Single Transistor Amplifiers (6/13/00)
Page 1
3.2 - SINGLE TRANSISTOR AMPLIFIERS
INTRODUCTION
Objective
The objective of this presentation is:
1.) Show how to characterize an amplifier
2.) Show the analysis of single transistor amplifiers using resistive loads
3.) Build the amplifier concepts necessary to consider integrated circuit amplifiers
Outline
• Characterizing an amplifer
• BJT Single transistor amplifiers
• MOS Single transistor amplifers
• Amplifiers with emitter/source degeneration
• Summary
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 2
CHARACTERIZING AMPLIFIERS
Characterization of Amplifiers
Amplifiers will be characterized by the following properties:
• Large-signal voltage transfer characteristics (.DC)
• Large-signal voltage swing limitations (.DC and .TRAN)
• Small-signal, frequency independent performance (.TF)
• Gain (.TF)
• Input resistance (.TF)
• Output resistance (.TF)
• Small-signal, frequency response (.AC)
• Other properties (.TEMP, .FOUR, etc.)
• Noise (.NOISE)
• Power dissipation (.OP)
• Slew rate (.TRAN)
• Etc.
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 3
Types of Single Transistor Amplifiers
VCC
RC
VCC
RC
vIN
RC
vOUT
VCC
VCC
vOUT
vOUT
vIN
vOUT
vIN
RE
RE
vIN
Common Emitter
Common Base
Common Collector
Emitter Degeneration
VDD
VDD
RD
VDD
RD
vIN
RD
vOUT
VDD
vOUT
vIN
vOUT
vIN
RS
RS
vIN
Common Source
vOUT
Common Gate
ECE 4430 - Analog Integrated Circuits and Systems
Common Drain
Source Degeneration
STA01
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 4
Signal Flow in Transistors
It is important to recognize that ac signals can only flow into and out of certain transistor terminals.
Illustration:
C
D
180°
180°
B
0°
0°
G
0°
0°
E
S
STA015
Rules:
The collector or drain can never be an input terminal.
The base or gate can never be an output terminal.
In addition it is important to note polarity reversals on these signal paths.
The base-collector or gate-drain path inverts. All other paths are noninverting.
(This of course assumes that there are no reactive elements causing phase shifts)
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 5
BJT SINGLE TRANSISTOR AMPLIFIERS
Common Emitter Amplifer
Large-Signal:
vOUT
iC
VCC
RC
vOUT
VCC
Forward
Active
Region
VCC
RC
VIN, IB
vIN
Saturation
Region
vCE(sat)
Common Emitter
0
VCC
0
Small-Signal:
IC
gm = V
t
vCE
0 0
Rin i
in
and
VA
ro = I
C
0.5V
iout
B
E
+
vin
-
gmvin
ro
RC
vIN
STA02
Rout
+
rπ
1.0V
C
vout
E
βο
roR C
vout -g m ·ro ·R C
iout
β o ·ro
R in = rπ =
and i = r + R
gm , Rout = r o + R C ,
vin = r o + R C
in
o
C
(One should also consider the case of a source resistance, RS, in series with the input)
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 6
Example 1 - Common Emitter BJT with Source Resistance
Find the small-signal input resistance, Rin, output resistance, Rout,
voltage gain, vout/vin, and current gain, iout/iin for the circuit
shown. Assume that βo is 100, VA = 100V, and Is = 10fA.
E
+
vin
-
RS=
10kΩ
rπ
iout
iout
ro
RL
RL=
10kΩ
RS=10kΩ
1mA
Rout
+
RC
Rout
vout
Rin iin
vin
Rin iin
+
vπ
- gmvπ
RC=
2.5kΩ
C=∞
Solution
Small-signal model is:
B
5V
C
C=∞
-5V
STA08
vout
E
STA09
IC 1mA
1+βo
V A 100V
101
gm = V = 26mV = 38.5mS, rπ = g = 38.5ms = 2.62kΩ and ro = I = 1mA = 100kΩ
t
m
C
R in = R S+rπ = 12.62kΩ, Rout = ro||RC||RL = 1.96kΩ,
vout vout v π   r π 
2.62
  -gmRout =
=

  = 
 12.62 (-38.5·1.96) = -15.66 V/V ⇒ 23.9dB
vin  v π vin Rin
and
iout ioutv π  gm(ro||RC)
 
iin =  v π iin  =  RL+ro||RC  rπ = (7.549mS)(2.62kΩ) = 19.78 A/A
The maximum voltage gain (RS → 0, RC → ∞, RL → ∞) is -VA/Vt = -100/0.026 = -3846V/V
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 7
Common Base Amplifer
Large-Signal:
iC
vOUT
VCC
RC
VCC
VCC
vOUT RL
Forward
Active
Region
VIN
Saturation
Region
vIN
STA04
0
vCB
VCC
0
0
-0.5
0
vIN
-0.6
Small-Signal:
gmvin
Rin i
in
E
B
+
vin
-
iout
Rout
+
rπ
ro
RC
C
vout
B STA05
rπ
vout
iout
-gm  β 
1
1
Neglecting ro, Rin = g + g ≈ g = β +1 , R out ≈ R C , v ≈ gmRC and i = g +g 1+β = -α

π
m
m
o
in
in
m
π
(One should also consider the case of a source resistance, RS, in series with the input)
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 8
Common Collector (Emitter Follower)
Large-Signal:
vOUT = vIN -vBE
vOUT
VCC
vIN
Forward
Active
Region
VBE ≈ 0.7V
vOUT
RE
0
STA06
vIN
0
Small-Signal:
Rin i
in
B
+
vin
C
vπ
+ rπ -
Rout
iout
+
gmvπ
ro
RE
E
vout
C STA07
rπ
gmRE
iout
1 v out
Neglecting ro again, Rin = rπ + (1+βο)RE , Rout = 1+β = g , v = 1+g R ≈ 1 and i = -(1+βo)
ο
m
in
m E
in
(One should also consider the case of a source resistance, RS, in series with the input)
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 9
MOS SINGLE TRANSISTOR AMPLIFIERS
Common Source Amplifier
Large-Signal:
vDS = VGS-VT
iD
vOUT Cutoff Region
Saturation
VDD
Region
vOUT
vI
VDD
RD
U
T=
RD
N-
V
T
VDD
vO
VIN
vIN
STA10
0
VDD
0
vDS
0
0 VT
Triode
Region
VDD
VIN
Small-Signal:
Rin i
in
iout
G
S
Rin = ∞,
Rout = r
+
vin
-
Rout
+
gmvin
rdsRD
,
ds + R D
ECE 4430 - Analog Integrated Circuits and Systems
rds
RD
vout -g m ·rds·R D
vin = r ds + R D
D
vout
S STA11
and
iout
iin = ∞
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 10
Common Gate Amplifier
Large-Signal:
iD
Cutoff
Region
VDD
RD
vOUT
vOUT
VDD
VDD
RD
Saturation
Region
VIN<VT
vIN
STA12
0 0
vDG
VDD
VT
Triode
Region
VIN = 0
-VT
vIN
Small-Signal:
gmvin
Rin i
in
iout
S
+
vin
G
Neglecting rds,
1
Rin = ≈ g ,
m
Rout
+
rds
Rout ≈ RD ,
ECE 4430 - Analog Integrated Circuits and Systems
RD
vout
vin ≈ gmRD
D
vout
G STA13
and
iout
iin = -1
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 11
Example 2
Find the values of Rin, Rout, and vout/vin of the common gate amplifier including rds. Assume that KN’ =
110µA/V2, VT = 0.7V, λN = 0.04V-1, W/L = 10µm/1µm , ID = 200µA and RD = 20kΩ.
Solution
First find the model parameters.
gm =
2KN’WID
= 2·110·10·200 = 663µS
L
1
106
and rds = λ I = 0.04·200 = 125kΩ
ΝD
Using the small-signal model shown we get,
vin = (iin-gmvin)rds + iinRD
gmvin
Rin i
in
iout
S
+
vin
G
Rout
+
rds
RD
D
vout
G STA14
vin rds+RD 145kΩ
Rin = i = 1+g r = 1+82.9 = 1.728kΩ (Compared to 1.51kΩ if we neglect rds)
in
m ds
Writing a nodal equation at the output gives
vout gm+gds 663+8
gmvin + gds(vin-vout) - GDvout → v = g +G = 8+50 = 11.57 V/V
in
ds D
(Compared to 13.26V/V if we neglect rds)
Rout = rds||RD = 17.24kΩ (Compared to 20kΩ if we neglect rds)
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 12
Common Drain (Source Follower)
Large-Signal:
v OUT = v IN - v GS
vOUT
VDD
vIN
vOUT
Saturation
Region
vGS
RS
0
STA15
vIN
0
Small-Signal:
G
+
vin
D
Neglecting rds gives,
Rin = ∞,
Rin +
iout
vgs -
Rout
+
gmvgs
rds
RS
vout
D STA16
RS
Rout = RS||(1/gm ) = 1+g R
m S
ECE 4430 - Analog Integrated Circuits and Systems
S
and
vout
gmRS
vin = 1+gmRS < 1
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 13
AMPLIFIERS WITH EMITTER/SOURCE DEGENERATION
Common Emitter with Emitter Degeneration
VCC
RC
Rin
iOUT
B
C
+
rπ
vπ
RB
ro
gmvπ
vin
vIN
Rout
+
vOUT
iIN
RB
E
RC
vout
RE
RE
-
-
STA17
Rin = RB+rπ+(1+βo)RE
βοRE 

Rout = ro 1 + R +R +r  + R E||(R B+rπ) ≈ (1+βo)ro
B E π

vout
vin = -
RC
βoR C
≈ - r +(1+β )R ≈ - R

 rπ +R B  
π
o E
E

Rin ro+RC+RE|| 1+β 


o 
gm rπro
ECE 4430 - Analog Integrated Circuits and Systems
|
max. gain
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 14
Common Source with Source Degeneration
VDD
RD
iOUT
vOUT
Rin
+
G
+
vin
vgs
-
iIN
vIN
RB
RG
D
Rout
+
gmvgs
S
rds
RD
vout
RS
RS
-
STA18
Rin = ∞
R out = rds[1 + (gm + gmbs)R S] + R S ≈ rdsgm R S
gmRD
RD
vout

vin ≈ - 1+gmRS → - R S max. gain
ECE 4430 - Analog Integrated Circuits and Systems
 P.E. Allen
Single Transistor Amplifiers (6/13/00)
Page 15
SUMMARY
BJT Single Transistor Amplifiers
Small-Signal Performance
Common Emitter
rπ
(Medium)
Common Base
rπ
(Low)
1+β
Output Resistance
ro
(High)
ro(1+βo)
(Very high)
rπ+(1+βo)RE
(High)
rπ +R S
1+βo (Very low)
Voltage Gain
-gmRL
gmRL
1
Current Gain
βo
-α
-(1+βo)
Small-Signal Performance
Common Source
Common Drain
Input Resistance
∞
Output Resistance
rdsRD
r ds + R D
Common Gate
rds+RD
1+gmrds
rdsRD
rds+RD
Voltage Gain
-g m ·rds·R D
r ds + R D
gmRD
0.8
Current Gain
∞
-1
∞
Input Resistance
o
Common Collector
MOS Single Transistor Amplifiers
ECE 4430 - Analog Integrated Circuits and Systems
∞
RS
1+gmRS
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