C8$!?%8?D484I$??4(,9:
(45,(&,/*),9$,-$1()$-,*0,
v
#4
5
( 4 ≡ 55555
$4
TX<^^V
c0();,MS<,TX<^8V,4$,1()-,&"*&,(45,/*++$-,&"$,!"#$$!%-%!(#($'0)!5,(0,;(.$),9:
+
( 4 = 55555,
.*
TX<^XV
α
K
( 4 = 55555 !# 55555
CI
CI
TX<^NV
62'7*#(02),4(&",MS<,TX<8^V,#$.$*+0,&"*&
407
408 Chapter 6 Bipolar Junction Transistors (BJTs)
!"$,#$+*&(2)0"(7,9$&4$$),(π,*)-,(4,/*),9$,123)-,9:,/2'9()();,&"$(#,#$07$/&(.$,-$1()(&(2)0,()
MS0<,TX<^OV,*)-,TX<^^V,*0,
v #4 = $ # ( π = $ 4 ( 4
!"305
( π = ( $ 4 ⁄ $ # )( 4
4"(/",:($+-0
( π = ( β + K )( 4
TX<^EV
L(;3#$,X<\E,(++30&#*&$0,&"$,-$1()(&(2),21,(π,*)-,(4<
ib
$
$
vbe
vbe
r+ #
%
vbe
ib
%
re #
ie
vbe
ie
Figure 6.38 !66/'$,)$&"L#$%+#0+@&"&$&2"#2@#(π#)"0#(4?
EXERCISE
6.37 I#;<=#%)7&"L#β# =#KPP#&'#9&)'+0#)$#)#0(#(266+($2,#(/,,+"$#2@#K#3I?#D&"0#$%+#7)6/+#2@#CI-#(4-#)"0#(π#)$
$%+#9&)'#*2&"$?
Ans. eP#3IZ]H#25 ΩH#M?G#UΩ
6.5.4 Voltage Gain
W$,"*.$,$0&*9+(0"$-,*92.$,&"*&,&"$,&#*)0(0&2#,0$)0$0,&"$,9*0$]$'(&&$#,0(;)*+, v#4,*)-,/*30$0,*
7#272#&(2)*+,/3##$)&,CIv#4,&2,1+24,(),&"$,/2++$/&2#,+$*-,*&,*,"(;",T(-$*++:,()1()(&$V,('7$-*)/$
+$.$+<,=),&"(0,4*:,&"$,&#*)0(0&2#,(0,*/&();,*0,*,.2+&*;$%/2)&#2++$-,/3##$)&,023#/$<,!2,29&*(),*)
23&73&,.2+&*;$,0(;)*+5,4$,'*:,12#/$,&"(0,/3##$)&,&2,1+24,&"#23;",*,#$0(0&2#5,*0,(0,-2)$,(),L(;<
X<\XT*V<,!"$),&"$,&2&*+,/2++$/&2#,.2+&*;$,v-*,4(++,9$
v -* = + -- ] $ - > -
= + -- ] ( . - + $ E )> = ( + -- ] . - > - ) ] $ E > = + -* ] $ E > -
TX<^DV
6.5 Small-Signal Operation and Models
R$#$,&"$,S3*)&(&:,+-*,(0,&"$,-/,9(*0,.2+&*;$,*&,&"$,/2++$/&2#5,*)-,&"$,0(;)*+,.2+&*;$,(0,;(.$),9:
v E4 = ] $ E > - = ] C I v #4 > -
TX<XOV
= ( ] C I > - ) v #4
!"30,&"$,.2+&*;$,;*(),21,&"(0,*'7+(1($#,/v,(0
v
E4
5 = ]CI >/ v ≡ 55555
v #4
TX<X?V
R$#$, *;*(), 4$, )2&$, &"*&, 9$/*30$, CI, (0, -(#$/&+:, 7#272#&(2)*+, &2, &"$, /2++$/&2#, 9(*0, /3##$)&5
&"$ ;*(),4(++,9$,*0,0&*9+$,*0,&"$,/2++$/&2#,9(*0,/3##$)&,(0,'*-$<,K390&(&3&();,12#,CI,1#2'
MS<,TX<8^V,$)*9+$0,30,&2,$A7#$00,&"$,;*(),(),&"$,12#'
.- >5
/ v = ] 5555555555
+,
TX<XPV
4"(/",(0,(-$)&(/*+,&2,&"$,$A7#$00(2),4$,-$#(.$-,(),K$/&(2),X<8,TMS<,X<\?V<,,,,,
EXERCISE
6.38 !"#$%+#(&,(/&$#2@#D&L?#W?NW:)>-#+)*#&'#)04/'$+0#$2#1&+60#)#0(#(266+($2,#(/,,+"$#2@#K#3I?#[+$#+--#=#KG#]>- =#KP#UΩ-#)"0#β# =#KPP?#D&"0#$%+#726$)L+#L)&"# v E4 ⁄ v #4 ? !@#v#4#=#P?PPG#'&" ω ?#726$-#@&"0#v-:?>#)"0#$):?>?
Ans. ] ePP#]Z]H #G#Q#M#'&" ω ?#726$'H#KP#+#M#'&" ω ?#µI
6.5.5 Separating the Signal and the DC Quantities
!"$, *)*+:0(0, *92.$, ()-(/*&$0, &"*&, $.$#:, /3##$)&, *)-, .2+&*;$, (), &"$, *'7+(1($#, /(#/3(&, 21
L(;< X<\XT*V,(0,/2'720$-,21,&42,/2'72)$)&0Y,*,-/,/2'72)$)&,*)-,*,0(;)*+,/2'72)$)&<,L2#
()0&*)/$5, v)*,=,+)*,+,v#45,.-,=,.-,+,$E5,*)-,02,2)<,!"$,-/,/2'72)$)&0,*#$,-$&$#'()$-,1#2',&"$
-/,/(#/3(&,;(.$),(),L(;<,X<\XT9V,*)-,1#2',&"$,#$+*&(2)0"(70,('720$-,9:,&"$,&#*)0(0&2#,TMS0<,X<\X
&"#23;",X<\EV<,J),&"$,2&"$#,"*)-5,*,#$7#$0$)&*&(2),21,&"$,0(;)*+,27$#*&(2),21,&"$,BC!,/*)
9$,29&*()$-,9:,$+('()*&();,&"$,-/,023#/$05,*0,0"24),(),L(;<,X<\D<,J90$#.$,&"*&,0()/$,&"$,.2+&%
*;$,21,*),(-$*+,-/,0377+:,-2$0,)2&,/"*);$5,&"$,0(;)*+,.2+&*;$,*/#200,(&,4(++,9$,>$#2<,L2#,&"(0
#$*02),4$,"*.$,#$7+*/$-,+--,*)-,+)*,4(&",0"2#&,/(#/3(&0<,R*-,&"$,/(#/3(&,/2)&*()$-,(-$*+,-/
RC
C
ib " vbe /r+
B
vbe
$
%
$
vce
$
vbe
%
ic " gm vbe
%
E
vbe
ie " r
e
Figure 6.39 =%+# )3*6&@&+,# (&,(/&$# 2@# D&L?# W?NW:)># .&$%# $%+
0(# '2/,(+'# :+)*# )"0# +--># +6&3&")$+0# :'%2,$5(&,(/&$+0>?# =%/'
2"61#$%+#'&L")6#(23*2"+"$'#),+#*,+'+"$?#b2$+#$%)$#$%&'#&'#)#,+*5
,+'+"$)$&2"#2@#$%+#'&L")6#2*+,)$&2"#2@#$%+#;<=#)"0#"2$#)"#)($/)6
)3*6&@&+,#(&,(/&$?
409
410 Chapter 6 Bipolar Junction Transistors (BJTs)
/3##$)&,023#/$05,&"$0$,423+-,"*.$,9$$),#$7+*/$-,9:,27$),/(#/3(&0<,Q2&$5,"24$.$#5,&"*&,&"$
/(#/3(&,21,L(;<,X<\D,(0,30$13+,2)+:,(),02,1*#,*0,(&,0"240,&"$,.*#(230,0(;)*+,/3##$)&0,*)-,.2+&%
*;$0`,(&,(0,!%?,*),*/&3*+,*'7+(1($#,/(#/3(&5,0()/$,&"$,-/,9(*0,/(#/3(&,(0,)2&,0"24)<
L(;3#$,X<\D,*+02,0"240,&"$,$A7#$00(2)0,12#,&"$,/3##$)&,()/#$'$)&0,T$E5,$#5,*)-,$4V,29&*()$4"$),*,0'*++,0(;)*+,v#4,(0,*77+($-<,!"$0$,#$+*&(2)0"(70,/*),9$,#$7#$0$)&$-,9:,*,/(#/3(&<,K3/",*,/(#%
/3(&,0"23+-,"*.$,&"#$$,&$#'()*+0[65,B5,*)-,M[*)-,0"23+-,:($+-,&"$,0*'$,&$#'()*+,/3##$)&0,()-(%
/*&$-,(),L(;<,X<\D<,!"$,#$03+&();,/(#/3(&,(0,&"$),40U$F'&4!?8?%8?D48?('!B$B?%(8'B8G'(8'B8BI'&&MB$C!'&
%"4('?$%!8$B8E%!E4(!45W,*)-,&"30,(&,/*),9$,/2)0(-$#$-,*),$S3(.*+$)&,0'*++%0(;)*+,/(#/3(&,'2-$+<
6.5.6 The Hybrid-π Model
@),$S3(.*+$)&,/(#/3(&,'2-$+,12#,&"$,BC!,(0,0"24),(),L(;<,X<8OT*V<,!"(0,'2-$+,#$7#$0$)&0,&"$,BC!
*0,*,.2+&*;$%/2)&#2++$-,/3##$)&,023#/$,*)-,$A7+(/(&+:,()/+3-$0,&"$,()73&,#$0(0&*)/$,+22G();,()&2
&"$,9*0$5,(π <,!"$,'2-$+,29.(230+:,:($+-0,$E,=,CIv#4,*)-, $ # = v#4 ⁄ ( π ? ,Q2&,02,29.(2305,"24$.$#5,(0
&"$,1*/&,&"*&,&"$,'2-$+,*+02,:($+-0,&"$,/2##$/&,$A7#$00(2),12#,$4<,!"(0,/*),9$,0"24),*0,12++240Y
@&,&"$,$'(&&$#,)2-$,4$,"*.$
v
v
#4
#4
5 + C I v #4 = 55555
5 ( K + CI (π )
$ 4 = 55555
(π
(π
v #4
(π 5 ( K + β ) = v #4 ## 55555555555
5
= 55555
(π
K+β
= v #4 ⁄ ( 4
@,0+(;"&+:,-(11$#$)&,$S3(.*+$)&%/(#/3(&,'2-$+,/*),9$,29&*()$-,9:,$A7#$00();,&"$,/3##$)&
21,&"$,/2)&#2++$-,023#/$,TCIv#4V,(),&$#'0,21,&"$,9*0$,/3##$)&,$#,*0,12++240Y
C I v #4 = C I ( $ # ( π )
= ( C I ( π )$ # = β $ #
!"(0,#$03+&0,(),&"$,*+&$#)*&(.$,$S3(.*+$)&%/(#/3(&,'2-$+,0"24),(),L(;<,X<8OT9V<,R$#$,&"$,&#*)%
0(0&2#,(0,#$7#$0$)&$-,*0,*,/3##$)&%/2)&#2++$-,/3##$)&,023#/$5,4(&",&"$,/2)&#2+,/3##$)&,9$();,$#<
ic
ib
B
C
+
vbe
–
ic
ib
C
B
rp
+
vbe
–
gmvbe
ie
rp
bib
gm = IC /VT
rp = b/gm
E
ie
(a)
E
Figure 6.40 =.2#'6&L%$61#0&@@+,+"$#7+,'&2"'#2@#$%+#%19,&05π#320+6#@2,#$%+#'3)665'&L")6#2*+,)$&2"#2@#$%+
;<=?#=%+#+V/&7)6+"$#(&,(/&$#&"#;'<#,+*,+'+"$'#$%+#;<=#)'#)#726$)L+5(2"$,266+0#(/,,+"$#'2/,(+#:)#$,)"'(2"5
0/($)"(+#)3*6&@&+,>-#)"0#$%)$#&"#;&<#,+*,+'+"$'#$%+#;<=#)'#)#(/,,+"$5(2"$,266+0#(/,,+"$#'2/,(+#:)#(/,,+"$
)3*6&@&+,>?
6.5 Small-Signal Operation and Models
!"$,&42,'2-$+0,21,L(;<,X<8O,*#$,0('7+(1($-,.$#0(2)0,21,4"*&,(0,G)24),*0,&"$,":9#(-%π
'2-$+<,!"(0,(0,&"$,'20&,4(-$+:,30$-,'2-$+,12#,&"$,BC!<
=&, (0, ('72#&*)&, &2, )2&$, &"*&, &"$, 0'*++%0(;)*+, $S3(.*+$)&, /(#/3(&0, 21, L(;<, X<8O, '2-$+, &"$
27$#*&(2), 21, &"$, BC!, '?8 '8 C$F4!8 #$'B8 "%$!?<, !"(0, 0"23+-, 9$, 29.(230, 1#2', &"$, 1*/&, &"*&
&"$ '2-$+,7*#*'$&$#0,CI,*)-,(π,-$7$)-,2),&"$,.*+3$,21,&"$,-/,9(*0,/3##$)&,.- 5,*0,()-(/*&$-,()
L(;<,X<8O<,=&,(0,()&$#$0&();,*)-,30$13+,&2,)2&$,&"*&,&"$,'2-$+0,21,L(;<,X<8O,T*V,*)-,T9V,*#$,&"$
0'*++%0(;)*+,.$#0(2)0,21,&"$,'2-$+0,21,L(;<,X<^T/V,*)-,T-V5,#$07$/&(.$+:<,K7$/(1(/*++:5,290$#.$
&"*&,(π ,(0,&"$,()/#$'$)&*+,#$0(0&*)/$,21,1)<
EXERCISE
6.39 L2#,&"$,'2-$+,(),L(;<,X<8OT9V,0"24,&"*&,$E,=,CIv#488*)-, $ 4 = v #4 ⁄ ( 4 ?
6.5.7 The T Model
@+&"23;", &"$,":9#(-%π, '2-$+, T(),2)$,21,(&0, &42,.*#(*)&0,0"24),(),L(;<,X<8OV, /*),9$,30$&2 /*##:,23&,0'*++%0(;)*+,*)*+:0(0,21,*):,&#*)0(0&2#,/(#/3(&5,&"$#$,*#$,0(&3*&(2)0,(),4"(/",*)
*+&$#)*&(.$, '2-$+5, 0"24), (), L(;<, X<8?5, (0, '3/", '2#$, /2).$)($)&<, !"(0, '2-$+5, /*++$-, &"$
@ "*2!+5,(0,0"24),(),&42,.$#0(2)0,(),L(;<,X<8?<, !"$,'2-$+,21,L(;<,X<8?T*V,#$7#$0$)&0,&"$
BC!,*0,*,.2+&*;$%/2)&#2++$-,/3##$)&,023#/$,4(&",&"$,/2)&#2+,.2+&*;$,9$();,v#4<,R$#$5,"24$.$#5
&"$,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#5,+22G();,()&2,&"$,$'(&&$#5,(0,$A7+(/(&+:,0"24)<,L#2'
L(;<,X<8?T*V,4$,0$$,/+$*#+:,&"*&,&"$,'2-$+,:($+-0,&"$,/2##$/&,$A7#$00(2)0,12#,$E,*)-,$4<,L2#,$#
4$,)2&$,&"*&,*&,&"$,9*0$,)2-$,4$,"*.$,,
C
ic
,i e
ib
B
$
vbe
ie
re
%
E
(a)
(b)
Figure 6.41 =.2#'6&L%$61#0&@@+,+"$#7+,'&2"'#2@#.%)$#&'#U"2."#)'#$%+#,8I%54&#2@#$%+#;<=?#=%+#(&,(/&$#&"
;'< &'#)#726$)L+5(2"$,266+0#(/,,+"$#'2/,(+#,+*,+'+"$)$&2"#)"0#$%)$#&"#;&<#&'#)#(/,,+"$5(2"$,266+0#(/,,+"$#'2/,(+
,+*,+'+"$)$&2"?# =%+'+# 320+6'# +T*6&(&$61# '%2.# $%+# +3&$$+,# ,+'&'$)"(+# (4# ,)$%+,# $%)"# $%+# 9)'+# ,+'&'$)"(+# (π
@+)$/,+0#&"#$%+#%19,&05π#320+6?
411
412 Chapter 6 Bipolar Junction Transistors (BJTs)
v
v
#4
#4
5 ( K ] CI (4 )
$ # = 55555
5 ] C I v #4 = 55555
(4
(4
v #4
v #4 β 5
5 ( K ] α ) = 55555
5 K ] 55555555555
= 55555
(4
(4 β+K
v
v
#4
#4
5 = 55555
5
= 555555555555555555555
( β + K )( 4
(π
)'#'%2/60#9+#$%+#()'+?
=1,(),&"$,'2-$+,21,L(;<,X<8?T*V,&"$,/3##$)&,21,&"$,/2)&#2++$-,023#/$,(0,$A7#$00$-,(),&$#'0
21,&"$,$'(&&$#,/3##$)&,*0
C I v #4 = C I ( $ 4 ( 4 )
= ( C I ( 4 )$ 4 = α $ 4
4$,29&*(),&"$,*+&$#)*&(.$,!,'2-$+,0"24),(),L(;<,X<8?T9V<,R$#$,&"$,BC!,(0,#$7#$0$)&$-,*0,*
/3##$)&%/2)&#2++$-,/3##$)&,023#/$,93&,4(&",&"$,/2)&#2+,0(;)*+,9$();,$4<
!$#&'#&"$+,+'$&"L#)"0#/'+@/6#$2#"2$+#$%)$#$%+#320+6'#2@#D&L?#W?eK:)>#)"0#:9>#),+#$%+#'3)665
'&L")6#7+,'&2"'#2@#$%+#320+6'#&"#D&L?#W?G:)>#)"0#:9>-#,+'*+($&7+61?#C*+(&@&()661#29'+,7+#$%)$#(4
&'#$%+#&"(,+3+"$)6#,+'&'$)"(+#2@#1*?
6.5.8 Small-Signal Models of the pnp Transistor
@+&"23;",&"$,0'*++%0(;)*+,'2-$+0,(),L(;0<,X<8O,*)-,X<8?,4$#$,-$.$+27$-,12#,&"$,/*0$,21,&"$
!"!,&#*)0(0&2#5,&"$:,*77+:,$S3*++:,4$++,&2,&"$,"!",&#*)0(0&2#,A$?D8!%8ED'!C48$!8"%&'($?$4B<
6.5.9 Application of the Small-Signal Equivalent Circuits
=%+# )7)&6)9&6&$1# 2@# $%+# '3)665'&L")6# ;<=# (&,(/&$# 320+6'# 3)U+'# $%+# )")61'&'# 2@# $,)"'&'$2,
)3*6&@&+,#(&,(/&$'#)#'1'$+3)$&(#*,2(+''?#=%+#*,2(+''#(2"'&'$'#2@#$%+#@2662.&"L#'$+*'8
1. M+('()*&$,&"$,0(;)*+,023#/$,*)-,-$&$#'()$,&"$,-/,27$#*&();,72()&,21,&"$,BC!,*)-,(),7*#%
&(/3+*#,&"$,-/,/2++$/&2#,/3##$)&,.-<
2. 6*+/3+*&$, &"$, .*+3$0, 21, &"$, 0'*++%0(;)*+, '2-$+, 7*#*'$&$#0Y, C I = . - ⁄ + , - , ( π = β ⁄ C I *)-, ( 4 = + , ⁄ . * = α ⁄ C I ?
3. M+('()*&$,&"$,-/,023#/$0,9:,#$7+*/();,$*/",-/,.2+&*;$,023#/$,4(&",*,0"2#&,/(#/3(&,*)-,$*/"
-/,/3##$)&,023#/$,4(&",*),27$),/(#/3(&<
4. U$7+*/$,&"$,BC!,4(&",2)$,21,(&0,0'*++%0(;)*+,$S3(.*+$)&,/(#/3(&,'2-$+0<,@+&"23;",*):
2)$,21,&"$,'2-$+0,/*),9$,30$-5,2)$,'(;"&,9$,'2#$,/2).$)($)&,&"*),&"$,2&"$#0,12#,&"$,7*#%
&(/3+*#,/(#/3(&,9$();,*)*+:>$-<,!"(0,72()&,4(++,9$,'*-$,/+$*#$#,+*&$#,(),&"(0,/"*7&$#<
5. @)*+:>$,&"$,#$03+&();,/(#/3(&,&2,-$&$#'()$,&"$,#$S3(#$-,S3*)&(&($0,T$<;<5,.2+&*;$,;*()5,()73&
#$0(0&*)/$V<,!"$,7#2/$00,4(++,9$,(++30&#*&$-,9:,&"$,12++24();,$A*'7+$0<
6.5 Small-Signal Operation and Models
Example 6.14
Y+#.&'%#$2#)")61h+#$%+#$,)"'&'$2,#)3*6&@&+,#'%2."#&"#D&L?#W?eM:)>#$2#0+$+,3&"+#&$'#726$)L+#L)&"# v % ⁄ v $ ?
I''/3+#β# =#KPP?
VCC
10 V
$10 V
2.3 mA
VC
100 k
RBB
3 k&
3k
RC
vo
0.023 mA
vi
VBB
$3.1 V
$3 V
100 k&
$0.7 V
2.323 mA
3V
(a )
(b)
Re
RBB
vi
RBB " 100 k&
B
$
vi
$
%
vo
$
%
r+
$
vbe
C
gm vbe
%
vo
RC " 3 k&
E
(d)
%
(c)
Figure 6.42 ET)3*6+#W?Ke8#;'<#)3*6&@&+,#(&,(/&$H#;&<#(&,(/&$#@2,#0(#)")61'&'H#;)<#)3*6&@&+,#(&,(/&$#.&$%#0(#'2/,(+'
,+*6)(+0#91#'%2,$#(&,(/&$'H#;2<-)3*6&@&+,#(&,(/&$#.&$%#$,)"'&'$2,#,+*6)(+0#91#&$'#%19,&05π, '3)665'&L")6#320+6'?
Solution
Y+#'%)66#@2662.#$%+#@&7+5'$+*#*,2(+''#2/$6&"+0#)927+8
1. !"$,1(#0&,0&$7,(),&"$,*)*+:0(0,/2)0(0&0,21,-$&$#'()();,&"$,S3($0/$)&,27$#*&();,72()&<,L2#,&"(0,73#%
720$,4$,*003'$,&"*&,v$,=,O,*)-,&"30,29&*(),&"$,-/,/(#/3(&,0"24),(),L(;<,X<8PT9V<,!"$,-/,9*0$,/3#%
#$)&,4(++,9$
413
414 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.14 continued
+ )) ] + )*
5
. ) = 55555555555555555555555
> ))
N ] P?d
! 5555555555555555 = P?PMN#3I
KPP
=%+#0(#(266+($2,#(/,,+"$#.&66#9+
. - = β . ) #=#KPP × P?PMN = M?N#3I
=%+#0(#726$)L+#)$#$%+#(266+($2,#.&66#9+
+ - = + -- ] . - > = +?O,−,P<\,× 3 = +3.1 _
C&"(+#+)#)$#+P?d#]#&'#6+''#$%)"#+- -#&$#@2662.'#$%)$#&"#$%+#V/&+'(+"$#(2"0&$&2"#$%+#$,)"'&'$2,#.&66#9+
2*+,)$&"L#&"#$%+#)($&7+#320+?#=%+#0(#)")61'&'#&'#&66/'$,)$+0#&"#D&L?#W?eM:9>?
2. R*.();,-$&$#'()$-,&"$,27$#*&();,72()&5,4$,/*),)24,7#2/$$-,&2,-$&$#'()$,&"$,0'*++%0(;)*+,'2-$+
7*#*'$&$#0Y
+
MG#3]
( 4 = 55555,5 = 55555555555555555555555555555555555555 = KP?f#Ω
.*
( M?N ⁄ P?aa )#3I
.M?N#3I
5 = 555555555555555555 = aM#3IZ]
C I = 55555
MG#3]
+,
β
KPP
( π = 555555 = 555555555 = K?Pa#UΩ
CI
aM
3. U$7+*/();,+)),*)-,+--8,4(&",0"2#&,/(#/3(&0,#$03+&0,(),&"$,/(#/3(&,(),L(;<,X<8PT/V<
4. !2,/*##:,23&,&"$,0'*++%0(;)*+,*)*+:0(05,(&,(0,$S3*++:,/2).$)($)&,&2,$'7+2:,$(&"$#,21,&"$,&42,":9#(-%
π5,$S3(.*+$)&%/(#/3(&,'2-$+0,21,L(;<,X<8O,&2,#$7+*/$,&"$,&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,X<8PT/V<
c0();,&"$,1(#0&,#$03+&0,(),&"$,*'7+(1($#,$S3(.*+$)&,/(#/3(&,;(.$),(),L(;<,X<8PT-V<,
5. I")61'&'#2@#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?eM:0>#*,2(++0'#)'#@2662.'8
(π
v #4 = v $ 55555555555555555555
( π + > ))
K?Pa
= v $ 5555555555555555 = P?PKK v $
KPK?Pa
TX<X\V
!"$,23&73&,.2+&*;$,v%,(0,;(.$),9:
v % = ] C I v #4 > -
= ] aM × P?PKK v $ × N = ] N?Pe v $
=%/'#$%+#726$)L+#L)&"#.&66#9+
v
/ v = 5555% = ] N?Pe #]Z]
v$
TX<X8V
6.5 Small-Signal Operation and Models
Example 6.15
=2#L)&"#32,+#&"'&L%$#&"$2#$%+#2*+,)$&2"#2@#$,)"'&'$2,#)3*6&@&+,'-#.+#.&'%#$2#(2"'&0+,#$%+#.)7+@2,3'#)$#7),5
&2/'#*2&"$'#&"#$%+#(&,(/&$#)")61h+0#&"#$%+#*,+7&2/'#+T)3*6+?#D2,#$%&'#*/,*2'+#)''/3+#$%)$#v$#%)'#)#$,&)"L/6),
.)7+@2,3?#D&,'$#0+$+,3&"+#$%+#3)T&3/3#)3*6&$/0+#$%)$#v$#&'#)662.+0#$2#%)7+?#=%+"-#.&$%#$%+#)3*6&$/0+#2@
v$#'+$#$2#$%&'#7)6/+-#L&7+#$%+#.)7+@2,3'#2@#$%+#$2$)6#V/)"$&$&+'#$):?>-#v)*:?>-#$-:?>-#)"0#v-:?>?
Solution
B"+#(2"'$,)&"$#2"#'&L")6#)3*6&$/0+#&'#$%+#'3)665'&L")6#)**,2T&3)$&2"-#.%&(%#'$&*/6)$+'#$%)$#v#4#'%2/60#"2$
+T(++0#)92/$#KP#3]?#!@#.+#$)U+#$%+#$,&)"L/6),#.)7+@2,3# v#4#$2#9+#MP#3]#*+)U5$25*+)U#)"0#.2,U#9)(U5
.),0-#EV?#:W?WN>#()"#9+#/'+0#$2#0+$+,3&"+#$%+#3)T&3/3#*2''&96+#*+)U#2@#v$ v #4
KP
vt % = 5555555555555 = 5555555555555 = P?aK#]
P?PKK
P?PKK
=2# (%+(U# .%+$%+,# $%+# $,)"'&'$2,# ,+3)&"'# &"# $%+# )($&7+# 320+# .&$%# v$# %)7&"L# )# *+)U# 7)6/+
vt $ = P?aK#]- .+#%)7+#$2#+7)6/)$+#$%+#(266+($2,#726$)L+?#=%+#726$)L+#)$#$%+#(266+($2,#.&66#(2"'&'$#2@#)#$,&)"5
L/6),#.)7+#v%#'/*+,&3*2'+0#2"#$%+#0(#7)6/+#+-#=#N?K#]?#=%+#*+)U#726$)L+#2@#$%+#$,&)"L/6),#.)7+@2,3#.&66
9+
vt % = vt $ × L)&" = P?aK × N?Pe = M?dd#]
!$#@2662.'#$%)$#.%+"#$%+#2/$*/$#'.&"L'#"+L)$&7+-#$%+#(266+($2,#726$)L+#,+)(%+'#)#3&"&3/3#2@#N?K#Q#M?dd =
P?NN ]-#.%&(%#&'#62.+,#$%)"#$%+#9)'+#726$)L+#91#6+''#$%)"#P?e#]?#=%/'#$%+#$,)"'&'$2,#.&66#,+3)&"#&"#$%+
)($&7+#320+#.&$%# v$#%)7&"L#)#*+)U#7)6/+#2@#P?aK#]?#b+7+,$%+6+''-#$2#9+#2"#$%+#')@+#'&0+-#.+#.&66#/'+#)
'23+.%)$#62.+,#7)6/+#@2,# vt $ #2@#)**,2T&3)$+61#P?f#]-#)'#'%2."#&"#D&L?#W?eN:)>-#)"0#(23*6+$+#$%+#)")61'&'
2@#$%&'#*,296+3#/$&6&h&"L#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?eM:0>?#=%+#'&L")6#(/,,+"$#&"#$%+#9)'+#.&66#9+#$,&)"5
L/6),-#.&$%#)#*+)U#7)6/+# $t# #2@
vt $
P?f
5 = 5555555555555555555555555 = P?PPf#3I
$t# = 5555555555555555555
> )) + ( π
KPP + K?Pa
=%&'# $,&)"L/6),5.)7+# (/,,+"$# .&66# 9+# '/*+,&3*2'+0# 2"# $%+# V/&+'(+"$# 9)'+# (/,,+"$# .)-# )'# '%2."# &"# D&L?
W?eN:9>?#=%+#9)'+Q+3&$$+,#726$)L+#.&66#(2"'&'$#2@#)#$,&)"L/6),5.)7+#(23*2"+"$#'/*+,&3*2'+0#2"#$%+#0(
+)*#$%)$#&'#)**,2T&3)$+61#P?d#]?#=%+#*+)U#7)6/+#2@#$%+#$,&)"L/6),#.)7+@2,3#.&66#9+
(
( π + > ))
K?Pa
KPP + K?Pa
π
vt #4 = vt $ 55555555555555555555 = P?f 5555555555555555555555555 = f?W#3]
=%+#$2$)6#v)*#&'#'U+$(%+0#&"#D&L?#W?eN:(>?
=%+#'&L")6#(/,,+"$#&"#$%+#(266+($2,#.&66#9+#$,&)"L/6),#&"#.)7+@2,3-#.&$%#)#*+)U#7)6/+# t$E #L&7+"#91
t$ E = β t$ # = KPP × P?PPf = P?f#3I
=%&'#(/,,+"$#.&66#9+#'/*+,&3*2'+0#2"#$%+#V/&+'(+"$#(266+($2,#(/,,+"$#.-#:=M?N#3I>-#)'#'%2."#&"#D&L?
W?eN:0>?
=%+#'&L")6#726$)L+#)$#$%+#(266+($2,#()"#9+#29$)&"+0#91#3/6$&*61&"L#v$#91#$%+#726$)L+#L)&"H#$%)$ &'-#
vt % = N?Pe × P?f = M?eN#]
D&L/,+# W?eN:+># '%2.'# )# 'U+$(%# 2@# $%+# $2$)6# (266+($2,# 726$)L+# v-# 7+,'/'# $&3+?# b2$+# $%+# *%)'+# ,+7+,')6
9+$.++"#$%+#&"*/$#'&L")6#v$#)"0#$%+#2/$*/$#'&L")6#v%?
D&")661-#.+#29'+,7+#$%)$#+)(%#2@#$%+#$2$)6#V/)"$&$&+'#&'#$%+#'/3#2@#)#0(#V/)"$&$1#:@2/"0#@,23#$%+#0(#(&,5
(/&$#&"#D&L?#W?eM9>-#)"0#)#'&L")6#V/)"$&$1#:@2/"0#@,23#$%+#(&,(/&$#&"#D&L?#W?eM0>?
415
416 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.15 continued
vi
$0.8 V
vˆ i
0
t
%0.8 V
(a)
iB (mA)
iˆb " 0.008 mA
ib
0.03
0.02
iB
0.01
IB " 0.023 mA
0
t
(b)
vBE
vbe
0.7 V
vˆ be " 8.6 mV
vBE
VBE
0
t
(c)
iC (mA)
ic
IC " 2.3 mA
3
2
1
iC
iˆc " 0.8 mA
IC
0
vC (V)
t
(d)
vˆ o " 2.43 V
vo
6
vo
4
2
VC " 3.1 V
vC
0
0.67 V
(e)
t
Figure 6.43 C&L")6# .)7+@2,3'# &"# $%+
(&,(/&$#2@#D&L?#W?eM?
6.5 Small-Signal Operation and Models
Example 6.16
Y+#"++0#$2#)")61h+#$%+#(&,(/&$#2@#D&L?#W?ee:)>#$2#0+$+,3&"+#$%+#726$)L+#L)&"#)"0#$%+#'&L")6#.)7+@2,3'
)$#7),&2/'#*2&"$'?#=%+#()*)(&$2,#--K#&'#)#(2/*6&"L#()*)(&$2,#.%2'+#*/,*2'+#&'#$2#(2/*6+#$%+#'&L")6#v$#$2
$%+#+3&$$+,#.%&6+#962(U&"L#0(?#!"#$%&'#.)1#$%+#0(#9&)'#+'$)96&'%+0#91#+ +#)"0#+ Q#$2L+$%+,#.&$%#>*#)"0#>.&66# "2$# 9+# 0&'$/,9+0# .%+"# $%+# '&L")6# v$# &'# (2""+($+0?# D2,# $%+# */,*2'+# 2@# $%&'# +T)3*6+-# --K# .&66# 9+
)''/3+0#$2#9+#7+,1#6),L+#'2#)'#$2#)($#)'#)#*+,@+($#'%2,$#(&,(/&$#)$#'&L")6#@,+V/+"(&+'#2@#&"$+,+'$?#C&3&5
6),61-#)"2$%+,#7+,1#6),L+#()*)(&$2,#--M#&'#/'+0#$2#(2/*6+#$%+#2/$*/$#'&L")6#v%#$2#2$%+,#*),$'#2@#$%+#'1'$+3?#
V $ " $10 V
$10 V
0.93 mA
RE " 10 k&
10 k&
$0.7 V
vi
$
%
CC1
CC2
vo
%5.4 V
0.92 mA
RC " 5 k&
5 k&
V % " %10 V
%10 V
(b)
(a)
E
RE
vi
$
%
RE
ie
re
B
vi
v
ie " % i
re
vo " % ,ie RC
,RC
"
v
re i
$
%
,ie
C
vo
RC
vo
RC
(c )
(d)
Figure 6.44 ;'<#(&,(/&$H#;&<#0(#)")61'&'H8;)<#(&,(/&$#.&$%#$%+#0(#'2/,(+'#+6&3&")$+0H#;2<#'3)665'&L")6#)")61'&'#/'&"L
$%+##=#320+6#@2,#$%+#;<=?
417
418 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.16 continued
Solution
\+,+#)L)&"#.+#'%)66#@2662.#$%+#@&7+5'$+*#*,2(+''#2/$6&"+0#)$#$%+#9+L&""&"L#2@#C+($&2"#W?G?a8
1. L(;3#$,X<88T9V,0"240,&"$,/(#/3(&,4(&",&"$,0(;)*+,023#/$,*)-,&"$,/237+();,/*7*/(&2#0,$+('()*&$-<
!"$,-/,27$#*&();,72()&,/*),9$,-$&$#'()$-,*0,12++240Y
+KP ] +
+KP ] P?d
. * = 555555555555555555555*5 #!# 55555555555555555555555 = P?aN#3I
KP
>*
I''/3&"L#β#=#KPP-#$%+"#α#=#P?aa-#)"0
. - = P?aa. * = P?aM#3I
+ - = −KP + . - > = −KP + P?aM × G = ] G?e #]
!"30,&"$,&#*)0(0&2#,(0,(),&"$,*/&(.$,'2-$<
2. W$,)24,-$&$#'()$,&"$,0'*++%0(;)*+,7*#*'$&$#0,*0,12++240Y
.P?aM
5 d 555555555555
C I d 55555
5 d NW?f ,'@o_
+,
P?PMG
+
P?PMG
( 4 d 55555,5 d 5555555555555 d Md?M Ω
P?aM
.*
,,,,,,, α d P?aa
β d KPP
β
KPP
( π d 555555 d 5555555555 d M?dM UΩ
NW?f
CI
3. !2,7#$7*#$,&"$,/(#/3(&,12#,0'*++%0(;)*+,*)*+:0(05,4$,#$7+*/$,&"$,-/,023#/$0,4(&",0"2#&,/(#/3(&0<,!"$
#$03+&();,/(#/3(&,(0,0"24),(),L(;<,X<88T/V<,J90$#.$,&"*&,4$,"*.$,*+02,$+('()*&$-,&"$,&42,/237+();
/*7*/(&2#05,0()/$,&"$:,*#$,*003'$-,&2,9$,*/&();,*0,7$#1$/&,0"2#&,/(#/3(&0<
4. W$,*#$,)24,#$*-:,&2,#$7+*/$,&"$,BC!,4(&",2)$,21,&"$,123#,$S3(.*+$)&,/(#/3(&,'2-$+0,21,L(;0<,X<8O
*)-,X<8?<,@+&"23;",*):,21,&"$,123#,4(++,42#G5,&"$,!,'2-$+0,21,L(;<,X<8?,4(++,9$,'2#$,/2).$)($)&
9$/*30$,&"$,9*0$,(0,;#23)-$-<,K$+$/&();,&"$,.$#0(2),(),L(;<,X<8?T9V,#$03+&0,(),&"$,*'7+(1($#,$S3(.%
*+$)&,/(#/3(&,0"24),(),L(;<,X<88T-V<
5. I")61'&'#2@#$%+#(&,(/&$#&"#D&L?#W?ee:0>#$2#0+$+,3&"+#$%+#2/$*/$#726$)L+#v%#)"0#%+"(+#$%+#726$)L+
L)&"# v % ⁄ v $ #&'#'$,)&L%$@2,.),0#)"0#&'#L&7+"#&"#$%+#@&L/,+?#=%+#,+'/6$#&'
v
/ v = 5555% = KfN?N#]Z]
v$
b2$+#$%)$#$%+#726$)L+#L)&"#&'#*2'&$&7+-#&"0&()$&"L#$%)$#$%+#2/$*/$#&'#&"#*%)'+#.&$%#$%+#&"*/$ '&L")6?
=%&'#*,2*+,$1#&'#0/+#$2#$%+#@)($#$%)$#$%+#&"*/$#'&L")6#&'#)**6&+0#$2#$%+#+3&$$+,#,)$%+,#$%)"#$2#$%+#9)'+)'#.)'#02"+#&"#ET)3*6+#W?Ke?#Y+#'%2/60#+3*%)'&h+#$%)$#$%+#*2'&$&7+ L)&"#%)'#"2$%&"L#$2#02#.&$%
$%+#@)($#$%)$#$%+#$,)"'&'$2,#/'+0#&"#$%&'#+T)3*6+#&'#2@#$%+#"!"#$1*+?
J+$/,"&"L#$2#$%+#V/+'$&2"#2@#)662.)96+#'&L")6#3)L"&$/0+-#.+#29'+,7+#@,23#D&L?#W?ee:0>#$%)$# v4##=# v$?
=%/'-#&@#'3)665'&L")6#2*+,)$&2"#&'#0+'&,+0#:@2,#6&"+),&$1>-#$%+"#$%+#*+)U#2@#v$#'%2/60#9+#6&3&$+0#$2#)**,2T&5
3)$+61#KP#3]?#Y&$%# +t$ #'+$#$2#$%&'#7)6/+-#)'#'%2."#@2,#)#'&"+5.)7+#&"*/$#&"#D&L?#W?eG-#$%+#*+)U#)3*6&$/0+#)$
$%+#(266+($2,-#+t % -#.&66#9+
+t % = KfN?N × P?PK = K?fNN#]
6.5 Small-Signal Operation and Models
1.83
Figure 6.45 !"*/$#)"0#2/$*/$#.)7+@2,3'#@2,#$%+#(&,(/&$#2@#D&L?#W?ee?#B9'+,7+#$%)$#$%&'#)3*6&@&+,#&'#"2"&"7+,$&"L-#)
*,2*+,$1#2@#$%+#L,2/"0+0#9)'+#(2"@&L/,)$&2"?
,,,
EXERCISE
6.40
=2#&"(,+)'+#$%+#726$)L+#L)&"#2@#$%+#)3*6&@&+,#)")61h+0#&"#ET)3*6+#W?KW-#$%+#(266+($2,#,+'&'$)"(+
>-#&' &"(,+)'+0#$2#d?G#UΩ?#D&"0#$%+#"+.#7)6/+'#2@#+- -#/v -#)"0#$%+#*+)U#)3*6&$/0+#2@#$%+#2/$*/$#'&"+
.)7+#(2,,+'*2"0&"L#$2#)"#&"*/$#'&"+#.)7+#v$#2@#KP53]#*+)U?
Ans. QN?K#]H#MdG#]Z]H#M?dG#]
6.5.10 Performing Small-Signal Analysis Directly
on the Circuit Diagram
!"#32'$#()'+'#2"+#'%2/60#+T*6&(&$61#,+*6)(+#+)(%#;<=#.&$%#&$'#'3)665'&L")6#320+6#)"0#)")5
61h+#$%+#,+'/6$&"L#(&,(/&$-#)'#.+#%)7+#02"+#&"#$%+#+T)3*6+'#)927+?#=%&'#'1'$+3)$&(#*,2(+0/,+
&'# *),$&(/6),61# ,+(233+"0+0# @2,# 9+L&""&"L# '$/0+"$'?# ET*+,&+"(+0# (&,(/&$# 0+'&L"+,'-# %2.5
+7+,-#2@$+"#*+,@2,3#)#@&,'$52,0+,#)")61'&'#0&,+($61#2"#$%+#(&,(/&$?#D&L/,+#W?eW#&66/'$,)$+'#$%&'
*,2(+''#@2,#$%+#$.2#(&,(/&$'#.+#)")61h+0#&"#ET)3*6+'#W?Ke#)"0#W?KW?#=%+#,+)0+,#&'#/,L+0#$2#@2662.
$%&'#0&,+($#)")61'&'#*,2(+0/,+#:$%+#'$+*'#),+#"/39+,+0>?#B9'+,7+#$%)$#$%+#+V/&7)6+"$5(&,(/&$
320+6#&'#$I"&$E$?&H#/$&6&h+0H#.+#),+#2"61#')7&"L#$%+#'$+*#2@#0,).&"L#$%+#(&,(/&$#.&$%#$%+#;<=
,+*6)(+0#91#&$'#320+6?#X&,+($#)")61'&'-#%2.+7+,-#%)'#)"#)00&$&2")6#7+,1#&3*2,$)"$#9+"+@&$8#!$
419
420 Chapter 6 Bipolar Junction Transistors (BJTs)
RC 3 ic " b ib
ic
ib
$
RBB
4 vo " %RC ic "%b RC ib
vi $
%
"%
1
%
r+
vo
5 Av # v "%
vi
2 ib "
RBB $ r+
i
b RC
RBB $ r+
vi
b RC
RBB $ r+
(a)
RE
1
re
ie
vi
2 ie "
$
%
vi
re
4
, RC
vi
vo " ic RC "
re
3 ic " , ie
,v
"%
re i
RC
, RC
v
5 Av # vo "$
re
i
(b)
Figure 6.46 O+,@2,3&"L# '&L")6# )")61'&'# 0&,+($61# 2"
$%+# (&,(/&$# 0&)L,)3# .&$%# $%+# ;<=# '3)665'&L")6# 320+6
&3*6&(&$61# +3*621+08# # :'># F&,(/&$# @2,# ET)3*6+# W?KeH
:&> F&,(/&$#@2,#ET)3*6+#W?KW?
*,27&0+'# &"'&L%$# ,+L),0&"L# $%+# '&L")6# $,)"'3&''&2"# $%,2/L%# $%+# (&,(/&$?# C/(%# &"'&L%$# ()"
*,27+# &"7)6/)96+# &"# 0+'&L"-# *),$&(/6),61# )$# $%+# '$)L+# 2@# '+6+($&"L# )# (&,(/&$# (2"@&L/,)$&2"
)**,2*,&)$+#@2,#)#L&7+"#)**6&()$&2"?
6.5.11 Augmenting the Small-Signal Models to Account
for the Early Effect
!"$,M*#+:,$11$/&5,-(0/300$-,(),K$/&(2),X<P5,/*30$0,&"$,/2++$/&2#,/3##$)&,&2,-$7$)-,)2&,2)+:,2)
v)*,93&,*+02,2), v-*<,!"$,-$7$)-$)/$,2), v-*,/*),9$,'2-$+$-,9:,*00(;)();,*,1()(&$,23&73&,#$0(0%
&*)/$,&2,&"$,/2)&#2++$-,/3##$)&,023#/$,(),&"$,":9#(-%π,'2-$+5,*0,0"24),(),L(;<,X<8N<,!"$,23&73&
#$0(0&*)/$,(%,4*0,-$1()$-,(),MS<,TX<?DV`,(&0,.*+3$,(0,;(.$),9:, ( % d + / ⁄ .′- - ,4"$#$,+/ ,(0,&"$,M*#+:
.2+&*;$,*)-, .′- ,(0,&"$,-/,9(*0,/3##$)&,4(&"23&,&*G();,&"$,M*#+:,$11$/&,()&2,*//23)&<,W$,4(++,)2#%
'*++:,-#27,&"$,7#('$,*)-,H30&,30$, ( % d + / ⁄ .- <,Q2&$,&"*&,(),&"$,'2-$+0,21,L(;<,X<8N,4$,"*.$
#$)*'$-,v#4,*0,vπ 5,(),2#-$#,&2,/2)12#',4(&",&"$,+(&$#*&3#$<
6.5 Small-Signal Operation and Models
ib
B
C
$
v+
gm v+
r+
B
ro
C
r+
( ib
ro
%
E
E
(a)
(b)
Figure 6.47 =%+#%19,&05π#'3)665'&L")6#320+6-#&"#&$'#$.2#7+,'&2"'-#.&$%#$%+#,+'&'$)"(+#(%#&"(6/0+0?#
!"$,S3$0&(2),*#(0$0,*0,&2,&"$,$11$/&,21,(%,2),&"$,27$#*&(2),21,&"$,&#*)0(0&2#,*0,*),*'7+(1($#<
=),*'7+(1($#,/(#/3(&0,(),4"(/",&"$,$'(&&$#,(0,;#23)-$-,T*0,(),&"$,/(#/3(&,21,L(;<,X<8PV5,(%,0('7+:
*77$*#0,(),7*#*++$+,4(&",>-<,!"305,(1,4$,()/+3-$,(%,(),&"$,$S3(.*+$)&,/(#/3(&,21,L(;<,X<8PT-V5,12#
$A*'7+$5,&"$,23&73&,.2+&*;$,v%,9$/2'$0
v % = ] C I v #4 ( > - qq ( % )
!"30,&"$,;*(),4(++,9$,02'$4"*&,#$-3/$-<,J9.(230+:,(1,(%,!,>- 5,&"$,#$-3/&(2),(),;*(),4(++,9$
)$;+(;(9+$5,*)-,2)$,/*),(;)2#$,&"$,$11$/&,21,(%<,=),;$)$#*+5,(),03/",*,/2)1(;3#*&(2),(%,/*),9$
)$;+$/&$-,(1,(&,(0,;#$*&$#,&"*),?O>-<
W"$),&"$,$'(&&$#,21,&"$,&#*)0(0&2#,(0,)2&,;#23)-$-5,()/+3-();,(%,(),&"$,'2-$+,/*),/2'7+(%
/*&$,&"$,*)*+:0(0<,W$,4(++,'*G$,/2''$)&0,#$;*#-();,(%,*)-,(&0,()/+30(2),2#,$A/+30(2),2),1#$%
S3$)&, 2//*0(2)0, &"#23;"23&, &"$, 922G<, W$, 0"23+-, *+02, )2&$, &"*&, (), ()&$;#*&$-%/(#/3(&, BC!
*'7+(1($#05,(%,7+*:0,*,-2'()*)&,#2+$,*)-,E'!!%?,9$,)$;+$/&$-5,*0,4(++,9$,0$$),(),6"*7&$#,N<,J1
/23#0$5,(1,2)$,(0,7$#12#'();,*),*//3#*&$,*)*+:0(0,21,*),*+'20&%1()*+,-$0(;),30();,/2'73&$#%
*(-$-,*)*+:0(05,&"$),(%,/*),9$,$*0(+:,()/+3-$-<,
L()*++:5,(&,0"23+-,9$,)2&$-,&"*&,$(&"$#,21,&"$,!,'2-$+0,(),L(;<,X<8?,/*),9$,*3;'$)&$-,&2
*//23)&,12#,&"$,M*#+:,$11$/&,9:,()/+3-();,(%,9$&4$$),/2++$/&2#,*)-,$'(&&$#<
EXERCISE
6.41 =%+#$,)"'&'$2,#&"#D&L?#EW?eK#&'#9&)'+0#.&$%#)#(2"'$)"$#(/,,+"$#'2/,(+#.8=#K#3I#)"0#%)'#β#=#KPP
)"0#+/#=#KPP#]?#
:)>#D&"0#$%+#0(#726$)L+'#)$#$%+#9)'+-#+3&$$+,-#)"0#(266+($2,?#
:9>#D&"0#CI-#(π -#)"0#(%?#
:(>#!@#$+,3&")6#r#&'#(2""+($+0#$2#L,2/"0-#m#$2#)#'&L")6#'2/,(+#v'&L#.&$%#)#'2/,(+#,+'&'$)"(+#>'&L#=#M UΩ)"0#s#$2#)"#f5UΩ#62)0#,+'&'$)"(+-#/'+#$%+#%19,&05π#320+6#2@#D&L?#W?ed:)>-#$2#0,).#$%+#'3)665'&L")6
+V/&7)6+"$#(&,(/&$#2@#$%+#)3*6&@&+,?#:b2$+#$%)$#$%+#(/,,+"$#'2/,(+#.#'%2/60#9+#,+*6)(+0#.&$%#)"#2*+"
(&,(/&$?>#F)6(/6)$+#$%+#27+,)66#726$)L+#L)&"#vH Zv'&L?#!@#(%#&'#"+L6+($+0-#.%)$#&'#$%+#+,,2,#&"#+'$&3)$&"L
$%+#L)&"#3)L"&$/0+_#:7%?4O#I"#&"@&"&$+#()*)(&$)"(+#&'#/'+0#$2#&"0&()$+#$%)$#$%+#()*)(&$)"(+#&'#'/@@&5
(&+"$61#6),L+#$%)$#&$#)($'#)'#)#'%2,$#(&,(/&$#)$#)66#'&L")6#@,+V/+"(&+'#2@#&"$+,+'$?#\2.+7+,-#$%+#()*)(&$2,
'$&66#962(U'#0(?>
421
422 Chapter 6 Bipolar Junction Transistors (BJTs)
-
-
Figure E6.41
Ans. :)>#−P?K#]-#−P?f#]-#+M#]H#:9>#eP#3IZ]-#M?G#UΩ-#KPP#UΩH#:(>#−dd#]Z]-#+N?ao#
6.5.12 Summary
=%+#)")61'&'#)"0#0+'&L"#2@#;<=#)3*6&@&+,#(&,(/&$'#&'#L,+)$61#@)(&6&$)$+0#&@#$%+#,+6)$&2"'%&*'
9+$.++"# $%+# 7),&2/'# '3)665'&L")6# 320+6# *),)3+$+,'# ),+# )$# 12/,# @&"L+,$&*'?# D2,# +)'1# ,+@+,5
+"(+-#$%+'+#),+#'/33),&h+0#&"#=)96+#W?e?#B7+,#$&3+-#%2.+7+,-#.+#+T*+($#$%+#,+)0+,#$2#9+
)96+#$2#,+()66#$%+'+#@,23#3+32,1?#D&")661-#"2$+#$%)$#$%+#3)$+,&)6#&"#=)96+#W?e#)**6&+'#+V/)661
.+66#$2#92$%#$%+#!"!#)"0#$%+#"!"#$,)"'&'$2,'#.&$%#"2#(%)"L+#&"#*26),&$&+'?
6.6 Basic BJT Amplifier Configurations
!$#&'#/'+@/6#)$#$%&'#*2&"$#$2#$)U+#'$2(U#2@#.%+,+#.+#),+#)"0#.%+,+#.+#),+#L2&"L#&"#2/,
'$/01#2@#;<=#)3*6&@&+,'?#!"#C+($&2"#W?e#.+#+T)3&"+0#$%+#+''+"(+#2@#$%+#/'+#2@#$%+#;<=
)'# )"# )3*6&@&+,?# =%+,+# .+# @2/"0# $%)$# )632'$56&"+),# )3*6&@&()$&2"# ()"# 9+# 29$)&"+0# 91
9&)'&"L#$%+#;<=#)$#)"#)**,2*,&)$+#*2&"$#&"#&$'#)($&7+#,+L&2"#2@#2*+,)$&2"#)"0#91#U++*&"L
$%+# '&L")6# v #4 # :2,# v π ># '3)66?# =%+"# &"# C+($&2"# W?G# .+# $22U# )# (62'+,# 622U# )$# $%+# '3)665
'&L")6# 2*+,)$&2"# 2@# $%+# ;<=# # )"0# 0+7+62*+0# (&,(/&$# 320+6'# $2# ,+*,+'+"$# $%+# $,)"'&'$2,$%/'# @)(&6&$)$&"L# $%+# 0+$+,3&")$&2"# 2@# )3*6&@&+,# *),)3+$+,'# '/(%# )'# 726$)L+# L)&"# )"0
&"*/$#)"0#2/$*/$#,+'&'$)"(+'?#
Y+#),+#"2.#,+)01#$2#(2"'&0+,#$%+#7),&2/'#*2''&96+#(2"@&L/,)$&2"'#2@#;<=#)3*6&@&+,')"0#.+#.&66#02#$%)$#&"#$%+#*,+'+"$#'+($&2"?#=2#@2(/'#2/,#)$$+"$&2"#2"#$%+#')6&+"$#@+)$/,+'
2@#$%+#7),&2/'#(2"@&L/,)$&2"'-#.+#'%)66#*,+'+"$#$%+3#&"#$%+&,#32'$#'&3*6+-#2,#R'$,&**+05
02."-S#7+,'&2"?#=%/'-#.+#.&66#"2$#'%2.#$%+#0(#9&)'&"L#),,)"L+3+"$'-#6+)7&"L#$%+#'$/01
2@# 9&)'# 0+'&L"# $2# $%+# "+T$# '+($&2"?# D&")661-# &"# C+($&2"# W?f# .+# .&66# 9,&"L# +7+,1$%&"L
$2L+$%+,#)"0#*,+'+"$#*,)($&()6#(&,(/&$'#@2,#0&'(,+$+5(&,(/&$#;<=#)3*6&@&+,'-#")3+61-#$%2'+
)3*6&@&+,# (&,(/&$'# $%)$# ()"# 9+# (2"'$,/($+0# /'&"L# 0&'(,+$+# (23*2"+"$'?# =%+# '$/01# 2@
&"$+L,)$+05(&,(/&$#)3*6&@&+,'#9+L&"'#&"#F%)*$+,#d?
6.6 Basic BJT Amplifier Configurations
Table 6.4 Small-Signal Models of the BJT
\19,&05π##A20+6
# ( β $ # )#]+,'&2"
:CIvπ>#]+,'&2"
ib
B
C
B
C
$
v!
r!
gmv!
%
r!
ro
E
E
:α $>#]+,'&2"
:CIvπ>#]+,'&2"
C
C
#i
g mv !
B
ro
$
v!
ro
"ib
B
ro
re
re
%
i
E
E
A20+6#O),)3+$+,'#&"#=+,3'#2@#XF#;&)'#F/,,+"$'
.5
C I = 55555
+,
+,
+
( 4 = 55555,5 = α 555555
..*
+,
+
( π = 55555,5 = β 555555
..)
!"#=+,3'#2@#CI
α
( 4 = 555555
CI
β
( π = 555555
CI
!"#=+,3'#2@#(4
α
C I = 5555
(4
K
K
C I + 5555 = 5555
(π
(4
( π = ( β + K )( 4
J+6)$&2"'%&*'#9+$.++"#α#)"0#β
α
β = 555555555555
K]α
β
α = 555555555555
β+K
K
β + K = 555555555555
K]α
+/
5
( % = 55555555
.-
423
424 Chapter 6 Bipolar Junction Transistors (BJTs)
6.6.1 The Three Basic Configurations
=%+,+#),+#$%,++#9)'&(#(2"@&L/,)$&2"'#@2,#(2""+($&"L#$%+#;<=#)'#)"#)3*6&@&+,?#E)(%#2@#$%+'+#(2"5
@&L/,)$&2"'#&'#29$)&"+0#91#(2""+($&"L#2"+#2@#$%+#$%,++#;<=#$+,3&")6'#$2#L,2/"0-#$%/'#(,+)$&"L#)
$.25*2,$#"+$.2,U#.&$%#$%+#L,2/"0+0#$+,3&")6#9+&"L#E%II%!#$2#$%+#&"*/$#)"0#2/$*/$#*2,$'?#D&L5
/,+#W?ef#'%2.'#$%+#,+'/6$&"L#$%,++#(2"@&L/,)$&2"'#.&$%#$%+#9&)'&"L#),,)"L+3+"$'#23&$$+0?
!"#$%+#(&,(/&$#2@#D&L?#W?ef:)>#$%+#+3&$$+,#$+,3&")6#&'#(2""+($+0#$2#L,2/"0-#$%+#&"*/$#726$)L+
'&L")6# v $ #&'#)**6&+0#9+$.++"#$%+#9)'+#)"0#L,2/"0-#)"0#$%+#2/$*/$#726$)L+#'&L")6# v % #&'#$)U+"
9+$.++"#$%+#(266+($2,#)"0#L,2/"0-#)(,2''#$%+#,+'&'$)"(+# > - ?#=%&'#(2"@&L/,)$&2"-#$%+,+@2,+-#&'
()66+0#$%+#L,2/"0+05+3&$$+,#2,#)*""*05!"#$$!%-;A8<-)3*6&@&+,?#!$#&'#91#@),#$%+#32'$#*2*/5
6),#;<=#)3*6&@&+,#(2"@&L/,)$&2"#)"0#&'#$%+#2"+#.+#%)7+#/$&6&h+0#&"#C+($&2"'#W?e#)"0#W?G#$2
'$/01#;<=#)3*6&@&+,#2*+,)$&2"?
$
$
RC
RC
vi
vo
vo
$
%
vi
$
%
%
%
(a) Common-Emitter (CE)
vi
(b) Common-Base (CB)
$
$
%
RL
vo
%
(c) Common-Collector (CC)
or Emitter Follower
Figure 6.48 =%+#$%,++#9)'&(#(2"@&L/,)$&2"'#2@#;<=#)3*6&@&+,?#=%+#9&)'&"L#),,)"L+3+"$'#),+#"2$#'%2."?
6.6 Basic BJT Amplifier Configurations
!"$, )*""*05&'(!- ;AB<, 2#, ;#23)-$-%9*0$, *'7+(1($#, (0, 0"24), (), L(;<, X<8ET9V<, =&, (0
29&*()$-,9:,/2))$/&();,&"$,9*0$,&2,;#23)-5,*77+:();,&"$,()73&, v $ ,9$&4$$),&"$,$'(&&$#,*);#23)-5,*)-,&*G();,&"$,23&73&, v %,*/#200,&"$,#$0(0&*)/$, > - ,/2))$/&$-,9$&4$$),&"$,/2++$/&2#
*)-,;#23)-<,W$,"*.$,$)/23)&$#$-,*,6B,*'7+(1($#,(),MA*'7+$,X<?8<
L()*++:5,L(;<,X<8ET/V,0"240,&"$,)*""*05)*++!)$*%-;AA<,2#,;#23)-$-%/2++$/&2#,*'7+(1($#<
=&,(0,29&*()$-,9:,/2))$/&();,&"$,/2++$/&2#,&$#'()*+,&2,;#23)-5,*77+:();,&"$,()73&,.2+&*;$,0(;%
)*+, v $ ,9$&4$$),9*0$,*)-,;#23)-5,*)-,&*G();,&"$,23&73&,.2+&*;$,0(;)*+, v %,9$&4$$),&"$,$'(&&$#
*)-,;#23)-5,*/#200,*,+2*-,#$0(0&*)/$, > X <,L2#,#$*02)0,&"*&,4(++,9$/2'$,*77*#$)&,0"2#&+:5,&"(0
/2)1(;3#*&(2),(0,'2#$,/2''2)+:,/*++$-,&"$,!"#$$!%-3*++*:!%<,
J3#,0&3-:,21,&"$,&"#$$,9*0(/,BC!,*'7+(1($#,/2)1(;3#*&(2)0,4(++,#$.$*+,&"*&,$*/","*0,-(0%
&()/&+:,-(11$#$)&,*&&#(93&$0,*)-,"$)/$,*#$*0,21,*77+(/*&(2)<?8
6.6.2 Characterizing Amplifiers15
;+@2,+#.+#9+L&"#2/,#'$/01#2@#$%+#0&@@+,+"$#;<=#)3*6&@&+,#(2"@&L/,)$&2"'-#.+#(2"'&0+,#%2.#$2
(%),)($+,&h+#$%+#*+,@2,3)"(+#2@#)"#)3*6&@&+,#)'#)#(&,(/&$#9/&60&"L#962(U?#I"#&"$,20/($&2"#$2
$%&'#$2*&(#.)'#*,+'+"$+0#&"#C+($&2"#K?G?
D&L/,+#W?ea:)>#'%2.'#)"#)3*6&@&+,#@+0#.&$%#)#'&L")6#'2/,(+#%)7&"L#)"#2*+"5(&,(/&$#726$)L+
v '&L #)"0#)"#&"$+,")6#,+'&'$)"(+# > '&L ? #=%+'+#()"#9+#$%+#*),)3+$+,'#2@#)"#)($/)6#'&L")6#'2/,(+
2,-#&"#)#()'()0+#)3*6&@&+,-#$%+#=%p7+"&"#+V/&7)6+"$#2@#$%+#2/$*/$#(&,(/&$#2@#)"2$%+,#'$)L+#*,+5
(+0&"L#$%+#2"+#/"0+,#'$/01?#=%+#)3*6&@&+,#&'#'%2."#.&$%#)#62)0#,+'&'$)"(+# > X #(2""+($+0#$2
$%+#2/$*/$#$+,3&")6?#\+,+-# > X #()"#9+#)"#)($/)6#62)0#,+'&'$)"(+#2,#$%+#&"*/$#,+'&'$)"(+#2@#)
'/((++0&"L#)3*6&@&+,#'$)L+#&"#)#()'()0+#)3*6&@&+,?
L(;3#$,X<8DT9V,0"240,&"$,*'7+(1($#,/(#/3(&,4(&",&"$,*'7+(1($#,9+2/G,#$7+*/$-,9:,(&0,$S3(.*+$)&%
/(#/3(&,'2-$+<,!"$,()73&,#$0(0&*)/$, > &" ,#$7#$0$)&0,&"$,+2*-();,$11$/&,21,&"$,*'7+(1($#,()73&,2)
&"$,0(;)*+,023#/$<,=&,(0,123)-,1#2'
v
> &" ≡ 5555$
$$
*)-,&2;$&"$#,4(&",&"$,#$0(0&*)/$, > '&L ,12#'0,*,.2+&*;$,-(.(-$#,&"*&,#$-3/$0, v '&L ,&2,&"$,.*+3$, v $
&"*&,*77$*#0,*&,&"$,()73&,21,&"$,*'7+(1($#,7#27$#5
> &"
> &" e > '&L
v $ d 5555555555555555555555 v '&L
TX<X^V
=&,(0,('72#&*)&,&2,)2&$,&"*&,(),;$)$#*+, > &" ,'*:,-$7$)-,2),&"$,+2*-,#$0(0&*)/$, > X ? ,J)$,21,&"$,&"#$$
/2)1(;3#*&(2)0,4$,*#$,0&3-:();,(),&"(0,0$/&(2)5,&"$,$'(&&$#,12++24$#5,$A"(9(&0,03/",-$7$)-$)/$<
!"$,0$/2)-,7*#*'$&$#,12#,/"*#*/&$#(>();,*'7+(1($#,7$#12#'*)/$,(0,&"$,*4!05)#%)/#$-1*+$5
'6!-6'#0- / v % - --$1()$-,*0
v
/ v% ≡ 5555%
v$
>X d ∞
!"$,&"(#-,*)-,1()*+,7*#*'$&$#,(0,&"$,23&73&,#$0(0&*)/$, > % ? ,J90$#.$,1#2',L(;<,X<8DT9V,&"*&, > %
(0, &"$, #$0(0&*)/$, 0$$), +22G();, 9*/G, ()&2, &"$, *'7+(1($#, 23&73&, &$#'()*+, 4(&", v $ , 0$&, &2, >$#2<
!"30, > %,/*),9$,-$&$#'()$-5,*&,+$*0&,/2)/$7&3*++:5,*0,()-(/*&$-,(),L(;<,X<8DT/V,4(&"
v
> % d 55553
$3
Ke
=%+#FE-#F;-#)"0#FF#(2"@&L/,)$&2"'#),+#$%+#;<=#(2/"$+,*),$'#2@#$%+#ABCDE=#FC-#Fn-#)"0#FX#(2"5
@&L/,)$&2"'-#,+'*+($&7+61?
KG
=%&'#'+($&2"#()"#9+#'U&**+0#&@#$%+#,+)0+,#%)'#)6,+)01#'$/0&+0#C+($&2"#G?W?MH#&$#*,+'+"$'#'/9'$)"$&)661#$%+
')3+#3)$+,&)6?
425
426 Chapter 6 Bipolar Junction Transistors (BJTs)
ii
Rsig
vsig $
%
io
$
$
vi
RL vo
%
%
(a)
Rsig
Ro
io
$
vsig $
%
vi
$
Rin
RL
$
A v %
vo
vo i
%
%
(b)
$
$
vi " 0
vx
%
%
ix
Ro
(c)
Figure 6.49 ;'<#I"#)3*6&@&+,#@+0#.&$%#)#'&L")6#'2/,(+#:v'&L -# >'&L>#)"0#*,27&0&"L#&$'#2/$*/$#)(,2''#)#62)0
,+'&'$)"(+#>X?;&<#=%+#(&,(/&$#&"#;'<#.&$%#$%+#)3*6&@&+,#,+*,+'+"$+0#91#&$'#+V/&7)6+"$#(&,(/&$#320+6?-;)<#X+$+,5
3&"&"L#$%+#2/$*/$#,+'&'$)"(+#>%#2@#$%+#)3*6&@&+,?
B$/*30$, > % ,(0,-$&$#'()$-,4(&", v $ d P K ,(&0,.*+3$,-2$0,)2&,-$7$)-,2), > '&L ?
!"$,/2)&#2++$-,023#/$, / v% v $ ,*)-,&"$,23&73&,#$0(0&*)/$, > % ,#$7#$0$)&,&"$,!"p.$)(),$S3(.*%
+$)&,21,&"$,*'7+(1($#,23&73&,/(#/3(&5,*)-,&"$,23&73&,.2+&*;$, v % ,/*),9$,123)-,1#2'
>X
>X e >%
v % d 555555555555555555 / v% v $
TX<XXV
!"30,&"$,.2+&*;$,;*(),21,&"$,*'7+(1($#,7#27$#5, / v - ,/*),9$,123)-,*0
v
>X
5
/ v ≡ 5555% d / v% 55555555555555555
v$
>X e >%
TX<XNV
*)-,&"$,2.$#*++,.2+&*;$,;*(), Q v 5,
v
Q v ≡ 555555%5
v '&L
/*),9$,-$&$#'()$-,9:,/2'9()();,MS0<,TX<X^V,*)-,TX<XXV5
> &"
5 /
Q v d 555555555555555555555
> &" e > '&L v
TX<XEV
6.6 Basic BJT Amplifier Configurations
6.6.3 The Common-Emitter (CE) Amplifier
B@#$%+#$%,++#9)'&(#;<=#)3*6&@&+,#(2"@&L/,)$&2"'-#$%+#(2332"#+3&$$+,#&'#$%+#32'$#.&0+61#/'+0?
=1*&()661-#&"#)"#)3*6&@&+,#@2,3+0#91#()'()0&"L#)#"/39+,#2@#'$)L+'-#$%+#9/6U#2@#$%+#726$)L+#L)&"
&'#29$)&"+0#91#/'&"L#2"+#2,#32,+#(2332"5+3&$$+,#'$)L+'#&"#$%+#()'()0+?
D&L/,+#W?GP:)>#'%2.'#)#(2332"5+3&$$+,#)3*6&@&+,#:.&$%#$%+#9&)'&"L#),,)"L+3+"$#23&$$+0>
@+0#.&$%#)#'&L")6#'2/,(+# v '&L #%)7&"L#)#'2/,(+#,+'&'$)"(+# > '&L ? #Y+#.&'%#$2#)")61h+#$%+#(&,(/&$
$2#0+$+,3&"+# > &" - # / v% - # > % - #)"0#Q v ? #D2,#$%&'#*/,*2'+#.+#'%)66#)''/3+#$%)$# > - #&'#*),$#2@#$%+
)3*6&@&+,H#$%/'#&@#)#62)0#,+'&'$)"(+# > X #&'#(2""+($+0#$2#$%+#)3*6&@&+,#2/$*/$-#&$#)**+),'#&"#*),5
)66+6#.&$%# > - ?
Characteristic Parameters of the CE Amplifier J+*6)(&"L# $%+# ;<=# .&$%# &$'# %19,&05 π
320+6-#.+#29$)&"#$%+#FE#)3*6&@&+,#+V/&7)6+"$#(&,(/&$#'%2."#&"#D&L?#W?GP:9>?#Y+#'%)66#/'+#$%&'#+V/&75
)6+"$#(&,(/&$#$2#0+$+,3&"+#$%+#(%),)($+,&'$&(#*),)3+$+,'#2@#$%+#)3*6&@&+,# > &" -# / v% -#)"0# > % #)'#@2662.'?
!"$,()73&,#$0(0&*)/$, > &" ,(0,123)-,9:,()07$/&(2),&2,9$
TX<XDV
> &" d ( π
J90$#.$,&"*&, > &" ,-2$0,)2&,-$7$)-,2),&"$,23&73&,0(-$,21,&"$,*'7+(1($#`,"$)/$5,&"(0,*'7+(1($#,(0
0*(-,&2,9$,/0#+'$!%'+<
!"$,23&73&,.2+&*;$, v % ,/*),9$,123)-,9:,'3+&(7+:();,&"$,/3##$)&, ( C I v π ) ,9:,&"$,&2&*+,#$0(0%
&*)/$,9$&4$$),&"$,23&73&,)2-$,*)-,;#23)-5,
v % d ] ( C I v π ) ( > - || ( % )
$
Rsig
RC
$
vsig $
%
vo
vi
%
Rin
%
Ro
(a)
Rsig
$
vsig
$
%
v+ " vi
$
gmvp
r+
ro
RC
vo
%
%
Rin " r+
||
Ro " RC ro
(b)
Figure 6.50 ;'<#F2332"5+3&$$+,#)3*6&@&+,#@+0#.&$%#)#'&L")6#v'&L#@,23#)#L+"+,)$2,#.&$%#)#,+'&'$)"(+#>'&L?
;&< =%+#(2332"5+3&$$+,#)3*6&@&+,#(&,(/&$#.&$%#$%+#;<=#,+6)(+0#.&$%#&$'#%19,&05π#320+6?
427
428 Chapter 6 Bipolar Junction Transistors (BJTs)
K()/$, vπ d v$ 5,&"$,27$)%/(#/3(&,.2+&*;$,;*(), / v% ≡ v % ⁄ v $ ,/*),9$,29&*()$-,*0
/ v % d ] C I ( > - || ( % )
TX<NOV
J90$#.$,&"*&,&"$,&#*)0(0&2#,23&73&,#$0(0&*)/$, ( % ,#$-3/$0,&"$,'*;)(&3-$,21,&"$,.2+&*;$,;*()<,=)
-(0/#$&$%/(#/3(&,*'7+(1($#05,4"(/",*#$,21,()&$#$0&,&2,30,(),&"(0,/"*7&$#5, > - ,(0,303*++:,'3/"
+24$#,&"*), ( % ,*)-,&"$,$11$/&,21, ( % ,2),#$-3/();, / v % ,(0,0+(;"&,T+$00,&"*),?Oj,2#,02V<,!"30,()
'*):,/*0$0,4$,/*),)$;+$/&, ( % ,*)-,$A7#$00, / v% ,0('7+:,*0,
/ v% ! ( ] C I > - )
TX<N?V
!"$, #$*-$#, (0, /*3&(2)$-5, "24$.$#5, &"*&, )$;+$/&();, ( % , (0, *++24$-, 2)+:, (), -(0/#$&$%/(#/3(&
-$0(;)<,@0,4(++,9$,0$$),(),6"*7&$#,N5, ( % ,7+*:0,*,/$)&#*+,#2+$,(),=6,*'7+(1($#0<,
!"$,23&73&,#$0(0&*)/$, > % ,(0,&"$,#$0(0&*)/$,0$$),+22G();,9*/G,()&2,&"$,23&73&,&$#'()*+,4(&"
v $ ,0$&,&2,>$#2<,L#2',L(;<,X<^OT9V,4$,0$$,&"*&,4(&", v $ ,0$&,&2,>$#25, v π ,4(++,9$,>$#2,*)-, C I v π
4(++,9$,>$#25,#$03+&();,()
> % d > - || ( %
TX<NPV
R$#$, ( % ,"*0,&"$,9$)$1(/(*+,$11$/&,21,#$-3/();,&"$,.*+3$,21, > % ? ,=),-(0/#$&$,/(#/3(&05,"24$.$#5
&"(0,$11$/&,(0,0+(;"&,*)-,4$,/*),'*G$,&"$,*77#2A('*&(2)
>% ! >-
TX<N\V
!"(0,/2)/+3-$0,&"$,*)*+:0(0,21,&"$,*'7+(1($#,7#27$#<,Q245,4$,/*),'*G$,&"$,12++24();,290$#.*%
&(2)0Y
1. !"$, ()73&, #$0(0&*)/$, > &" d ( π d β ⁄ C I , (0, '2-$#*&$, &2, +24, (), .*+3$, T&:7(/*++:5, (), &"$
G(+2"',#*);$V<,J9.(230+:, > &" ,(0,-(#$/&+:,-$7$)-$)&,2), β ,*)-,(0,().$#0$+:,7#272#&(2)*+
&2,&"$,/2++$/&2#,9(*0,/3##$)&, . - <,!2,29&*(),*,"(;"$#,()73&,#$0(0&*)/$5,&"$,9(*0,/3##$)&,/*)
9$,+24$#$-5,93&,&"(0,*+02,+24$#0,&"$,;*()<,!"(0,(0,*,0(;)(1(/*)&,-$0(;),&#*-$%211<,=1,*,'3/"
"(;"$#,()73&,#$0(0&*)/$,(0,-$0(#$-5,&"$),*,'2-(1(/*&(2),21,&"$,6M,/2)1(;3#*&(2),T&2,9$
-(0/300$-,0"2#&+:V,2#,*),$'(&&$#%12++24$#,0&*;$,/*),9$,$'7+2:$-<
2. =%+#2/$*/$#,+'&'$)"(+# > % ! > - #&'#320+,)$+#$2#%&L%#&"#7)6/+#:$1*&()661-#&"#$%+#U&62%3
,)"L+>?#J+0/(&"L# > - #$2#62.+,# > % #&'#/'/)661#"2$#)#7&)96+#*,2*2'&$&2"#9+()/'+#$%+#726$5
)L+#L)&"#&'#)6'2#,+0/(+0?#I6$+,")$&7+61-#&@#)#7+,1#62.#2/$*/$#,+'&'$)"(+#:&"#$%+#2%3'#$2
$+"'#2@#2%3'#,)"L+>#&'#"++0+0-#)"#+3&$$+,5@2662.+,#'$)L+#&'#()66+0#@2,-#)'#.&66#9+#0&'5
(/''+0#&"#C+($&2"#W?W?W?
3. =%+#2*+"5(&,(/&$#726$)L+#L)&"# / v% #()"#9+#%&L%-#3)U&"L#$%+#FE#(2"@&L/,)$&2"#$%+#.2,U5
%2,'+#&"#;<=#)3*6&@&+,#0+'&L"?#^"@2,$/")$+61-#%2.+7+,-#$%+#9)"0.&0$%#2@#$%+#FE#)3*6&5
@&+,#&'#'+7+,+61#6&3&$+0?#Y+#'%)66#'$/01#)3*6&@&+,#@,+V/+"(1#,+'*2"'+#&"#F%)*$+,#a?
Overall Voltage Gain =2#0+$+,3&"+#$%+#27+,)66#726$)L+#L)&"# Q v #.+#@&,'$#0+$+,3&"+#$%+
@,)($&2"#2@# v '&L #$%)$#)**+),'#)$#$%+#)3*6&@&+,#&"*/$#*,2*+,-#$%)$#&'-# v $ H
(π
v $ d v '&L 5555555555555555555
( π e > '&L
TX<N8V
Z$7$)-();,2),&"$,#$+*&(.$,.*+3$0,21, ( π ,*)-, > '&L - ,0(;)(1(/*)&,+200,21,0(;)*+,0&#$);&",/*),2//3#
*&, &"$, ()73&5, 4"(/", (0, 29.(230+:, 3)-$0(#*9+$, *)-, /*), 9$, *.2(-$-, 9:, #*(0();, &"$, ()73&
6.6 Basic BJT Amplifier Configurations
#$0(0&*)/$5,*0,-(0/300$-,*92.$<,@&,&"(0,72()&5,4$,0"23+-,#$'()-,&"$,#$*-$#,&"*&,&2,'*()&*(),*
#$*02)*9+:,+()$*#,27$#*&(2)5, v $ ,0"23+-,)2&,$A/$$-,*923&,^,'_,&2,?O,'_5,4"(/",720$0,*,/2)%
0&#*()&,2),&"$,.*+3$,21, v '&L ?
=1,*,+2*-,#$0(0&*)/$, > X ,(0,/2))$/&$-,&2,&"$,23&73&,&$#'()*+,21,&"$,*'7+(1($#5,&"(0,#$0(0&*)/$
4(++,*77$*#,(),7*#*++$+,4(&", > - ? ,=&,12++240,&"*&,&"$,.2+&*;$,;*(), / v,/*),9$,29&*()$-,9:,0('%
7+:,#$7+*/();, > - ,(),&"$,$A7#$00(2),21, / v% ,(),MS<,TX<NOV,9:, > - || > X 5
/ v d ] C I ( > - || > X || ( % )
TX<N^V
W$,/*),)24,30$,&"(0,$A7#$00(2),12#, / v ,&2;$&"$#,4(&", ( v $ ⁄ v '&L ) ,1#2',MS<,TX<N8V,&2,29&*(),&"$
2.$#*++,.2+&*;$,;*(), Q v,*0,
v
(π
C ( > || > X || ( % )
Q v ≡ 555555%5 d ] 5555555555555555555
v '&L
( π e > '&L I -
TX<NXV
EXERCISE
6.41 ^'+# / v% #&"#EV?#:W?dP>#$2L+$%+,#.&$%# > % #&"#EV?#:W?dM>#$2#29$)&"# / v ? #C%2.#$%)$#$%+#,+'/6$#&'#&0+"$&()6
$2#$%)$#&"#EV?#:W?dG>?
Alternative Gain Expressions =%+,+#),+#)6$+,")$&7+#@2,3'#@2,# / v #)"0# Q v #$%)$#()"#1&+60
(2"'&0+,)96+#&"'&L%$#9+'&0+'#9+&"L#&"$/&$&7+#)"0#+)'1#$2#,+3+39+,?#=%+#+T*,+''&2"#@2,# / v #()"
9+#29$)&"+0#91#,+*6)(&"L# C I #&"#EV?#:W?dG>#.&$%# α ⁄ ( 4 H
( > - || > X || ( % )
5
/ v d ] α 55555555555555555555555555555555
(4
TX<NNV
B9'+,7&"L#$%)$# ( > - || > X || ( % ) #&'#$%+#$2$)6#,+'&'$)"(+#&"#$%+#(266+($2,#)"0# ( 4 #&'#$%+#$2$)6#,+'&'5
$)"(+#&"#$%+#+3&$$+,-#$%&'#+T*,+''&2"#'&3*61#'$)$+'#$%)$#$%+#726$)L+#L)&"#@,23#9)'+#$2#(266+($2,
&'#L&7+"#91#
=2$)6#,+'&'$)"(+#&"#(266+($2,
/ v d ] α 555555555555555555555555555555555555555555555555555555555555555555
=2$)6#,+'&'$)"(+#&"#+3&$$+,
TX<NEV
!"$,#$*02),12#,&"$,1*/&2#, α ,(0,&"*&,&"$,/2++$/&2#,/3##$)&,(0, α ,&('$0,&"$,$'(&&$#,/3##$)&<,J1
/23#0$, α ! K,*)-,/*),303*++:,9$,)$;+$/&$-5,*)-,&"$,$A7#$00(2),(),MS<,TX<NEV,(0,0('7+:,0&*&$*0,*,#$0(0&*)/$,#*&(2<,!"(0,$A7#$00(2),(0,*,;$)$#*+,2)$,*)-,*77+($0,&2,*):,BC!,*'7+(1($#,/(#%
/3(&,12#,1()-();,&"$,.2+&*;$,;*(),1#2',9*0$,&2,/2++$/&2#<
@,/2##$072)-();,$A7#$00(2),12#, Q v ,/*),9$,29&*()$-,9:,#$7+*/();, ( C I ( π ) ,(),&"$,)3'$#*%
&2#,21,MS<,TX<NXV,4(&", β - ,
( > - || > X || ( % )
5
Q v d ] β 55555555555555555555555555555555
> '&L e ( π
TX<NDV
4"(/",/*),9$,$A7#$00$-,(),42#-0,*0
=2$)6#,+'&'$)"(+#&"#(266+($2,
Q v d ] β 555555555555555555555555555555555555555555555555555555555555555555
=2$)6#,+'&'$)"(+#&"#9)'+
TX<EOV
429
430 Chapter 6 Bipolar Junction Transistors (BJTs)
J90$#.$,&"*&,"$#$,&"$,'3+&(7+(/*&(.$,1*/&2#,(0, β - ,4"(/",(0,&"$,#*&(2,21, $ E ,&2, $ # H ,&"(0,'*G$0
0$)0$,9$/*30$,4$,*#$,30();,&"$,#*&(2,21,#$0(0&*)/$0,(),&"$,/2++$/&2#,*)-,&"$,9*0$<,!"$,#$*-$#
(0,3#;$-,&2,#$1+$/&,2),&"$0$,$A7#$00(2)0,4"(+$,#$1$##();,&2,L(;<,X<^O<
Performing the Analysis Directly on the Circuit I'#3+"$&2"+0#&"#C+($&2"#W?G-#.&$%
*,)($&(+#2"+#()"#0&'*+"'+#.&$%#$%+#43"&$E$?#/'+#2@#$%+#;<=#+V/&7)6+"$#(&,(/&$#)"0#*+,@2,3#$%+
)")61'&'#0&,+($61#2"#$%+#(&,(/&$#'(%+3)$&(?#;+()/'+#&"#$%&'#.)1#2"+#,+3)&"'#(62'+,#$2#$%+#)($/)6
(&,(/&$-#$%&'#0&,+($#)")61'&'#()"#1&+60#L,+)$+,#&"'&L%$#&"$2#(&,(/&$#2*+,)$&2"?#I6$%2/L%#)$#$%&'
'$)L+#&"#6+),"&"L#+6+($,2"&(#(&,(/&$'#&$#&'#*+,%)*'#)#6&$$6+#+),61#$2#@2662.#$%&'#0&,+($#)")61'&'
,2/$+-#.+#'%2.#&"#D&L?#W?GK#$%+#FE#)3*6&@&+,#(&,(/&$#*,+*),+0#@2,#0&,+($#)")61'&'?#B9'+,7+#$%)$
.+#%)7+#R*/66+0#2/$S#$%+#,+'&'$)"(+# ( % #@,23#$%+#$,)"'&'$2,-#$%/'#3)U&"L#$%+#$,)"'&'$2,#(266+($2,
(2"0/($# C I v π #.%&6+#'$&66#)((2/"$&"L#@2,#$%+#+@@+($#2@# ( % ?
Rsig
vsig
$
%
ib
gmv+
" bib
$
ro
$
v+ " vi
RC
vo
%
%
Rin " r+
||
Ro " RC ro
||
vo " % gmv+ (RC ro)
Figure 6.51 O+,@2,3&"L#$%+#)")61'&'#0&,+($61#2"#$%+#(&,(/&$#.&$%#$%+#;<=#320+6#/'+0#&3*6&(&$61?
Example 6.17
I#FE#)3*6&@&+,#/$&6&h+'#)#;<=#.&$%# β d KPP #)"0# +/ d KPP #]-#&'#9&)'+0#)$# . - d K #3I#)"0#%)'#)#(266+($2,
,+'&'$)"(+# > - d G #U Ω? #D&"0# > &" - # > % - #)"0# / v% ? #!@#$%+#)3*6&@&+,#&'#@+0#.&$%#)#'&L")6#'2/,(+#%)7&"L#)#,+'&'$)"(+
2@#G#U Ω- #)"0#)#62)0#,+'&'$)"(+# > X d G #U Ω #&'#(2""+($+0#$2#$%+#2/$*/$#$+,3&")6-#@&"0#$%+#,+'/6$&"L# / v #)"0#Q v ?
!@# vt π #&'#$2#9+#6&3&$+0#$2#G#3]- #.%)$#),+#$%+#(2,,+'*2"0&"L# vt '&L #)"0# vt % #.&$%#$%+#62)0#(2""+($+0_
Solution
I$# . - d K #3I.K#3I 5
5 d 555555555555555555
d eP #3IZ]
C I d 55555
P?PMG#]
+,
β
KPP
( π d 555555 d 5555555555555555555555 d M?G #U Ω
eP#3IZ]
CI
+
KPP#]
( % d 55555/5 d 555555555555555 d KPP ,G Ω
K#3I
.-
6.6 Basic BJT Amplifier Configurations
!"$,*'7+(1($#,/"*#*/&$#(0&(/,7*#*'$&$#0,/*),)24,9$,123)-,*0
> &" d ( π d M?G #U Ω
/ v% d ] C I ( > - || ( % )
d ] eP#3IZ]#### , ( G#UΩ || KPP#UΩ )
d ] KaP?G#]Z]
> % d > - || ( %
d G || KPP d e?dW#UΩ
W(&",*,+2*-,#$0(0&*)/$, > X d G#UΩ ,/2))$/&$-,*&,&"$,23&73&5,4$,/*),1()-, / v ,9:,$(&"$#,21,&"$,12++24();
&42,*77#2*/"$0Y
>X
5
/ v d / v% 55555555555555555
>X e >%
G
d ] KaP?G × 5555555555555555555 d ] ad?W #]Z]
G e e?dW
2,
/ v d ] C I ( > - || > X || ( % )
d ] eP ( G || G || KPP ) d ] ad?W #]Z]
!"$,2.$#*++,.2+&*;$,;*(), Q v ,/*),)24,9$,-$&$#'()$-,*0
> &"
5 /
Q v d 555555555555555555555
> &" e > '&L v
M?G
d 5555555555555555 × ] ad?W d ] NM?G ,_o_
M?G e G
!@#$%+#3)T&3/3#)3*6&$/0+#2@# v π #&'#$2#9+#G#3]-#$%+#(2,,+'*2"0&"L#7)6/+#2@# vt '&L #.&66#9+
> &" e > '&L
M?G e G
vt '&L d 5555555555555555555555 vt π d 5555555555555555 × G d KG ,'_
> &"
M?G
)"0#$%+#)3*6&$/0+#2@#$%+#'&L")6#)$#$%+#2/$*/$#.&66#9+
vt % d Q v vt '&L## d NM?G × P?PKG d P?ea ,_
EXERCISE
6.42. =%+#0+'&L"+,#2@#$%+#)3*6&@&+,#&"#ET)3*6+#W?Kd#0+(&0+'#$2#62.+,#$%+#9&)'#(/,,+"$#$2#%)6@#&$'#2,&L&")6
7)6/+#&"#2,0+,#$2#,)&'+#$%+#&"*/$#,+'&'$)"(+#)"0#%+"(+#&"(,+)'+#$%+#@,)($&2"#2@# v '&L #$%)$#)**+),'#)$#$%+
&"*/$#2@#$%+#)3*6&@&+,#*,2*+,?#!"#)"#)$$+3*$#$2#3)&"$)&"#$%+#726$)L+#L)&"-#$%+#0+'&L"+,#0+(&0+'#$2
02/96+#$%+#7)6/+#2@# > - ? #D2,#$%+#"+.#0+'&L"-#0+$+,3&"+# > &" - # / v% - # > % - # / v - #)"0# Q v ? #!@#$%+#*+)U
)3*6&$/0+#2@# v π #&'#$2#9+#6&3&$+0#$2#G#3]-#.%)$#),+#$%+#(2,,+'*2"0&"L#7)6/+'#2@# vt '&L #)"0# vt % #:.&$%
$%+#62)0#(2""+($+0>_
Ans. G#U ΩH # ] KaP?G #]Z]H#a?G#U ΩH # ] WG?W #]Z]H# ] NM?f #]Z]H#KP#3]H#P?NN#]
431
432 Chapter 6 Bipolar Junction Transistors (BJTs)
6.6.4 The Common-Emitter Amplifier with an Emitter Resistance
!"(6/0&"L#)#,+'&'$)"(+#&"#$%+#+3&$$+,#)'#'%2."#&"#D&L?#W?GM:)>#()"#6+)0#$2#'&L"&@&()"$#(%)"L+'
&"#$%+#)3*6&@&+,#(%),)($+,&'$&('?#=%/'-#'/(%#)#,+'&'$2,#()"#9+#)"#+@@+($&7+#0+'&L"#$226#@2,#$)&5
62,&"L#$%+#)3*6&@&+,#(%),)($+,&'$&('#$2#@&$#$%+#0+'&L"#,+V/&,+3+"$'?
@)*+:0(0,21,&"$,/(#/3(&,(),L(;<,X<^PT*V,/*),9$,7$#12#'$-,9:,#$7+*/();,&"$,BC!,4(&",2)$,21
(&0,0'*++%0(;)*+,'2-$+0<,@+&"23;",*):,2)$,21,&"$,'2-$+0,21,L(;0<,X<8O,*)-,X<8?,/*),9$,30$-5
&"$, '20&, /2).$)($)&, 12#, &"(0, *77+(/*&(2), (0, 2)$, 21, &"$, &42, !, '2-$+0<, !"(0, (0, 9$/*30$, &"$
#$0(0&*)/$, > 4 , (), &"$, $'(&&$#, 4(++, *77$*#, (), 0$#($0, 4(&", &"$, $'(&&$#, #$0(0&*)/$, ( 4 , 21, &"$, !
'2-$+,*)-,/*),&"30,9$,*--$-,&2,(&5,0('7+(1:();,&"$,*)*+:0(0,/2)0(-$#*9+:<,=),1*/&5,4"$)$.$#
&"$#$,(0,*,#$0(0&*)/$,(),&"$,$'(&&$#,+$*-5,&"$,!,'2-$+,0"23+-,7#2.$,'2#$,/2).$)($)&,&2,30$
&"*),&"$,":9#(-% π ,'2-$+<
U$7+*/();,&"$,BC!,4(&",&"$,!,'2-$+,21,L(;<,X<8?T9V,#$03+&0,(),&"$,*'7+(1($#,0'*++%0(;)*+5
$S3(.*+$)&%/(#/3(&,'2-$+,0"24),(),L(;<,X<^PT9V<,Q2&$,&"*&,4$,"*.$,)2&,()/+3-$-,&"$,BC!,23&%
73&, #$0(0&*)/$, ( % `, 9$/*30$, &"(0, 423+-, /2'7+(/*&$, &"$, *)*+:0(0, /2)0(-$#*9+:<, K()/$, 12#, &"$
-(0/#$&$,*'7+(1($#,*&,"*)-,(&,&3#)0,23&,&"*&,&"$,$11$/&,21, ( % ,2),/(#/3(&,7$#12#'*)/$,(0,0'*++5,4$
0"*++,)2&,()/+3-$,(&,(),&"$,*)*+:0(0,"$#$<,!"(0,(0,)2&,&"$,/*0$5,"24$.$#5,12#,&"$,=6,.$#0(2),21
&"(0,/(#/3(&5,*)-,4$,0"*++,()-$$-,&*G$, ( % ,()&2,*//23)&,(),&"$,*)*+:0(0,(),6"*7&$#,N<
Rsig
$
$
vsig
RC
vi
$
%
Re
vo
%
%
Rin
Ro
C
ic
$
,ie
Rsig
$
vsig
$
%
RC
ib
B
vi
%
ie
re
vo
%
Ro
E
Re
Rin
(b)
Figure 6.52 =%+# FE# )3*6&@&+,# .&$%# )"# +3&$$+,# ,+'&'$)"(+# >4 H# ;'<# F&,(/&$# .&$%2/$# 9&)'# 0+$)&6'H
;&< EV/&7)6+"$#(&,(/&$#.&$%#$%+#;<=#,+*6)+0#.&$%#&$'#=#320+6?
6.6 Basic BJT Amplifier Configurations
!2,-$&$#'()$,&"$,*'7+(1($#,()73&,#$0(0&*)/$, > &" - ,4$,)2&$,1#2',L(;<,X<^PT9V,&"*&,
v
> &" ≡ 5555$
$#
4"$#$
$4
5
$ # d ( K ] α )$ 4 d 55555555555
βeK
TX<E?V
*)v
$
$ 4 d 555555555555555
5
(4 e >4
TX<EPV
> &" d ( β e K ) ( ( 4 e > 4 )
TX<E\V
!"305
!"(0, (0, *, .$#:, ('72#&*)&, #$03+&<, =&, 0&*&$0, &"*&, ?D48 $!"U?8 (4B$B?'!E48 &%%P$!C8 $!?%8 ?D48 #'B48 $B
( β e K ) ,?$I4B8?D48?%?'&8(4B$B?'!E48$!8?D484I$??4(5,*)-,(0,G)24),*0,&"$,%!(#($'0)!5%!3+!)$#*0
%/+!<,!"$,1*/&2#, ( β e K ) ,*#(0$0,9$/*30$,&"$,9*0$,/3##$)&,(0, K ⁄ ( β e K ) ,&('$0,&"$,$'(&&$#,/3#%
#$)&<,!"$,$A7#$00(2),12#, > &" ,(),MS<,TX<E\V,0"240,/+$*#+:,&"*&,()/+3-();,*,#$0(0&*)/$, > 4 ,(),&"$
$'(&&$#,/*),0390&*)&(*++:,()/#$*0$, > &" <,=)-$$-5,&"$,.*+3$,21, > &" ,(0,()/#$*0$-,9:,&"$,#*&(2
> &" ( .&$%#> 4 #&"(6/0+0 )
( β e K ) ( (4 e >4 )
55555555555555555555555555555555555555555555555555555 d 55555555555555555555555555555555555555
5
> &" ( .&$%2/$#> 4 )
( β e K )( 4
>
d K e 555554 ! K e C I > 4
(4
,
TX<E8V
!"30,&"$,/(#/3(&,-$0(;)$#,/*),30$,&"$,.*+3$,21, > 4 ,&2,/2)&#2+,&"$,.*+3$,21, > &" ?
!2,-$&$#'()$,&"$,.2+&*;$,;*(), / v% - ,4$,0$$,1#2',L(;<,X<^PT9V,&"*&
v% d ]$E >d ]α $4 >-
K390&(&3&();,12#, $ 4 ,1#2',MS<,TX<EPV,;(.$0
>5
/ v% d ] α 555555555555555
(4 e >4
TX<E^V
4"(/",(0,*,0('7+$,*77+(/*&(2),21,&"$,;$)$#*+,$A7#$00(2),(),MS<,TX<NEV<,R$#$5,21,/23#0$5,&"$
&2&*+,#$0(0&*)/$,(),&"$,$'(&&$#,(0, ( 4 e > 4 ?
!"$,27$)%/(#/3(&,.2+&*;$,;*(),(),MS<,TX<E^V,/*),9$,$A7#$00$-,*+&$#)*&(.$+:,*0
>α
5
/ v% d ] 5555 5555555555555555555555
(4 K e >4 ⁄ (4
CI >CI >5 ! ] 55555555555555555555
/ v% d ] 5555555555555555555555
5
K e >4 ⁄ (4
K e CI >4
TX<EXV
!"305,()/+3-();, > 4 ,#$-3/$0,&"$,.2+&*;$,;*(),9:,&"$,1*/&2#,( K e C I > 4 ) 5,4"(/",(0,&"$,0*'$,1*/%
&2#,9:,4"(/", > &" ,(0,()/#$*0$-<,!"(0,72()&0,23&,*),()&$#$0&();,&#*-$%211,9$&4$$),;*(),*)-,()73&
#$0(0&*)/$5, *, &#*-$%211, &"*&, &"$, -$0(;)$#, /*), $A$#/(0$, &"#23;", &"$, /"2(/$, 21, *), *77#27#(*&$
.*+3$,12#, > 4 ?
!"$,23&73&,#$0(0&*)/$, > % ,/*),9$,123)-,1#2',&"$,/(#/3(&,(),L(;<,X<^PT9V,9:,()07$/&(2)Y
>% d >-
433
434 Chapter 6 Bipolar Junction Transistors (BJTs)
=1,*,+2*-,#$0(0&*)/$, > X ,(0,/2))$/&$-,*&,&"$,*'7+(1($#,23&73&5, / v ,/*),9$,123)-,*0,
>X
5
/ v d / v% 55555555555555555
>X e >%
>>X
5 555555555555555555
5
d ] α 555555555555555
(4 e >4 >X e >> - || > X
5
d ] α 55555555555555555
(4 e >4
TX<ENV
4"(/",/23+-,"*.$,9$$),4#(&&$),-(#$/&+:,30();,MS<,TX<NEV<,!"$,2.$#*++,.2+&*;$,;*(), Q v ,/*)
)24,9$,123)-Y
> &"
> - || > X
5 × ] α 55555555555555555
5
Q v d 555555555555555555555
> &" e > '&L
(4 e >4
K390&(&3&();,12#, > &" ,1#2',MS<,TX<E\V,*)-,#$7+*/();, α ,4(&", β ⁄ ( β e K ) ,#$03+&0,(),
> - || > X
5
Q v d ] β 55555555555555555555555555555555555555555555555555555
> '&L e ( β e K ) ( ( 4 e > 4 )
TX<EEV
4"(/",(0,*,-(#$/&,*77+(/*&(2),21,&"$,;$)$#*+,$A7#$00(2),7#$0$)&$-,(),MS<,TX<EOV<,W$,290$#.$
&"*&,&"$,2.$#*++,.2+&*;$,;*(), Q v ,(0,+24$#,&"*),&"$,.*+3$,4(&"23&, > 4 ,9$/*30$,21,&"$,*--(&(2)*+
&$#', ( β e K )> 4 ,(),&"$,-$)2'()*&2#<,!"$,;*()5,"24$.$#5,(0,+$00,0$)0(&(.$,&2,&"$,.*+3$,21, β - ,*
-$0(#*9+$,#$03+&<
@)2&"$#, ('72#&*)&, /2)0$S3$)/$, 21, ()/+3-();, &"$, #$0(0&*)/$, > 4 , (), &"$, $'(&&$#, (0, &"*&, (&
$)*9+$0,&"$,*'7+(1($#,&2,"*)-+$,+*#;$#,()73&,0(;)*+0,4(&"23&,()/3##();,)2)+()$*#,-(0&2#&(2)<
!"(0,(0,9$/*30$,2)+:,*,1#*/&(2),21,&"$,()73&,0(;)*+,*&,&"$,9*0$5, v $ - ,*77$*#0,9$&4$$),&"$,9*0$
*)-,&"$,$'(&&$#<,K7$/(1(/*++:5,1#2',&"$,/(#/3(&,(),L(;<,X<^PT9V5,4$,0$$,&"*&
(4
K 5
55555 d 555555555555555
5 ! 55555555555555555555
v$
(4 e >4
K e CI >4
vπ
TX<EDV
!"305,12#,&"$,0*'$, v π 5,&"$,0(;)*+,*&,&"$,()73&,&$#'()*+,21,&"$,*'7+(1($#5, v $ - ,/*),9$,;#$*&$#
&"*),12#,&"$,6M,*'7+(1($#,9:,&"$,1*/&2#, ( K e C I > 4 )?
=2#'/33),&h+-#&"(6/0&"L#)#,+'&'$)"(+# > 4 #&"#$%+#+3&$$+,#2@#$%+#FE#)3*6&@&+,#,+'/6$'#&"#$%+
@2662.&"L#(%),)($+,&'$&('8
1. !"$,()73&,#$0(0&*)/$, > &" ,(0,()/#$*0$-,9:,&"$,1*/&2#, ( K e C I > 4 )?
2. =%+#726$)L+#L)&"#@,23#9)'+#$2#(266+($2,-# / v - #&'#,+0/(+0#91#$%+#@)($2,# ( K e C I > 4 )?
3. D2,#$%+#')3+#"2"6&"+),#0&'$2,$&2"-#$%+#&"*/$#'&L")6# v $ #()"#9+#&"(,+)'+0#91#$%+#@)($2,
( K e C I > 4 )?
4. =%+#27+,)66#726$)L+#L)&"#&'#6+''#0+*+"0+"$#2"#$%+#7)6/+#2@#β ?
5. =%+#%&L%5@,+V/+"(1#,+'*2"'+#&'#'&L"&@&()"$61#&3*,27+0#:)'#.+#'%)66#'++#&"#F%)*$+,#a>?
W(&",&"$,$A/$7&(2),21,;*(),#$-3/&(2)5,&"$0$,/"*#*/&$#(0&(/0,#$7#$0$)&,7$#12#'*)/$,('7#2.$'$)&0<
=)-$$-5,&"$,#$-3/&(2),(),;*(),(0,&"$,7#(/$,7*(-,12#,29&*()();,&"$,2&"$#,7$#12#'*)/$,('7#2.$'$)&0<
=),'*):,/*0$0,&"(0,(0,*,;22-,9*#;*()`,(&,(0,&"$,3)-$#+:();,7"(+2027":,12#,&"$,30$,21,)$;*&(.$,1$$-%
9*/G<,!"*&,&"$,#$0(0&*)/$, > 4 ,()&#2-3/$0,)$;*&(.$,1$$-9*/G,(),&"$,*'7+(1($#,/(#/3(&,/*),9$,0$$),9:
#$1$#$)/$,&2,L(;<,X<^PT*VY,W"(+$,G$$7();, v $ ,/2)0&*)&5,*003'$,&"*&,12#,02'$,#$*02),&"$,/2++$/&2#
/3##$)&,()/#$*0$0`,&"$,$'(&&$#,/3##$)&,*+02,4(++,()/#$*0$5,#$03+&();,(),*),()/#$*0$-,.2+&*;$,-#27
*/#200, > 4 ? , !"30, &"$, $'(&&$#, .2+&*;$, #(0$05, *)-, &"$, 9*0$]$'(&&$#, .2+&*;$, -$/#$*0$0<, !"$, +*&&$#
$11$/&, /*30$0, &"$, /2++$/&2#, /3##$)&, &2, -$/#$*0$5, /23)&$#*/&();, &"$, ()(&(*++:, *003'$-, /"*);$5, *)
()-(/*&(2),21,&"$,7#$0$)/$,21,)$;*&(.$,1$$-9*/G<,=),6"*7&$#,?O5,4"$#$,4$,0"*++,0&3-:,)$;*&(.$
6.6 Basic BJT Amplifier Configurations
435
1$$-9*/G, 12#'*++:5, 4$, 4(++, 1()-, &"*&, &"$, 1*/&2#, ( K e C I > 4 )- , 4"(/", *77$*#0, #$7$*&$-+:5, (0, &"$
a*'23)&,21,)$;*&(.$%1$$-9*/Gb,()&#2-3/$-,9:, > 4 ? ,L()*++:5,4$,)2&$,&"*&,&"$,)$;*&(.$%1$$-9*/G
*/&(2),21, > 4 ,;(.$0,(&,&"$,)*'$,!"#$$!%-2!6!0!%'$#*0-%!(#($'0)!<
Example 6.18
D2,#$%+#FE#)3*6&@&+,#'*+(&@&+0#&"#ET)3*6+#W?Kd-#.%)$#7)6/+#2@# > 4 #&'#"++0+0#$2#,)&'+# > &" #$2#)#7)6/+
@2/,#$&3+'#$%)$#2@# > '&L_#Y&$%# > 4 #&"(6/0+0-#@&"0# / v%- # > % - # / v - #)"0# Q v ? #I6'2-#&@# vt π #&'#6&3&$+0#$2#G#3].%)$#),+#$%+#(2,,+'*2"0&"L#7)6/+'#2@# vt '&L #)"0# vt % _
Solution
!2,29&*(), > &" d e > '&L d e × G d MP#UΩ 5,&"$,#$S3(#$-, > 4 ,(0,123)-,1#2'
MP d ( β e K ) # ( ( 4 e > 4 )
W(&", β d KPP- ,
( 4 e > 4 ! MPP#Ω
!"305
# > 4 d MPP ] MG d KdG#Ω
>5
/ v% d ] α 555555555555555
(4 e >4
GPPP 5 d ] MG #]Z]
! ] 55555555555555555555
MG e KdG
> % d > - d G#UΩ #:/"(%)"L+0>
>X
G 5
5 d ] MG × 55555555555
/ v d / v% 55555555555555555
d ] KM?G#]Z]
>X e >%
GeG
> &"
MP
Q v d 555555555555555555555
5 # / d ] 555555555555555 × KM?G d ] KP #]Z]
MP e G
> &" e > '&L v
D2,# vt π d G #3]-
( e>
(4
4
4
vt $ d vtπ 5555555555555555
KdG
d G K e 555555555 d eP#3]
MG
> &" e > '&L
vt '&L## d vt $ 5555555555555555555555
> &"
G d GP#3]
d eP K e 55555
5
MP
vt % d vt '&L × Q v
d GP × KP d GPP#3]#`#P?G#]
=%/'-#.%&6+ Q v #%)'#0+(,+)'+0#$2#)92/$#)#$%&,0#2@#&$'#2,&L&")6#7)6/+-#$%+#)3*6&@&+,#&'#)96+#$2#*,20/(+
)'#6),L+#)"#2/$*/$#'&L")6#)'#9+@2,+#@2,#$%+#')3+#"2"6&"+),#0&'$2,$&2"?
436 Chapter 6 Bipolar Junction Transistors (BJTs)
EXERCISE
6.43 C%2.#$%)$#.&$%# > 4 #&"(6/0+0-#)"0# v π #6&3&$+0#$2#)#3)T&3/3#7)6/+# vt π - #$%+#3)T&3/3#)662.)96+#&"*/$
'&L")6-# vt '&L - #&'#L&7+"#91
> > '&L
vt '&L d vt π K e 555554 e 5555555
5
(4
(π
!@#$%+#$,)"'&'$2,#&'#9&)'+0#)$# . - d P?G #3I#)"0#%)'#)# β #2@#KPP-#.%)$#7)6/+#2@# > 4 #&'#"++0+0#$2#*+,3&$
)"#&"*/$#'&L")6# vt '&L #2@#KPP#3]#@,23#)#'2/,(+#.&$%#)#,+'&'$)"(+# > '&L d KP#UΩ #.%&6+#6&3&$&"L# vt π #$2
KP#3]_#Y%)$#&'# > &" #@2,#$%&'#)3*6&@&+,_#!@#$%+#$2$)6#,+'&'$)"(+#&"#$%+#(266+($2,#&'#KP#U Ω- #.%)$# Q v
7)6/+#,+'/6$'_
Ans. NGP# Ω H#eP?e#U Ω H# ] Ka?f #]Z]
6.6.5 The Common-Base (CB) Amplifier
L(;3#$,X<^\T*V,0"240,*,/2''2)%9*0$,*'7+(1($#,4(&",&"$,9(*0();,/(#/3(&,2'(&&$-<,!"$,*'7+(1($#
(0,1$-,4(&",*,0(;)*+,023#/$,/"*#*/&$#(>$-,9:, v '&L ,*)-, > '&L ? ,K()/$, > '&L ,*77$*#0,(),0$#($0,4(&",&"$
$'(&&$#5,(&,(0,'2#$,/2).$)($)&,&2,#$7#$0$)&,&"$,&#*)0(0&2#,4(&",&"$,!,'2-$+,&"*),4(&",&"$,":9#(-%π
'2-$+<,Z2();,&"(05,4$,29&*(),&"$,*'7+(1($#,$S3(.*+$)&,/(#/3(&,0"24),(),L(;<,X<^\T9V<,Q2&$,&"*&
4$,"*.$,)2&,()/+3-$-, ( % <,!"(0,(0,9$/*30$,()/+3-();, ( % ,423+-,/2'7+(/*&$,&"$,*)*+:0(0,/2)0(-$#%
*9+:5,12#,(&,423+-,*77$*#,9$&4$$),&"$,23&73&,*)-,()73&,21,&"$,*'7+(1($#<,L2#&3)*&$+:5,(&,&3#)0,23&
&"*&,&"$,$11$/&,21, ( % ,2),&"$,7$#12#'*)/$,21,*,-(0/#$&$,6B,*'7+(1($#,(0,.$#:,0'*++<,W$,4(++,/2)%
0(-$#,&"$,$11$/&,21, ( % ,4"$),4$,0&3-:,&"$,=6,12#',21,&"$,6B,*'7+(1($#,(),6"*7&$#,N<
$
,ie
RC
vo
$
RC
re
vo
Rsig
Rsig
vsig
$
$
%
vi
%
Ro
vsig
ie
%
Ro " RC
$
$
%
vi
%
%
Rin
Rin " re
(a)
(b)
Figure 6.53 :'>#F;#)3*6&@&+,#.&$%#9&)'#0+$)&6'#23&$$+0H#:&>#I3*6&@&+,#+V/&7)6+"$#(&,(/&$#.&$%#$%+#;<=#,+*,+'+"$+0#91#&$'#=
A20+6?
6.6 Basic BJT Amplifier Configurations
L#2',()07$/&(2),21,&"$,$S3(.*+$)&,/(#/3(&,(),L(;<,X<^\T9V5,4$,0$$,&"*&,&"$,()73&,#$0(0&*)/$,(0
> &"## d ( 4
TX<DOV
!"(0, 0"23+-, "*.$, 9$$), $A7$/&$-5, 0()/$, 4$, *#$, +22G();, ()&2, &"$, $'(&&$#, *)-, &"$, 9*0$, (0
;#23)-$-<,!:7(/*++:, ( 4 ,(0,*,1$4,2"'0,&2,*,1$4,&$)0,21,2"'0`,&"30,&"$,6B,*'7+(1($#,"*0,*,+24
()73&,#$0(0&*)/$<
!2,-$&$#'()$,&"$,.2+&*;$,;*()5,4$,4#(&$,*&,&"$,/2++$/&2#,)2-$
v% d ]α $4 >-
*)-,0390&(&3&$,12#,&"$,$'(&&$#,/3##$)&,1#2'
v
$ 4 d ] 5555$
(4
&2,29&*()
v
α
/ v% ≡ 5555% d 5555 > - d C I > v$
(4
TX<D?V
4"(/",$A/$7&,12#,(&0,720(&(.$,0(;),(0,(-$)&(/*+,&2,&"$,$A7#$00(2),12#, / v% ,12#,&"$,6M,*'7+(1($#<
=%+#2/$*/$#,+'&'$)"(+#2@#$%+#F;#(&,(/&$#()"#9+#@2/"0#91#&"'*+($&2"#2@#$%+#(&,(/&$#&"#D&L?
W?GN:9>#)'
>% d >-
TX<DPV
4"(/",(0,&"$,0*'$,*0,(),&"$,/*0$,21,&"$,6M,*'7+(1($#,T4(&", ( % ,)$;+$/&$-V<
@+&"23;",&"$,;*(),21,&"$,6B,*'7+(1($#,7#27$#,"*0,&"$,0*'$,'*;)(&3-$,*0,&"*&,21,&"$,6M
*'7+(1($#5,&"(0,(0,303*++:,)2&,&"$,/*0$,12#,&"$,2.$#*++,.2+&*;$,;*()<,!"$,+24,()73&,#$0(0&*)/$,21
&"$,6B,*'7+(1($#,/*),/*30$,&"$,()73&,0(;)*+,&2,9$,0$.$#$+:,*&&$)3*&$-5,07$/(1(/*++:5
v
> &"
(4
555555$5 d 555555555555555555555
5 d 555555555555555555
5
v '&L
> '&L e > &"
> '&L e ( 4
TX<D\V
1#2',4"(/",4$,0$$,&"*&,$A/$7&,12#,0(&3*&(2)0,(),4"(/", > '&L ,(0,2),&"$,2#-$#,21, ( 4 - ,&"$,0(;)*+
&#*)0'(00(2),1*/&2#, v $ ⁄ v '&L ,/*),9$,.$#:,0'*++<,=&,(0,30$13+,*&,&"(0,72()&,&2,'$)&(2),&"*&,2)$,21
&"$,*77+(/*&(2)0,21,&"$,6B,/(#/3(&,(0,&2,*'7+(1:,"(;"%1#$S3$)/:,0(;)*+0,&"*&,*77$*#,2),*,/2*A%
(*+,/*9+$<,!2,7#$.$)&,0(;)*+,#$1+$/&(2),2),&"$,/*9+$5,&"$,6B,*'7+(1($#,(0,#$S3(#$-,&2,"*.$,*)
()73&, #$0(0&*)/$, $S3*+, &2, &"$, /"*#*/&$#(0&(/, #$0(0&*)/$, 21, &"$, /*9+$5, 4"(/", (0, 303*++:, (), &"$
#*);$,21,^O, Ω ,&2,N^, Ω?
=1,*,+2*-,#$0(0&*)/$, > X ,(0,/2))$/&$-,&2,&"$,*'7+(1($#,23&73&,&$#'()*+5,(&,4(++,*77$*#,(),7*#%
*++$+,4(&", > - ,*)-,&"30, / v ,/*),9$,-$&$#'()$-,*0,
/ v d C I ( > - || > X )
!"$,2.$#*++,.2+&*;$,;*(), Q v ,/*),)24,9$,29&*()$-,9:,'3+&(7+:();, / v ,4(&",&"$,$A7#$00(2),12#
v $ ⁄ v '&L ,(),MS<,TX<D\V5,
(4
5 C ( > || > X )
Q v d 555555555555555555
> '&L e ( 4 I > - || > X
5
d α 555555555555555555
> '&L e ( 4
TX<D8V
K()/$, α ! K5,4$,0$$,&"*&,&"$,2.$#*++,.2+&*;$,;*(),(0,0('7+:,&"$,#*&(2,21,&"$,&2&*+,#$0(0&*)/$,()
&"$,/2++$/&2#,/(#/3(&,&2,&"$,&2&*+,#$0(0&*)/$,(),&"$,$'(&&$#,/(#/3(&<,W$,*+02,)2&$,&"*&,&"$,2.$#*++
437
438 Chapter 6 Bipolar Junction Transistors (BJTs)
.2+&*;$,;*(),(0,*+'20&,()-$7$)-$)&,21,&"$,.*+3$,21, β ,T$A/$7&,&"#23;",&"$,0'*++,-$7$)-$)/$
21, α ,2), β V5,*,-$0(#*9+$,7#27$#&:<,J90$#.$,&"*&,12#, > '&L ,21,&"$,0*'$,2#-$#,*0, > - ,*)-, > X 5,&"$
;*(),4(++,9$,.$#:,0'*++<
=),03''*#:5,&"$,6B,*'7+(1($#,$A"(9(&0,*,.$#:,+24,()73&,#$0(0&*)/$, ( ( 4 ) 5,*),27$)%/(#/3(&
.2+&*;$,;*(),&"*&,(0,720(&(.$,*)-,$S3*+,(),'*;)(&3-$,&2,&"*&,21,&"$,6M,*'7+(1($#,T C I > - V5,*)-5
+(G$,&"$,6M,*'7+(1($#5,*,#$+*&(.$+:,"(;",23&73&,#$0(0&*)/$, ( > - ) <,B$/*30$,21,(&0,.$#:,+24,()73&
#$0(0&*)/$5,&"$,6B,/(#/3(&,'&%!4,(0,)2&,*&&#*/&(.$,*0,*,.2+&*;$,*'7+(1($#,$A/$7&,(),07$/(*+(>$*77+(/*&(2)05,03/",*0,&"$,/*9+$,*'7+(1($#,'$)&(2)$-,*92.$<,!"$,6B,*'7+(1($#,"*0,$A/$++$)&
"(;"%1#$S3$)/:,7$#12#'*)/$5,4"(/",*0,4$,0"*++,0$$,(),6"*7&$#0,N,*)-,D5,'*G$0,(&,30$13+,()
/2'9()*&(2),4(&",2&"$#,/(#/3(&0,(),&"$,('7+$'$)&*&(2),21,"(;"%1#$S3$)/:,*'7+(1($#0<
EXERCISES
6.44 F2"'&0+,#)#F;#)3*6&@&+,#/$&6&h&"L#)#;<=#9&)'+0#)$# . - d K #3I#)"0#.&$%# > - d G #U Ω? #X+$+,3&"+
> &" - # / v % - #)"0# > % - #!@#$%+#)3*6&@&+,#&'#62)0+0#&"# > X d G #U Ω- #.%)$#7)6/+#2@# / v #,+'/6$'_#Y%)$# Q v
&'#29$)&"+0#&@# > '&L d G #U Ω _
Ans. MG#ΩH#MPP#]Z]H#G#U ΩH# KPP #]Z]H#P?G#]Z]
6.45 I#F;#)3*6&@&+,#&'#,+V/&,+0#$2#)3*6&@1#)#'&L")6#0+6&7+,+0#91#)#(2)T&)6#()96+#%)7&"L#)#(%),)($+,&'$&(
,+'&'$)"(+#2@#GP Ω? #Y%)$#9&)'#(/,,+"$# . - #'%2/60#9+#/$&6&h+0#$2#29$)&"# > &" #$%)$#&'#3)$(%+0#$2#$%+
()96+#,+'&'$)"(+_#=2#29$)&"#)"#27+,)66#726$)L+#L)&"#2@#Q v #2@#eP#]Z]-#.%)$#'%2/60#$%+#$2$)6#,+'&'$)"(+
&"#$%+#(266+($2,#:&?+?-# > - || > X >#9+_
Ans. P?G#3IH#e#U Ω
6.6.6 The Common-Collector Amplifier or Emitter Follower
!"$,+*0&,21,&"$,9*0(/,BC!,*'7+(1($#,/2)1(;3#*&(2)0,(0,&"$,/2''2)%/2++$/&2#,*'7+(1($#5,*,.$#:
('72#&*)&,/(#/3(&,&"*&,1()-0,1#$S3$)&,*77+(/*&(2),(),&"$,-$0(;),21,92&",0'*++%0(;)*+,*'7+(1($#0
*)-,*'7+(1($#0,&"*&,*#$,#$S3(#$-,&2,"*)-+$,+*#;$,0(;)*+0,*)-,-$+(.$#,0390&*)&(*+,*'23)&0,21
0(;)*+,724$#,&2,*,+2*-<,!"(0,+*&&$#,.*#($&:,4(++,9$,0&3-($-,(),6"*7&$#,??<,@0,4$++5,&"$,/2''2)%
/2++$/&2#,*'7+(1($#,(0,3&(+(>$-,(),*,0(;)(1(/*)&,1*'(+:,21,-(;(&*+,+2;(/,/(#/3(&0,T6"*7&$#,?8V<
!"$,/(#/3(&,(0,'2#$,/2''2)+:,G)24),9:,&"$,*+&$#)*&(.$,)*'$,4I$??4(8G%&&%A4(`,&"$,#$*02)
12#,&"(0,4(++,9$/2'$,*77*#$)&,0"2#&+:<,
The Need for Voltage Buffers ;+@2,+#0+67&"L#&"$2#$%+#)")61'&'#2@#$%+#+3&$$+,#@2662.+,-#&$#&'
/'+@/6#$2#622U#)$#2"+#2@#&$'#32'$#(2332"#)**6&()$&2"'?#F2"'&0+,#$%+#'&$/)$&2"#0+*&($+0#&"#D&L?
W?Ge:)>?#I#'&L")6#'2/,(+#0+6&7+,&"L#)#'&L")6#2@#,+)'2")96+#'$,+"L$%#:MPP#3]>#.&$%#)"#&"$+,")6
,+'&'$)"(+#2@#KPP#U Ω- #&'#$2#9+#(2""+($+0#$2#)#K5U Ω #62)0#,+'&'$)"(+?#F2""+($&"L#$%+#'2/,(+#$2
$%+#62)0#0&,+($61#)'#&"#D&L?#W?Ge:9>#.2/60#,+'/6$#&"#'+7+,+#)$$+"/)$&2"#2@#$%+#'&L")6H#$%+#'&L")6
)**+),&"L#)(,2''#$%+#62)0#.&66#9+#2"61# K ⁄ ( KPP e K ) #2@#$%+#&"*/$#'&L")6-#2,#)92/$#M#3]?#
@),*+&$#)*&(.$,/23#0$,21,*/&(2),(0,03;;$0&$-,(),L(;<,X<^8T/V<,R$#$,4$,"*.$,()&$#720$-,*)
*'7+(1($#,9$&4$$),&"$,023#/$,*)-,&"$,+2*-<,J3#,*'7+(1($#5,"24$.$#5,(0,3)+(G$,&"$,*'7+(1($#0
4$,"*.$,9$$),0&3-:();,(),&"(0,/"*7&$#,&"30,1*#`,(&,"*0,*,.2+&*;$,;*(),21,3)(&:<,!"(0,(0,9$/*30$
23#, 0(;)*+, (0, *+#$*-:, 21, 0311(/($)&, 0&#$);&", *)-, 4$, -2, )2&, )$$-, &2, ()/#$*0$, (&0, *'7+(&3-$<
Q2&$5,"24$.$#5,&"*&,23#,*'7+(1($#,"*0,*),()73&,#$0(0&*)/$,21,?OO,G ΩH ,&"30,"*+1,&"$,()73&,0(;%
)*+,T?OO,'_V,4(++,*77$*#,*&,&"$,()73&,21,&"$,*'7+(1($#,7#27$#<,K()/$,&"$,*'7+(1($#,"*0,*,+24
6.6 Basic BJT Amplifier Configurations
Rsig " 100 k&
Rsig " 100 k&
$
vsig "
200 mV
$
%
vsig "
200 mV
RL " 1 k&
$
%
RL " 1 k&
! 2 mV
%
(b)
(a)
Ro " 10 &
Rsig " 100 k&
vsig "
200 mV
Avo" 1
$
RL "
1 k&
$
%
vo ! 99 mV
%
Rin " 100 k&
(c)
Figure 6.54 !66/'$,)$&"L#$%+#"++0#@2,#)#/"&$15L)&"#9/@@+,#)3*6&@+,?
23&73&,#$0(0&*)/$,T?O, Ω V5,DDj,21,&"(0,0(;)*+,TDD,'_V,4(++,*77$*#,*&,&"$,23&73&<,!"(0,(0,*,0(;%
)(1(/*)&,('7#2.$'$)&,2.$#,&"$,0(&3*&(2),4(&",&"$,023#/$,/2))$/&$-,-(#$/&+:,&2,&"$,+2*-<,@0
4(++,9$,0$$),0"2#&+:5,&"$,$'(&&$#,12++24$#,/*),$*0(+:,('7+$'$)&,&"$,3)(&:%;*(),&/33!%-'"4+#5
3#!%,0"24),(),L(;<,X<^8T/V<
Characteristic Parameters of the Emitter Follower D&L/,+#W?GG:)>#'%2.'#)#(2332"5
(266+($2,#)3*6&@&+,#2,#+3&$$+,#@2662.+,-#)'#.+#.&66#,+@+,#$2#&$#%+"(+@2,$%?#b2$+#$%)$#$%+#9&)'&"L
(&,(/&$#&'#"2$#'%2."?#=%+#+3&$$+,#@2662.+,#&'#@+0#.&$%#)#'&L")6#'2/,(+#: v '&L - # > '&L >#)"0#%)'#)
62)0#,+'&'$)"(+# > X #(2""+($+0#9+$.++"#+3&$$+,#)"0#L,2/"0?#=2#U++*#$%&"L'#'&3*6+-#.+#),+#)'5
'/3&"L#$%)$# > X #&"(6/0+'#92$%#$%+#)($/)6#62)0#)"0#)"1#2$%+,#,+'&'$)"(+#$%)$#3)1#9+#*,+'+"$#9+5
$.++"#+3&$$+,#)"0#L,2/"0?#b2,3)661#$%+#)($/)6# > X #.2/60#9+#3/(%#62.+,#&"#7)6/+#$%)"#'/(%
2$%+,#,+'&'$)"(+'#)"0#$%/'#.2/60#023&")$+?
K()/$,&"$,BC!,"*0,*,#$0(0&*)/$, > X ,/2))$/&$-,(),(&0,$'(&&$#5,(&,(0,'20&,/2).$)($)&,&2,30$
&"$,!,'2-$+,&2,#$7#$0$)&,&"$,BC!<,Z2();,&"(0,#$03+&0,(),&"$,$'(&&$#%12++24$#,$S3(.*+$)&,/(#%
/3(&,0"24),(),L(;<,X<^^T9V<,W$,"*.$,()/+3-$-, ( % ,0('7+:,9$/*30$,(&,(0,.$#:,$*0:,&2,-2,02<
R24$.$#5,)2&$,&"*&, ( % ,*77$*#0,(),7*#*++$+,4(&", > X5,*)-,(),-(0/#$&$,/(#/3(&0,(0,'3/",+*#;$#
&"*), > X ,*)-,/*),&"30,9$,)$;+$/&$-<,!"$,#$03+&();,0('7+(1($-,/(#/3(&,0"24),(),L(;<,X<^^T/V5
/*),)24,9$,30$-,&2,-$&$#'()$,&"$,/"*#*/&$#(0&(/,7*#*'$&$#0,21,&"$,*'7+(1($#<,
!"$,()73&,#$0(0&*)/$, > &" ,(0,123)-,1#2',
v
> &" d 5555$
$#
K390&(&3&();,12#, $ # d $ 4 ⁄ ( β e K ) ,4"$#$, $ 4 ,(0,;(.$),9:
v
$
$ 4 d 5555555555555555
(4 e >X
439
440 Chapter 6 Bipolar Junction Transistors (BJTs)
aie
Rsig
$
re
Rsig
vsig
$
vsig
ro
ie
$
%
$
%
vi
$
$
vi
RL
%
Rin
RL
vo
%
%
Ro
%
(b)
(a)
ib " (1%a) ie
Rsig
$
%
,ie
" ie / b$1
$
vsig
vo
ie
re
Ro " re
vi
$
RL
vo
%
%
Rin " (b$1) (re $ RL)
(c)
Figure 6.55 ;'<#F2332"5(266+($2,#)3*6&@&+,#2,#+3&$$+,5@2662.+,?#;&<#EV/&7)6+"$#(&,(/&$#29$)&"+0#91#,+*6)(&"L#$%+#;<=#.&$%#&$'#,
320+6?#b2$+#$%)$#(%#)**+),'#&"#*),)66+6#.&$%#>X?#C&"(+#&"#0&'(,+$+#(&,(/&$'#(P !#>X-#.+#'%)66#"+L6+($#&$-#$%/'#29$)&"&"L#$%+#'&3*6&@&+0
(&,(/&$#&"#;)<?
6.6 Basic BJT Amplifier Configurations
4$,29&*()
> &"## d ( β e K ) ( ( 4 e > X )
TX<D^V
*,#$03+&,&"*&,4$,/23+-,"*.$,4#(&&$),-(#$/&+:5,3&(+(>();,&"$,#$0(0&*)/$%#$1+$/&(2),#3+$<,Q2&$,&"*&
*0,$A7$/&$-,&"$,$'(&&$#,12++24$#,&*G$0,&"$,+24,+2*-,#$0(0&*)/$,*)-,#$1+$/&0,(&,&2,&"$,9*0$,0(-$5
4"$#$,&"$,0(;)*+,023#/$,(05,*1&$#,()/#$*0();,(&0,.*+3$,9:,*,1*/&2#, ( β e K )? ,=&,(0,&"(0,('7$-*)/$
&#*)012#'*&(2), 7#27$#&:, 21, &"$, $'(&&$#, 12++24$#, &"*&, '*G$0, (&, 30$13+, (), /2))$/&();, *, +24%
#$0(0&*)/$,+2*-,&2,*,"(;"%#$0(0&*)/$,023#/$5,&"*&,(05,&2,('7+$'$)&,*,9311$#,*'7+(1($#<
=%+#726$)L+#L)&"# / v #&'#L&7+"#91
v
>X
/ v ≡ 5555% d 5555555555555555
v$
>X e (4
TX<DXV
/ v% d K
TX<DNV
K$&&();, > X d ∞ ,:($+-0, / v% -
!"305, *0, $A7$/&$-5, &"$, 27$)%/(#/3(&, .2+&*;$, ;*(), 21, &"$, $'(&&$#, 12++24$#, 7#27$#, (0, 3)(&:?X
4"(/",'$*)0,&"*&,&"$,0(;)*+,.2+&*;$,*&,&"$,$'(&&$#,G%&&%AB,&"*&,*&,&"$,9*0$`,4"(/",(0,&"$,2#(;()
21,&"$,)*'$,a$'(&&$#,12++24$#<b
!2,-$&$#'()$, > % - ,#$1$#,&2,L(;<,X<^^T/V,*)-,+22G,9*/G,()&2,&"$,$'(&&$#,T(<$<5,9$"()-,2#,$A/+3-%
();, > X V,4"(+$,0$&&();, v $ d P ,T(<$<5,;#23)-();,&"$,9*0$V<,m23,4(++,0$$, ( 4 ,21,&"$,BC!5,&"30
>% d (4
TX<DEV
!"(0,#$03+&,&2;$&"$#,4(&", / v% d K ,:($+-0, / v ,(),MS<,TX<DXV5,&"30,/2)1(#'();,23#,$*#+($#,*)*+:0(0<
Overall Voltage Gain Y+# "2.# *,2(++0# $2# 0+$+,3&"+# $%+# 27+,)66# 726$)L+# L)&"# Q v - # )'
@2662.'8
v
> &"
555555$5 d 555555555555555555555
5
v '&L
> &" e > '&L
( β e K )( (4 e >X )
d 55555555555555555555555555555555555555555555555555555
5
( β e K ) ( ( 4 e > X ) e > '&L
v
v
v B$C
v B$C
%
5 d 5555555$5 × / v
Q v ≡ 5555555
K390&(&3&();,12#, / v ,1#2',MS<,TX<DXV5,#$03+&0,()
( β e K )> X
Q v d 5555555555555555555555555555555555555555555555555555555555555555555
( β e K )> X e ( β e K )( 4 e > '&L
TX<DDV
!"(0,$S3*&(2), ()-(/*&$0, &"*&, &"$, 2.$#*++, ;*()5, &"23;", +24$#,&"*),2)$5, /*), 9$, /+20$,&2, 2)$, (1
( β e K )> X ,(0,+*#;$#,2#,/2'7*#*9+$,(),.*+3$,&2, > '&L ? ,!"(0,*;*(),/2)1(#'0,&"$,*/&(2),21,&"$,$'(&%
&$#,12++24$#,(),-$+(.$#();,*,+*#;$,7#272#&(2),21, v '&L ,&2,*,+24%.*+3$-,+2*-,#$0(0&*)/$, > X ,$.$)
&"23;", > '&L ,/*),9$,'3/",+*#;$#,&"*), > X<,!"$,G$:,72()&,(0,&"*&, > X ,(0,'3+&(7+($-,9:, ( β e K )
KW
!"#*,)($&(+-#$%+#7)6/+#2@# / v% #.&66#9+#62.+,#$%)"-#9/$#(62'+#$2#/"&$1?#D2,#2"+#$%&"L-# ( % - #.%&(%#.+#%)7+
"+L6+($+0-#.2/60#3)U+# / v% d ( % ⁄ ( ( % e ( 4 )?#I6'2-#)'#)6,+)01#3+"$&2"+0-#$%+,+#3)1#9+#2$%+,#,+'&'$)"(+'
:+?L?-#@2,#9&)'&"L#*/,*2'+'>#)$$)(%+0#$2#$%+#+3&$$+,?
441
442 Chapter 6 Bipolar Junction Transistors (BJTs)
Rsig
Rsig / (b$1)
(b$1) re
vsig
$
%
(b$1) RL
re
$
vsig
$
%
RL
vo
%
(a)
$
vo
%
(b)
Figure 6.56 C&3*6+#+V/&7)6+"$#(&,(/&$'#@2,#$%+#+3&$$+,#@2662.+,#29$)&"+0#91#;'<#,+@6+($&"L#(4#)"0#>X#$2#$%+
9)'+#'&0+-#)"0#;&<#,+@6+($&"L#v'&L#)"0#>'&L#$2#$%+#+3&$$+,#'&0+?#b2$+#$%)$#$%+#(&,(/&$#&"#;&<#()"#9+#29$)&"+0#@,23
$%)$#&"#;'<#91#'&3*61#0&7&0&"L#)66#,+'&'$)"(+'#91#T β e K>?
9$12#$,(&,(0,a7#$0$)&$-,&2,&"$,023#/$<b,L(;3#$,X<^XT*V,0"240,*),$S3(.*+$)&,/(#/3(&,21,&"$,$'(&&$#
12++24$#,29&*()$-,9:,0('7+:,#$1+$/&();, ( 4 ,*)-, > X ,&2,&"$,9*0$,0(-$<,!"$,2.$#*++,.2+&*;$,;*()
Q v ≡ v % ⁄ v '&L ,/*),9$,-$&$#'()$-,-(#$/&+:,*)-,.$#:,0('7+:,1#2',&"(0,/(#/3(&,9:,30();,&"$,.2+&*;$
-(.(-$#,#3+$<,!"$,#$03+&,(0,&"$,$A7#$00(2),12#, Q v ,*+#$*-:,;(.$),(),MS<,TX<DDV<
Z(.(-();,*++,#$0(0&*)/$0,(),&"$,/(#/3(&,21,L(;<,X<^XT*V,9:, β e K ,-2$0,)2&,/"*);$,&"$,.2+&*;$
#*&(2, v % ⁄ v '&L ? ,!"30,4$,29&*(),*)2&"$#,$S3(.*+$)&,/(#/3(&5,0"24),(),L(;<,X<^XT9V5,&"*&,/*),9$
30$-,&2,-$&$#'()$, Q v ≡ v % ⁄ v '&L ,21,&"$,$'(&&$#,12++24$#<,@,;+*)/$,*&,&"(0,/(#/3(&,#$.$*+0,&"*&
(&,(0,0('7+:,&"$,$S3(.*+$)&,/(#/3(&,29&*()$-,9:,#$1+$/&();, v '&L ,*)-, > '&L ,1#2',&"$,9*0$,0(-$,&2
&"$,$'(&&$#,0(-$<,=),&"(0,#$1+$/&(2)5, v '&L ,-2$0,)2&,/"*);$5,93&, > '&L ,(0,-(.(-$-,9:, β e K<,!"305
4$,$(&"$#,#$1+$/&,&2,&"$,9*0$,0(-$,*)-,29&*(),&"$,/(#/3(&,(),L(;<,X<^XT*V,2#,#$1+$/&,&2,&"$,$'(&&$#
0(-$,*)-,29&*(),&"$,/(#/3(&,(),L(;<,X<^XT9V<,L#2',&"$,+*&&$#5, Q v ,/*),9$,123)-,*0,
v
>X
Q v ≡ 555555%5 d 5555555555555555555555555555555555555555555555555555
5
v '&L
> X e ( 4 e > '&L ⁄ ( β e K )
TX<?OOV
J90$#.$,&"*&,&"(0,$A7#$00(2),(0,&"$,0*'$,*0,&"*&,(),MS<,TX<DDV,$A/$7&,12#,-(.(-();,92&",&"$
)3'$#*&2#,*)-,-$)2'()*&2#,9:, β e K<
!"$,$A7#$00(2),12#, Q v ,(),MS<,TX<?OOV,"*0,*),()&$#$0&();,()&$#7#$&*&(2)Y,!"$,$'(&&$#,12+%
+24$#,#$-3/$0, > '&L ,9:,&"$,1*/&2#, ( β e K ) ,9$12#$,a7#$0$)&();,(&,&2,&"$,+2*-,#$0(0&*)/$, > XbY,*)
('7$-*)/$,&#*)012#'*&(2),&"*&,"*0,&"$,0*'$,9311$#();,$11$/&<
@&,&"(0,72()&,(&,(0,('72#&*)&,&2,)2&$,&"*&,*+&"23;",&"$,$'(&&$#,12++24$#,-2$0,)2&,7#2.(-$
.2+&*;$,;*(),(&,"*0,*,/3##$)&,;*(),21, β e K<
Thévenin Representation of the Emitter-Follower Output I# 32,+# L+"+,)6# ,+*,+5
'+"$)$&2"# 2@# $%+# +3&$$+,5@2662.+,# 2/$*/$# &'# '%2."# &"# D&L?# W?Gd:)>?# \+,+# Q v% # &'# $%+# 27+,)66
2*+"5(&,(/&$# 726$)L+# L)&"# $%)$# ()"# 9+# 29$)&"+0# 91# '+$$&"L# > X d ∞ # &"# $%+# (&,(/&$# 2@# D&L?
W?GW:9>-#)'#&66/'$,)$+0#&"#D&L?#W?Gd:9>?#=%+#,+'/6$#&'# Q v% d K?#=%+#2/$*/$#,+'&'$)"(+# > 2/$ #&'#5$GM
G4(4!?8@,23# > % ? #=2#0+$+,3&"+# > 2/$ #.+#'+$# v '&L #$2#h+,2#:,)$%+,#$%)"#'+$$&"L# v $ #$2#h+,2>?#IL)&"
.+#()"#/'+#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>#$2#02#$%&'-#)'#&66/'$,)$+0#&"#D&L?#W?Gd:(>?#Y+
'++#$%)$
> '&L
> 2/$## d ( 4 e 55555555555
5
βeK
TX<?O?V
6.6 Basic BJT Amplifier Configurations
443
Rsig / (b$1)
Rout
$
Gvo vsig
RL
$
%
vsig
vo
re
$
%
%
Gvo " 1
$
vo " vsig
%
(b)
(a)
Rsig / (b$1)
Rsig
re
E
Rsig
Rout " re $ %
b$1
(c)
Rsig
Rout " re$%
(b$1)
re
vsig
$
%
RL
Rin " (b$1) (re$RL)
(d)
Figure 6.57 ;'<#=%p7+"&"#,+*,+'+"$)$&2"#2@#$%+#2/$*/$#2@#$%+#+3&$$+,#@2662.+,?#:&>#B9$)&"&"L#Qv%#@,23#$%+
+V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>?#;)<#B9$)&"&"L#>2/$#@,23#$%+#+V/&7)6+"$#(&,(/&$#&"#D&L?#W?GW:9>#.&$%#v'&L#'+$#$2
h+,2?-;2<#=%+#+3&$$+,#@2662.+,#.&$%#>&"#)"0#>2/$#0+$+,3&"+0#'&3*61#91#622U&"L#&"$2#$%+#&"*/$#)"0#2/$*/$#$+,5
3&")6'-#,+'*+($&7+61?
D&")661-# .+# '%2.# &"# D&L?# W?Gd:0># $%+# +3&$$+,5@2662.+,# (&,(/&$# $2L+$%+,# .&$%# &$'# > &" # )"0
> 2/$ ? #B9'+,7+#$%)$# > &" #&'#0+$+,3&"+0#91#,+@6+($&"L# ( 4 #)"0# > X #$2#$%+#9)'+#'&0+#:91#3/6$&*615
&"L# $%+&,# 7)6/+'# 91# β e K>?# =2# 0+$+,3&"+# > 2/$ - # L,)9# %260# 2@# $%+# +3&$$+,# )"0# .)6U# :2,# 4/'$
622Uj>#9)(U.),0#.%&6+# v '&L d P? #s2/#.&66#'++# ( 4 #&"#'+,&+'#.&$%# > '&L - #.%&(%#9+()/'+#&$#&'#&"
$%+#9)'+#3/'$#9+#0&7&0+0#91#( β e K )?
W$,)2&$,&"*&,3)+(G$,&"$,6M,*)-,6B,*'7+(1($#0,4$,0&3-($-,$*#+($#5,&"$,$'(&&$#,12++24$#,(0,!%?
3)(+*&$#*+<,!"(0,(0,'*)(1$0&$-,9:,&"$,1*/&,&"*&, > &" ,-$7$)-0,2), > X ,*)-, > 2/$ ,-$7$)-0,2), > '&L ?
Example 6.19
!$#&'#,+V/&,+0#$2#0+'&L"#)"#+3&$$+,#@2662.+,#$2#&3*6+3+"$#$%+#9/@@+,#)3*6&@&+,#2@#D&L?#W?Ge:(>?#C*+(&@1#$%+
,+V/&,+0#9&)'#(/,,+"$# . * #)"0#$%+#3&"&3/3#7)6/+#$%+#$,)"'&'$2,# β #3/'$#%)7+?#X+$+,3&"+#$%+#3)T&3/3
)662.+0#7)6/+#2@# v B$C #&@# v π #&'#$2#9+#6&3&$+0#$2#G#3]#&"#2,0+,#$2#29$)&"#,+)'2")961#6&"+),#2*+,)$&2"?#Y&$%
v '&L# d MPP #3]-#0+$+,3&"+#$%+#'&L")6#726$)L+#)$#$%+#2/$*/$#&@# > X #&'#(%)"L+0#$2#M#U Ω- #)"0#$2#P?G#U Ω?
444 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.19 continued
Rsig " 100 k&
Ro " 10 &
vo
vsig
$
%
" 200 mV
RL " 1 k&
Rin " 100 k&
Figure 6.58 F&,(/&$#@2,#ET)3*6+#W?Ka?#
Solution
=%+#+3&$$+,5@2662.+,#(&,(/&$#&'#'%2."#&"#D&L?#W?Gf?#=2#29$)&"# > % d KP#Ω- #.+#9&)'#$%+#$,)"'&'$2,#$2
29$)&"# ( 4 d KP#Ω? #=%/'+
KP#Ω d 55555,5
.*
. * d M?G ,'@
!"$,()73&,#$0(0&*)/$, > &" ,4(++,9$
> &" d ( β e K ) ( ( 4 e > X )
KPP d ( β e K ) ( P?PK e K )
=%/'-#$%+#;<=#'%2/60#%)7+#)# β #.&$%#)#3&"&3/3#7)6/+#2@#af?#I#%&L%+,# β #.2/60#297&2/'61#9+#9+"+@&(&)6?
=%+#27+,)66#726$)L+#L)&"#()"#9+#0+$+,3&"+0#@,23
v
>X
Q v ≡ 555555%5 d 5555555555555555555555555555555555555555
5
v '&L
> '&L
> X e ( 4 e 5555555555555555
5
(β e K)
I''/3&"L# β d KPP -#$%+#7)6/+#2@# Q v #29$)&"+0#&'
Q v d P?G
=%/'#.%+"# v '&L d MPP #3]-#$%+#'&L")6#)$#$%+#2/$*/$#.&66#9+#KPP#3]?#C&"(+#$%+#KPP#3]#)**+),'#)(,2''#$%+
K5U Ω #62)0-#$%+#'&L")6#)(,2''#$%+#9)'+Q+3&$$+,#4/"($&2"#()"#9+#@2/"0#@,23
v%
v π d 555555 × ( 4
>X
KPP
d 555555555555 × KP d K #3]
KPPP
!@# vt π d G#3]#$%+"# v '&L #()"#9+#&"(,+)'+0#91#)#@)($2,#2@#G-#,+'/6$&"L#&"# vt '&L d K#]?
=2#29$)&"# v % #)'#$%+#62)0#&'#7),&+0-#.+#/'+#$%+#=%p7+"&"#+V/&7)6+"$#2@#$%+#+3&$$+,#@2662.+,-#'%2."#&"
D&L?#W?Gd:)>#.&$%# Q v% d K #)"0
> '&L
KPP
> 2/$## d 555555555555 e ( 4 d 555555555 e P?PK d K#UΩ
KPK
βeK
6.6 Basic BJT Amplifier Configurations
445
$2#29$)&"
>
> X e > 2/$
X
v % d v '&L 555555555555555555555
D2,# > X d M#UΩM
MeK
v % d MPP#3] × 555555555555 d KNN?N#3]
)"0#@2,# > X d P?G#UΩP?G
P?G e K
v % d MPP#3] × 5555555555555555 d WW?d#3]
EXERCISE
6.46 I"#+3&$$+,#@2662.+,#/$&6&h+'#)#$,)"'&'$2,#.&$%# β d KPP #)"0#&'#9&)'+0#)$# . - d G#3I?#!$#2*+,)$+'#9+5
$.++"#)#'2/,(+#%)7&"L#)#,+'&'$)"(+#2@#KP#U Ω #)"0#)#62)0#2@#K#U Ω? #D&"0# > &" - # Q v% - # > 2/$ - #)"0# Q v ?
Y%)$#&'#$%+#*+)U#)3*6&$/0+#2@# v '&L #$%)$#,+'/6$'#&"# v π #%)7&"L#)#*+)U#)3*6&$/0+#2@#G#3]_#D&"0#$%+
,+'/6$&"L#*+)U#)3*6&$/0+#)$#$%+#2/$*/$?
Ans. KPK?G#U Ω H#K#]Z]H#KPe# Ω H#P?aK#]Z]H#K?K#]H#K#]
6.6.7 Summary and Comparisons
L2#, $*0:, #$1$#$)/$, *)-, &2, $)*9+$, /2'7*#(02)05, 4$, 7#$0$)&, (), !*9+$, X<^, &"$, 12#'3+*0, 12#
-$&$#'()();,&"$,/"*#*/&$#(0&(/,7*#*'$&$#0,21,-(0/#$&$,BC!,*'7+(1($#0<,Q2&$,&"*&, ( % ,"*0,9$$)
)$;+$/&$-, &"#23;"23&<, @0, "*0, *+#$*-:, 9$$), '$)&(2)$-5, &"(0, (0, 7200(9+$, (), -(0/#$&$%/(#/3(&
*'7+(1($#0<,=),*--(&(2),&2,&"$,#$'*#G0,'*-$,&"#23;"23&,&"(0,0$/&(2),*923&,&"$,/"*#*/&$#(0&(/0
*)-,*77+(/*9(+(&:,21,&"$,.*#(230,/2)1(;3#*&(2)05,4$,'*G$,&"$,12++24();,/2)/+3-();,72()&0<
1. !"$,6M,/2)1(;3#*&(2),(0,&"$,2)$,9$0&,03(&$-,12#,#$*+(>();,&"$,93+G,21,&"$,;*(),#$S3(#$-,()
*),*'7+(1($#<,Z$7$)-();,2),&"$,'*;)(&3-$,21,&"$,;*(),#$S3(#$-5,$(&"$#,*,0();+$,0&*;$,2#,*
/*0/*-$,21,&42,2#,&"#$$,0&*;$0,/*),9$,30$-<
2. =)/+3-();,*,#$0(0&2#, > 4 ,(),&"$,$'(&&$#,+$*-,21,&"$,6M,0&*;$,7#2.(-$0,*,)3'9$#,21,7$#12#%
'*)/$,('7#2.$'$)&0,*&,&"$,$A7$)0$,21,;*(),#$-3/&(2)<
3. !"$,+24,()73&,#$0(0&*)/$,21,&"$,6B,*'7+(1($#,'*G$0,(&,30$13+,2)+:,(),07$/(1(/,*77+(/*&(2)0<
@0,4$,0"*++,0$$,(),6"*7&$#,D5,(&,"*0,*,'3/",9$&&$#,"(;"%1#$S3$)/:,#$072)0$,&"*),&"$,6M
*'7+(1($#<,!"(0,037$#(2#(&:,4(++,'*G$,(&,30$13+,*0,*,"(;"%1#$S3$)/:,*'7+(1($#5,$07$/(*++:
4"$),/2'9()$-,4(&",&"$,6M,/(#/3(&<,W$,0"*++,0$$,2)$,03/",/2'9()*&(2),(),6"*7&$#,N<
4. =%+# +3&$$+,# @2662.+,# @&"0'# )**6&()$&2"# )'# )# 726$)L+# 9/@@+,# @2,# (2""+($&"L# )# %&L%5
,+'&'$)"(+# '2/,(+# $2# )# 62.5,+'&'$)"(+# 62)0# )"0# )'# $%+# 2/$*/$# '$)L+# &"# )# 3/6$&'$)L+
)3*6&@&+,-#.%+,+#&$'#*/,*2'+#&'#$2#+V/&*#$%+#)3*6&@&+,#.&$%#)#62.#2/$*/$5,+'&'$)"(+?
446 Chapter 6 Bipolar Junction Transistors (BJTs)
?
TABLE 6.5 Characteristics of BJT Amplifiers)-#9-#(
> &"
/ v%
>%
/v
F2332"
+3&$$+,
:D&L?#W?GP>
( β e K )( 4
]CI >-
>-
] C I ( > - || > X )
F2332"
+3&$$+,#.&$%#
( β e K )( (4 e >4 )
> - || > X
5
] α 55555555555555555
(4
>4
CI >5
] 55555555555555555555
K e CI >4
>-
] C I ( > - || > X )
55555555555555555555555555555555
K e CI >4
Qv
> - || > X
5
] β 555555555555555555555555555555555555
> '&L e ( β e K )( 4
> - || > X
5
] β 55555555555555555555555555555555555555555555555555555
> '&L e ( β e K ) ( ( 4 e > 4 )
> - || > X
5
] α 55555555555555555
(4 e >4
:D&L?#W?GM>
F2332"#9)'+
:D&L?#W?GN>
(4
CI >-
>-
E3&$$+,
@2662.+,
:D&L?#W?GG>
( β e K )( (4 e >X )
K
(4
> || >
> '&L e ( 4
C I ( > - || > X )
> - || > X
5
α 55555555555555555
(4
X
5
α 555555555555555555
>X
5555555555555555
>X e (4
>X
5555555555555555555555555555555555555555555555555555
5
> X e ( 4 e > '&L ⁄ ( β e K )
# Q v% d K
> '&L
> 2/$ d ( 4 e 55555555555
5
βeK
'
D2,#$%+#&"$+,*,+$)$&2"#2@#>I-#/v%-#)"0#>%#,+@+,#$2#D&L?#W?ea?
#
#
#=%+#;<=#2/$*/$#,+'&'$)"(+#(%#%)'#9++"#"+L6+($+0-#.%&(%#&'#*+,3&$$+0#&"#$%+#0&'(,+$+5(&,(/&$#)3*6&@&+,'#'$/0&+0#&"#$%&'#(%)*$+,?#D2,#&"$+L,)$+05(&,(/&$#)3*6&5
@&+,'#:F%)*$+,#d>-#(
%#3/'$#)6.)1'#9+#$)U+"#&"$2#)((2/"$?
E
#C+$$&"L#β = ∞ ##(α = 1)#)"0#,+*6)(&"L8(4#.&$%#KZCI-#>-#.&$%#>1-#)"0#>4#.&$%#>B#,+'/6$'#&"#$%+#(2,,+'*2"0&"L#@2,3/6)'#@2,#ABCDE=#)3*6&@&+,'#:=)96+#G?e>?
6.7 Biasing in BJT Amplifier Circuits
R*.();,0&3-($-,&"$,.*#(230,/2)1(;3#*&(2)0,21,BC!,*'7+(1($#05,4$,)24,*--#$00,&"$,('72#&*)&
S3$0&(2),21,9(*0();,*)-,(&0,#$+*&(2)0"(7,&2,0'*++%0(;)*+,9$"*.(2#<,!"$,9(*0();,7#29+$',(0,&"*&
21,$0&*9+(0"();,*,/2)0&*)&,-/,/3##$)&,(),&"$,/2++$/&2#,21,&"$,BC!<,!"(0,/3##$)&,"*0,&2,9$,/*+/3%
+*9+$5,7#$-(/&*9+$5,*)-,()0$)0(&(.$,&2,.*#(*&(2)0,(),&$'7$#*&3#$,*)-,&2,&"$,+*#;$,.*#(*&(2)0,()
&"$,.*+3$,21,β,$)/23)&$#$-,*'2);,&#*)0(0&2#0,21,&"$,0*'$,&:7$<,@)2&"$#,('72#&*)&,/2)0(-$#%
*&(2),(),9(*0,-$0(;),(0,+2/*&();,&"$,-/,9(*0,72()&,(),&"$,$- ]v-*,7+*)$,&2,*++24,12#,'*A('3'
23&73&,0(;)*+,04();,T0$$,&"$,-(0/300(2),(),K$/&(2),X<8<XV<,=),&"(0,0$/&(2)5,4$,0"*++,-$*+,4(&"
.*#(230,*77#2*/"$0,&2,02+.();,&"$,9(*0,7#29+$',(),&#*)0(0&2#,/(#/3(&0, -$0(;)$-,4(&",-(0/#$&$
-$.(/$0<,B(*0,'$&"2-0,12#,()&$;#*&$-%/(#/3(&,-$0(;),*#$,7#$0$)&$-,(),6"*7&$#,N<
B$12#$, 7#$0$)&();,&"$, a;22-b, 9(*0();, 0/"$'$05, 4$, 0"23+-, 72()&, 23&, 4":, &42, 29.(230
*##*);$'$)&0,*#$,!%?,;22-<,L(#0&5,*&&$'7&();,&2,9(*0,&"$,BC!,9:,1(A();,&"$,.2+&*;$,+)*,9:5,12#
()0&*)/$5,30();,*,.2+&*;$,-(.(-$#,*/#200,&"$,724$#,0377+:,+--5,*0,0"24),(),L(;<,X<^DT*V5,(0,)2&
*,.(*9+$,*77#2*/"Y,!"$,.$#:,0"*#7,$A72)$)&(*+,#$+*&(2)0"(7,$- ]v)*,'$*)0,&"*&,*):,0'*++,*)()$.(&*9+$,-(11$#$)/$0,(),+)*,1#2',&"$,-$0(#$-,.*+3$,4(++,#$03+&,(),+*#;$,-(11$#$)/$0,(),.-,*)(),+-*<,K$/2)-5,9(*0();,&"$,BC!,9:,$0&*9+(0"();,*,/2)0&*)&,/3##$)&,(),&"$,9*0$5,*0,0"24),()
L(;<,X<^DT9V5,4"$#$, . ) ! ( ( + -- ] P?d ) ⁄ > ) - ,(0,*+02,)2&,*,#$/2''$)-$-,*77#2*/"<,R$#$,&"$
&:7(/*++:,+*#;$,.*#(*&(2)0,(),&"$,.*+3$,21,β,*'2);,3)(&0,21,&"$,0*'$,-$.(/$,&:7$,4(++,#$03+&,()
/2##$072)-();+:,+*#;$,.*#(*&(2)0,(),.-,*)-,"$)/$,(),+-*<
6.7 Biasing in BJT Amplifier Circuits
VCC
VCC
RB1
RB
RC
RC
IC
IC
IB
$
RB2
VCE
VCE
$
IB
VBE
VBE
%
%
(b)
(a)
Figure 6.59 =.2#297&2/'#'(%+3+'#@2,#9&)'&"L#$%+#;<=8#;'<#91#@&T&"L# +)*H#;&<#91#@&T&"L#.)?#;2$%#,+'/6$
&" .&0+# 7),&)$&2"'# &"# .-# )"0# %+"(+# &"# +-*# )"0# $%+,+@2,+# ),+# (2"'&0+,+0# $2# 9+# R9)0?S# b+&$%+,# '(%+3+# &'
,+(233+"0+0?
6.7.1 The Classical Discrete-Circuit Bias Arrangement
L(;3#$, X<XOT*V, 0"240, &"$, *##*);$'$)&, '20&, /2''2)+:, 30$-, 12#, 9(*0();, *, -(0/#$&$%/(#/3(&
&#*)0(0&2#,*'7+(1($#,(1,2)+:,*,0();+$,724$#,0377+:,(0,*.*(+*9+$<,!"$,&$/")(S3$,/2)0(0&0,21,037%
7+:();,&"$,9*0$,21,&"$,&#*)0(0&2#,4(&",*,1#*/&(2),21,&"$,0377+:,.2+&*;$,+--,&"#23;",&"$,.2+&*;$
-(.(-$#,>?5,>P<,=),*--(&(2)5,*,#$0(0&2#,>*,(0,/2))$/&$-,&2,&"$,$'(&&$#<
VCC
VBB " VCC
%
R2
R1 $ R2
&
RC
RC
R1
VCC
IB
RB " R1 $ R2
R2
RE
(a)
L
IC
IE
RE
(b)
Figure 6.60 F6)''&()6# 9&)'&"L# @2,# ;<='# /'&"L# )# '&"L6+# *2.+,# '/**618# ;'<# (&,(/&$H# ;&<# (&,(/&$# .&$%# $%+
726$)L+#0&7&0+,#'/**61&"L#$%+#9)'+#,+*6)(+0#.&$%#&$'#=%p7+"&"#+V/&7)6+"$?
L(;3#$,X<XOT9V,0"240,&"$,0*'$,/(#/3(&,4(&",&"$,.2+&*;$,-(.(-$#,)$&42#G,#$7+*/$-,9:,(&0
!"p.$)(),$S3(.*+$)&5
>M
5+
+ )) = 5555555555555555
> K + > M --
TX<?OPV
447
448 Chapter 6 Bipolar Junction Transistors (BJTs)
>K >M
5
> ) = 5555555555555555
>K + >M
TX<?O\V
!"$,/3##$)&,.*,/*),9$,-$&$#'()$-,9:,4#(&();,*,q(#/""211,+227,$S3*&(2),12#,&"$,9*0$]$'(&&$#]
;#23)-,+2275,+*9$+$-,F5,*)-,0390&(&3&();, . ) = . * ⁄ ( β + K ) 8
+ )) ] + )*
5
. * = 555555555555555555555555555555555555555
>* + >) ⁄ ( β + K )
TX<?O8V
!2,'*G$,.*,()0$)0(&(.$,&2,&$'7$#*&3#$,*)-, β,.*#(*&(2)5?N,4$,-$0(;),&"$,/(#/3(&,&2,0*&(01:,&"$
12++24();,&42,/2)0&#*()&0Y
+)) #!#+)*
TX<?O^V
>
> *# ! 55555555555
# )5
β+K
TX<?OXV
62)-(&(2), TX<?O^V, $)03#$0, &"*&, 0'*++, .*#(*&(2)0, (), +)*, T!, O<N, _V, 4(++, 9$, 04*'7$-, 9:, &"$
'3/",+*#;$#,+))<,!"$#$,(0,*,+('(&5,"24$.$#5,2),"24,+*#;$,+)),/*),9$Y,L2#,*,;(.$),.*+3$,21,&"$
0377+:,.2+&*;$,+--5,&"$,"(;"$#,&"$,.*+3$,4$,30$,12#,+))5,&"$,+24$#,4(++,9$,&"$,03',21,.2+&*;$0
*/#200, >-, *)-, &"$, /2++$/&2#]9*0$, H3)/&(2), T+-)V<, J), &"$, 2&"$#, "*)-5, 4$, 4*)&, &"$, .2+&*;$
*/#200,>-,&2,9$,+*#;$,(),2#-$#,&2,29&*(),"(;",.2+&*;$,;*(),*)-,+*#;$,0(;)*+,04();,T9$12#$,&#*)%
0(0&2#,/3&211V<,W$,*+02,4*)&,+-),T2#,+-*V,&2,9$,+*#;$,&2,7#2.(-$,*,+*#;$,0(;)*+,04();,T9$12#$
&#*)0(0&2#,0*&3#*&(2)V<,!"305,*0,(0,&"$,/*0$,(),*):,-$0(;)5,4$,"*.$,* 0$&,21,/2)1+(/&();,#$S3(#$%
'$)&05,*)-,&"$,02+3&(2),'30&,9$,*,&#*-$%211<,@0,* #3+$,21,&"3'95,2)$,-$0(;)0,12#,+)),*923&
K
K
K
555 +-- - + ,T2#,+ V,*923&, 555 +-- - ,*)-,. > ,*923&, 555 +-- ?
-)
-*
- N
N
N
62)-(&(2),TX<?OXV,'*G$0,.*,()0$)0(&(.$,&2,.*#(*&(2)0,(),β,*)-,/23+-,9$,0*&(01($-,9:,0$+$/&%
();,>),0'*++<,!"(0,(),&3#),(0,*/"($.$-,9:,30();,+24,.*+3$0,12#,>?,*)-,>P<,F24$#,.*+3$0,12#,>?
*)-,>P5,"24$.$#5,4(++,'$*),*,"(;"$#,/3##$)&,-#*(),1#2',&"$,724$#,0377+:5,*)-,4(++,#$03+&,()
*, +24$#();, 21, &"$, ()73&, #$0(0&*)/$, 21, &"$, *'7+(1($#, T(1, &"$, ()73&, 0(;)*+, (0, /237+$-, &2, &"$
9*0$V5?E,4"(/",(0,&"$,&#*-$%211,().2+.$-,(),&"(0,7*#&,21,&"$,-$0(;)<,=&,0"23+-,9$,)2&$-,&"*&
/2)-(&(2),TX<?OXV,'$*)0,&"*&,4$,4*)&,&2,'*G$,&"$,9*0$,.2+&*;$,()-$7$)-$)&,21,&"$,.*+3$,21
β,*)-,-$&$#'()$-,02+$+:,9:,&"$,.2+&*;$,-(.(-$#<,!"(0,4(++,29.(230+:,9$,0*&(01($-,(1,&"$,/3##$)&
(),&"$,-(.(-$#, (0,'*-$,'3/", +*#;$#, &"*), &"$, 9*0$,/3##$)&<,!:7(/*++:, 2)$, 0$+$/&0, >?, *)-, >P
03/",&"*&,&"$(#,/3##$)&,(0,(),&"$,#*);$,21,.*,&2,O<?.*<
L3#&"$#,()0(;"&,#$;*#-();,&"$,'$/"*)(0',9:,4"(/",&"$,9(*0,*##*);$'$)&,21,L(;<,X<XOT*V,0&*%
9(+(>$0, &"$, -/, $'(&&$#, T*)-, "$)/$, /2++$/&2#V, /3##$)&, (0, 29&*()$-, 9:, /2)0(-$#();, &"$, 1$$-9*/G
*/&(2),7#2.(-$-,9:,>*<,62)0(-$#,&"*&,12#,02'$,#$*02),&"$,$'(&&$#,/3##$)&,()/#$*0$0<,!"$,.2+&*;$
-#27,*/#200,>*5,*)-,"$)/$,+*,4(++,()/#$*0$,/2##$072)-();+:<,Q245,(1,&"$,9*0$,.2+&*;$,(0,-$&$#%
'()$-,7#('*#(+:,9:,&"$,.2+&*;$,-(.(-$#,>?5,>P5,4"(/",(0,&"$,/*0$,(1,>),(0,0'*++5,(&,4(++,#$'*()
/2)0&*)&5, *)-, &"$, ()/#$*0$, (), +*, 4(++, #$03+&, (), *, /2##$072)-();, -$/#$*0$, (), +)*<, !"(0, (), &3#)
#$-3/$0,&"$,/2++$/&2#,T*)-,$'(&&$#V,/3##$)&5,*,/"*);$,27720(&$,&2,&"*&,2#(;()*++:,*003'$-<,!"30
>*,7#2.(-$0,*,!4C'?$F48G445#'EP,*/&(2),&"*&,0&*9(+(>$0,&"$,9(*0,/3##$)&<,!"(0,0"23+-,#$'()-,&"$
#$*-$#,21,&"$,#$0(0&*)/$,>4,&"*&,4$,()/+3-$-,(),&"$,$'(&&$#,+$*-,21,&"$,6M,*'7+(1($#,(),K$/&(2)
X<X<8<,W$,0"*++,0&3-:,)$;*&(.$,1$$-9*/G,12#'*++:,(),6"*7&$#,?O<
;&)'#0+'&L"#'++U'#$2#'$)9&6&h+#+&$%+,#.*#2,#.-#'&"(+#.-#=#α.*#)"0#α#7),&+'#7+,1#6&$$6+?#=%)$#&'-#)#'$)96+#.*
.&66#,+'/6$#&"#)"#+V/)661#'$)96+#.--#)"0#7&(+#7+,')?
Kf
!@#$%+#&"*/$#'&L")6#&'#(2/*6+0#$2#$%+#$,)"'&'$2,#9)'+-#$%+#$.2#9&)'#,+'&'$)"(+'#>?,*)-8>P#+@@+($&7+61#)**+),
&"#*),)66+6#9+$.++"#$%+#9)'+#)"0#L,2/"0?#=%/'-#62.#7)6/+'#@2,#>?,*)-8>P,.&66#,+'/6$#&"#62.+,&"L#>&"?
Kd
6.7 Biasing in BJT Amplifier Circuits
449
Example 6.20
Y+#.&'%#$2#0+'&L"#$%+#9&)'#"+$.2,U#2@#$%+#)3*6&@&+,#&"#D&L?#W?WP#$2#+'$)96&'%#)#(/,,+"$#.*#=#K#3I#/'&"L#)
*2.+,#'/**61#+--# =# +KM#]?#=%+#$,)"'&'$2,#&'#'*+(&@&+0#$2#%)7+#)#"23&")6#β#7)6/+#2@#KPP?
Solution
Y+#'%)66#@2662.#$%+#,/6+#2@#$%/39#3+"$&2"+0#)927+#)"0#)662()$+#2"+5$%&,0#2@#$%+#'/**61#726$)L+#$2#$%+
726$)L+#0,2*#)(,2''#>M#)"0#)"2$%+,#2"+5$%&,0#$2#$%+#726$)L+#0,2*#)(,2''#>- -#6+)7&"L#2"+5$%&,0#@2,#*2''&96+
"+L)$&7+#'&L")6#'.&"L#)$#$%+#(266+($2,?#=%/'+ ) = +e#]
+ * = e ] + )* #!#N?N#]
*)-,>*,(0,-$&$#'()$-,1#2'
+
N?N
> * = 55555*5 = 5555555 = N?N#UΩ
.*
K
L#2',&"$,-(0/300(2),*92.$,4$,0$+$/&,*,.2+&*;$,-(.(-$#,/3##$)&,21, P?K. * = P?K × K = P?K#3I? ,Q$;+$/&();
&"$,9*0$,/3##$)&5,4$,1()KM
> K + > M = 5555555 = KMP#UΩ
P?K
*)>M
55555555555555555
5+
= e#]
> K + > M -!"30,>P,=,8O,GΩ,*)-,>?,=,EO,GΩ<,
@&,&"(0,72()&5,(&,(0,-$0(#*9+$,&2,1()-,*,'2#$,*//3#*&$,$0&('*&$,12#,.*5,&*G();,()&2,*//23)&,&"$,)2)>$#2
9*0$,/3##$)&<,c0();,MS<,TX<?O8V5
e ] P?d
. * = 55555555555555555555555555555555555555555555555555555555555555 = P?aN#3I
( fP qq eP ) ( UΩ )
N?N ( UΩ ) + 5555555555555555555555555555555555
KPK
!"(0,(0,S3(&$,*,9(&,+24$#,&"*),?,'@5,&"$,.*+3$,4$,*#$,*('();,12#<,=&,(0,$*0:,&2,0$$,1#2',&"$,*92.$,$S3*%
&(2),&"*&,*,0('7+$,4*:,&2,#$0&2#$,.*,&2,(&0,)2'()*+,.*+3$,423+-,9$,&2,#$-3/$,>*,1#2',\<\,GΩ,9:,&"$,'*;)(%
&3-$,21,&"$,0$/2)-,&$#',(),&"$,-$)2'()*&2#,TO<PXN,GΩV<,!"30,*,'2#$,03(&*9+$,.*+3$,12#,>*,(),&"(0,/*0$
423+-,9$,>*,=,\,GΩ5,4"(/",#$03+&0,(),.*,=,?<O?,'@,!,?,'@<?D
=&,0"23+-,9$,)2&$-,&"*&,(1,4$,*#$,4(++();,&2,-#*4,*,"(;"$#,/3##$)&,1#2',&"$,724$#,0377+:,*)-,&2,*//$7&
*,+24$#,()73&,#$0(0&*)/$,12#,&"$,*'7+(1($#5,&"$),4$,'*:,30$,*,.2+&*;$%-(.(-$#,/3##$)&,$S3*+5,0*:5,&2,.*,T(<$<5
?,'@V5,#$03+&();,(),>?,=,E,GΩ,*)-,>P,=,8,GΩ<,W$,0"*++,#$1$#,&2,&"$,/(#/3(&,30();,&"$0$,+*&&$#,.*+3$0,*0
-$0(;),P5,12#,4"(/",&"$,*/&3*+,.*+3$,21,.*,30();,&"$,()(&(*+,.*+3$,21,>*,21,\<\,GΩ,4(++,9$
e ] P?d
. * = 555555555555555555555555555 = P?aa#!#K#3I
N?N + P?PMd
?D
I6$%2/L%#,+0/(&"L# >*88 ,+'$2,+'# .*#$2#$%+#0+'&L"#7)6/+#2@# ?,'@-#&$#02+'#"2$#'267+#$%+#*,296+3#2@#$%+
0+*+"0+"(+#2@#$%+#7)6/+#2@#.*#2"#β. C++#ET+,(&'+#W?ed?
Ka
450 Chapter 6 Bipolar Junction Transistors (BJTs)
Example 6.20 continued
=),&"(0,/*0$5,-$0(;),P5,4$,)$$-,)2&,/"*);$,&"$,.*+3$,21,>*<
D&")661-#$%+#7)6/+#2@#>-#()"#9+#0+$+,3&"+0#@,23#
KM ] +
> - = 55555555555555555-5
.C/9'$&$/$&"L# . - = α . * #= P?aa × K = P?aa#3I#!#K#3I #,+'/6$'-#@2,#92$%#0+'&L"'-#&"
KM ] f
> - = 555555555555555 = e#UΩ
K
EXERCISE
6.47 D2,#0+'&L"#K#&"#ET)3*6+#W?MP-#()6(/6)$+#$%+#+T*+($+0#,)"L+#2@#.*#&@#$%+#$,)"'&'$2,#/'+0#%)'#β#&"#$%+
,)"L+#2@#GP#$2#KGP?#ET*,+''#$%+#,)"L+#2@#.*#)'#)#*+,(+"$)L+#2@#$%+#"23&")6#7)6/+#:.*#!#K#3I>#295
$)&"+0#@2,#β =#KPP?#J+*+)$#@2,#0+'&L"#M?
Ans. D2,#0+'&L"#K8#P?ae#3I#$2#K?Pe#3I-#)#KPo#,)"L+H#@2,#0+'&L"#M8#P?afe#3I#$2#P?aaG#3I-#)#K?Ko
,)"L+?
6.7.2 A Two-Power-Supply Version of the Classical
Bias Arrangement
@, 02'$4"*&, 0('7+$#, 9(*0, *##*);$'$)&, (0, 7200(9+$, (1, &42, 724$#, 0377+($0, *#$, *.*(+*9+$5, *0
0"24),(),L(;<,X<X?<,W#(&();,*,+227,$S3*&(2),12#,&"$,+227,+*9$+$-,F,;(.$0
+ ** ] + )*
. * = 5555555555555555555555555555555555555555
,
>* + >) ⁄ ( β + K )
TX<?ONV
Figure 6.61 ;&)'&"L# $%+# ;<=# /'&"L# $.2# *2.+,# '/**6&+'?# J+'&'$2,# >)# &'
"++0+0#2"61#&@#$%+#'&L")6#&'#$2#9+#()*)(&$&7+61#(2/*6+0#$2#$%+#9)'+?#B$%+,5
.&'+-#$%+#9)'+#()"#9+#(2""+($+0#0&,+($61#$2#L,2/"0-#2,#$2#)#L,2/"0+0#'&L")6
'2/,(+-#,+'/6$&"L#&"#)632'$#$2$)6#β 5&"0+*+"0+"(+#2@#$%+#9&)'#(/,,+"$?
6.7 Biasing in BJT Amplifier Circuits
!"(0,$S3*&(2),(0,(-$)&(/*+,&2,MS<,TX<?O8V,$A/$7&,12#,+**,#$7+*/();,+))<,!"30,&"$,&42,/2)0&#*()&0
21,MS0<,TX<?O^V,*)-,TX<?OXV,*77+:,"$#$,*0,4$++<,Q2&$,&"*&,(1,&"$,&#*)0(0&2#,(0,&2,9$,30$-,4(&",&"$
9*0$,;#23)-$-,T(<$<5,(),&"$,/2''2)%9*0$,/2)1(;3#*&(2)V5,&"$),>),/*),9$,$+('()*&$-,*+&2;$&"$#<
J),&"$,2&"$#,"*)-5,(1,&"$,()73&,0(;)*+,(0,&2,9$,/237+$-,&2,&"$,9*0$5,&"$),>),(0,)$$-$-<,W$,0"*++
0&3-:,/2'7+$&$,/(#/3(&0,21,&"$,.*#(230,BC!,*'7+(1($#,/2)1(;3#*&(2)0,(),K$/&(2),X<E<
EXERCISE
D6.48 =%+#9&)'#),,)"L+3+"$#2@#D&L?#W?WK#&'#$2#9+#/'+0#@2,#)#(2332"59)'+#)3*6&@&+,?#X+'&L"#$%+#(&,(/&$
$2#+'$)96&'%#)#0(#+3&$$+,#(/,,+"$#2@#K#3I#)"0#*,27&0+#$%+#%&L%+'$#*2''&96+#726$)L+#L)&"#.%&6+#)65
62.&"L#@2,#)#3)T&3/3#'&L")6#'.&"L#)$#$%+#(266+($2,#2@#±M#]?#^'+#+KP5]#)"0#−G5]#*2.+,#'/**6&+'?
Ans. >),=,O`,>*,=,8<\,GΩ`,>-,=,E<8,GΩ
6.7.3 Biasing Using a Collector-to-Base Feedback Resistor
L(;3#$, X<XPT*V, 0"240, *, 0('7+$, 93&, $11$/&(.$, *+&$#)*&(.$, 9(*0();, *##*);$'$)&, 03(&*9+$, 12#
/2''2)%$'(&&$#,*'7+(1($#0<,!"$,/(#/3(&,$'7+2:0,*,#$0(0&2#,>),/2))$/&$-,9$&4$$),&"$,/2++$/%
&2#,*)-,&"$,9*0$<,U$0(0&2#,>),7#2.(-$0,)$;*&(.$,1$$-9*/G5,4"(/","$+70,&2,0&*9(+(>$,&"$,9(*0
72()&,21,&"$,BC!<,W$,0"*++,0&3-:,1$$-9*/G,12#'*++:,(),6"*7&$#,?O<
@)*+:0(0,21,&"$,/(#/3(&,(0,0"24),(),L(;<,X<XPT9V5,1#2',4"(/",4$,/*),4#(&$,
+ -- = . * > - + . ) > ) + + )*
.*
5 > + + )*
= . * > - + 55555555555
β+K )
!"30,&"$,$'(&&$#,9(*0,/3##$)&,(0,;(.$),9:
+ -- ] + )*
5
. * = 555555555555555555555555555555555555555
>- + >) ⁄ ( β + K )
(a)
iE is sum
on top
and on
bottom all
can do
KCL
TX<?OEV
(b)
Figure 6.62 ;'<#I#(2332"5+3&$$+,#$,)"'&'$2,#)3*6&@&+,#9&)'+0#91#)#@++09)(U#,+'&'$2,#>)?#;&<#I")61'&'#2@
$%+#(&,(/&$#&"#;'<?
451
452 Chapter 6 Bipolar Junction Transistors (BJTs)
=&,(0,()&$#$0&();,&2,)2&$,&"*&,&"(0,$S3*&(2),(0,(-$)&(/*+,&2,MS<,TX<?ODV5,4"(/",;2.$#)0,&"$,27$#*&(2)
21,&"$,&#*-(&(2)*+,9(*0,/(#/3(&5,$A/$7&,&"*&,+--,#$7+*/$0,+)),*)-,>-,#$7+*/$0,>*<,=&,12++240,&"*&,&2
29&*(), *, .*+3$, 21, .*, &"*&, (0,()0$)0(&(.$, &2, .*#(*&(2),21, β5,4$, 0$+$/&, > ) ⁄ ( β + K ) #*#> - ?,Q2&$5
"24$.$#5,&"*&,&"$,.*+3$, 21,>),-$&$#'()$0,&"$,*++24*9+$,)$;*&(.$,0(;)*+, 04();,*&,&"$,/2++$/&2#
0()/$
>)
5,
+ -) = . ) > ) = . * 55555555555
β+K
TX<?ODV
EXERCISE
D6.49 X+'&L"#$%+#(&,(/&$#2@#D&L?#W?WM#$2#29$)&"#)#0(#+3&$$+,#(/,,+"$#2@#K#3I-#3)T&3/3#L)&"-#)"0#)#±M5]
'&L")6#'.&"L#)$#$%+#(266+($2,H#$%)$#&'-#0+'&L"#@2,#+-*#=#+M?N#]?#[+$#+--#=#KP#]#)"0#β# =#KPP?
Ans. >),=,?XP,GΩ`,>-,=,N<N,GΩ<,Q2&$,&"*&,(1,0&*)-*#-,^j,#$0(0&2#,.*+3$0,*#$,30$-,T@77$)-(A,lV
4$,0$+$/&,>),=,?XO,GΩ,*)-,>-,=,N<^,GΩ<,!"(0,#$03+&0,(),.*,=,?<OP,'@,*)-,+-,=,+P<\,_<
6.7.4 Biasing Using a Constant-Current Source
!"$,BC!,/*),9$,9(*0$-,30();,*,/2)0&*)&%/3##$)&,023#/$,.,*0,()-(/*&$-,(),&"$,/(#/3(&,21,L(;<
X<X\T*V<,!"(0,/(#/3(&,"*0,&"$,*-.*)&*;$,&"*&,&"$,$'(&&$#,/3##$)&,(0,()-$7$)-$)&,21,&"$,.*+3$0,21
β,*)-,>)<,!"30,>),/*),9$,'*-$,+*#;$5,$)*9+();,*),()/#$*0$,(),&"$,()73&,#$0(0&*)/$,*&,&"$,9*0$
4(&"23&,*-.$#0$+:,*11$/&();,9(*0,0&*9(+(&:<,L3#&"$#5,/3##$)&%023#/$,9(*0();,+$*-0,&2,0(;)(1(/*)&
-$0(;),0('7+(1(/*&(2)5,*0,4(++,9$/2'$,29.(230,(),+*&$#,0$/&(2)0,*)-,/"*7&$#0<
@,0('7+$,('7+$'$)&*&(2),21,&"$,/2)0&*)&%/3##$)&,023#/$,.,(0,0"24),(),L(;<,X<X\T9V<,!"$
/(#/3(&, 3&(+(>$0, *, 7*(#, 21, '*&/"$-, &#*)0(0&2#0, V?, *)-, VP5, 4(&", V?, /2))$/&$-, *0, *, -(2-$, 9:
0"2#&();,(&0,/2++$/&2#,&2,(&0,9*0$<,=1,4$,*003'$,&"*&,V?,*)-,VP,"*.$,"(;", β,.*+3$05,4$,/*)
)$;+$/&,&"$(#,9*0$,/3##$)&0<,!"30,&"$,/3##$)&,&"#23;",V?,4(++,9$,*77#2A('*&$+:,$S3*+,&2,.UML5
+ -- ] ( ] + ** ) ] + )*
5
. JED = 55555555555555555555555555555555555555555555555
>
0.7
TX<??OV
VCC
IREF
I
R
V
Q1
$
VBE
%
Q2
%VEE
(a)
(b)
Figure 6.63 ;'<#I#;<=#9&)'+0#/'&"L#)#(2"'$)"$5(/,,+"$#'2/,(+#.?#;&<#F&,(/&$#@2,#&3*6+3+"$&"L#$%+#(/,,+"$
'2/,(+#.?
6.8 Discrete-Circuit BJT Amplifiers
Q245,0()/$,V?,*)-,VP,"*.$,&"$,0*'$,+)*5,&"$(#,/2++$/&2#,/3##$)&0,4(++,9$,$S3*+5,#$03+&();,(),
+ -- + + ** ] + )*
. = . JED = 55555555555555555555555555555555555555
>
TX<???V
Q$;+$/&();,&"$,M*#+:,$11$/&,(),VP5,&"$,/2++$/&2#,/3##$)&,4(++,#$'*(),/2)0&*)&,*&,&"$,.*+3$
;(.$),9:,&"(0,$S3*&(2),*0,+2);,*0,VP,#$'*()0,(),&"$,*/&(.$,#$;(2)<,!"(0,/*),9$,;3*#*)&$$-,9:
G$$7();,&"$,.2+&*;$,*&,&"$,/2++$/&2#5,+5,;#$*&$#,&"*),&"*&,*&,&"$,$'(&&$#,T−+**V,9:,*&,+$*0&,O<\_<
!"$,/2))$/&(2),21,V?,*)-,VP,(),L(;<,X<X\T9V,(0,G)24),*0,*,)/%%!0$-"#%%*%<,W$,4(++,0&3-:
/3##$)&,'(##2#0,(),-$&*(+,(),6"*7&$#,N<,,
EXERCISE
6.50 D2,#$%+#(&,(/&$#&"#D&L?#W?WN:)>#.&$%#+--#=#KP#]-#.#=#K#3I-#β#=#KPP-#>)#=#KPP#UΩ-#)"0#>-#=#d?G#UΩ-#@&"0
$%+#0(#726$)L+#)$#$%+#9)'+-#$%+#+3&$$+,-#)"0#$%+#(266+($2,?#D2,#+**#=#KP#]-#)"0#"+L6+($&"L#9)'+#(/,,+"$'@&"0#$%+#,+V/&,+0#7)6/+#2@#>#&"#2,0+,#@2,#$%+#(&,(/&$#2@#D&L?#W?WN:9>#$2#&3*6+3+"$#$%+#(/,,+"$#'2/,(+#.?
Ans. −K#]H#−K?d#]H#+M?W#]H#Ka?N#UΩ
6.8 Discrete-Circuit BJT Amplifiers
Y&$%#2/,#'$/01#2@#;<=#)3*6&@&+,#9)'&('#(23*6+$+-#.+#"2.#*/$#+7+,1$%&"L#$2L+$%+,#91#*,+'+"$5
&"L#*,)($&()6#(&,(/&$'#@2,#0&'(,+$+5(&,(/&$#)3*6&@&+,'?#=%+'+#(&,(/&$'-#.%&(%#/$&6&h+#$%+#)3*6&@&+,
(2"@&L/,)$&2"'#'$/0&+0#&"#C+($&2"#W?W#)"0#2"+#2@#$%+#9&)'&"L#3+$%20'#2@#C+($&2"#W?d-#()"#9+
)''+396+0#/'&"L#2@@5$%+5'%+6@#0&'(,+$+#$,)"'&'$2,'-#,+'&'$2,'-#)"0#()*)(&$2,'?#=%2/L%#*,)($&()6
)"0#(),+@/661#'+6+($+0#$2#&66/'$,)$+#'23+#&3*2,$)"$#*2&"$'-#$%+#(&,(/&$'#*,+'+"$+0#&"#$%&'#'+($&2"
'%2/60#9+#,+L),0+0#)'#+T)3*6+'#2@#0&'(,+$+5(&,(/&$-#9&*26),5$,)"'&'$2,#)3*6&@&+,'?#!"0++0-#$%+,+
&'# )# L,+)$# 7),&+$1# 2@# '/(%# (&,(/&$'-# )# "/39+,# 2@# .%&(%# ),+# +T*62,+0# &"# $%+# +"052@5(%)*$+,
*,296+3'?
!"#$%&'#'+($&2"#.+#*,+'+"$#)#'+,&+'#2@#+T+,(&'+#*,296+3'-#ET+,(&'+'#W?GK#$2#W?GG-#.%&(%#),+
(),+@/661#0+'&L"+0#$2#&66/'$,)$+#&3*2,$)"$#)'*+($'#2@#$%+#)3*6&@&+,#(&,(/&$'#'$/0&+0?#=%+'+#+T+,5
(&'+'#),+#)6'2#&"$+"0+0#$2#+")96+#$%+#,+)0+,#$2#'++#32,+#(6+),61#$%+#0&@@+,+"(+'#9+$.++"#$%+#7),5
&2/'#(&,(/&$#(2"@&L/,)$&2"'?#Y+#'$,2"L61#/,L+#$%+#,+)0+,#$2#'267+#$%+'+#+T+,(&'+'?#I'#/'/)6-#$%+
)"'.+,'#),+#*,27&0+0?
6.8.1 The Basic Structure
D&L/,+#W?We#'%2.'#$%+#9)'&(#(&,(/&$#$%)$#.+#'%)66#/$&6&h+#$2#&3*6+3+"$#$%+#7),&2/'#(2"@&L/,)5
$&2"'#2@#0&'(,+$+#;<=#)3*6&@&+,'?#I32"L#$%+#7),&2/'#9&)'&"L#'(%+3+'#*2''&96+#@2,#0&'(,+$+#;<=
)3*6&@&+,'#:C+($&2"#W?d>-#.+#%)7+#'+6+($+0-#@2,#'&3*6&(&$1#)"0#+@@+($&7+"+''-#$%+#2"+#+3*621&"L
(2"'$)"$5(/,,+"$#9&)'&"L?#D&L/,+#W?We#&"0&()$+'#$%+#0(#(/,,+"$'#&"#)66#9,)"(%+'#)"0#$%+#0(#726$5
)L+'#)$#)66#"20+'?#Y+#'%2/60#"2$+#$%)$#2"+#.2/60#.)"$#$2#'+6+($#)#6),L+#7)6/+#@2,#>)#&"#2,0+,#$2
U++*#$%+#&"*/$#,+'&'$)"(+#)$#$%+#9)'+#6),L+?#\2.+7+,-#.+#)6'2#.)"$#$2#6&3&$#$%+#0(#726$)L+#0,2*
)(,2''#>)#)"0#+7+"#32,+#&3*2,$)"$61#$%+#7),&)9&6&$1#2@#$%&'#0(#726$)L+#,+'/6$&"L#@,23#$%+#7),&)5
$&2"#&"# β#7)6/+'#)32"L#$,)"'&'$2,'#2@#$%+#')3+#$1*+?#=%+#0(#726$)L+#+)#0+$+,3&"+'#$%+#)662.5
)96+#"+L)$&7+#'&L")6#'.&"L#)$#$%+#(266+($2,?##
453
454 Chapter 6 Bipolar Junction Transistors (BJTs)
VCC
IC " #I
RC
VC " VCC % #RC I
VB " %
IB " I'(" $ 1)
IRB
"$1
$
RB
VBE
%
VE " %
&" $ 1 $ V &
IRB
BE
I
%VEE
Figure 6.64 ;)'&(#'$,/($/,+#2@#$%+#(&,(/&$#/'+0#$2#,+)6&h+#'&"L6+5'$)L+-#0&'(,+$+5(&,(/&$#;<=#)3*6&@&+,#(2"5
@&L/,)$&2"'?
,,,,,,,,,,,,,
EXERCISE
6.51 F2"'&0+,#$%+#(&,(/&$#2@#D&L?#W?We#@2,#$%+#()'+#+--#=#+**#=#KP#]-#.#=#K#3I-#>)#=#KPP#UΩ-#>-#=#f#UΩ)"0#β#=#KPP?#D&"0#)66#0(#(/,,+"$'#)"0#726$)L+'?#Y%)$#),+#$%+#)662.)96+#'&L")6#'.&"L'#)$#$%+#(266+($2,
&"#92$%#0&,+($&2"'_#\2.#02#$%+'+#7)6/+'#(%)"L+#)'#β#&'#(%)"L+0#$2#GP_#=2#MPP_#D&"0#$%+#7)6/+'#2@
$%+#;<=#'3)665'&L")6#*),)3+$+,'#)$#$%+#9&)'#*2&"$#:.&$%#β# =#KPP>?#=%+#E),61#726$)L+#+/#=#KPP#]?
Ans. C++#D&L?#EW?GK?#C&L")6#'.&"L8#@2,# β# =#KPP-#+f#]-#QN?e#]H#@2,# β#=#GP-#+f#]-#Qe?e#]H#@2,
β = MPP-#+f ]-#QM?a#]?
$10 V
C
8 k&
0.99 ! 1 mA
!$2 V
! 0.01 mA
%1 V
ai
B
C
$
%1.7 V
100 k&
vp
%
rp
gmvp
B
ro
i
re
1 mA
b " 100
a " 0.99
%10 V
(a)
Figure E6.51
E
VA " 100 V
gm " 40 mA'V
re " 25 &
(b)
E
ro " 100 k&
rp " 2.5 k&
ro
6.8 Discrete-Circuit BJT Amplifiers
455
6.8.2 The Common-Emitter (CE) Amplifier
@0, '$)&(2)$-, (), K$/&(2), X<X5, &"$, 6M, /2)1(;3#*&(2), (0, &"$, '20&, 4(-$+:, 30$-, 21, *++, BC!
*'7+(1($#,/(#/3(&0<,L(;3#$,X<X^T*V,0"240,*,6M,*'7+(1($#,('7+$'$)&$-,30();,&"$,/(#/3(&,21
L(;<, X<X8<, !2,$0&*9+(0", *, (#60'+- 6%*/02,T2#,*),')-6%*/025,*0,(&,(0,02'$&('$0,/*++$-V,*&,&"$
$'(&&$#5,*,+*#;$,/*7*/(&2#,-*5,303*++:,(),&"$,#*);$,21,'(/#21*#*-0,2#,&$)0,21,'(/#21*#*-0,(0
/2))$/&$-,9$&4$$),$'(&&$#,*)-,;#23)-<,!"(0,/*7*/(&2#,(0 #$S3(#$-,&2,7#2.(-$,*,.$#:,+24
('7$-*)/$,&2,;#23)-,T(-$*++:5,>$#2,('7$-*)/$`,(<$<5,(),$11$/&5,*,0"2#&,/(#/3(&V,*&,*++,0(;)*+
1#$S3$)/($0,21,()&$#$0&<,=),&"(0,4*:5,&"$,$'(&&$#,0(;)*+,/3##$)&,7*00$0,&"#23;",-*,&2,;#23)*)-,&"30,#H"'BB4B,&"$,23&73&,#$0(0&*)/$,21,&"$,/3##$)&,023#/$,.,T*)-,*):,2&"$#,/(#/3(&,/2'%
72)$)&, &"*&, '(;"&, 9$, /2))$/&$-, &2, &"$, $'(&&$#V`, "$)/$, -* (0, /*++$-, *, &94'((- )'4')#$*%<
J9.(230+:5,&"$,+24$#,&"$,0(;)*+,1#$S3$)/:5,&"$,+$00,$11$/&(.$,&"$,9:7*00,/*7*/(&2#,9$/2'$0<
!"(0,(003$,4(++,9$,0&3-($-,(),K$/&(2),D<?<P<,L2#,23#,73#720$0,"$#$,4$,0"*++,*003'$,&"*&,-*
VCC (0 V)
RC
CC2
vc
CC1
Rsig
vsig
vo
ii
RL
$
$
v p " vi
vi
RB
$
%
%
0V
%
Ro
CE
I
Rin
%VEE
(a)
Rsig
ii
B
$
vsig
$
%
vi
C
vo = –gmv+(RC || RL || ro)
$
vp
RB
Rib = rp
RC
RL
gmvp
%
%
Rin = RB||rp
ro
rp
E
Ro = RC ||ro
(b)
Figure 6.65 ;'<#I#(2332"5+3&$$+,#)3*6&@&+,#/'&"L#$%+#'$,/($/,+#2@#D&L?#W?We?#;&<#EV/&7)6+"$#(&,(/&$
29$)&"+0#91#,+*6)(&"L#$%+#$,)"'&'$2,#.&$%#&$'#%19,&05π#320+6?
456 Chapter 6 Bipolar Junction Transistors (BJTs)
(0, */&();, *0, *, 7$#1$/&, 0"2#&, /(#/3(&, *)-, &"30, (0, $0&*9+(0"();, *, >$#2, 0(;)*+, .2+&*;$, *&, &"$
$'(&&$#<
=), 2#-$#,)2&, &2,-(0&3#9,&"$,-/,9(*0, /3##$)&0,*)-,.2+&*;$05,&"$,0(;)*+,&2,9$,*'7+(1($-5
0"24), *0, *, .2+&*;$, 023#/$, v0(;, 4(&", *), ()&$#)*+, #$0(0&*)/$, >0(;5, (0, /2))$/&$-, &2, &"$, 9*0$
&"#23;",*,+*#;$,/*7*/(&2#,--?<,6*7*/(&2#,--?5,G)24),*0,*,)*/4+#06-)'4')#$*%5,(0,#$S3(#$&2,*/&,*0,*,7$#1$/&,0"2#&,/(#/3(&,*&,*++,0(;)*+,1#$S3$)/($0,21,()&$#$0&,4"(+$,9+2/G();,-/<,R$#$
*;*(),4$,0"*++,*003'$,&"(0,&2,9$,&"$,/*0$,*)-,-$1$#,-(0/300(2),21,('7$#1$/&,0(;)*+,/23%
7+();5,*#(0();,*0,*,#$03+&,21,&"$,#(0$,21,&"$,('7$-*)/$,21,--?,*&,+24,1#$S3$)/($05,&2,K$/&(2)
D<?<P<,@&,&"(0,H3)/&3#$5,4$,0"23+-,72()&,23&,&"*&,(),0(&3*&(2)0,4"$#$,&"$,0(;)*+,023#/$,/*)
7#2.(-$,*,-/,7*&",12#,&"$,-/,9*0$,/3##$)&,.),4(&"23&,0(;)(1(/*)&+:,/"*);();,&"$,9(*0,72()&5,4$
'*:,/2))$/&,&"$,023#/$,-(#$/&+:,&2,&"$,9*0$5,&"30,-(07$)0();,4(&",--?,*0,4$++,*0,>)<,M+('()*&%
();,>),"*0,&"$,*--$-,9$)$1(/(*+,$11$/&,21,#*(0();,&"$,()73&,#$0(0&*)/$,21,&"$,*'7+(1($#<
!"$,.2+&*;$,0(;)*+,#$03+&();,*&,&"$,/2++$/&2#5, vE5,(0,/237+$-,&2,&"$,+2*-,#$0(0&*)/$,>X,.(*
*)2&"$#,/237+();,/*7*/(&2#,--P<,W$,0"*++,*003'$,&"*&,--P,*+02,*/&0,*0,*,7$#1$/&,0"2#&,/(#/3(&
*&,*++,0(;)*+,1#$S3$)/($0,21,()&$#$0&`,&"30,&"$,23&73&,.2+&*;$, v%,=, vE<,Q2&$,&"*&,>X,/*),9$,*)
*/&3*+,+2*-,#$0(0&2#,&2,4"(/",&"$,*'7+(1($#,(0,#$S3(#$-,&2,7#2.(-$,(&0,23&73&,.2+&*;$,0(;)*+5,2#
(&,/*),9$,&"$,()73&,#$0(0&*)/$,21,*,0390$S3$)&,*'7+(1($#,0&*;$,(),/*0$0,4"$#$,'2#$,&"*),2)$
0&*;$,21,*'7+(1(/*&(2),(0,)$$-$-<,TW$,4(++,0&3-:,'3+&(0&*;$,*'7+(1($#0,(),6"*7&$#,E<V
!2,-$&$#'()$,&"$,/"*#*/&$#(0&(/,7*#*'$&$#0,21,&"$,6M,*'7+(1($#5,&"*&,(05,(&0,()73&,#$0(0%
&*)/$5,.2+&*;$,;*()5,*)-,23&73&,#$0(0&*)/$5,4$,#$7+*/$,&"$,BC!,4(&",(&0,":9#(-%π5,0'*++%0(;)*+
'2-$+<, !"$, #$03+&();, 0'*++%0(;)*+, $S3(.*+$)&, /(#/3(&, 21, &"$, 6M, *'7+(1($#, (0, 0"24), (), L(;<
X<X^T9V<,
!"$,$S3(.*+$)&,/(#/3(&,21,L(;<,X<X^T9V,/*),9$,30$-,&2,-$&$#'()$,&"$,*'7+(1($#,/"*#*/&$#(0%
&(/,7*#*'$&$#0, > &" 5, / v 5, > %5,*)-, Q v ,(),$A*/&+:,&"$,0*'$,4*:,4$,30$-,12#,&"$,a0&#(77$-%-24)b
.$#0(2), 21, &"$, 6M, *'7+(1($#, (), K$/&(2), X<X<\<, W$, *+02, 0"24, 02'$, 21, &"$, *)*+:0(0, -2)$
-(#$/&+:,2),&"$,/(#/3(&,(&0$+1,(),L(;<,X<X^T*V<
J90$#.$,&"*&,&"$,2)+:,-(11$#$)/$,9$&4$$),&"$,/(#/3(&,(),L(;<,X<X^T9V,*)-,&"$,0('7+(1($.$#0(2),(),L(;<,X<^OT9V,(0,&"$,9(*0,#$0(0&*)/$, > ) ,&"*&,*77$*#0,*/#200,&"$,*'7+(1($#,()73&,*)&"30,/"*);$0, > &" ,&2
> &"## d > ) || ( π
TX<??PV
!@# > ) ! ( π #.+#()"#"+L6+($#&$'#+@@+($-#)"0#.+#),+#9)(U#$2#$%+#'&3*6+,#(&,(/&$#2@#D&L?#W?GP:9>
)"0# $%+# @2,3/6)'# 0+,&7+0# &"# C+($&2"# W?W?N?# =%2'+# @2,3/6)'-# .&$%# ( % # "+L6+($+0-# .+,+# *,+5
'+"$+0#&"#$%+#FE#+"$,1#&"#=)96+#W?e?
!@# > ) #&'#"2$#3/(%#L,+)$+,#$%)"# ( π -#$%+"#&$#3/'$#9+#$)U+"#&"$2#)((2/"$#&"#$%+#)")61'&'?#=%&'
&'#)#'&3*6+#$)'U-#)"0#.+#/,L+#$%+#,+)0+,'#$2#4/'$#.2,U#$%+&,#.)1#$%,2/L%#$%+#(&,(/&$#,)$%+,
$%)"# ,+61&"L#2"#3+32,&h+0#@2,3/6)'?#I'# )#(%+(U-# %2.+7+,-#$%+,+# &'#)# '&3*6+# )**,2)(%#$2
)0)*$#$%+#FE#@2,3/6)'#2@#=)96+#W?e#$2#$%+#()'+#)$#%)"08#I**61#$%+#=%p7+"&"#$%+2,+3#$2#$%+
"+$.2,U# (23*2'+0# 2@# v '&L - # > '&L - # )"0# > ) - # $%/'# ,+0/(&"L# &$# $2# )# L+"+,)$2,# v′'&L d
( > ) ⁄ ( > ) e > '&L ) ) v '&L #)"0#)#,+'&'$)"(+# >′ '&L d > '&L || > ) ? #b2.#$%+#@2,3/6)'#&"#$%+#FE#+"$,1#&"
=)96+#W?e#()"#9+#(%)"L+0#)'#@2662.'8#J+*6)(+#$%+#+T*,+''&2"#@2,# > &" #91#$%)$#&"#EV?#:W?KKM>H
3/6$&*61#$%+#+T*,+''&2"#@2,# Q v #91#$%+#@)($2,# > ) ⁄ ( > ) e > '&L ) H #)"0#,+*6)(+# > '&L #&"#$%)$#+T*,+'5
'&2"#91# ( > '&L || > ) )?
6.8 Discrete-Circuit BJT Amplifiers
EXERCISE
6.52 F2"'&0+,#$%+#FE#)3*6&@&+,#2@#D&L?#W?WG:)>#.%+"#9&)'+0#)'#&"#ET+,(&'+#W?GK?#!"#*),$&(/6),-#,+@+,#$2
D&L? EW?GK#@2,#$%+#9&)'#(/,,+"$'#)"0#$%+#7)6/+'#2@#$%+#+6+3+"$'#2@#$%+#;<=#320+6#)$#$%+#9&)'#*2&"$?#E7)65
/)$+#>&"#:.&$%2/$#)"0#.&$%#>)#$)U+"#&"$2#)((2/"$>-#/v%#:.&$%2/$#)"0#.&$%#(%#$)U+"#&"$2#)((2/"$>-#)"0
>2#:.&$%2/$#)"0#.&$%#(%#$)U+"#&"$2#)((2/"$>?#D2,#>X#=#G#UΩ-#@&"0#/v?#!@#>'&L#=#G#UΩ-#@&"0#$%+#27+,)66
726$)L+#L)&"#Qv?#!@#$%+#'&"+5.)7+# vπ#&'#$2#9+#6&3&$+0#$2#G#3]#*+)U-#.%)$#&'#$%+#3)T&3/3#)662.+0
*+)U#)3*6&$/0+#2@#v'&L#)"0#$%+#(2,,+'*2"0&"L#*+)U#)3*6&$/0+#2@#v%_
Ans. P<^,GΩ5,P<8,GΩ`,]\PO,_o_5,]PDX,_o_`,E,GΩ5,N<8,GΩ`,]??D,_o_`,]\D,_o_`,?^ '_`,O<X,_
6.8.3 The Common-Emitter Amplifier with an Emitter Resistance
I'#0+32"'$,)$+0#&"#C+($&2"#W?W?e-#)#"/39+,#2@#9+"+@&(&)6#,+'/6$'#()"#9+#29$)&"+0#91#(2""+($5
&"L#)#,+'&'$)"(+# > 4 #&"#$%+#+3&$$+,#2@#$%+#$,)"'&'$2,?#=%&'#&'#'%2."#&"#D&L?#W?WW:)>#.%+,+# > 4 #&'2@# (2/,'+-# /"91*)''+0?# D&L/,+# W?WW:9># '%2.'# $%+# '3)665'&L")6-# +V/&7)6+"$5(&,(/&$# 320+6?
B9'+,7+#$%)$#$%+#2"61#0&@@+,+"(+#9+$.++"#$%&'#(&,(/&$#)"0#$%+#'&3*6&@&+0#7+,'&2"#'$/0&+0#&"
C+($&2"#W?W?e#&'#$%+#&"(6/'&2"#2@#$%+#9&)'#,+'&'$)"(+# > ) -#.%&(%#/"@2,$/")$+61#()"#6&3&$#$%+
&"(,+)'+#&"# > &" #0/+#$2# > 4 - #'&"(+
> &" d > ) || [ ( β e K ) ( ( 4 e > 4 ) ]
TX<??\V
=%+#)")61'&'#2@#$%+#(&,(/&$'#&"#D&L?#W?WW#&'#'$,)&L%$@2,.),0#)"0#&'#&66/'$,)$+0#&"#$%+#@&L/,+?#=%+
@2,3/6)'#L&7+"#&"#=)96+#W?e#()"#9+#)0)*$+0#$2#)**61#$2#$%+#(&,(/&$#%+,+#91#,+*6)(&"L#$%+#@2,5
3/6)#@2,# > &" #.&$%#$%)$#&"#EV?#:W?KKN>-#,+*6)(&"L# > '&L #91# >′'&L d > '&L || > ) - #)"0#3/6$&*61&"L#$%+
+T*,+''&2"# @2,# Q v # 91# $%+# @)($2,# > ) ⁄ ( > ) e > '&L ) ?# B"(+# )L)&"-# .+# 02# "2$# ,+(233+"0# $%&'
)**,2)(%#2@#*6/LL&"L#&"$2#@2,3/6)'H#,)$%+,-#'&"(+#+)(%#(&,(/&$#$%+#,+)0+,#.&66#+"(2/"$+,#.&66
9+#0&@@+,+"$-#&$#&'#3/(%#32,+#/'+@/6#$2#.2,U#2"+k'#.)1#$%,2/L%#$%+#(&,(/&$#/'&"L#$%+#)")61'&'
3+$%20'#'$/0&+0#)'#)#L/&0+?
EXERCISE
6.53# F2"'&0+,#$%+#+3&$$+,50+L+"+,)$+0#FE#(&,(/&$#2@#D&L?#W?WW#.%+"#9&)'+0#)'#&"#ET+,(&'+#W?GK?#!"#*),5
$&(/6),-#,+@+,#$2#D&L?#EW?GK#@2,#$%+#9&)'#(/,,+"$'#)"0#@2,#$%+#7)6/+'#2@#$%+#+6+3+"$'#2@#$%+#;<=#320+6
)$#$%+#9&)'#*2&"$?#[+$#$%+#)3*6&@&+,#9+#@+0#@,23#)#'2/,(+#%)7&"L#>'&L#=#G#UΩ-#)"0#6+$#>X#=#G#UΩ?#D&"0
$%+#7)6/+#2@#>4#$%)$#,+'/6$'#&"#>&"#+V/)6#$2#@2/,#$&3+'#$%+#'2/,(+#,+'&'$)"(+#>'&L?#D2,#$%&'#7)6/+#2@#>4@&"0#/v%-#>2-#/v -#)"08Qv ?#!@#vπ#&'#$2#9+#6&3&$+0#$2#G#3]-#.%)$#&'#$%+#3)T&3/3#7)6/+#v'&L#()"#%)7+#.&$%
)"0#.&$%2/$#>4#&"(6/0+0_#D&"0#$%+#(2,,+'*2"0&"L#v%?
Ans. PP^,Ω`,]\P,_o_`,E,GΩ`,]?P<\,_o_`,]D<E,_o_`,XP<^,'_`,?^,'_`,O<X,_
457
458 Chapter 6 Bipolar Junction Transistors (BJTs)
VCC (0 V)
RC
CC2
vo
CC1
Rsig
ii
ib
ic = ,ie
$
vp
$
%
vsig $
%
vo = –,ie(RC||RL)
vi R
B
Ro
CE
0V
Rib
%
vi
re $ Re
ie "
Re
RL
Rin
I
%VEE
(a)
C
vo = –,ie(RC||RL)
ic
RC
aie
Rsig
ii
ib
$
vsig
$
%
vi
%
Rin = RB||Rib
RB
RL
B
$
ie
vp
re
%
E
Rib = (b + 1)(re + Re)
ie "
Ro = RC
vi
re $ Re
Re
(b)
Figure 6.66 ;'<# I# (2332"5+3&$$+,# )3*6&@&+,# .&$%# )"# +3&$$+,# ,+'&'$)"(+# >4?# ;&<# EV/&7)6+"$# (&,(/&$
29$)&"+0#91#,+*6)(&"L#$%+#$,)"'&'$2,#.&$%#&$'#=#320+6?
6.8 Discrete-Circuit BJT Amplifiers
6.8.4 The Common-Base (CB) Amplifier
L(;3#$,X<XNT*V,0"240,*,6B,*'7+(1($#,9*0$-,2),&"$,/(#/3(&,21,L(;<,X<X8<,J90$#.$,&"*&,0()/$
92&", &"$, -/, *)-, */, .2+&*;$0, *&, &"$, 9*0$, *#$, >$#25, 4$, "*.$, /2))$/&$-, &"$, 9*0$, -(#$/&+:, &2
;#23)-5, &"30, $+('()*&();, #$0(0&2#, >), *+&2;$&"$#<, 6237+();, /*7*/(&2#0, --?, *)-8 --P, 7$#12#'
0('(+*#,13)/&(2)0,&2,&"20$,(),&"$,6M,/(#/3(&<
!"$,0'*++%0(;)*+5,$S3(.*+$)&%/(#/3(&,'2-$+,21,&"$,*'7+(1($#,(0,0"24),(),L(;<,X<XNT9V<,!"(0
/(#/3(&,(0,(-$)&(/*+,&2,&"*&,(),L(;<,X<^\T9V5,4"(/",4$,*)*+:>$-,(),-$&*(+,(),K$/&(2),X<X<^<,!"30
&"$,*)*+:0(0,21,K$/&(2),X<X<^5,*)-,()-$$-,&"$,#$03+&0,03''*#(>$-,(),&"$,6B,$)&#:,(),!*9+$
X<85,*77+:,-(#$/&+:,"$#$<
VCC (0 V)
RC
CC2
vo
vo
aie
RL
re
CC1
ii
Rsig
Ro
ie
$
vsig
$
%
I
vi
%
Rin
%VEE
(a)
C
aie
vo = –,ie (RC ||RL )
RC
RL
B
ie = –vi /re
Ro = RC
re
Rsig
ii
E
$
vsig
$
%
vi
%
Rin= re
(b)
Figure 6.67 ;'<#I#(2332"59)'+#)3*6&@&+,#/'&"L#$%+
'$,/($/,+#2@#D&L?#W?We?#;&<#EV/&7)6+"$#(&,(/&$#29$)&"+0#91
,+*6)(&"L#$%+#$,)"'&'$2,#.&$%#&$'#=#320+6?
459
460 Chapter 6 Bipolar Junction Transistors (BJTs)
EXERCISE
6.54 F2"'&0+,#$%+#F;# )3*6&@&+,# 2@#D&L?#W?WW:)>#.%+"#0+'&L"+0#/'&"L#$%+#;<=#)"0#(23*2"+"$#7)6/+'
'*+(&@&+0#&"#ET+,(&'+#W?GK?#C*+(&@&()661-#,+@+,#$2#D&L?#EW?GK#@2,#$%+#9&)'#V/)"$&$&+'#)"0#$%+#7)6/+'#2@
$%+#(23*2"+"$'#2@#$%+#;<=#'3)665'&L")6#320+6?#[+$#>'&L#=#>X#=#G#UΩ?#D&"0#$%+#7)6/+'#2@#>&"-#/v%-#>%/v -# v $ ⁄ v '&L - #)"0#Qv?#=2#.%)$#7)6/+#'%2/60#>'&L#9+#,+0/(+0#:/'/)661#"2$#*2''&96+#$2#02j>#$2#29$)&"#)"
27+,)66#726$)L+#L)&"#+V/)6#$2#$%)$#@2/"0#@2,#$%+#FE#)3*6&@&+,#&"#ET+,(&'+#W?GM-#$%)$#&'-#QNa#]Z]_
Ans. P^,Ω`,+\PO,_o_`,E,GΩ`,+?P\,_o_`,O<OO^,_o_`,O<X,_o_`,^8,Ω
6.8.5 The Emitter Follower
@),$'(&&$#%12++24$#,/(#/3(&,9*0$-,2),&"$,0&#3/&3#$,21,L(;<,X<X8,(0,0"24),(),L(;<,X<XET*V<
J90$#.$,&"*&,0()/$,&"$,/2++$/&2#,(0,&2,9$,*&,0(;)*+,;#23)-5,4$,"*.$,$+('()*&$-,&"$,/2++$/&2#
#$0(0&*)/$,>-<,!"$,()73&,0(;)*+,(0,/*7*/(&(.$+:,/237+$-,&2,&"$,9*0$5,*)-,&"$,23&73&,0(;)*+,(0
/*7*/(&(.$+:,/237+$-,1#2',&"$,$'(&&$#,&2,*,+2*-,#$0(0&*)/$,>X<,,,,,,
$VCC
CC1
Rsig
CC2
vsig
$
%
$
RB
RL
I
vo
%
Rin
Ro , Rout
%VEE
(a)
Rsig
ib " (1 % a)ie "
aie
ie
b$1
$
ie
re
vsig
$
%
RB
vi
$
RL
%
%
Rin
Rib
vo
Ro , Rout
(b)
Figure 6.68 ;'<#I"#+3&$$+,5@2662.+,#(&,(/&$#9)'+0#2"#$%+#'$,/($/,+#2@#D&L?#W?We?#;&<#C3)665'&L")6#+V/&7)5
6+"$#(&,(/&$#2@#$%+#+3&$$+,#@2662.+,#.&$%#$%+#$,)"'&'$2,#,+*6)(+0#91#&$'#=#320+6?
6.8 Discrete-Circuit BJT Amplifiers
J+*6)(&"L#$%+#;<=#.&$%#&$'#=#320+6#)"0#"+L6+($&"L# ( % - #.+#29$)&"#$%+#+V/&7)6+"$#(&,(/&$
'%2."#&"#D&L?#W?Wf:9>?#=%&'#(&,(/&$#&'#&0+"$&()6#$2#$%)$#&"#$%+#'$,&**+0502."#()'+#)")61h+0#&"
C+($&2"#W?W?W#+T(+*$#%+,+#.+#%)7+#$%+#9&)'#,+'&'$)"(+# > ) ? #b2$+#$%)$#&$#&'#7+,1#&3*2,$)"$#$2
'+6+($#)'#6),L+#)#7)6/+#@2,# > ) #)'#*+,3&$$+0#91#0(#9&)'#(2"'&0+,)$&2"'-#'&"(+#)#62.# > ) #(2/60
0+@+)$# $%+# */,*2'+# 2@# $%+# +3&$$+,# @2662.+,?# =2# )**,+(&)$+# $%&'# *2&"$# ,+()66# $%)$# $%+# 32'$
&3*2,$)"$#@+)$/,+#2@#$%+#+3&$$+,#@2662.+,#&'#$%)$#&$#3/6$&*6&+'# > X #91# ( β e K )-#$%/'#*,+'+"$&"L#)
%&L%#&"*/$#,+'&'$)"(+#$2#$%+#'&L")6#'2/,(+?#\+,+-#%2.+7+,-# > ) #)**+),'#&"#*),)66+6#.&$%#$%&'
&"(,+)'+0#,+'&'$)"(+-#,+'/6$&"L#&"
> &"## d > ) || ( β e K ) ( ( 4 e > X )
TX<??8V
=%/'#&0+)661-# > ) #'%2/60#9+#3/(%#6),L+,#$%)"# ( β e K ) # ( ( 4 e > X )?
IL)&"#.+#/,L+#$%+#,+)0+,#$2#)")61h+#$%+#(&,(/&$#9+&"L#'$/0&+0#:%+,+-#D&L?#W?Wf>#0&,+($61.&$%2/$#$%+#"++0#$2#,+@+,#9)(U#$2#3+32,&h+0#@2,3/6)'?#I'#)#(%+(U-#%2.+7+,-#.+#"2$+#$%)$
$%+#,+'/6$'#*,+'+"$+0#&"#=)96+#W?e#&"#$%+#+3&$$+,5@2662.+,#+"$,1#)**61#$2#$%+#(&,(/&$#&"#D&L?
W?Wf:9># .&$%# $%+# @2662.&"L# )0)*$)$&2"'8# J+*6)(+# $%+# +T*,+''&2"# @2,# > &" # .&$%# $%)$# &"# EV?
:W?KKe>H#3/6$&*61#$%+#+T*,+''&2"#@2,# Q v #91#$%+#@)($2,# > ) ⁄ ( > ) e > '&L ) H #)"0#,+*6)(+# > '&L #&"#$%+
+T*,+''&2"#@2,# Q v #91# ( > '&L || > ) )? #I6'2-#$%+#+V/&7)6+"$#(&,(/&$'#&"#D&L?#W?GW#()"#9+#)0)*$+0#$2
$%+# (&,(/&$# &"# D&L?# W?Wf# 91# ,+*6)(&"L# v '&L # 91# ( > ) ⁄ ( > ) e > '&L ) ) v '&L # )"0# > '&L # 91# ( > '&L || > ) )?
D&")661-#$%+#=%p7+"&"#+V/&7)6+"$#&"#D&L#W?Gd:)>#()"#9+#3)0+#$2#)**61#$2#$%+#(&,(/&$#&"#D&L?
W?Wd#91#/'&"L# Q v% d > ) ⁄ ( > ) e > '&L ) #)"0# > 2/$ d ( 4 e ( > '&L || > ) ) ⁄ ( β e K ) ?
EXERCISE
6.55 =%+#+3&$$+,#@2662.+,#&"#D&L?#W?Wf:)>#&'#/'+0#$2#(2""+($#)#'2/,(+#.&$%#>'&L#=#KP#UΩ#$2#)#62)0#>X#=#K#UΩ?
=%+#$,)"'&'$2,#&'#9&)'+0#)$#.#=#G#3I-#/$&6&h+'#)#,+'&'$)"(+#>)#=#eP#UΩ-#)"0#%)'#β#=#KPP?#D&"0#>$#-#>&"Qv -#Qv %-#)"0#>2/$?#!@#&"#2,0+,#$2#6&3&$#"2"6&"+),#0&'$2,$&2"-#$%+#9)'+Q+3&$$+,#'&L")6#726$)L+#&'#6&3&$+0#$2
KP#3]#*+)U-#.%)$#&'#$%+#(2,,+'*2"0&"L#)3*6&$/0+#)$#$%+#2/$*/$_#Y%)$#.&66#$%+#27+,)66#726$)L+#L)&"
9+(23+#&@#>X#&'#(%)"L+0#$2#M#UΩ_#=2#GPP#Ω_
Ans. ?O?<^,GΩ`,PE<N,GΩ`,O<N\E,_o_`,O<E,_o_`,E8,Ω`,P,_`,O<NXE,_o_`,O<XE^,_o_<
6.8.6 The Amplifier Frequency Response
=%/'#@),-#.+#%)7+#)''/3+0#$%)$#$%+#L)&"#2@#;<=#)3*6&@&+,'#&'#(2"'$)"$#&"0+*+"0+"$#2@#$%+
@,+V/+"(1#2@#$%+#&"*/$#'&L")6?#=%&'#.2/60#&3*61#$%)$#;<=#)3*6&@&+,'#%)7+#&"@&"&$+#9)"0.&0$%.%&(%#2@#(2/,'+#&'#"2$#$,/+?#=2#&66/'$,)$+-#.+#'%2.#&"#D&L?#W?Wa#)#'U+$(%#2@#$%+#3)L"&$/0+#2@
$%+# L)&"# 2@# )# (2332"5+3&$$+,# )3*6&@&+,# 7+,'/'# @,+V/+"(1?# B9'+,7+# $%)$# $%+,+# &'# &"0++0# )
.&0+#@,+V/+"(1#,)"L+#27+,#.%&(%#$%+#L)&"#,+3)&"'#)632'$#(2"'$)"$?#=%&'#297&2/'61#&'#$%+
/'+@/6# @,+V/+"(1# ,)"L+# 2@# 2*+,)$&2"# @2,# $%+# *),$&(/6),# )3*6&@&+,?# =%/'# @),-# .+# %)7+# 9++"
)''/3&"L#$%)$#2/,#)3*6&@&+,'#),+#2*+,)$&"L#&"#$%&'#@,+V/+"(1#9)"0-#()66+0#$7!-"#2&'02?
461
462 Chapter 6 Bipolar Junction Transistors (BJTs)
Vo
Vsig (dB)
Low-frequency
band
Midband
High-frequency band
• All capacitances can be neglected
• Gain falls off
due to the internal
capacitive effects in
the BJT
• Gain falls off
due to the effects
of CC1, CC2,
and CE
3 dB
20 log (AM ( (dB)
fL
fH
f (Hz)
(log scale)
Figure 6.69 CU+$(%#2@#$%+#3)L"&$/0+#2@#$%+#L)&"#2@#)#FE#)3*6&@&+,#7+,'/'#@,+V/+"(1?#=%+#L,)*%#0+6&"+)$+'#$%+
$%,++#@,+V/+"(1#9)"0'#,+6+7)"$#$2#@,+V/+"(15,+'*2"'+#0+$+,3&")$&2"?
D&L/,+#W?Wa#&"0&()$+'#$%)$#)$#62.+,#@,+V/+"(&+'-#$%+#3)L"&$/0+#2@#)3*6&@&+,#L)&"#@)66'#2@@?
=%&'#&'#9+()/'+#$%+#(2/*6&"L#)"0#91*)''#()*)(&$2,'#"2#62"L+,#%)7+#62.#&3*+0)"(+'?#J+()66
$%)$#.+#)''/3+0#$%)$#$%+&,#&3*+0)"(+'#.+,+#'3)66#+"2/L%#$2#)($#)'#'%2,$#(&,(/&$'?#I6$%2/L%
$%&'#()"#9+#$,/+#)$#3&09)"0#@,+V/+"(&+'-#)'#$%+#@,+V/+"(1#2@#$%+#&"*/$#'&L")6#&'#62.+,+0-#$%+
,+)($)"(+# K ⁄ Z ω - #2@#+)(%#2@#$%+'+#()*)(&$2,'#9+(23+'#'&L"&@&()"$-#)"0#&$#()"#9+#'%2."#$%)$
$%&'#,+'/6$'#&"#$%+#27+,)66#726$)L+#L)&"#2@#$%+#)3*6&@&+,#0+(,+)'&"L?
D&L/,+# W?Wa# &"0&()$+'# )6'2# $%)$# $%+# L)&"# 2@# $%+# )3*6&@&+,# @)66'# 2@@# )$# $%+# %&L%5@,+V/+"(1
+"0?#=%&'#&'#0/+#$2#$%+#&"$+,")6#()*)(&$&7+#+@@+($'#&"#$%+#;<=?#!"#F%)*$+,#N#.+#9,&+@61#&"$,25
0/(+0##'/(%#()*)(&$&7+#+@@+($'#&"#2/,#'$/01#2@#$%+#"!#4/"($&2"?#!"#F%)*$+,#a#.+#'%)66#'$/01#$%+
&"$+,")6# ()*)(&$&7+# +@@+($'# 2@# $%+# ;<=# )"0# .&66# )/L3+"$# $%+# %19,&05π# 320+6# .&$%# ()*)(&5
$)"(+'#$%)$#320+6#$%+'+#+@@+($'?
Y+#.&66#/"0+,$)U+#)#0+$)&6+0#'$/01#2@#$%+#@,+V/+"(1#,+'*2"'+#2@#;<=#)3*6&@&+,'#&"#F%)*5
$+,#a?#D2,#$%+#$&3+#9+&"L-#%2.+7+,-#&$#&'#&3*2,$)"$#@2,#$%+#,+)0+,#$2#,+)6&h+#$%)$#@2,#+7+,1#;<=
)3*6&@&+,-#$%+,+#&'#)#@&"&$+#9)"0#27+,#.%&(%#$%+#L)&"#&'#)632'$#(2"'$)"$?#=%+#92/"0),&+'#2@
$%&'#/'+@/6#@,+V/+"(1#9)"0#2,#3&09)"0-#),+#$%+#$.2#@,+V/+"(&+'#GX#)"0#GY#)$#.%&(%#$%+#L)&"
0,2*'#91#)#(+,$)&"#"/39+,#2@#0+(&9+6'#:/'/)661#N#0;>#9+62.#&$'#7)6/+#)$#3&09)"0?#I'#&"0&5
()$+0#&"#D&L?#W?Wa-#$%+#)3*6&@&+,#&'02:#2$7-#2,#N50;#9)"0.&0$%-#&'#0+@&"+0#)'#$%+#0&@@+,+"(+
9+$.++"#$%+#62.+,#: GX>#)"0#/**+,#2,#%&L%+,#: GY>#N50;#@,+V/+"(&+'8
)"0#'&"(+#/'/)661# G X * G Y -
)2 d G Y ] G X
TX<??^V
)2 ! G Y
TX<??XV
I#@&L/,+52@53+,&$#@2,#$%+#)3*6&@&+,#&'#&$'#6'#0,&'02:#2$7-4%*2/)$-#0+@&"+0#)'#
Q) d / [ )2
TX<??NV
.%+,+# / [ #&'#$%+#3)L"&$/0+#2@#$%+#)3*6&@&+,#L)&"#&"#$%+#3&09)"0?#!$#.&66#9+#'++"#&"#F%)*$+,#a
$%)$#&"#)3*6&@&+,#0+'&L"#&$#&'#/'/)661#*2''&96+#$2#$,)0+#2@@#L)&"#@2,#9)"0.&0$%?#B"+#.)1#$2#)((235
*6&'%#$%&'-#@2,#&"'$)"(+-#&'#91#&"(6/0&"L#,+'&'$)"(+# > 4 #&"#$%+#+3&$$+,#2@#$%+#FE#)3*6&@&+,?
6.9 Transistor Breakdown and Temperature Effects
6.9 Transistor Breakdown and Temperature Effects
Y+#(2"(6/0+#$%&'#(%)*$+,#.&$%#)#9,&+@#0&'(/''&2"#2@#$.2#&3*2,$)"$#"2"&0+)6#+@@+($'#&"#$%+
;<=8#726$)L+#9,+)U02."-#)"0#$%+#0+*+"0+"(+#2@# β #2"# . - #)"0#$+3*+,)$/,+?
6.9.1 Transistor Breakdown
!"$,'*A('3',.2+&*;$0,&"*&,/*),9$,*77+($-,&2,*,BC!,*#$,+('(&$-,9:,&"$,MBC,*)-,6BC,9#$*G%
-24),$11$/&0,&"*&,12++24,&"$,*.*+*)/"$,'3+&(7+(/*&(2),'$/"*)(0',-$0/#(9$-,(),K$/&(2),\<^<\<
62)0(-$#, 1(#0&, &"$, /2''2)%9*0$, /2)1(;3#*&(2)<, !"$, $-− v-), /"*#*/&$#(0&(/0, (), L(;<, X<NOT9V
()-(/*&$,&"*&,12#,$*,=,O,T(<$<5,4(&",&"$,$'(&&$#,27$)%/(#/3(&$-V,&"$,/2++$/&2#]9*0$,H3)/&(2),9#$*G0
-24),*&,*,.2+&*;$,-$)2&$-,9:,)+-)N<,L2#,$*,r,O5,9#$*G-24),2//3#0,*&,.2+&*;$0,0'*++$#,&"*)
)+-)N<,!:7(/*++:5,12#,-(0/#$&$,BC!05,)+-)N,(0,;#$*&$#,&"*),^O,_<
Q$A&, /2)0(-$#, &"$, /2''2)%$'(&&$#, /"*#*/&$#(0&(/0, 21, L(;<, X<N?5, 4"(/", 0"24, 9#$*G-24)
2//3##();,*&,*,.2+&*;$,)+-*N<,R$#$5,*+&"23;",9#$*G-24),(0,0&(++,21,&"$,*.*+*)/"$,&:7$5,&"$,$11$/&0
2),&"$,/"*#*/&$#(0&(/0,*#$,'2#$,/2'7+$A,&"*),(),&"$,/2''2)%9*0$,/2)1(;3#*&(2)<,W$,4(++,)2&
$A7+*(),&"$0$,(),-$&*(+`,(&,(0,0311(/($)&,&2,72()&,23&,&"*&,&:7(/*++:,)+-*N,(0,*923&,"*+1,)+-)N<,J)
&#*)0(0&2#,-*&*,0"$$&05,)+-*N,(0,02'$&('$0,#$1$##$-,&2,*0,&"$,(/($'#0#06-1*+$'6!,X+-*N<
B#$*G-24),21,&"$,6BC,(),$(&"$#,&"$,/2''2)%9*0$,2#,/2''2)%$'(&&$#,/2)1(;3#*&(2),(0,)2&
-$0&#3/&(.$,*0,+2);,*0,&"$,724$#,-(00(7*&(2),(),&"$,-$.(/$,(0,G$7&,4(&"(),0*1$,+('(&0<,!"(05,"24%
$.$#5,(0,)2&,&"$,/*0$,4(&",&"$,9#$*G-24),21,&"$,$'(&&$#]9*0$,H3)/&(2)<,!"$,MBC,9#$*G0,-24),()
*),*.*+*)/"$,'*))$#,*&,*,.2+&*;$,)+*)N8 '3/",0'*++$#,&"*),)+-)N<,!:7(/*++:5,)+*)N,(0,(),&"$
#*);$,21,X,_,&2,E,_5,*)-,&"$,9#$*G-24),(0,-$0&#3/&(.$,(),&"$,0$)0$,&"*&,&"$,β,21,&"$,&#*)0(0&2#,(0
7$#'*)$)&+:,#$-3/$-<,!"(0,-2$0,)2&,7#$.$)&,30$,21,&"$,MBC,*0,*,>$)$#,-(2-$,&2,;$)$#*&$,#$1$#%
$)/$,.2+&*;$0,(),=6,-$0(;)<,=),03/",*77+(/*&(2)0,2)$,(0,)2&,/2)/$#)$-,4(&",&"$,β%-$;#*-*&(2)
$11$/&<,@,/(#/3(&,*##*);$'$)&,&2,7#$.$)&,MBC,9#$*G-24),(),=6,*'7+(1($#0,4(++,9$,-(0/300$-,()
6"*7&$#, ?P<, !#*)0(0&2#, 9#$*G-24), *)-, &"$, '*A('3', *++24*9+$, 724$#, -(00(7*&(2), *#$
('72#&*)&,7*#*'$&$#0,(),&"$,-$0(;),21,724$#,*'7+(1($#0,T6"*7&$#,??V,<
<
iC
Saturation
region
Active region
aIE1
iE " IE1
iE " IE2
aIE2
iC
vCB
iE " 0
iE
(a)
vCB
0
0.4 % 0.5 V
BVCBO
Expanded
scale
(b)
Figure 6.70 =%+#;<=#(2332"59)'+#(%),)($+,&'$&('#&"(6/0&"L#$%+#$,)"'&'$2,#9,+)U02."#,+L&2"?
463
464 Chapter 6 Bipolar Junction Transistors (BJTs)
Figure 6.71 !".(FG!(+$11$34.1)''.#(+",#,+'.#)*')+*()3+?%2)3&('".(9#.,@2$/3(#.&)$37
EXERCISE
6.56 H",'()*('".($%'-%'(0$?',&.($6('".(+)#+%)'()3(:)&7(I;7J;()6('".('#,3*)*'$#(!"!#$(=(<K(LM
µA
Figure E6.56
Ans. !"#$%
6.9.2 Dependence of β on IC and Temperature
!"#$%&"$%'('")*(+",-'.#(/.(",0.(,**%1.2('",'('".('#,3*)*'$#(+$11$34.1)''.#(2+(+%##.3'(&,)35( β
$#( % &' 5()*(+$3*',3'(6$#(,(&)0.3('#,3*)*'$#7(83(6,+'5( β (2.-.32*($3('".(2+(+%##.3'(,'(/")+"('".('#,34
*)*'$#()*(9),*.25(,*(*"$/3()3(:)&7(;7<=7(!".(-">*)+,?(-#$+.**.*('",'(&)0.(#)*.('$('")*(2.-.32.3+.
,#.(9.>$32('".(*+$-.($6('")*(9$$@7(A$'.5("$/.0.#5('",'('".#.()*(,(+%##.3'(#,3&.($0.#(/")+"( β ()*
")&".*'7(A$#1,??>5($3.(9),*.*('".('#,3*)*'$#('$($-.#,'.(,'(,(+%##.3'(/)'")3('")*(#,3&.7
:)&%#.(;7<=(,?*$(*"$/*('".(2.-.32.3+.($6( β ($3('.1-.#,'%#.7(!".(6,+'('",'( β ()3+#.,*.*
/)'"('.1-.#,'%#.(+,3(?.,2('$(*.#)$%*(-#$9?.1*()3('#,3*)*'$#*('",'($-.#,'.(,'(?,#&.(-$/.#(?.04
.?*(B*..(C",-'.#(DDE7
6.9 Transistor Breakdown and Temperature Effects
465
µ
Figure 6.72 =1*&()6#0+*+"0+"(+#2@#β#2"#.-#)"0#2"#$+3*+,)$/,+#&"#)"#&"$+L,)$+05(&,(/&$#"*"#'&6(2"#$,)"'&'5
$2,#&"$+"0+0#@2,#2*+,)$&2"#),2/"0#K#3I?
Summary
Z$7$)-();,2),&"$,9(*0,/2)-(&(2)0,2),(&0,&42,H3)/&(2)05
&"$,BC!,/*),27$#*&$,(),2)$,21,&"#$$,7200(9+$,'2-$0Y,/3&%
211,T92&",H3)/&(2)0,#$.$#0$,9(*0$-V5,*/&(.$,T&"$,MBC,12#%
4*#-,9(*0$-,*)-,&"$,6BC,#$.$#0$,9(*0$-V5,*)-,0*&3#*&(2)
T92&",H3)/&(2)0,12#4*#-,9(*0$-V<,U$1$#,&2,!*9+$,X<?<
L2#,*'7+(1($#,*77+(/*&(2)05,&"$,BC!,(0,27$#*&$-,(),&"$,*/%
&(.$,'2-$<,K4(&/"();,*77+(/*&(2)0,'*G$,30$,21,&"$,/3&%
211,*)-,0*&3#*&(2),'2-$0<,
@,BC!,27$#*&();,(),&"$,*/&(.$,'2-$,7#2.(-$0,*,/2++$/&2#
/3##$)&, $ - = . 6 4 v)* Z+, ? ,!"$,9*0$,/3##$)&, $ ) = $ - ⁄ β *)-,&"$,$'(&&$#,/3##$)&,$*,=,$-,+,$)<,@+025,$-,=,α $*5,*)-,&"30
β = α ⁄ ( K ] α ) ,*)-, α = β ⁄ ( β + K ) ? ,K$$,!*9+$,X<P<
=2# +"'/,+# 2*+,)$&2"# &"# $%+# )($&7+# 320+-# $%+# (266+($2,
726$)L+#2@#)"#!"!#$,)"'&'$2,#3/'$#9+#U+*$#%&L%+,#$%)"#)*5
*,2T&3)$+61# P?e# ]# 9+62.# $%+# 9)'+# 726$)L+?# D2,# )# "!"
$,)"'&'$2,#$%+#(266+($2,#726$)L+#3/'$#9+#62.+,#$%)"#)*5
*,2T&3)$+61#P?e#]#)927+#$%+#9)'+#726$)L+?#B$%+,.&'+$%+#F;<#9+(23+'#@2,.),0#9&)'+0-#)"0#$%+#$,)"'&'$2,#+"5
$+,'#$%+#')$/,)$&2"#,+L&2"?
@&, *, /2)0&*)&, /2++$/&2#, /3##$)&5, &"$, '*;)(&3-$, 21, &"$
9*0$]$'(&&$#,.2+&*;$,-$/#$*0$0,9:,*923&,P,'_,12#,$.$#:
?°6,#(0$,(),&$'7$#*&3#$<
!"$,BC!,4(++,9$,*&,&"$,$-;$,21,0*&3#*&(2),4"$), v -* ,(0
#$-3/$-,&2,*923&,O<\,_<,=),0*&3#*&(2)5, v -* ! P?M,_5,*)&"$,#*&(2,21, $ - ,&2, $ ) ,(0,+24$#,&"*), β ,T(<$<5, β @2,(+0 < β )
=),&"$,*/&(.$,'2-$5, $ - ,0"240,*,0+(;"&,-$7$)-$)/$,2), v -* ?
!"(0,7"$)2'$)2)5,G)24),*0,&"$,M*#+:,$11$/&5,(0,'2-$+$9:,*0/#(9();,*,1()(&$,T(<$<5,)2)()1()(&$V,23&73&,#$0(0&*)/$,&2
&"$,BC!Y, ( % d + / ⁄ . ′ - 5,4"$#$, + / ,(0,&"$,M*#+:,.2+&*;$
*)-, . ′ - ,(0,&"$,-/,/2++$/&2#,/3##$)&,4(&"23&,&"$,M*#+:,$11$/&
&*G$),()&2,*//23)&<,=),-(0/#$&$,/(#/3(&05, ( % ,7+*:0,*,'()2#
#2+$, *)-, /*), 303*++:, 9$, )$;+$/&$-<, !"(0, (0, !%?, &"$, /*0$5
"24$.$#5,(),()&$;#*&$-%/(#/3(&,-$0(;),T6"*7&$#,NV<
!"$,-/,*)*+:0(0,21,&#*)0(0&2#,/(#/3(&0,(0,;#$*&+:,0('7+(%
1($-,9:,*003'();,&"*&, + )* !,O<N,_<,U$1$#,&2,!*9+$,X<\<,
!2,27$#*&$,*0,*,+()$*#,*'7+(1($#5,&"$,BC!,(0,9(*0$-,(),&"$
*/&(.$,#$;(2),*)-,&"$,0(;)*+,v#4,(0,G$7&,0'*++,Tv#4,*,+,V<
L2#,0'*++,0(;)*+05,&"$,BC!,13)/&(2)0,*0,*,+()$*#,.2+&*;$%
/2)&#2++$-,/3##$)&,023#/$,4(&",*,&#*)0/2)-3/&*)/$, C I =
. - ⁄ + , ? ,!"$,()73&,#$0(0&*)/$,9$&4$$),9*0$,*)-,$'(&&$#5
+22G();,()&2,&"$,9*0$5,(0, ( π = β ⁄ C I ? ,!"$,()73&,#$0(0&%
$)/$,9$&4$$),9*0$,*)-,$'(&&$#5,+22G();,()&2,&"$,$'(&&$#,(0
(4 ! K ⁄ C I <,!*9+$,X<8,7#2.(-$0,*,03''*#:,21,&"$,0'*++%
0(;)*+,'2-$+0,*)-,&"$,$S3*&(2)0,12#,-$&$#'()();,&"$(#,7*%
#*'$&$#0<
B(*0,-$0(;),0$$G0,&2,$0&*9+(0",*,-/,/2++$/&2#,/3##$)&,&"*&
(0,*0,()-$7$)-$)&,21,&"$,.*+3$,21,β,*0,7200(9+$<
!"$,&"#$$,9*0(/,BC!,*'7+(1($#,/2)1(;3#*&(2)0,*#$,0"24)
(),L(;<,X<8E<,@,03''*#:,21,&"$(#,/"*#*/&$#(0&(/,7*#*'$%
&$#0,(0,7#2.(-$-,(),!*9+$,X<^<
466 Chapter 6 Bipolar Junction Transistors (BJTs)
!"$,6M,*'7+(1($#,(0,30$-,&2,29&*(),&"$,93+G,21,&"$,#$%
S3(#$-,.2+&*;$,;*(),(),*,/*0/*-$,*'7+(1($#<,=&,"*0,*,+*#;$
.2+&*;$,;*(),*)-,*,'2-$#*&$,()73&,#$0(0&*)/$,93&,*,#$+*%
&(.$+:,"(;",23&73&,#$0(0&*)/$,*)-,+('(&$-,"(;"%1#$S3$)/:
#$072)0$,T6"*7&$#,DV<
=%+# &"*/$# ,+'&'$)"(+# 2@# $%+# (2332"5+3&$$+,# )3*6&@&+,
()"#9+#&"(,+)'+0#91#&"(6/0&"L#)"#/"91*)''+0#,+'&'$)"(+
&"#$%+#+3&$$+,#6+)0?#=%&'#+3&$$+,50+L+"+,)$&2"#,+'&'$)"(+
*,27&0+'# 2$%+,# *+,@2,3)"(+# &3*,27+3+"$'# )$# $%+# +T5
*+"'+#2@#,+0/(+0#726$)L+#L)&"?
!"$,6B,*'7+(1($#,"*0,*,.$#:,+24,()73&,#$0(0&*)/$,*)-,(0
30$13+,(),*,+('(&$-,)3'9$#,21,07$/(*+,*77+(/*&(2)0<,=&,-2$05
"24$.$#5, "*.$, *), $A/$++$)&, "(;"%1#$S3$)/:, #$072)0$
T6"*7&$#,DV,*)-,&"30,/*),9$,/2'9()$-,4(&",&"$,6M,*'7+(%
1($#,&2,29&*(),*),$A/$++$)&,*'7+(1($#,/(#/3(&,T6"*7&$#,NV<
!"$,$'(&&$#,12++24$#,"*0,*,"(;",()73&,#$0(0&*)/$,*)-,*
+24,23&73&,#$0(0&*)/$<,!"305,(&,(0,30$13+,*0,*,9311$#,*'%
7+(1($#, &2, /2))$/&, *, "(;"%#$0(0&*)/$, 0(;)*+, 023#/$, &2, *
+24%#$0(0&*)/$, +2*-<, @)2&"$#, ('72#&*)&, *77+(/*&(2), 21
&"$,$'(&&$#,12++24$#,(0,*0,&"$,+*0&,0&*;$,T/*++$-,&"$,23&73&
0&*;$V,21,*,/*0/*-$,*'7+(1($#<
@,0:0&$'*&(/,7#2/$-3#$,&2,*)*+:>$,*),*'7+(1($#,/(#/3(&,/2)%
0(0&0,21,#$7+*/();,$*/",BC!,4(&",2)$,21,(&0,0'*++%0(;)*+5
$S3(.*+$)&,/(#/3(&,'2-$+0<,Z6,.2+&*;$,023#/$0,*#$,#$7+*/$9:,0"2#&,/(#/3(&0,*)-,-/,/3##$)&,023#/$0,9:,27$),/(#/3(&0<
!"$,*)*+:0(0,/*),&"$),9$,7$#12#'$-,2),&"$,#$03+&();,$S3(.%
*+$)&,/(#/3(&<=1,*,#$0(0&*)/$,(0,/2))$/&$-,(),0$#($0,4(&",&"$
$'(&&$#,+$*-,21,&"$,BC!5,&"$,!,'2-$+,(0,&"$,'20&,/2).$)($)&
&2,30$<,J&"$#4(0$5,&"$,":9#(-% π ,'2-$+,(0,$'7+2:$-<
!"$,#$0(0&*)/$,#$1+$/&(2),#3+$,(0,*,724$#13+,&22+,(),&"$,*)*+%
:0(0,21,BC!,*'7+(1($#,/(#/3(&0Y,@++,#$0(0&*)/$0,(),&"$,$'(&&$#
/(#/3(&,()/+3-();,&"$,$'(&&$#,#$0(0&*)/$, ( 4 ,/*),9$,#$1+$/&$&2, &"$, 9*0$, 0(-$, 9:, '3+&(7+:();, &"$', 9:, ( β e K )<, 62)%
.$#0$+:5,4$,/*),#$1+$/&,*++,#$0(0&*)/$0,(),&"$,9*0$,/(#/3(&,&2
&"$,$'(&&$#,0(-$,9:,-(.(-();,&"$',9:, ( β e K )<
Z(0/#$&$%/(#/3(&, BC!, *'7+(1($#0, 3&(+(>$, +*#;$, /237+();
*)-, 9:7*00, /*7*/(&2#0<, MA*'7+$, /(#/3(&0, *#$, ;(.$), ()
K$/&(2),X<E<,@0,4(++,9$,0$$),(),6"*7&$#,N5,&"(0,(0,)2&,&"$
/*0$,(),=6,*'7+(1($#0<
PROBLEMS
Computer Simulation Problems
O,296+3'# &0+"$&@&+0# 91# $%&'# &(2"# ),+# &"$+"0+0# $2# 0+32"5
'$,)$+#$%+#7)6/+#2@#/'&"L#CO!FE#'&3/6)$&2"#$2#7+,&@1#%)"0#)")61'&'
)"0#0+'&L"-#)"0#$2#&"7+'$&L)$+#&3*2,$)"$#&''/+'#'/(%#)'#)662.)96+
'&L")6# '.&"L# )"0# )3*6&@&+,# "2"6&"+),# 0&'$2,$&2"?# !"'$,/($&2"'# $2
)''&'$#&"#'+$$&"L#/*#OC*&(+#)"0#A/6$&'&3#'&3/6)$&2"'#@2,#)66#$%+
&"0&()$+0#*,296+3'#()"#9+#@2/"0#&"#$%+#(2,,+'*2"0&"L#@&6+'#2"#$%+
0&'(?#b2$+#$%)$#&@#)#*),$&(/6),#*),)3+$+,#7)6/+#&'#"2$#'*+(&@&+0#&"
$%+#*,296+3#'$)$+3+"$-#12/#),+#$2#3)U+#)#,+)'2")96+#)''/3*$&2"?
u#0&@@&(/6$#*,296+3H#uu#32,+#0&@@&(/6$H#uuu#7+,1#(%)66+"L&"L#)"0Z
2,#$&3+5(2"'/3&"LH#X8#0+'&L"#*,296+3?
Section 6.1: Device Structure and Physical
operation
6.1 !"$, &$#'()*+, .2+&*;$0, 21, .*#(230, !"!, &#*)0(0&2#0, *#$
'$*03#$-, -3#();, 27$#*&(2), (), &"$(#, #$07$/&(.$, /(#/3(&0, 4(&"
&"$,12++24();,#$03+&0Y
Case
E
B
C
?
P
\
8
^
X
O,,
O,
−O<N
−O<N
−P<N
O
O<N
O<E
O
O
−P<O
O
O<N
O<?
O<N
−O<X
O
^<O
Mode
=), &"(0, &*9+$5,4"$#$, &"$, $)&#($0, *#$,(), .2+&05,O, ()-(/*&$0, &"$
#$1$#$)/$,&$#'()*+,&2,4"(/",&"$,9+*/G,T)$;*&(.$V,7#29$,21,&"$
.2+&'$&$#,(0,/2))$/&$-<,L2#,$*/",/*0$5,(-$)&(1:,&"$,'2-$,21
27$#*&(2),21,&"$,&#*)0(0&2#<
6.2 !42, &#*)0(0&2#05, 1*9#(/*&$-, 4(&", &"$, 0*'$, &$/")2+2;:
93&,"*.();,-(11$#$)&,H3)/&(2),*#$*05,4"$),27$#*&$-,*&,*,9*0$%
$'(&&$#, .2+&*;$,21,O<N^,_5,"*.$,/2++$/&2#,/3##$)&0,21,O<P,'@
*)-,^,'@<,L()-,.6,12#,$*/",-$.(/$<,W"*&,*#$,&"$,#$+*&(.$,H3)/%
&(2),*#$*0f
6.3 =), *, 7*#&(/3+*#, &$/")2+2;:5, *, 0'*++, BC!, 27$#*&();, *&
v )* d Mf+ , ,/2)-3/&0,*,/2++$/&2#,/3##$)&,21,?OO,µ@<,W"*&
(0, &"$, /2##$072)-();, 0*&3#*&(2), /3##$)&f, L2#, *, &#*)0(0&2#, ()
&"$,0*'$,&$/")2+2;:,93&,4(&",*),$'(&&$#,H3)/&(2),&"*&,(0,\P
&('$0, +*#;$#5, 4"*&, (0, &"$, 0*&3#*&(2), /3##$)&f, W"*&, /3##$)&
4(++, &"(0, &#*)0(0&2#, /2)-3/&, *&, v )* d Mf+ , f, W"*&, (0, &"$
9*0$]$'(&&$#, .2+&*;$, 21, &"$, +*&&$#, &#*)0(0&2#, *&, $- d ? '@f
@003'$,*/&(.$%'2-$,27$#*&(2),(),*++,/*0$0<
6.4 !42, &#*)0(0&2#0, "*.$, MBC, *#$*0, *0, 12++240Y, /*?, d
@*? d 8OO µ' × 8OO µ', *)-, @*P d O<8 µ' × O<P µ'<, =1, &"$
&42,&#*)0(0&2#0,*#$,27$#*&$-,(),&"$,*/&(.$,'2-$,*)-,/2)-3/&
$S3*+,/2++$/&2#,/3##$)&05,4"*&,-2,:23,$A7$/&,&"$,-(11$#$)/$
(),&"$(#, v )* ,.*+3$0,&2,9$f
6.5 L()-, &"$, /2++$/&2#, /3##$)&0, &"*&, :23, 423+-, $A7$/&, 12#
27$#*&(2), *&, v )* d dPP , '_, 12#, &#*)0(0&2#0, 12#, 4"(/"
Problems 467
] KM
] Kf
,@,*)-, . 6 d KP ,@<,L2#,&"$,&#*)0(0&2#,4(&",&"$
+*#;$#, MBC5, 4"*&, (0, &"$, v )* , #$S3(#$-, &2, 7#2.(-$, *, /2++$/&2#
/3##$)&, $S3*+, &2, &"*&, 7#2.(-$-, 9:, &"$, 0'*++$#, &#*)0(0&2#, *&
v )* d dPP ,'_f,@003'$,*/&(.$%'2-$,27$#*&(2),(),*++,/*0$0<
6.6 =),&"(0,7#29+$'5,4$,/2)&#*0&,&42,BC!,()&$;#*&$-%/(#/3(&
6.7 62)0(-$#,*),!"!,&#*)0(0&2#,4"20$,9*0$]$'(&&$#,-#27,(0
O<NX,_,*&,*,/2++$/&2#,/3##$)&,21,?O,'@<,W"*&,/3##$)&,4(++,(&
/2)-3/&,*&,v)*,=,O<NO,_f,W"*&,(0,(&0,9*0$]$'(&&$#,.2+&*;$,12#
$-,=,?O,µ@f
6.8 =),*,7*#&(/3+*#,BC!5,&"$,9*0$,/3##$)&,(0,?O,µ@5,*)-,&"$
/2++$/&2#,/3##$)&,(0,XOO,µ@<,L()-,β,*)-,α 12#,&"(0,-$.(/$<
6.9 L()-,&"$,.*+3$0,21,β,&"*&,/2##$072)-,&2,α,.*+3$0,21,O<^5
O<E5,O<D5,O<D^5,O<DD5,O<DD^5,*)-,O<DDD<
6.10 L()-,&"$,.*+3$0,21,α ,&"*&,/2##$072)-,&2,β,.*+3$0,21,?5
P5,?O5,PO5,?OO5,POO5,?OOO5,*)-,POOO<
+)*,T'_V
.-,T'@V
.),Tµ@V
.*8T'@V
α
β
.6
a
b
c
d
e
XDO
?<OOO
^O
XDO
?<OOO
^EO
NEO
?O<?O
?PO
EPO
?<ONO
N
O<?\N
?O^O
N^<OO
6.16 @, 7*#&(/3+*#, BC!, 4"$), 27$#*&$-, (), &"$, */&(.$, '2-$
/2)-3/&0,*,/2++$/&2#,/3##$)&,21,?O,'@,*)-,"*0, v)*,=,O<NO,_
*)-,$),=,?OO,µ@<,c0$,&"$0$,-*&*,&2,/#$*&$,07$/(1(/,&#*)0(0&2#
'2-$+0,21,&"$,12#',0"24),(),L(;0<,X<^T*V,&2,T-V<
6.17 c0();, &"$, !"!, &#*)0(0&2#, '2-$+, 21, L(;<, X<^T9V5, /2)%
0(-$#,&"$,/*0$,21,*,&#*)0(0&2#,12#,4"(/",&"$,9*0$,(0,/2))$/&$&2, ;#23)-5, &"$, /2++$/&2#, (0, /2))$/&$-, &2, *, ?O%_, -/, 023#/$
&"#23;",*,P%GΩ,#$0(0&2#5,*)-,*,\%'@,/3##$)&,023#/$,(0,/2)%
)$/&$-, &2, &"$, $'(&&$#, 4(&", &"$, 72+*#(&:, 02, &"*&, /3##$)&, (0
-#*4),23&,21,&"$,$'(&&$#,&$#'()*+<,=1, β,=,?OO,*)-,.6,=,?O]?^
@5,1()-,&"$,.2+&*;$0,*&,&"$,$'(&&$#,*)-,&"$,/2++$/&2#,*)-,/*+%
/3+*&$,&"$,9*0$,/3##$)&<
D 6.18 62)0(-$#,*),!"!, &#*)0(0&2#,27$#*&$-,(),&"$,*/&(.$
*6.11 K"24,&"*&,12#,*,&#*)0(0&2#,4(&", α,/+20$,&2,3)(&:5,(1, α
/"*);$0, 9:, *, 0'*++, 7$#%3)(&, *'23)&, ( ∆ α ⁄ α ) 5, &"$, /2##$%
072)-();,7$#%3)(&,/"*);$,(),β,(0,;(.$),*77#2A('*&$+:,9:,
α
∆
555555β5 # ! β ∆
5555555
α
β
6.12 @),!"!,&#*)0(0&2#,21,*,&:7$,4"20$,β,(0,07$/(1($-,&2,#*);$
'2-$,*)-,#$7#$0$)&$-,9:,&"$,'2-$+,21,L(;<,X<^T-V<,F$&,&"$
&#*)0(0&2#,9$,/2))$/&$-,*0,()-(/*&$-,9:,&"$,$S3(.*+$)&,/(#%
/3(&,0"24),(),L(;<,X<XT9V<,=&,(0,#$S3(#$-,&2,/*+/3+*&$,&"$,.*+%
3$0,21, > ) ,*)-, > - ,&"*&,4(++,$0&*9+(0",*,/2++$/&2#,/3##$)&, . 21, ? '@, *)-, *, /2++$/&2#%&2%$'(&&$#, .2+&*;$, + -* , 21, ?, _<
!"$, BC!, (0, 07$/(1($-, &2, "*.$, β d KMG , *)] KG
. 6 d G × KP ,@<
1#2',XO,&2,\OO,(0,/2))$/&$-,(),*,/(#/3(&,4(&",$'(&&$#,;#23)-$-5
/2++$/&2#,*&,+D,_5,*)-,*,/3##$)&,21,PO,µ@,()H$/&$-,()&2,&"$,9*0$<
6*+/3+*&$, &"$, #*);$, 21, /2++$/&2#, *)-, $'(&&$#, /3##$)&0, &"*&, /*)
#$03+&<,W"*&,(0,&"$,'*A('3',724$#,-(00(7*&$-,(),&"$,&#*)0(0&2#f
T7%?4O,g$#"*70,:23,/*),0$$,4":,&"(0,(0,*,9*-,4*:,&2,$0&*9+(0"
&"$,27$#*&();,/3##$)&,(),&"$,/2++$/&2#,21,*,BC!<V
6.19 @),!"!8&#*)0(0&2#,"*0,*,6BC,4(&",*),*#$*,?^O,&('$0,&"*&
] KG
21,&"$,MBC<,=1, . 6 d G × KP @5,1()-,&"$,.2+&*;$,-#27,*/#200
MBC, *)-, */#200, 6BC, 4"$), $*/", (0, 12#4*#-, 9(*0$-, *)-, /2)%
-3/&();,*,/3##$)&,21,?,'@<,@+02,1()-,&"$,12#4*#-,/3##$)&,$*/"
H3)/&(2),423+-,/2)-3/&,4"$),12#4*#-,9(*0$-,4(&",O<^ _<
6.13 @,BC!,(0,07$/(1($-,&2,"*.$, . 6 d G × KP
] KG
,@,*)-, β
&"*&,1*++0,(),&"$,#*);$,21,^O,&2,POO<,=1,&"$,&#*)0(0&2#,(0,27$#%
*&$-, (), &"$, */&(.$, '2-$, 4(&", v )* , 0$&, &2, O<X^O, _5, 1()-, &"$
$A7$/&$-,#*);$,21, $ - - , $ ) - ,*)-, $ * ?
6.14 I$*03#$'$)&0,'*-$,2),*,)3'9$#,21,&#*)0(0&2#0,27$#%
*&();,(),&"$,*/&(.$,'2-$,4(&", $ * d K ,'@,()-(/*&$,9*0$,/3#%
#$)&0,21,^O,µ@5,?O,µ@5,*)-,P^,µ@<,L2#,$*/",-$.(/$5,1()-, $ - β - ,*)-, α ?
6.15 I$*03#$'$)&,21,+)*,*)-,&42,&$#'()*+,/3##$)&0,&*G$)
2),*,)3'9$#,21,!"!,&#*)0(0&2#0,27$#*&();,(),&"$,*/&(.$,'2-$
*#$,&*93+*&$-,9$+24<,L2#,$*/"5,/*+/3+*&$,&"$,'(00();,/3##$)&
.*+3$,*0,4$++,*0,α5,β5,*)-,.6,*0,()-(/*&$-,9:,&"$,&*9+$<
6.20 W$,4(0",&2,().$0&(;*&$,&"$,27$#*&(2),21,&"$,!"!,&#*)%
0(0&2#, (), 0*&3#*&(2), 30();, &"$, '2-$+, 21, L(;<, X<D<, F$&
] KG
. 6 d KP @5, v)* d P?d _5, β d KPP ,*)-,.6- o.6 d ?OO<,L2#
$*/",21,&"#$$,.*+3$0,21, v -* ,T)*'$+:5,,O<8,_5,O<\,_5,*)-,O<?
_V5,1()-, v )- - , $ )- - , $ ) - , $ - - ,*)-, $ - ⁄ $ ) ? ,@+02,1()-, v -* ,&"*&
#$03+&0,(), $ - d P<
*6.21 c0$, MS0<, TX<?8V5, TX<?^V5, *)-, TX<?XV, &2, 0"24, &"*&, *)
!"!,&#*)0(0&2#,27$#*&$-,(),0*&3#*&(2),$A"(9(&0,*,/2++$/&2#%&2%
$'(&&$#,.2+&*;$5,+-*')$ ,;(.$),9:
. 6- K e β @2,(+0
5 555555555555555555555555555555
+ -*')$ d + , 6" 555555
. 6 K ] β @2,(+0 ⁄ β
PROBLEMS
1*9#(/*&(2),&$/")2+2;($0Y,L2#,&"$,a2+-b, &$/")2+2;:5,*, &:7(/*+
] KG
!"!,&#*)0(0&2#,"*0, . 6 d G × KP ,@5,*)-,12#,&"$,a)$4b,&$/"%
] Kf
)2+2;:,*,&:7(/*+,!"!,&#*)0(0&2#,"*0, . 6 d G × KP ,@<,!"$0$
&:7(/*+,-$.(/$0,"*.$,.*0&+:,-(11$#$)&,H3)/&(2),*#$*0,*)-,9*0$
4(-&"<, L2#, 23#, 73#720$, "$#$, 4$, 4(0", &2, -$&$#'()$, &"$, v )*
#$S3(#$-,&2,$0&*9+(0",*,/2++$/&2#,/3##$)&,21,?,'@,(),$*/",21,&"$
&42,&:7(/*+,-$.(/$0<,@003'$,*/&(.$%'2-$,27$#*&(2)<
Transistor
CHAPTER 6
. 6 d KP
CHAPTER 6
PROBLEMS
468 Chapter 6 Bipolar Junction Transistors (BJTs)
c0$, &"(0, #$+*&(2)0"(7, &2, $.*+3*&$, + -*')$ , 12#, β @2,(+0 d GP5
?O5,^5,*)-,?,12#,*,&#*)0(0&2#,4(&", β d KPP ,*)-,4(&",*,6BC
*#$*,?OO,&('$0,&"*&,21,&"$,MBC<
6.22 62)0(-$#,&"$,"!",+*#;$%0(;)*+,'2-$+,21,L(;<,X<??T9V
*77+($-,&2,*,&#*)0(0&2#,"*.();,.6,=,?O−?\,@,*)-, β,=,8O<,=1,&"$
$'(&&$#, (0, /2))$/&$-, &2, ;#23)-5, &"$, 9*0$, (0, /2))$/&$-, &2, *
/3##$)&,023#/$,&"*&,73++0,PO µ@,23&,21,&"$,9*0$,&$#'()*+5,*)&"$ /2++$/&2#,(0,/2))$/&$-,&2,*,)$;*&(.$,0377+:,21 −?O,_,.(*
*,?O%GΩ,#$0(0&2#5,1()-,&"$,/2++$/&2#,.2+&*;$5,&"$,$'(&&$#,/3#%
#$)&5,*)-,&"$,9*0$,.2+&*;$<
6.23 @8"!",&#*)0(0&2#,"*0, v*),=,O<E,_,*&,*,/2++$/&2#,/3##$)&
6.26 W"(+$, L(;<, X<^, 7#2.(-$0, 123#, 7200(9+$, +*#;$%0(;)*+
$S3(.*+$)&,/(#/3(&0,12#,&"$,!"!,&#*)0(0&2#5,2)+:,&42,$S3(.*+$)&
/(#/3(&0,12#,&"$,"!",&#*)0(0&2#,*#$,7#2.(-$-,(),L(;<,X<??<,K37%
7+:,&"$,'(00();,&42< ,
6.27 B:,*)*+2;:,&2,&"$,!"!,/*0$,0"24),(),L(;<,X<D5,;(.$,&"$
$S3(.*+$)&,/(#/3(&,21,*,"!",&#*)0(0&2#,(),0*&3#*&(2)<
Section 6.2: Current–Voltage
Characteristics
6.28 L2#,&"$,/(#/3(&0,(),L(;<,gX<PE5,*003'$,&"*&,&"$,&#*)0(0%
&2#0,"*.$,.$#:,+*#;$,β<,K2'$,'$*03#$'$)&0,"*.$,9$$),'*-$
21,?,@<,W"*&,-2,:23,$A7$/&,v*),&2,9$/2'$,*&,$-,=,?O,'@f,@&
$- =,^,@f
2), &"$0$, /(#/3(&05, 4(&", &"$, #$03+&0, ()-(/*&$-, (), &"$, 1(;3#$<
L()-,&"$,.*+3$0,21,&"$,2&"$#,+*9$+$-,.2+&*;$0,*)-,/3##$)&0<,,,
6.24 @,"!",&#*)0(0&2#,'2-$+$-,4(&",&"$,/(#/3(&,(),L(;<,X<??
T9V,(0,/2))$/&$-,4(&",(&0,9*0$,*&,;#23)-5,/2++$/&2#,*&,]?<O,_5
*)-,*,?O%'@,/3##$)&,(0,()H$/&$-,()&2,(&0,$'(&&$#<,=1,&"$,&#*)%
0(0&2#,(0,0*(-,&2,"*.$ β,=,?O5,4"*&,*#$,(&0,9*0$,*)-,/2++$/&2#
/3##$)&0f, =), 4"(/", -(#$/&(2), -2, &"$:, 1+24f, =1, .6, =, ?O]?^, @5
4"*&,.2+&*;$,#$03+&0,*&,&"$,$'(&&$#f,W"*&,-2$0,&"$,/2++$/&2#
/3##$)&,9$/2'$,(1,*,&#*)0(0&2#,4(&", β =,?OOO,(0,0390&(&3&$-f
T7%?4O, !"$, 1*/&, &"*&, &"$, /2++$/&2#, /3##$)&, /"*);$0, 9:, +$00
&"*), ?Oj, 12#, *, +*#;$, /"*);$, 21, β, (++30&#*&$0, &"*&, &"(0, (0, *
;22-,4*:,&2,$0&*9+(0",*,07$/(1(/,/2++$/&2#,/3##$)&<V
6.29 I$*03#$'$)&0,2),&"$,/(#/3(&0,21,L(;<,gX<PD,7#2-3/$
+*9$+$-, .2+&*;$0, *0, ()-(/*&$-<, L()-, &"$, .*+3$, 21, β, 12#, $*/"
6.25 @,"!",724$#,&#*)0(0&2#,27$#*&$0,4(&",*),$'(&&$#%&2%
/2++$/&2#,.2+&*;$,21,^,_5,*),$'(&&$#,/3##$)&,21,?O,@5,*)-,+*)
=,O<E^,_<,L2#,β, =,?^5,4"*&,9*0$,/3##$)&,(0,#$S3(#$-f,W"*&
(0,.6,12#,&"(0,&#*)0(0&2#f,62'7*#$,&"$,$'(&&$#]9*0$,H3)/&(2)
*#$*,21,&"(0,&#*)0(0&2#,4(&",&"*&,21,*,0'*++%0(;)*+,&#*)0(0&2#
&"*&, /2)-3/&0, $-, =, ?, '@, 4(&", v*), =, O<NO, _<, R24, '3/"
+*#;$#,(0,(&f
&#*)0(0&2#<
6.30, @, .$#:, 0('7+$, /(#/3(&, 12#, '$*03#();, β , 21, *), !"!
&#*)0(0&2#, (0, 0"24), (), L(;<, gX<\O<, =), *, 7*#&(/3+*#, -$0(;)5
+ -- , (0, 7#2.(-$-, 9:, *, D%_, 9*&&$#:`, I, (0, *, /3##$)&, '$&$#
4(&", *, ^O%µ@, 13++, 0/*+$, *)-, #$+*&(.$+:, +24, #$0(0&*)/$, &"*&
:23,/*),)$;+$/&,12#,23#,73#720$0,"$#$<,@003'();,&"*&,&"$
&#*)0(0&2#,"*0, + )* d P?d ,_,*&, . * d K ,'@5,4"*&,.*+3$,21
>,423+-,$0&*9+(0",*,#$0(0&2#,/3##$)&,21,?,'@f,Q245,&2,4"*&
.*+3$,21, β ,-2$0,*,'$&$#,#$*-();,21,13++,0/*+$,/2##$072)-f
W"*&,(0, β ,(1,&"$,'$&$#,#$*-();,(0,?o^,21,13++,0/*+$f,?o?O,21
13++,0/*+$f
6.31, U$7$*&, MA$#/(0$, X<?\, 12#, &"$, 0(&3*&(2), (), 4"(/", &"$
724$#,0377+($0,*#$,#$-3/$-,&2, ± K?G ,_<
5.6 k&
15 k&
V3
15 k&
%4 V
V7
V4
V2
0V
2.4 k&
(b)
Figure P6.28
I5
10 k&
(c)
$
0.7 V
%
I6
5 k&
(d)
Problems 469
PROBLEMS
$6.3 V
100 k&
200 k&
1 k&
(a)
(c)
(b)
Figure P6.29
$5 V
VCC
RE
RC
M
RC
%5 V
Figure P6.32
Figure P6.30
D 6.32,Z$0(;),&"$,/(#/3(&,(),L(;<,gX<\P,&2,$0&*9+(0",*,/3#%
#$)&,21,?,'@,(),&"$,$'(&&$#,*)-,*,.2+&*;$,21, ] K ,_,*&,&"$,/2+%
+$/&2#<,!"$,&#*)0(0&2#, v *) d P?We ,_,*&, . * d P?K ,'@5,*)β d KPP <, !2, 4"*&, .*+3$, /*), > - , 9$, ()/#$*0$-, 4"(+$, &"$
/2++$/&2#,/3##$)&,#$'*()0,3)/"*);$-f
$ 1.5 V
RC
IC
VC
D 6.33 MA*'()*&(2), 21, &"$, &*9+$, 21, 0&*)-*#-, .*+3$0, 12#
#$0(0&2#0,4(&",^j,&2+$#*)/$,(),@77$)-(A,l,#$.$*+0,&"*&,&"$
/+20$0&,.*+3$0,&2,&"20$,123)-,(),&"$,-$0(;),21,MA*'7+$,X<PO
*#$, ^<?, GΩ, *)-, X<E, GΩ<, L2#, &"$0$, .*+3$0, 30$, *77#2A('*&$
/*+/3+*&(2)0,T$<;<5,+)* !,O<N,_,*)-, α,!,?V,&2,-$&$#'()$,&"$
.*+3$0, 21 /2++$/&2#, /3##$)&, *)-, /2++$/&2#, .2+&*;$, &"*&, *#$
+(G$+:,&2,#$03+&<
D 6.34 Z$0(;), &"$, /(#/3(&, (), L(;<, gX<\8, &2, $0&*9+(0"
. - d P?K , '@, *)-, + - d P?G , _<, !"$, &#*)0(0&2#, $A"(9(&0
v )* ,21,O<E,_,*&, $ - d K ,'@5,*)-, β d KPP<
RE
% 1.5 V
Figure P6.34
CHAPTER 6
$7 V
6.35 L2#,$*/",21,&"$,/(#/3(&0,0"24),(),L(;<,gX<\^5,1()-,&"$
$'(&&$#5,9*0$5,*)-,/2++$/&2#,.2+&*;$0,*)-,/3##$)&0<,c0$,β,=,^O5
93&,*003'$, +)* = P?f#] ,()-$7$)-$)&,21,/3##$)&,+$.$+<
CHAPTER 6
$1.5 V
$1.5 V
2.2 k&
1 k&
Q1
Q2
2.2 k&
1 k&
%1.5 V
%1.5 V
(a)
(b)
$3 V
$3 V
1.1 k&
$1.0 V
1 k&
$1.5 V
Q3
T*V W"*&,-2$0,v*),9$/2'$,(1,&"$,H3)/&(2),&$'7$#*&3#$,#(0$0
&2,^O°6f
T9V =1,&"$,&#*)0(0&2#,(0,27$#*&$-,*&,*,1(A$-,$'(&&$#]9*0$,.2+&*;$
21,NOO,'_5,4"*&,$'(&&$#,/3##$)&,1+240,*& PO°6f,@&,^O°6f
6.40 62)0(-$#,*,&#*)0(0&2#,12#,4"(/",&"$,9*0$]$'(&&$#,.2+&*;$
-#27, (0, O<N, _, *&, ?O, '@<, W"*&, /3##$)&, 1+240, 12#, v)* =, O<^, _f
M.*+3*&$,&"$,#*&(2,21,&"$,0+27$0,21,&"$,$-]v)*8 /3#.$,*&, v)*,d,NOO
'_,*)-,*&,v)*,d,^OO,'_<,!"$,+*#;$,#*&(2,/2)1(#'0,&"$,72()&,&"*&
&"$,BC!,"*0,*),a*77*#$)&,&"#$0"2+-b,*&, v )* ! P?G] <
6.41 =),g#29+$',X<8O5,&"$,0&*&$-,.2+&*;$0,*#$,'$*03#$-,*&
P^°6<,W"*&,.*+3$0,/2##$072)-,*&,]P^°6f,@&,?P^°6f
6.42 c0$,MS<,TX<?EV,&2,7+2&,$-,.$#030,v-*,12#,*),!"!,&#*)0(0%
&2#,"*.();,.6,=,?O−?^,@,*)-,+/,=,?OO,_<,g#2.(-$,/3#.$0,12#
v)*,=,O<X^5,O<NO5,O<NP5,O<N\5,*)-,O<N8,.2+&0<,K"24,&"$,/"*#*/%
&$#(0&(/0,12#,v-*,37,&2,?^,_<
*6.43 =),&"$,/(#/3(&,0"24),(),L(;<,gX<8\5,/3##$)&,023#/$,.,(0
?<? '@5, *)-, *&, P^ ° 6, v )* d WfP , '_, *&, $ - d K , '@<, @&
P^ ° 6, 4(&", β d KPP 5, 4"*&, /3##$)&0, 1+24, (), > K , *)-, > M f
W"*&,.2+&*;$,423+-,:23,$A7$/&,*&,)2-$,Mf,Q2&();,&"*&,&"$,&$'%
7$#*&3#$, /2$11(/($)&, 21, v )* , 12#, . - , /2)0&*)&, (0, ] M , '_o ° 65
4"*&,(0,&"$,!6,21, v * f,L2#,*),*'9($)&,&$'7$#*&3#$,21,N^ ° 65
4"*&, .2+&*;$, 423+-, :23, $A7$/&, *&, )2-$, Mf, 6+$*#+:, 0&*&$, *):
0('7+(1:();,*003'7&(2)0,:23,'*G$<
Q4
560 &
(c)
6.39,@,7*#&(/3+*#,"!",&#*)0(0&2#,27$#*&();,*&,*),$'(&&$#,/3##$)&
21,O<^,'@,*&,PO°6,"*0,*),$'(&&$#]9*0$,.2+&*;$,21,XDP,'_<
470 &
(d)
Figure P6.35
R2
68 k&
R1
6.8 k&
E
6.36 !"$,/3##$)&,.-)N,21,*,0'*++,&#*)0(0&2#,(0,'$*03#$-,&2
9$,?O,)@,*&,P^°6<,=1,&"$,&$'7$#*&3#$,21,&"$,-$.(/$,(0,#*(0$&2,?P^°65,4"*&,-2,:23,$A7$/&,.-)N,&2,9$/2'$f
*6.37 @3;'$)&, &"$, '2-$+, 21, &"$, !"!, BC!, 0"24), (), L(;<
X<?ET*V,9:,*,/3##$)&,023#/$,#$7#$0$)&();,.-)N<,@003'$,&"*&,(%
(0,.$#:,+*#;$,*)-,&"30,/*),9$,)$;+$/&$-<,=),&$#'0,21,&"(0,*--(%
&(2)5,4"*&,-2,&"$,&$#'()*+,/3##$)&0,$)5,$-5,*)-,$*,9$/2'$f,=1
&"$,9*0$,+$*-,(0,27$)%/(#/3(&$-,4"(+$,&"$,$'(&&$#,(0,/2))$/&$&2,;#23)-5,*)-,&"$,/2++$/&2#,(0,/2))$/&$-,&2,*,720(&(.$,037%
7+:5,1()-,&"$,$'(&&$#,*)-,/2++$/&2#,/3##$)&0<
6.38 @,BC!,4"20$,$'(&&$#,/3##$)&,(0,1(A$-,*&,?,'@,"*0,*
9*0$]$'(&&$#,.2+&*;$,21,O<XD,_,*&,P^°6<,W"*&,9*0$]$'(&&$#
.2+&*;$,423+-,:23,$A7$/&,*&,O°6f,@&,?OO°6f
I
Figure P6.43
6.44 L2#, *, 7*#&(/3+*#, !"!, &#*)0(0&2#, 27$#*&();, *&, *, v)*, 21
XNO '_,*)-,.-,=,P,'@5,&"$,$- ]v-*,/"*#*/&$#(0&(/,"*0,*,0+27$
]G
21,P,×, KP
.,!2,4"*&,.*+3$,21,23&73&,#$0(0&*)/$,-2$0,&"(0
/2##$072)-f,W"*&,(0,&"$,.*+3$,21,&"$,M*#+:,.2+&*;$,12#,&"(0
&#*)0(0&2#f,L2#,27$#*&(2),*&,PO,'@5,4"*&,423+-,&"$,23&73&
#$0(0&*)/$,9$/2'$f
Ω
PROBLEMS
470 Chapter 6 Bipolar Junction Transistors (BJTs)
Problems 471
(&0,23&73&,#$0(0&*)/$,*&,?,'@f,@&,?OO,µ@f
()/#$*0$-,(),2#-$#,12#,&"$,&#*)0(0&2#,&2,27$#*&$,*&,&"$,$-;$,21
0*&3#*&(2)f
6.46 I$*03#$'$)&0,21,&"$,$- ]v-*,/"*#*/&$#(0&(/,21,*,0'*++%
$3 V
RB " 10 k&
6.47 l(.$, &"$, "!", $S3(.*+$)&, /(#/3(&, '2-$+0, &"*&, /2##$%
072)-,&2,&"20$,0"24),(),L(;<,X<?E,12#,&"$,!"!,/*0$<
VC
6.48 @,BC!,27$#*&();,*&,$),=,E,µ@,*)-,$-,=,?<P,'@,3)-$#%
;2$0,*,#$-3/&(2),(),9*0$,/3##$)&,21,O<E,µ@<,=&,(0,123)-,&"*&
4"$), v-*, (0, "$+-, /2)0&*)&5, &"$, /2##$072)-();, #$-3/&(2), ()
/2++$/&2#,/3##$)&,(0,O<?,'@<,W"*&,*#$,&"$,.*+3$0,21,β,*)-,&"$
()/#$'$)&*+, β, 2#, β'E, &"*&, *77+:f, =1, &"$, 9*0$, /3##$)&, (0
()/#$*0$-,1#2',E,µ@,&2,?O,µ@,*)-,v-*,(0,()/#$*0$-,1#2',E,_
&2,?O,_5,4"*&,/2++$/&2#,/3##$)&,#$03+&0f,@003'$,+/,=,?OO,_<
6.49 L2#, &"$, /(#/3(&, (), L(;<, gX<8D, +$&, + -- d G , _5
> - d K , G Ω- , *)-, > ) d MP , G Ω? , !"$, BC!, "*0, β d GP?
L()-,&"$,.*+3$,21, +)) ,&"*&,#$03+&0,(),&"$,&#*)0(0&2#,27$#*&();,
:)>#&"#$%+#)($&7+#320+#.&$%# + - d K #]H#
:9>#)$#$%+#+0L+#2@#')$/,)$&2"H
T/V,-$$7,(),0*&3#*&(2),4(&", β @2,(+0 d KP?
1 k&
Figure P6.51
Section 6.3: BJT Circuits at DC
6.52 !"$,&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,gX<^P,"*0,*,.$#:,"(;"
β<,L()-,+*,*)-,+-,12#,+),T*V,+?<^,_5,T9V,+?,_5,*)-,T/V,O,_<,
3V
VCC
1k
IC
VBB
VB
RC
VC
VC
RB
VE
1k
Figure P6.49
D *6.50 62)0(-$#, &"$, /(#/3(&, 21, L(;<, gX<8D, 12#, &"$
/*0$, +)) d +-- <,=1,&"$,BC!,(0,0*&3#*&$-5,30$,&"$,$S3(.*+$)&
/(#/3(&, 21, L(;<, X<PO, &2, -$#(.$, *), $A7#$00(2), 12#, β @2,(+0 , ()
&$#'0,21, + -- ,*)-, ( > ) ⁄ > - )<,@+02,-$#(.$,*),$A7#$00(2),12#
&"$, &2&*+, 724$#, -(00(7*&$-, (), &"$, /(#/3(&<, L2#, + -- d G , _5
-$0(;),&"$,/(#/3(&,&2,29&*(),27$#*&(2),*&,*,12#/$-, β ,*0,/+20$
&2,?O,*0,7200(9+$,4"(+$,+('(&();,&"$,724$#,-(00(7*&(2),&2,)2
+*#;$#,&"*),PO,'W<,c0$,?j,#$0(0&2#0,T0$$,@77$)-(A,lV<
6.51 !"$, "!", &#*)0(0&2#, (), &"$, /(#/3(&, (), L(;<, gX<^?, "*0
β d GP<, K"24, &"*&, &"$, BC!, (0, 27$#*&();, (), &"$, 0*&3#*&(2)
'2-$,*)-,1()-, β @2,(+0 ,*)-,+ - ? ,!2,4"*&,.*+3$,0"23+-, > ) ,9$
Figure P6.52
6.53 !"$,&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,gX<^P,"*0,*,.$#:,"(;"
β<, L()-, &"$, "(;"$0&, .*+3$, 21, +), 12#, 4"(/", &"$, &#*)0(0&2#, 0&(++
27$#*&$0, (), &"$, */&(.$, '2-$<, @+025, 1()-, &"$, .*+3$, 21, +), 12#
4"(/",&"$,&#*)0(0&2#,27$#*&$0,(),0*&3#*&(2),4(&",*,12#/$-,β,21,?<
6.54 62)0(-$#, &"$, 27$#*&(2), 21, &"$, /(#/3(&, 0"24), (), L(;<
gX<^8,12#,+),*&,]?,_5,O,_5,*)-,+?,_<,@003'$,&"*&, β,(0,.$#:
"(;"<,W"*&,.*+3$0,21,+*,*)-,+-,#$03+&f,@&,4"*&,.*+3$,21,+)
-2$0,&"$,$'(&&$#,/3##$)&,#$-3/$,&2,2)$%&$)&",21,(&0,.*+3$,12#
+) =,O,_f,L2#,4"*&,.*+3$,21,+),(0,&"$,&#*)0(0&2#,H30&,*&,&"$
$-;$,21,/2)-3/&(2)f,W"*&,.*+3$0,21,+*,*)-,+-,/2##$072)-f
PROBLEMS
0(;)*+,&#*)0(0&2#,27$#*&();,*&, v)*,=,NPO,'_,0"24,&"*&,$-,=
?<E,'@,*&,v-*,=,P,_,*)-,&"*&,$-,=,P<8,'@,*&,v-*,=,?8,_<,W"*&
(0, &"$, /2##$072)-();, .*+3$, 21, $-, )$*#, 0*&3#*&(2)f, @&, 4"*&
.*+3$,21, v-*,(0,$-,=,P<O,'@f,W"*&,(0,&"$,.*+3$,21,&"$,M*#+:
.2+&*;$,12#,&"(0,&#*)0(0&2#f,W"*&,(0,&"$,23&73&,#$0(0&*)/$,&"*&
/2##$072)-0,&2,27$#*&(2),*&,v)*,=,NPO,'_f
CHAPTER 6
6.45 L2#,*,BC!,"*.();,*),M*#+:,.2+&*;$,21,?^O,_5,4"*&,(0
CHAPTER 6
PROBLEMS
472 Chapter 6 Bipolar Junction Transistors (BJTs)
L2#, 4"*&, .*+3$, 21, +), -2$0, &"$, &#*)0(0&2#, #$*/", &"$, $-;$, 21
0*&3#*&(2)f,W"*&,.*+3$0,21,+-,*)-,+*,/2##$072)-f,L()-,&"$
.*+3$, 21, +), 12#, 4"(/", &"$, &#*)0(0&2#, 27$#*&$0, (), 0*&3#*&(2)
4(&",*,12#/$-,β,21,P<
6.57 @, 0();+$, '$*03#$'$)&, ()-(/*&$0, &"$, $'(&&$#, .2+&*;$
21, &"$, &#*)0(0&2#, (), &"$, /(#/3(&, 21, L(;<, g^<^N, &2, 9$, ?<P, _<
c)-$#,&"$,*003'7&(2),&"*&, + )* =,O<N,_5,4"*&,*#$,+)5,.)5,.*5
.-5,+-5,β5,*)-,α f,T7%?4O,=0)h&,(&,03#7#(0();,4"*&,*,+(&&+$,'$*%
03#$'$)&,/*),+$*-,&2fV
$5 V
$5 V
2 k&
5 k&
VC
VE
VB
VB
50 k&
VE
2 k&
VC
5 k&
%5 V
%5 V
Figure P6.57
Figure P6.54
6.55 L2#,&"$,&#*)0(0&2#,0"24),(),L(;<,gX<^^5,*003'$, α,!,?
*)-,v)* =,O<^,_,*&,&"$,$-;$,21,/2)-3/&(2)<,W"*&,*#$,&"$,.*+3$0
21,+*,*)-,+-,12#,+) =,O,_f,L2#,4"*&,.*+3$,21,+),-2$0,&"$,&#*)%
0(0&2#,/3&,211f,K*&3#*&$f,=),$*/",/*0$5,4"*&,.*+3$0,21,+*,*)+- #$03+&f
D 6.58 Z$0(;),*,/(#/3(&,30();,*,"!",&#*)0(0&2#,12#,4"(/", α
!, ?, 30();, &42, #$0(0&2#0, /2))$/&$-, *77#27#(*&$+:, &2, ±^, _, 02
&"*&,.* =,P,'@,*)-,+)- =,P<^,_<,W"*&,$A*/&,.*+3$0,21,>*,*)-,>423+-,9$,)$$-$-f,Q245,/2)03+&,*,&*9+$,21,0&*)-*#-,^j,#$0(0&2#
.*+3$0, T$<;<5, &"*&, 7#2.(-$-, (), @77$)-(A, lV, &2, 0$+$/&, 03(&*9+$
7#*/&(/*+, .*+3$0<, W"*&, .*+3$0, 21, #$0(0&2#0, "*.$, :23, /"20$)f
W"*&,*#$,&"$,.*+3$0,21,.*,*)-,+)-,&"*&,#$03+&f
6.59 =),&"$,/(#/3(&,0"24),(),L(;<,gX<^D5,&"$,&#*)0(0&2#,"*0
β =,^O<,L()-,&"$,.*+3$0,21,+)5,+*5,*)-,+-<,=1,>),(0,#*(0$-,&2
5 mA
VC
?OO GΩ5, 4"*&, .2+&*;$0, #$03+&f, W(&", >), =, ?OO, GΩ5, 4"*&
.*+3$, 21, β, 423+-, #$&3#), &"$, .2+&*;$0, &2, &"$, .*+3$0, 1(#0&
/*+/3+*&$-f
1 k&
VB
$5 V
RE
2.2 k&
VE
1 mA
1 k&
VE
VB
Figure P6.55
D 6.56 62)0(-$#, &"$, /(#/3(&, (), L(;<, gX<^P, 4(&", &"$, 9*0$
.2+&*;$,+),29&*()$-,30();,*,.2+&*;$,-(.(-$#,*/#200,&"$,\%_
0377+:<, @003'();, &"$, &#*)0(0&2#, β, &2, 9$, .$#:, +*#;$, T(<$<5
(;)2#();, &"$, 9*0$, /3##$)&V5, -$0(;), &"$, .2+&*;$, -(.(-$#, &2
29&*(),+),=,?<^,_<,Z$0(;),12#,*,O<?%'@,/3##$)&,(),&"$,.2+&%
*;$,-(.(-$#<,Q245,(1,&"$,BC!, β, =,?OO5,*)*+:>$,&"$,/(#/3(&,&2
-$&$#'()$,&"$,/2++$/&2#,/3##$)&,*)-,&"$,/2++$/&2#,.2+&*;$<
RB
20 k&
VC
RC
2.2 k&
%5 V
Figure P6.59
Problems 473
$3 V
&#*)0(0&2#,(0,27$#*&();,(),&"$,*/&(.$,'2-$<,W"*&,(0,&"$,+*#;$0&
.*+3$, &"*&, >-, /*), "*.$, 4"(+$, &"$, &#*)0(0&2#, #$'*()0, (), &"$
*/&(.$,'2-$f
$3 V
1.6 k&
1.6 k&
V3
V2
PROBLEMS
6.61 L2#, &"$, /(#/3(&, (), L(;<, gX<X?5, 1()-, +)5, +*5, *)+-,12#8>) = ?OO,GΩ5,?O,GΩ5,*)-,?,GΩ<,F$&,β = ?OO<
22 k&
I4
V1
2.2 k&
1 mA
%3 V
(b)
(a)
$3 V
$3 V
3.3 k&
1.6 k&
V7
22 k&
56 k&
V6
V9
V5
5.1 k&
2.2 k&
Figure P6.61
6.62 L2#,&"$,/(#/3(&0,(),L(;<,gX<XP5,1()-,.*+3$0,12#,&"$,+*9$+$)2-$,.2+&*;$0,*)-,9#*)/",/3##$)&0<,@003'$,β, &2,9$,.$#:,"(;"<
%3 V
%3 V
*6.63 U$7$*&,&"$,*)*+:0(0,21,&"$,/(#/3(&0,(),g#29+$',X<XP
30();,β,=,?OO<,L()-,*++,&"$,+*9$+$-,)2-$,.2+&*;$0,*)-,9#*)/"
(d)
(c)
/3##$)&0<
$3 V
D **6.64 =&,(0,#$S3(#$-,&2,-$0(;),&"$,/(#/3(&,(),L(;<,gX<X8
02,&"*&,*,/3##$)&,21,?,'@,(0,$0&*9+(0"$-,(),&"$,$'(&&$#,*)-,*
.2+&*;$,21,−5,_,*77$*#0,*&,&"$,/2++$/&2#<,!"$,&#*)0(0&2#,&:7$
30$-,"*0,*,)2'()*+,β,21,?OO<,R24$.$#5,&"$,β,.*+3$,/*),9$,*0
+24,*0,^O,*)-,*0,"(;",*0,?^O<,m23#,-$0(;),0"23+-,$)03#$,&"*&
&"$,07$/(1($-,$'(&&$#,/3##$)&,(0,29&*()$-,4"$), β,=,?OO,*)&"*&,*&,&"$,$A&#$'$,.*+3$0,21, β,&"$,$'(&&$#,/3##$)&,-2$0,)2&
/"*);$,9:,'2#$,&"*),?Oj,21,(&0,)2'()*+,.*+3$<,@+025,-$0(;)
12#,*0,+*#;$,*,.*+3$,12#,>),*0,7200(9+$<,l(.$,&"$,.*+3$0,21,>)5
>*5,*)-,>-,&2,&"$,)$*#$0&,G(+2"'<,W"*&,(0,&"$,$A7$/&$-,#*);$
21, /2++$/&2#, /3##$)&, *)-, /2++$/&2#, .2+&*;$, /2##$072)-();, &2
&"$,13++,#*);$,21,β,.*+3$0f
D 6.65 !"$,"!",&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,gX<X^,"*0
β =,^O<,L()-,&"$,.*+3$,12#,>-,&2,29&*(),+-,=,+\,_<,W"*&,"*7%
91 k&
3.3 k&
V11
V10
V12
150 k&
5.1 k&
%3 V
7$)0, (1, &"$, &#*)0(0&2#, (0, #$7+*/$-, 4(&", *)2&"$#, "*.();
β = ?OOf,
V8
$0.7 V
(e)
Figure P6.62
CHAPTER 6
6.60 =),&"$,/(#/3(&,0"24),(),L(;<,gX<^D5,&"$,&#*)0(0&2#,"*0
β =,^O<,L()-,&"$,.*+3$0,21,+)5,+*5,*)-,+-5,*)-,.$#(1:,&"*&,&"$
474 Chapter 6 Bipolar Junction Transistors (BJTs)
PROBLEMS
$9 V
2 k&
E
80 k&
100 &
D2
CHAPTER 6
Q2
Q1
R
D1
C
2 k&
100 &
2 k&
40 k&
Figure P6.64
Figure P6.66
5V
$5 V
9.1 k&
5.1 k&
V2
V1
100 k&
*6.67 L2#,&"$,/(#/3(&,0"24),(),L(;<,gX<XN5,1()-,&"$,+*9$+$)2-$,.2+&*;$0,12#Y
T*V β,=,∞
T9V β,=,?OO
D *6.68 c0();,β,=,∞5,-$0(;),&"$,/(#/3(&,0"24),(),L(;<,gX<XE
02,&"*&,&"$,9(*0,/3##$)&0,(),V?5,VP5,*)-,V\,*#$,?,'@5,?,'@5
*)-,P,'@5,#$07$/&(.$+:5,*)-,+\,=,O5,+^,=,−P,_5,*)-,+N,=,?,_<
Q2
V3
Figure P6.65
**6.66 62)0(-$#,&"$,/(#/3(&,0"24),(),L(;<,gX<XX<,=&,#$0$'9+$0
&"*&,(),L(;<,X<PD,93&,()/+3-$0,2&"$#,1$*&3#$0<,L(#0&5,)2&$,-(2-$0
1?,*)-,1P,*#$,()/+3-$-,&2,'*G$,-$0(;),T*)-,*)*+:0(0V,$*0($#,*)&2,7#2.(-$,&$'7$#*&3#$,/2'7$)0*&(2),12#,&"$,$'(&&$#]9*0$,.2+&%
*;$0,21,V?,*)-,VP<,K$/2)-5,)2&$,#$0(0&2#,>,4"20$,73#720$,(0,&2
7#2.(-$, )$;*&(.$, 1$$-9*/G, T'2#$, 2), &"(0, +*&$#, (), &"$, 922GsV<
c0();, + )* ,*)-,+1 =,O<N,_,()-$7$)-$)&,21,/3##$)&,*)-,β =,∞5
1()-,&"$,.2+&*;$0,+)?5,+*?5,+-?5,+)P5,+*P5,*)-,+-P5,()(&(*++:,4(&",>
27$)%/(#/3(&$-,*)-,&"$),4(&",>,/2))$/&$-<,U$7$*&,12#,β =,?OO5
()(&(*++:,4(&",>,27$)%/(#/3(&$-,&"$),/2))$/&$-<
V5
Q1
V4
9.1 k&
4.3 k&
%5 V
Figure P6.67
L2#,$*/",#$0(0&2#5,0$+$/&,&"$,)$*#$0&,0&*)-*#-,.*+3$,3&(+(>();
&"$,&*9+$,21,0&*)-*#-,.*+3$0,12#,^j,#$0(0&2#0,(),@77$)-(A,l<
Q245,12#,β,=,?OO5,1()-,&"$,.*+3$0,21,+\5,+85,+^5,+X5,*)-,+N<
*6.69 L2#,&"$,/(#/3(&,(),L(;<,gX<XD5,1()-,+),*)-,+*,12#,v.,=,O _5
+P _5,−P<^,_5,*)-,−^,_<,!"$,BC!0,"*.$,β,=,?OO<
**6.70 L()-, *77#2A('*&$, .*+3$0, 12#, &"$, /2++$/&2#, .2+&%
*;$0,(),&"$,/(#/3(&0,21,L(;<,gX<NO<,@+025,/*+/3+*&$,12#/$-,β
12#, $*/", 21, &"$, &#*)0(0&2#0<, TY$!?O, =)(&(*++:5, *003'$, *++
&#*)0(0&2#0, *#$, 27$#*&();, (), 0*&3#*&(2)5, *)-, .$#(1:, &"$
*003'7&(2)<
Problems 475
2.5 V
R3
R2
R5
V4
Q1
V3
PROBLEMS
V7
Q2
Q3
V5
V2
V6
R4
R1
R6
2.5 V
%5 V
Figure P6.68
Figure P6.69
5V
5V
5V
CHAPTER 6
$5 V
5V
Figure P6.70
Section 6.4: Applying the BJT in Amplifier
Design
6.71 @,BC!,*'7+(1($#,/(#/3(&,03/",*0,&"*&,(),L(;<,X<\\T*V
(0,27$#*&$-,4(&",+--,d,e^,_,*)-,(0,9(*0$-,*&,+-*8 ,d,e?,_<
L()-, &"$, .2+&*;$, ;*()5, &"$, '*A('3', *++24$-, 23&73&, )$;*%
&(.$,04();,4(&"23&,&"$,&#*)0(0&2#,$)&$#();,0*&3#*&(2)5,*)-,&"$
/2##$072)-();,'*A('3',()73&,0(;)*+,7$#'(&&$-<
6.72 L2#,&"$,*'7+(1($#,/(#/3(&,(),L(;<,X<\\T*V,4(&",+-- =,+^ _
*)-,>- =,?,GΩ5,1()-,+-*,*)-,&"$,.2+&*;$,;*(),*&,&"$,12++24();
-/,/2++$/&2#,9(*0,/3##$)&0Y,O<^,'@5,?,'@5,P<^,'@5,8,'@5,*)-
8<^,'@<,L2#,$*/"5,;(.$,&"$,'*A('3',7200(9+$,720(&(.$%,*))$;*&(.$%23&73&, 0(;)*+, 04();, *0, -$&$#'()$-, 9:, &"$, )$$-, &2
G$$7,&"$,&#*)0(0&2#,(),&"$,*/&(.$,#$;(2)<,g#$0$)&,:23#,#$03+&0,()
*,&*9+$<
D 6.73 62)0(-$#, &"$, 6M, *'7+(1($#, /(#/3(&, 21, L(;<, X<\\T*V
4"$),27$#*&$-,4(&",*,-/,0377+:,+-- =,+^,_<,=&,(0,#$S3(#$-,&2
1()-,&"$,72()&,*&,4"(/",&"$,&#*)0(0&2#,0"23+-,9$,9(*0$-`,&"*&,(05
1()-,&"$,.*+3$,21,+-*,02,&"*&,&"$,23&73&,0()$%4*.$,0(;)*+, vE4
#$03+&();, 1#2', *), ()73&, 0()$%4*.$, 0(;)*+, v#4, 21, ^%'_, 7$*G
*'7+(&3-$,"*0,&"$,'*A('3',7200(9+$,'*;)(&3-$<,W"*&,(0,&"$
CHAPTER 6
PROBLEMS
476 Chapter 6 Bipolar Junction Transistors (BJTs)
7$*G,*'7+(&3-$,21,&"$,23&73&,0()$,4*.$,*)-,&"$,.*+3$,21,&"$
;*(),29&*()$-f,@003'$,+()$*#,27$#*&(2),*#23)-,&"$,9(*0,72()&<
TY$!?O,!2,29&*(),&"$,'*A('3',7200(9+$,23&73&,*'7+(&3-$,12#
*,;(.$),()73&5,:23,)$$-,&2,9(*0,&"$,&#*)0(0&2#,*0,/+20$,&2,&"$
$-;$, 21, 0*&3#*&(2), *0, 7200(9+$, 4(&"23&, $)&$#();, 0*&3#*&(2), *&
*):,&('$5,&"*&,(05,4(&"23&,v-*,-$/#$*0();,9$+24,O<\,_<V
6.74 @,-$0(;)$#,/2)0(-$#0,*,)3'9$#,21,+24%.2+&*;$,BC!
*'7+(1($#, -$0(;)0, 3&(+(>();, 724$#, 0377+($0, 4(&", .2+&*;$
+ -- ,21,?<O5,?<^5,P<O5,2#,\<O,_<,L2#,&#*)0(0&2#0,&"*&,0*&3#*&$
*&, + -* d P?N _5,4"*&,(0,&"$,+*#;$0&,7200(9+$,.2+&*;$,;*()
*/"($.*9+$,4(&",$*/",21,&"$0$,0377+:,.2+&*;$0f,=1,(),$*/"
/*0$, 9(*0();, (0, *-H30&$-, 02, &"*&, + -* d + -- ⁄ M5, 4"*&
;*()0, *#$, */"($.$-f, =1, *, )$;*&(.$%;2();, 23&73&, 0(;)*+
04();,21,O<8_,(0,#$S3(#$-5,*&,4"*&, + -* ,0"23+-,&"$,&#*)%
0(0&2#, 9$, 9(*0$-, &2, 29&*(), '*A('3', ;*()f, W"*&, (0, &"$
;*(), */"($.$-, 4(&", $*/", 21, &"$, 0377+:, .2+&*;$0f, Q2&(/$
&"*&,*++,21,&"$0$,;*()0,*#$,()-$7$)-$)&,21,&"$,.*+3$,21, . /"20$)sV
$5 V
10 k&
vO
vI
10 k&
Figure P6.76
$VCC " $5 V
vI
vI
D *6.75,@,BC!,*'7+(1($#,03/",*0,&"*&,(),L(;<,X<\\T*V,(0,&2
9$,-$0(;)$-,&2,03772#&,#$+*&(.$+:,3)-(0&2#&$-,0()$%4*.$,23&73&
0(;)*+0,21,7$*G,*'7+(&3-$0,\,.2+&,4(&"23&,&"$,BC!,$)&$#();
0*&3#*&(2),2#,/3&211,*)-,&2,"*.$,*,.2+&*;$,;*(),21, / v ,_o_<
K"24, &"*&, &"$, '()('3', 0377+:, .2+&*;$, + -- , )$$-$-, (0
;(.$),9:
+ -- d + -*')$ e \ e / v + ,
@+025,1()-, + -- 5,07$/(1($-,&2,&"$,)$*#$0&,O<^,_5,12#,&"$,12+%
+24();,0(&3*&(2)0Y
T*V, / v d ] MP ,_o_5, \ d P?M ,_
T9V, / v d ] GP ,_o_5, \ d P?G ,_
T/V, / v d ] KPP ,_o_5, \ d P?G ,_
T-V, / v d ] KPP ,_o_5, \ d K?P ,_
T$V, / v d ] MPP ,_o_5, \ d K?P ,_
T1V, / v d ] GPP ,_o_5, \ d K?P ,_
T;V, / v d ] GPP ,_o_5, \ d M?P ,_
vO
vO
RC
RC
%VCC " %5 V
(b)
(a)
Figure P6.77
Z$#(.$,&"(0,$A7#$00(2),()/+3-();,&"$,M*#+:,$11$/&5,9:,039%
0&(&3&();,
$- = .6 4
v)* ⁄ +, v -*
5
K + 5555555
+/
&"#EV?#:W?Me>#)"0#&"(6/0&"L#$%+#@)($2,# ( K + v -* ⁄ + / ) #&"#EV?
:W?Mf>?#C%2.#$%)$#$%+#L)&"#+T*,+''&2"#(%)"L+'#$2
( + -- ] + -* ) ⁄ +
].- >- ⁄ +,
/ v = 555555555555555555555555555555555555
= ] 555555555555555555555555555555555555555,
.- >+ -- ] + -*
K + 555555555555555555555
K + 555555555555555555555555
+ / + + -*
+ / + + -*
6.76 !"$,&#*)0(0&2#,(),&"$,/(#/3(&,21,L(;<,gX<NX,(0,9(*0$-,*&
*,-/,/2++$/&2#,/3##$)&,21,O<8,'@<,W"*&,(0,&"$,.2+&*;$,;*()f
TY$!?O,c0$,!"p.$)()h0,&"$2#$',&2,/2).$#&,&"$,/(#/3(&,&2,&"$
12#',(),L(;<,X<\\*V<
L2#,&"$,/*0$,+-- =,^,_,*)-,+-* =,P<^,_5,4"*&,(0,&"$,;*()
4(&"23&,*)-,4(&",&"$,M*#+:,$11$/&,&*G$),()&2,*//23)&f,F$&
+/ =,?OO,_<
6.77 KG$&/", *)-, +*9$+, &"$, .2+&*;$, &#*)01$#, /"*#*/&$#(0&(/0
6.79 W"$), &"$, *'7+(1($#, /(#/3(&, 21, L(;< X<\\T*V, (0, 9(*0$-
21,&"$,"!",/2''2)%$'(&&$#,*'7+(1($#0,0"24),(),L(;<,gX<NN<
*6.78 =), -$#(.();, &"$, $A7#$00(2), 12#, 0'*++%0(;)*+, .2+&%
*;$, ;*(), /v, (), MS<, TX<\?V, 4$, )$;+$/&$-, &"$, M*#+:, $11$/&<
4(&",*,/$#&*(),+)*5,&"$,-/,.2+&*;$,*&,&"$,/2++$/&2#,(0,123)&2,9$,+P,_<,L2#,+--,=,+^,_,*)-,>- =,? GΩ5,1()-,.-,*)-,&"$
0'*++%0(;)*+,.2+&*;$,;*()<,L2#,*,/"*);$,∆v)*,=,+^,'_5,/*+%
/3+*&$,&"$,#$03+&();,∆vN<,6*+/3+*&$,(&,&42,4*:0Y,9:,1()-();
Problems 477
*6.80 62)0(-$#,&"$,*'7+(1($#,/(#/3(&,21,L(;<,X<\\T*V,4"$)
27$#*&$-,4(&",*,0377+:,.2+&*;$,+--,=,+\_<
6.81 !"$,$00$)/$,21,&#*)0(0&2#,27$#*&(2),(0,&"*&,*,/"*);$,()
v)*5, ∆v)*5, 7#2-3/$0, *, /"*);$, (), $-5, ∆$-<, B:, G$$7();, ∆v)*
0'*++5, ∆$-, (0, *77#2A('*&$+:, +()$*#+:, #$+*&$-, &2, ∆v)*5, ∆$-, =
CI∆v)*5, 4"$#$, CI, (0, G)24), *0, &"$, &#*)0(0&2#, &#*)0/2)-3/%
&*)/$<,B:,7*00();,∆$-,&"#23;",>-5,*),23&73&,.2+&*;$,0(;)*+
∆vN, (0, 29&*()$-<, c0$, &"$, $A7#$00(2), 12#, &"$, 0'*++%0(;)*+
.2+&*;$, ;*(), (), MS< TX<\OV, &2, -$#(.$, *), $A7#$00(2), 12#, CI<
L()-,&"$,.*+3$,218CI,12#,*,&#*)0(0&2#,9(*0$-,*&,.- =,?,'@<
VCC
iC
VBB
$
RB
vCE
iB
%
Figure P6.82
12#,$)8= PO µ@5,^O,µ@5,EO,µ@5,*)-,?OO,µ@<,L2#,&"$,73#720$
21,&"(0,0G$&/"5,*003'$,&"*&,$-,=, β$),*&, v-*,=,O<,@+025,0G$&/"
&"$,+2*-,+()$,29&*()$-,12#,+--,=,?O,_,*)-,>-,=,?,GΩ<,=1,&"$
-/,9(*0,/3##$)&,()&2,&"$,9*0$,(0,^O,µ@5,4#(&$,&"$,$S3*&(2),12#
&"$,/2##$072)-();,$- −v-*,/3#.$<,@+025,4#(&$,&"$,$S3*&(2),12#
&"$,+2*-,+()$5,*)-,02+.$,&"$,&42,$S3*&(2)0,&2,29&*(),+-*,*).-<, =1, &"$, ()73&, 0(;)*+, /*30$0, *, 0()302(-*+, 0(;)*+, 21, \O%µ@
7$*G, *'7+(&3-$, &2, 9$, 037$#('720$-, 2), .)5, 1()-, &"$, /2##$%
072)-();,0(;)*+,/2'72)$)&0,21,$-,*)-,v-*<
*6.84 62)0(-$#, &"$, 27$#*&(2), 21, &"$, /(#/3(&, 0"24), (), L(;<
gX<E8,*0,v),#(0$0,0+24+:,1#2',>$#2<,L2#,&"(0,&#*)0(0&2#5,*003'$
β =, ^O5, v)*, *&, 4"(/", &"$, &#*)0(0&2#, /2)-3/&0, (0, O<^, _5, v)*
4"$), 13++:, /2)-3/&();, (0, O<N, _5, 0*&3#*&(2), 9$;()0, *&, v)- =
O<8,_5,*)-,&"$,&#*)0(0&2#,(0,-$$7+:,(),0*&3#*&(2),*&,v)- =,O<X_<
KG$&/",*)-,+*9$+,v*,*)-,v-,.$#030,v)<,L2#,4"*&,#*);$,21,v),(0
$-,$00$)&(*++:,>$#2f,W"*&,*#$,&"$,.*+3$0,21,v*5,$*5,$-5,*)-,v-,12#
v) =,?,_,*)-,\,_f,L2#,4"*&,.*+3$,21,v),-2$0,0*&3#*&(2),9$;()f
W"*&,(0,$),*&,&"(0,72()&f,L2#, v) =,8,_,*)-,X,_5,4"*&,*#$,&"$
.*+3$0,21,v*5,v-5,$*5,$-5,*)-,$)f,@3;'$)&,:23#,0G$&/",9:,*--();
*,7+2&,21,$)<
$6 V
6.82 !"$,73#720$,21,&"(0,7#29+$',(0,&2,(++30&#*&$,&"$,*77+(%
/*&(2), 21, ;#*7"(/*+, *)*+:0(0, &2, &"$, /(#/3(&, 0"24), (), L(;<
gX<EP<,KG$&/", $ - ] v -* ,/"*#*/&$#(0&(/,/3#.$0,12#,&"$,BC!,12#
$ ) d K ,µ@5,?O,µ@5,PO,µ@5,*)-,8O,µ@<,@003'$,&"$,+()$0,&2
9$, "2#(>2)&*+, T(<$<5, )$;+$/&, &"$, M*#+:, $11$/&V5, *)-, +$&
β d KPP<, L2#, + -- d G , _, *)-, > - d K , G Ω- , 0G$&/", &"$
+2*-, +()$<, W"*&, 7$*G%&2%7$*G, /2++$/&2#, .2+&*;$, 04();, 4(++
#$03+&,12#, $ ) ,.*#:();,2.$#,&"$,#*);$,?O,µ@,&2,8O,µ@f,=1,&"$
K
BC!,(0,9(*0$-,*&, + -* d M555 + -- - ,1()-,&"$,.*+3$,21, . - ,*). ) ? ,=1,*&,&"(0,/3##$)&, + )* d P?d ,_,*)-,(1, > ) d KPP ,G Ω1()-,&"$,#$S3(#$-,.*+3$,21,+ ))<
*6.83 KG$&/",&"$,$- −v-*8/"*#*/&$#(0&(/0,21,*),!"!,&#*)0(0&2#
"*.();,β,=,?OO,*)-,+/,=,?OO,_<,KG$&/",/"*#*/&$#(0&(/,/3#.$0
RC
PROBLEMS
T*V W"*&,(0,&"$,&"$2#$&(/*+,'*A('3',.2+&*;$,;*(),&"*&,&"(0
*'7+(1($#,/*),7#2.(-$f
T9V W"*&, .*+3$, 21, +-*, '30&, &"(0, *'7+(1($#, 9$, 9(*0$-, *&, &2
7#2.(-$,*,.2+&*;$,;*(),21,]EO,_o_f
T/V =1,&"$,-/,/2++$/&2#,/3##$)&,.-,*&,&"$,9(*0,72()&,(),T9V,(0
&2,9$,O<^,'@5,4"*&,.*+3$,21,>-,0"23+-,9$,30$-f
T-V W"*&,(0,&"$,.*+3$,21,+)*,#$S3(#$-,&2,7#2.(-$,&"$,9(*0,72()&
'$)&(2)$-,*92.$f,@003'$,&"*&,&"$,BC!,"*0,.6 =,?O]?^,@<
T$V =1,*,0()$%4*.$,0(;)*+, v#4,"*.();,*,^%'_,7$*G,*'7+(&3-$
(0,037$#('720$-,2),+)*5,1()-,&"$,/2##$072)-();,23&73&,.2+&%
*;$,0(;)*+,vE4,&"*&,4(++,9$,037$#('720$-,2),+-*,*003'();,+()%
$*#,27$#*&(2),*#23)-,&"$,9(*0,72()&<
T1V 6"*#*/&$#(>$, &"$, 0(;)*+, /3##$)&, $E, &"*&, 4(++, 9$, 037$#%
('720$-,2),&"$,-/,9(*0,/3##$)&,.-<
T;V W"*&, (0, &"$, .*+3$, 21, &"$, -/, 9*0$, /3##$)&, .), *&, &"$, 9(*0
72()&f, @003'$, β =, ?OO<,6"*#*/&$#(>$,&"$,0(;)*+, /3##$)&, $#
&"*&,4(++,9$,037$#('720$-,2),&"$,9*0$,/3##$)&,.)<
T"V Z(.(-();, &"$, *'7+(&3-$, 21, v#4, 9:, &"$, *'7+(&3-$, 21, $#5
$.*+3*&$,&"$,()/#$'$)&*+,T2#,0'*++%0(;)*+V,()73&,#$0(0&*)/$,21
&"$,*'7+(1($#<
T(V KG$&/",*)-,/+$*#+:,+*9$+,/2##$+*&$-,;#*7"0,12#,v)*5,v-*5,$-5
*)-,$)<,Q2&$,&"*&,$*/",;#*7",/2)0(0&0,21,*,-/,2#,*.$#*;$,.*+3$
*)-,*,037$#('720$-,0()$,4*.$<,B$,/*#$13+,21,&"$,7"*0$,#$+*%
&(2)0"(70,21,&"$,0()$,4*.$0<
CHAPTER 6
∆$-, 30();, &"$, &#*)0(0&2#, $A72)$)&(*+, /"*#*/&$#(0&(/5, *)*77#2A('*&$+:, 30();, &"$, 0'*++%0(;)*+, .2+&*;$, ;*()<, U$7$*&
12#,∆v)* =,]^,'_<,K3''*#(>$,:23#,#$03+&0,(),* &*9+$<
1 k&
vC
vB
vE
1 k&
Figure P6.84
CHAPTER 6
PROBLEMS
478 Chapter 6 Bipolar Junction Transistors (BJTs)
6.90 @,&#*)0(0&2#,27$#*&();,4(&",)2'()*+,CI,21,^O,'@o_,"*0
*,β,&"*&,#*);$0,1#2',^O,&2,?^O<,@+025,&"$,9(*0,/(#/3(&5,9$();,+$00
Section 6.5: Small-Signal Operation
and Models
6.85 62)0(-$#, *, &#*)0(0&2#, 9(*0$-, &2, 27$#*&$, (), &"$, */&(.$
'2-$,*&,*,-/,/2++$/&2#,/3##$)&,.-<,6*+/3+*&$,&"$,/2++$/&2#,0(;%
)*+,/3##$)&,*0,*,1#*/&(2),21,.-,T(<$<5, $ E ⁄ . - > 12#,()73&,0(;)*+0
v#4,21,+?,'_5,−?,'_5,+P,'_5,−P,'_5,+^,'_5,−^,'_5,+E
'_5,−E,'_5,+?O,'_5,−?O,'_5,+?P,'_5,*)-,−?P,'_<,=)
$*/",/*0$,-2,&"$,/*+/3+*&(2),&42,4*:0Y
T*V 30();,&"$,$A72)$)&(*+,/"*#*/&$#(0&(/5,*)-,
T9V 30();,&"$,0'*++%0(;)*+,*77#2A('*&(2)<,
6.86 @),!"!,BC!,4(&",;#23)-$-,$'(&&$#,(0,27$#*&$-,4(&",+)*
=,O<NOO,_5,*&,4"(/",&"$,/2++$/&2#,/3##$)&,(0,O<^,'@<,@,?O%GΩ
#$0(0&2#,/2))$/&0,&"$,/2++$/&2#,&2,*,+?O%_,0377+:<,W"*&,(0,&"$
#$03+&();, /2++$/&2#, .2+&*;$, +-f, Q245, (1, *, 0(;)*+, *77+($-, &2
&"$ 9*0$,#*(0$0,v)*,&2,NO^,'_5,1()-,&"$,#$03+&();,&2&*+,/2++$/&2#
/3##$)&,$-,*)-,&2&*+,/2++$/&2#,.2+&*;$, v-,30();,&"$,$A72)$)&(*+
$- ]v)*,#$+*&(2)0"(7<,L2#,&"(0,0(&3*&(2)5,4"*&,*#$,v#4,*)-,vEf,6*+%
/3+*&$, &"$, .2+&*;$, ;*(), v E ⁄ v #4 ? , 62'7*#$, 4(&", &"$, .*+3$
29&*()$-,30();,&"$,0'*++%0(;)*+,*77#2A('*&(2)5,&"*&,(05,−CI>-<
6.87 @,&#*)0(0&2#,4(&", β,=,?PO,(0,9(*0$-,&2,27$#*&$,*&,*,-/
/2++$/&2#,/3##$)&,21,O<X,'@<,L()-,&"$,.*+3$0,21,CI5,(π 5,*)-,(4<
U$7$*&,12#,*,9(*0,/3##$)&,21,XO,µ@<,
6.88 @,"!",BC!,(0,9(*0$-,&2,27$#*&$,*&,.-,=,?<O,'@<,W"*&
(0,&"$,*002/(*&$-,.*+3$,21,CIf,=1,β,=,?OO5,4"*&,(0,&"$,.*+3$,21
&"$,0'*++%0(;)*+,#$0(0&*)/$,0$$),+22G();,()&2,&"$,$'(&&$#,T(4Vf
=)&2, &"$, 9*0$, T(πVf, =1, &"$, /2++$/&2#, (0, /2))$/&$-, &2, *, ^%GΩ
+2*-5,4(&",*,0(;)*+,21,^%'_,7$*G,*77+($-,9$&4$$),9*0$,*)$'(&&$#5,4"*&,23&73&,0(;)*+,.2+&*;$,#$03+&0f
D 6.89 @,-$0(;)$#,4(0"$0,&2,/#$*&$,*,BC!,*'7+(1($#,4(&",*
CI, 21, P^, '@o_, *)-, *, 9*0$, ()73&, #$0(0&*)/$, 21, \OOO, Ω, 2#
'2#$<,W"*&,$'(&&$#%9(*0,/3##$)&,0"23+-,"$,/"220$f,W"*&,(0
&"$,'()('3',β, "$,/*),&2+$#*&$,12#,&"$,&#*)0(0&2#,30$-f,
,,α
a
c
3)-$#,&"$,/2)0&#*()&,&"*&,+--,(0,1(A$-<,F$&,&"$,()73&,0(;)*+, v#4
=, +t #4 ,0() ω ?5,4"$#$, +t #4 ,(0,&"$,'*A('3',.*+3$,12#,*//$7&%
*9+$,+()$*#(&:<,L2#,&"$,-$0(;),&"*&,#$03+&0,(),&"$,+*#;$0&,0(;)*+
*&,&"$ /2++$/&2#5,4(&"23&,&"$,BC!,+$*.();,&"$,*/&(.$,#$;(2)5
0"24,&"*&
+t #4
5
> - . - = ( + -- ] P?N ]+t #4 ) K + 55555
+,
*)-,1()-,*),$A7#$00(2),12#,&"$,.2+&*;$,;*(),29&*()$-<,L2#,+-=,\,_,*)-, +t #4 ,=,^,'_5,1()-,&"$,-/,.2+&*;$,*&,&"$,/2++$/&2#5
&"$,*'7+(&3-$,21,&"$,23&73&,.2+&*;$,0(;)*+5,*)-,&"$,.2+&*;$
;*()<
6.93 !"$, &*9+$, 9$+24, 03''*#(>$0, 02'$, 21, &"$, 9*0(/
*&&#(93&$0,21,*,)3'9$#,21,BC!0,21,-(11$#$)&,&:7$05,27$#*&();
*0,*'7+(1($#0,3)-$#,.*#(230,/2)-(&(2)0<,g#2.(-$,&"$,'(00();
$)&#($0<,T7%?4O,=0)h&,(&,#$'*#G*9+$,"24,'3/",&42,7*#*'$&$#0
/*),#$.$*+fV
6.94 @,BC!,(0,9(*0$-,&2,27$#*&$,(),&"$,*/&(.$,'2-$,*&,*,-/
/2++$/&2#,/3##$)&,21,O<^,'@<,=&,"*0,*,β,21,?OO<,l(.$,&"$,123#
0'*++%0(;)*+,'2-$+0,TL(;0<,X<8O,*)-,X<8?V,21,&"$,BC!,/2'%
7+$&$,4(&",&"$,.*+3$0,21,&"$(#,7*#*'$&$#0<
6.95 !"$,&#*)0(0&2#,*'7+(1($#,(),L(;<,gX<D^,(0,9(*0$-,4(&",*
/3##$)&,023#/$8.,*)-,"*0,*,.$#:,"(;",β<,L()-,&"$,-/,.2+&*;$,*&
&"$, /2++$/&2#5, +-<, @+025, 1()-, &"$, .*+3$, 21, CI<, U$7+*/$, &"$
&#*)0(0&2#,4(&",&"$,0('7+(1($-,":9#(-%π,'2-$+,21,L(;<,X<8OT*V
d
e
?<OOO
β
88.-,T'@V
88.*,T'@V
88.),T'@V
88CI,T'@o_V
88(4,TΩV
88(π,TΩV
b
6.91 =),&"$,/(#/3(&,21,L(;<,X<\X5,+)*,(0,*-H30&$-,02,&"*&,+-8=
?,_<,=1,+--,=,\,_5,>-,=,P,GΩ5,*)-,*,0(;)*+,v#4,=,O<OO^,0(),ω?
.2+&0,(0,*77+($-5,1()-,$A7#$00(2)0,12#,&"$,&2&*+,()0&*)&*)$230
S3*)&(&($0,$-,T?V5, v-8 T?V5,*)-,$),T?V<,!"$,&#*)0(0&2#,"*0, β,=,EO<
W"*&,(0,&"$,.2+&*;$,;*()f
D *6.92 W$,4(0",&2,-$0(;),&"$,*'7+(1($#,/(#/3(&,21,L(;<,X<\X
g#$0$)&,:23#,#$03+&0,(),&"$,12#',21,*,&*9+$,&"*&,()/+3-$0,*,/2+%
3'),12#,&"$,$##2#,()&#2-3/$-,9:,&"$,0'*++%0(;)*+,*77#2A('*%
&(2)<,62''$)&,2),&"$,#*);$,21,.*+(-(&:,21,&"$,0'*++%0(;)*+
*77#2A('*&(2)<
Transistor
&"*),(-$*+5,*++240,*,±POj,.*#(*&(2),(),.-<,W"*&,*#$,&"$,$A&#$'$
.*+3$0,123)-,21,&"$,#$0(0&*)/$,+22G();,()&2,&"$,9*0$f,
f
g
O<DO
?OO
?<OO
,∞
?<OO
?<OO
^
O<OPO
?<?O
NOO
P^
?OO
?O<?,GΩ
Problems 479
ix
$ v
% x
8.2 k&
PROBLEMS
v
r = ix
x
Figure P6.98
9$,#$7+*/$-,9:,2)$,21,&"$,0'*++%0(;)*+,'2-$+0, 21,L(;0<,X<8O
*)-, X<8?<, c0$, &"$, '2-$+, 21, L(;<, X<8?T9V, *)-, 0"24, &"*&, &"$
#$03+&();, &42%&$#'()*+, -$.(/$5, G)24), *0, *, -(2-$, /2))$/&$&#*)0(0&2#5,"*0,*,0'*++%0(;)*+,#$0(0&*)/$,(,$S3*+,&2, ( 4 ?
I " 0.5 mA
6.99,L(;3#$,gX<DD,0"240,*,7*#&(/3+*#,/2)1(;3#*&(2),21,BC!
Figure P6.95
6.96 L2#, &"$, /2)/$7&3*+, /(#/3(&, 0"24), (), L(;<, X<\D5, >-, =
\ GΩ5,CI8=,^O,'@o_5,*)-, β =,?OO<,=1,*,7$*G%&2%7$*G,23&73&
.2+&*;$, 21, ?, _, (0, '$*03#$-, *&, &"$, /2++$/&2#5, 4"*&, *#$, &"$
7$*G%&2%7$*G,.*+3$0,21,v#4,*)-,$#f
*'7+(1($#05, G)24), *0, a$'(&&$#, 12++24$#<b, !"$, 9(*0, *##*);$%
'$)&,(0,)2&,0"24)<,U$7+*/$,&"$,BC!,4(&",(&0,!,$S3(.*+$)&%
/(#/3(&,'2-$+,21,L(;<,X<8?T9V<,K"24,&"*&
v
> &"## ≡ 5555$ d ( β e K ) ( ( 4 e > 4 )
$#
v%
>4
5555 d 555555555555555
5
v$
>4 e (4
6.97, L(;3#$, gX<DN, 0"240, &"$, /(#/3(&, 21, *), *'7+(1($#, 1$4(&",*,0(;)*+,023#/$, v '&L ,4(&",*,023#/$,#$0(0&*)/$, > '&L ? ,!"$
9(*0,/(#/3(&#:,(0,)2&,0"24)<,U$7+*/$,&"$,BC!,4(&",(&0,":9#(-%
π , $S3(.*+$)&, /(#/3(&, 21, L(;<, X<8OT*V<, L()-, &"$, ()73&, #$0(0%
&*)/$, > &" ≡ v π ⁄ $ # 5,&"$,.2+&*;$,&#*)0'(00(2),1#2',023#/$,&2
*'7+(1($#,()73&5, v π ⁄ v '&L - ,*)-,&"$,.2+&*;$,;*(),1#2',9*0$,&2
/2++$/&2#5, v % ⁄ v π <,c0$,&"$0$,&2,0"24,&"*&,&"$,2.$#*++,.2+&*;$
;*(), v % ⁄ v '&L ,(0,;(.$),9:
v
β >555555%5 d ] 5555555555555555555
v '&L
( π e > '&L
ib
vi
$
$
%
Re
vo
$
Rsig
ib
%
Rin
$
vsig $
%
RC
vo
v+
%
Rin
Figure P6.99
6.100 L2#,&"$,/(#/3(&,0"24),(),L(;<,gX<?OO5,-#*4,*,/2'%
%
Figure P6.97
6.98,L(;3#$,gX<DE,0"240,*,&#*)0(0&2#,4(&",&"$,/2++$/&2#,/2)%
)$/&$-,&2,&"$,9*0$<,!"$,9(*0,*##*);$'$)&,(0,)2&,0"24)<,K()/$,*
>$#2, v )- ,('7+($0,27$#*&(2),(),&"$,*/&(.$,'2-$5,&"$,BC!,/*)
CHAPTER 6
T)2&$,&"*&,&"$,-/,/3##$)&,023#/$,.,0"23+-,9$,#$7+*/$-,4(&",*)
27$),/(#/3(&V<,R$)/$,1()-,&"$,.2+&*;$,;*(), v E ⁄ v $ ?
7+$&$,0'*++%0(;)*+,$S3(.*+$)&,/(#/3(&,3&(+(>();,*),*77#27#(*&$
! '2-$+, 12#, &"$, BC!, T30$, α, =, O<DDV<, m23#, /(#/3(&, 0"23+0"24, &"$, .*+3$0, 21, *++, /2'72)$)&05, ()/+3-();, &"$, '2-$+
7*#*'$&$#0<, W"*&, (0, &"$, ()73&, #$0(0&*)/$, >()f, 6*+/3+*&$, &"$
2.$#*++,.2+&*;$,;*(), ( v % ⁄ v '&L )?
6.101 =),&"$,/(#/3(&,0"24),(),L(;<,gX<?O?5,&"$,&#*)0(0&2#,"*0
*,β,21,POO<,W"*&,(0,&"$,-/,.2+&*;$,*&,&"$,/2++$/&2#f,L()-,&"$
()73&, #$0(0&*)/$0, >$#, *)-, >(), *)-, &"$, 2.$#*++, .2+&*;$, ;*()
PROBLEMS
480 Chapter 6 Bipolar Junction Transistors (BJTs)
.*+3$0,21,(45,CI5,*)-,(π,#$03+&f,W"*&,(0,&"$,2.$#*++,.2+&*;$,;*()f
T7%?4O8m23,/*),0$$,&"*&,&"(0,/(#/3(&5,30();,9*0$%/3##$)&,/2)%
&#2+,21,9(*05,(0,.$#:,β%0$)0(&(.$,*)-,303*++:,!%?8(4E%II4!545<V
$9 V
10 k&
C2
vo
CHAPTER 6
!
RL
10 k&
Q1
Rsig
C1
50 &
!
vsig $
%
0.5 mA
Figure P6.100
$5 V
$1.5 V
10 mA
10 k&
!
vb
vo
vsig $
%
L(;<, X<88T*V<, !"$, 724$#, 0377+($0, *.*(+*9+$, *#$, ±^, _<, !"$
()73&, 0(;)*+, 023#/$, "*0, *, #$0(0&*)/$, 21, ^O, Ω5, *)-, (&, (0
#$S3(#$-,&"*&,&"$,*'7+(1($#,()73&,#$0(0&*)/$,'*&/",&"(0,.*+3$<
TQ2&$,&"*&,>(),=,(4 ,tt,>*,!,(4<V,!"$,*'7+(1($#,(0,&2,"*.$,&"$
;#$*&$0&,7200(9+$,.2+&*;$,;*(),*)-,&"$,+*#;$0&,7200(9+$,23&73&
0(;)*+,93&,#$&*(),0'*++%0(;)*+,+()$*#,27$#*&(2),T(<$<5,&"$,0(;)*+
/2'72)$)&,*/#200,&"$,9*0$]$'(&&$#,H3)/&(2),0"23+-,9$,+('%
(&$-,&2,)2,'2#$,&"*),?O,'_V<,L()-,*77#27#(*&$,.*+3$0,12#,>*
*)-,>-<,W"*&,(0,&"$,.*+3$,21,.2+&*;$,;*(),#$*+(>$-f
*6.107 !"$,&#*)0(0&2#,(),&"$,/(#/3(&,0"24),(),L(;<,gX<?ON,(0
9(*0$-, &2, 27$#*&$, (), &"$, */&(.$, '2-$<, @003'();, &"*&, β, (0
!
1 k&
RC
100 &
Rin
D 6.105 U$-$0(;), &"$, /(#/3(&, 21, L(;<, X<88, 9:, #*(0();, &"$
#$0(0&2#,.*+3$0,9:,*,1*/&2#,!,&2,()/#$*0$,&"$,#$0(0&*)/$,0$$)
9:,&"$,()73&, v$,&2,N^,Ω<,W"*&,.*+3$,21,.2+&*;$,;*(),#$03+&0f
l#23)-$-%9*0$,/(#/3(&0,21,&"(0,G()-,*#$,30$-,(),0:0&$'0,03/"
*0, /*9+$, !_5, (), 4"(/"5, 12#, "(;"$0&%S3*+(&:, 0(;)*+();5, +2*#$0(0&*)/$0, )$$-, &2, 9$, a'*&/"$-b, &2, &"$, $S3(.*+$)&, #$0(0%
&*)/$0,21,&"$,()&$#/2))$/&();,/*9+$0<
D **6.106 ,Z$0(;),*),*'7+(1($#,30();,&"$,/2)1(;3#*&(2),21
Rin
Rsig
6.104 U$/2)0(-$#,&"$,/(#/3(&,0"24),(),L(;<,X<88T*V,3)-$#
&"$,/2)-(&(2),&"*&,&"$,0(;)*+,023#/$,"*0,*),()&$#)*+,#$0(0&*)/$
21,?OO,Ω<,W"*&,-2$0,&"$,2.$#*++,.2+&*;$,;*(),9$/2'$f,W"*&
(0,&"$,+*#;$0&,()73&,0(;)*+,.2+&*;$,&"*&,/*),9$,30$-,4(&"23&
23&73&%0(;)*+,/+(77();f
Rib
.$#:, +*#;$5, 1()-, &"$, /2++$/&2#, 9(*0, /3##$)&, .-<, U$7+*/$, &"$
&#*)0(0&2#,4(&",&"$, 0'*++%0(;)*+, $S3(.*+$)&, /(#/3(&, '2-$+,21
L(;<,X<8?T9V,T#$'$'9$#,&2,#$7+*/$,&"$,-/,724$#,0377+:,4(&",*
0"2#&,/(#/3(&V<,@)*+:>$,&"$,#$03+&();,*'7+(1($#,$S3(.*+$)&,/(#%
/3(&,&2,0"24,&"*&
v %K
>*
5555555 = 5555555555555555
,
v$
>* + (4
Figure P6.101
5V
( v % ⁄ v '&L )? ,L2#,*),23&73&,0(;)*+,21,±O<8,_5,4"*&,.*+3$0,21,v0(;
*)-,v#,*#$,#$S3(#$-f
3.3
6.102 62)0(-$#, &"$, *3;'$)&$-, ":9#(-%π, '2-$+, 0"24), ()
L(;<,X<8NT*V<,Z(0#$;*#-();,"24,9(*0();,(0,&2,9$,-2)$5,4"*&,(0
&"$,+*#;$0&,7200(9+$,.2+&*;$,;*(),*.*(+*9+$,12#,*,0(;)*+,023#/$
/2))$/&$-, -(#$/&+:, &2, &"$, 9*0$, *)-, *, .$#:%"(;"%#$0(0&*)/$
+2*-f,6*+/3+*&$,&"$,.*+3$,21,&"$,'*A('3',7200(9+$,;*(),12#
+/,=,P^,_,*)-,+/ =,P^O,_<
6.103 U$/2)0(-$#,&"$,*'7+(1($#,0"24),(),L(;<,X<8P,*)-,*)*%
+:>$-, (), MA*'7+$, X<?8,3)-$#, &"$,/2)-(&(2),&"*&, β,(0,)2&,4$++
/2)&#2++$-<,L2#,4"*&,.*+3$,21, β,-2$0,&"$,/(#/3(&,9$;(),&2,0*&3%
#*&$f,W$,/*),/2)/+3-$,&"*&,+*#;$,β,(0,-*);$#230,(),&"(0,/(#/3(&<
Q245, /2)0(-$#, &"$, $11$/&, 21, #$-3/$-, β5, 0*:5, &2, β, =, P^<, W"*&
3.6
Figure P6.107
Problems 481
io
L()-,&"$,.*+3$0,21,&"$0$,.2+&*;$,;*()0,T12#, α,! ?V<,Q245,(1
&"$, &$#'()*+, +*9$+$-, v%?, (0, /2))$/&$-, &2, ;#23)-5, 4"*&, -2$0
&"$,.2+&*;$,;*(), v %M ⁄ v $ ,9$/2'$f
$
Ro
vo
%
Figure P6.110
6.111, @), *+&$#)*&(.$, $S3(.*+$)&, /(#/3(&, 21, *), *'7+(1($#, 1$4(&", *, 0(;)*+, 023#/$, ( v '&L - > '&L ) , *)-, /2))$/&$-, &2, *, +2*> X ,(0,0"24),(),L(;<,gX<???<,R$#$, Q v% ,(0,&"$,27$)%/(#/3(&
2.$#*++,.2+&*;$,;*()5
v
Q v% d 555555%5
v '&L
>X d ∞
:)># b2# 32,+# $%)"# KPo# 2@# $%+# '&L")6# '$,+"L$%# &'# 62'$# &"# $%+
(2""+($&2"#$2#$%+#)3*6&@&+,#&"*/$?
:9>#!@#$%+#62)0#,+'&'$)"(+#(%)"L+'#@,23#$%+#"23&")6#7)6/+#2@
M#U Ω #$2#)#62.#7)6/+#2@#K#U Ω -#$%+#(%)"L+#&"#2/$*/$#726$)L+
&'#6&3&$+0#$2#KPo#2@#"23&")6#7)6/+?
T/V,!"$,)2'()*+,2.$#*++,.2+&*;$,;*(),(0,?O,_o_<
*)-, > 2/$ ,(0,&"$,23&73&,#$0(0&*)/$,4(&", v '&L ,0$&,&2,>$#2<,!"(0
(0,-(11$#$)&,1#2', > % ? ,K"24,&"*&
6.110,L(;3#$,gX<??O,0"240,*),*+&$#)*&(.$,$S3(.*+$)&,/(#/3(&
#$7#$0$)&*&(2),21,*),*'7+(1($#<,=1,&"(0,/(#/3(&,(0,&2,9$,$S3(.*+$)&
&2,&"*&,(),L(;<,X<^OT9V,0"24,&"*&, Q I d / v% ⁄ > % ? ,@+02,/2)%
.()/$,:23#0$+1,&"*&,&"$,&#*)0/2)-3/&*)/$, Q I ,(0,-$1()$-,*0
@+02,0"24,&"*&,&"$,2.$#*++,.2+&*;$,;*()
$
Q I d 555%5
v$
>X d P
*)-, "$)/$, (0, G)24), *0, &"$, 0"2#&%/(#/3(&, &#*)0/2)-3/&*)/$<
Q24,(1,&"$,*'7+(1($#,(0,1$-,4(&",*,0(;)*+,023#/$, ( v '&L - > '&L )
*)-,(0,/2))$/&$-,&2,*,+2*-,#$0(0&*)/$, > X 5,0"24,&"*&,&"$,;*()
21,&"$,*'7+(1($#,7#27$#, / v ,(0,;(.$),9:, / v d Q I ( > % || > X )
*)-,&"$,2.$#*++,.2+&*;$,;*(), Q v ,(0,;(.$),9:
>$
5 /
Q v% d 5555555555555555555
> $ e > '&L v%
4"$#$, > $ d > &"
**6.112, I20&, 7#*/&(/*+, *'7+(1($#0, "*.$, ()&$#)*+, 1$$-9*/G
&"*&,'*G$,&"$',)2)3)(+*&$#*+<,=),03/",*,/*0$5, > &" ,-$7$)-0
2), > X ? ,!2,(++30&#*&$,&"(0,72()&,4$,0"24,(),L(;<,gX<??P,&"$
$S3(.*+$)&,/(#/3(&,21,*),*'7+(1($#,(),4"(/",*,1$$-9*/G,#$0(0%
&*)/$, > G , '2-$+0, &"$, ()&$#)*+, 1$$-9*/G, '$/"*)(0', &"*&, (0
7#$0$)&, (), &"(0, *'7+(1($#<, =&, (0, > G , &"*&, '*G$0, &"$, *'7+(1($#
)2)3)(+*&$#*+<,K"24,&"*&
Rout
$
vsig $
%
vi
> G e ( > M || > X )
5 ,
> &" d > K || 5555555555555555555555555555555555555
K e C I ( > M || > X )
%
io
$
Rin
<
>X
5
Q v d Q v% 55555555555555555555
> X e > 2/$
> &"
5 Q ( > || > X )
Q v d 555555555555555555555
> &" e > '&L I %
Rsig
>X d ∞
$
Gvovsig %
Figure P6.111
u O,296+3'#W?KPf#$2#W?KKK#),+#&0+"$&()6#$2#*,296+3'#G?fP#$2#G?fe?
RL v o
%
PROBLEMS
%
6.108 @),*'7+(1($#,4(&",*),()73&,#$0(0&*)/$,21,?OO,G Ω 5,*)
D 6.109,K7$/(1:,&"$,7*#*'$&$#0, > &" - , / v% - ,*)-, > % ,21,*)
*'7+(1($#,&"*&,(0,&2,9$,/2))$/&$-,9$&4$$),*,?OO%G Ω ,023#/$
*)-,*,P%G Ω ,+2*-<,!"$,*'7+(1($#,(0,#$S3(#$-,&2,'$$&,&"$,12+%
+24();,07$/(1(/*&(2)0Y
G m vi
Rin
vi
Section 6.6: Basic BJT Amplifier
Configurations, u
27$)%/(#/3(&, .2+&*;$, ;*(), 21, ?OO, _o_5, *)-, *), 23&73&, #$0(0%
&*)/$, 21, ?OO, Ω- , (0, /2))$/&$-, 9$&4$$), *, ?O%G Ω , 0(;)*+
023#/$,*)-,*,?%G Ω ,+2*-<,L()-,&"$,2.$#*++,.2+&*;$,;*(), Q v ?
@+02, 1()-, &"$, /3##$)&, ;*()5, -$1()$-, *0, &"$, #*&(2, 21, &"$, +2*/3##$)&,&2,&"$,/3##$)&,-#*4),1#2',&"$,0(;)*+,023#/$<
$
CHAPTER 6
v %M
]α >5555555 = 5555555555555555
v$
>* + (4
PROBLEMS
482 Chapter 6 Bipolar Junction Transistors (BJTs)
ii
Rsig
Rf
$
vsig $
%
vi
$
R1
g mvi
RL vo
R2
%
CHAPTER 6
%
Rin
Ro
Figure P6.112
K ] ( K ⁄ CI >G )
5
/ v% d ] C I > M 5555555555555555555555555555555
K e ( >M ⁄ >G )
> % d > M || > G
M.*+3*&$, > &" - , / v% - , *)-, > % , 12#, &"$, /*0$, > K d KPP , G Ω> G d K , I Ω- , C I d KPP , '@o_5, > M d KPP Ω- , *)> X d K ,G Ω? ,W"(/",21,&"$,*'7+(1($#,/"*#*/&$#(0&(/,7*#*'$%
&$#0, (0, '20&, *11$/&$-, 9:, > G , T(<$<5, #$+*&(.$, &2, &"$, /*0$, 4(&"
> G d ∞ Vf,L2#, > '&L d KPP ,G Ω 5,-$&$#'()$,&"$,2.$#*++,.2+&%
*;$,;*()5,Q v - ,4(&",*)-,4(&"23&, > G ,7#$0$)&<
6.113, @, 6M, *'7+(1($#, 3&(+(>$0, *, BC!, 4(&", β d KPP , *)+ / d GP ,_5,9(*0$-,*&, . - d P?G ,'@`,(&,"*0,*,/2++$/&2#,#$0(0%
&*)/$, > - d KP ,G Ω? ,@003'$, > ) ! ( π <,L()-, > &" - , > % - ,*)/ v% ?,=1,&"$,*'7+(1($#,(0,1$-,4(&",*,0(;)*+,023#/$,"*.();,*,#$0(0%
&*)/$,21,?O,G Ω- ,*)-,*,+2*-,#$0(0&*)/$, > X d KP ,G Ω ,(0,/2)%
)$/&$-,&2,&"$,23&73&,&$#'()*+5,1()-,&"$,#$03+&();, / v ,*)-,Q v<,=1
&"$,7$*G,.2+&*;$,21,&"$,0()$,4*.$,*77$*#();,9$&4$$),9*0$,*)$'(&&$#, (0, &2, 9$, +('(&$-, &2, ^, '_5, 4"*&, vt '&L , (0, *++24$-5, *)4"*&,23&73&,.2+&*;$,0(;)*+,*77$*#0,*/#200,&"$,+2*-f
T-V,=1,(&,(0,)2&,7200(9+$,&2,#$0&#(/&, β ,&2,&"$,#*);$,123)-,(),T/V5
*)-,&"$,-$0(;)$#,"*0,&2,/2)&$)-,4(&", β ,(),&"$,#*);$,^O,&2
?^O5,4"*&,.*+3$,21,9(*0,/3##$)&, . - ,423+-,#$03+&,(), Q v ,1*++%
();,(),*,#*);$,21, ± MP j,21,*,)$4,)2'()*+,.*+3$f,W"*&,(0
&"$,)2'()*+,.*+3$,21, Q v ,(),&"(0,/*0$f
D 6.115,=),&"(0,7#29+$'5,4$,().$0&(;*&$,&"$,$11$/&,21,/"*);%
();,&"$,9(*0,/3##$)&, . - ,2),&"$,2.$#*++,.2+&*;$,;*(), Q v ,21,*
6M,*'7+(1($#<,62)0(-$#,&"$,0(&3*&(2),21,*,6M,*'7+(1($#,27$#%
*&();,4(&",*,0(;)*+,023#/$,"*.();, > '&L d KP ,G Ω ,*)-,"*.();
> - || > X d KP ,G Ω? ,!"$,BC!,(0,07$/(1($-,&2,"*.$, β d KPP
*)-, + / d MG ,_<,c0$,MS<,TX<NDV,&2,1()-, Q v ,*&, . - d P?K
'@5, O<P, '@5, O<^, '@5, ?<O, '@5, *)-, ?<P^, '@<, J90$#.$, &"$
$11$/&, 21, ( % , 2), +('(&();, Q v , *0, . - , (0, ()/#$*0$-<, L()-, &"$
.*+3$,21, . - ,&"*&,#$03+&0,(), Q v d GP ,_o_<,
6.116 !42, (-$)&(/*+, 6M, *'7+(1($#0, *#$, /2))$/&$-, (), /*0%
/*-$<,!"$,1(#0&,0&*;$,(0,1$-,4(&",*,023#/$, v '&L ,"*.();,*,#$0(0%
&*)/$, > '&L d KP , G Ω? , @, +2*-, #$0(0&*)/$, > X d KP , G Ω , (0
D *6.114, =), &"(0, 7#29+$', 4$, ().$0&(;*&$, &"$, $11$/&, 21, &"$
/2))$/&$-,&2,&"$,/2++$/&2#,21,&"$,0$/2)-,0&*;$<,M*/",BC!,(0
9(*0$-, *&, . - d P?MG , '@, *)-, "*0, β d KPP , *)-, *, .$#:
+*#;$, + / ? , M*/", 0&*;$, 3&(+(>$0, *, /2++$/&2#, #$0(0&*)/$
> - d KP,G Ω?
>′X
5
Q v ! 55555555555555555555555555555555555555555555
( > '&L ⁄ β ) e ( K ⁄ C I )
T*V KG$&/",&"$,$S3(.*+$)&,/(#/3(&,21,&"$,&42%0&*;$,*'7+(1($#<
T9V 6*+/3+*&$, &"$, .2+&*;$, &#*)0'(00(2), 1#2', &"$, 0(;)*+
023#/$,&2,&"$,()73&,21,&"$,1(#0&,0&*;$<
T/V,6*+/3+*&$,&"$,.2+&*;$,;*(),21,&"$,1(#0&,0&*;$5, / vK<
T-V,6*+/3+*&$,&"$,.2+&*;$,;*(),21,&"$,0$/2)-,0&*;$5, / vM ?
T$V,L()-,&"$,2.$#*++,.2+&*;$,;*()5, v %M ⁄ v '&L ?
()$.(&*9+$, .*#(*9(+(&:, 21, β , 2), &"$, #$*+(>$-, ;*(), 21, &"$, 6M
*'7+(1($#<,L2#,&"(0,73#720$5,30$,&"$,2.$#*++,;*(),$A7#$00(2)
(),MS<,TX<NDV<,@003'$, ( % ,(0,0311(/($)&+:,+*#;$,&2,9$,)$;+(;(%
9+$,*)-,&"30,0"24,&"*&
4"$#$, >′X d > X || > - <
62)0(-$#,&"$,/*0$, > X′ d KP ,G Ω ,*)-, > '&L d KP ,G Ω- ,*)-,+$&
&"$,BC!,9$,9(*0$-,*&, . - d K ,'@<,!"$,BC!,"*0,*,)2'()*+, β
21,?OO<,
:)>#Y%)$#&'#$%+#"23&")6#7)6/+#2@# Q v _#
:9>#!@# β #()"#9+#)"1.%+,+#9+$.++"#GP#)"0#KGP-#.%)$#&'#$%+
(2,,+'*2"0&"L#,)"L+#2@# Q v _
T/V,=1,(),*,7*#&(/3+*#,-$0(;)5,(&,(0,#$S3(#$-,&2,'*()&*(), Q v
4(&"(), ± MP j, 21, (&0, )2'()*+, .*+3$5, 4"*&, (0, &"$, '*A('3'
*++24*9+$,#*);$,21, β f
6.117,@,6M,*'7+(1($#,3&(+(>$0,*,BC!,4(&", β d KPP ,9(*0$*&, . - d P?G , '@, *)-, "*0, *, /2++$/&2#, #$0(0&*)/$, > - d KP
G Ω ,*)-,*,#$0(0&*)/$, > 4 d KGP#Ω ,/2))$/&$-,(),&"$,$'(&&$#<
L()-, > &" - , / v% - ,*)-, > % ? ,=1,&"$,*'7+(1($#,(0,1$-,4(&",*,0(;)*+
023#/$,"*.();,*,#$0(0&*)/$,21,?O,G Ω 5,*)-,*,+2*-,#$0(0&*)/$
> X d KP ,G Ω ,(0,/2))$/&$-,&2,&"$,23&73&,&$#'()*+5,1()-,&"$
#$03+&();, / v ,*)-, Q v? ,=1,&"$,7$*G,.2+&*;$,21,&"$,0()$,4*.$
*77$*#();,9$&4$$),9*0$,*)-,$'(&&$#,(0,&2,9$,+('(&$-,&2,^,'_5
4"*&, vt '&L ,(0,*++24$-5,*)-,4"*&,23&73&,.2+&*;$,0(;)*+,*77$*#0
*/#200,&"$,+2*-f
Problems 483
T(V,=)73&,#$0(0&*)/$, > &" d MP ,G Ω?
T((V,W"$),1$-,1#2',*,0(;)*+,023#/$,4(&",*,7$*G,*'7+(&3-$,21
O<?,_,*)-,*,023#/$,#$0(0&*)/$,21,PO,G Ω 5,&"$,7$*G,*'7+(&3-$
21, v π ,(0,^,'_<
K7$/(1:, > 4 ,*)-,&"$,9(*0,/3##$)&, . - <,!"$,BC!,"*0, β d KPP?
=1,&"$,&2&*+,#$0(0&*)/$,(),&"$,/2++$/&2#,(0,^,G Ω5,1()-,&"$,2.$#%
*++, .2+&*;$, ;*(), Q v , *)-, &"$, 7$*G, *'7+(&3-$, 21, &"$, 23&73&
0(;)*+, v % ?
D 6.123,@),$'(&&$#,12++24$#,(0,#$S3(#$-,&2,-$+(.$#,*, P?G %_
7$*G,0()302(-,&2,*, M %G Ω ,+2*-<,=1,&"$,7$*G,*'7+(&3-$,21, v #4
(0,&2,9$,+('(&$-,&2,^,'_5,4"*&,(0,&"$,+24$0&,.*+3$,21, . * ,*&
4"(/",&"$,BC!,/*),9$,9(*0$-f,@&,&"(0,9(*0,/3##$)&5,4"*&,*#$
&"$, '*A('3', *)-, '()('3', /3##$)&0, &"*&, &"$, BC!, 4(++, 9$
/2)-3/&();,T*&,&"$,720(&(.$,*)-,)$;*&(.$,7$*G0,21,&"$,23&73&
0()$,4*.$Vf,=1,&"$,#$0(0&*)/$,21,&"$,0(;)*+,023#/$,(0,POO,G Ω4"*&,.*+3$