# Document 13436440 ```Lecture 21
Frequency Response of Amplifiers
(I)
Common-Emitter Amplifier
Outline
•
•
•
•
Review frequency domain analysis
BJT and MOSFET models for
frequency response
Frequency Response of Intrinsic
Common-Emitter Amplifier
Effect of transistor parameters on fT
Howe and Sodini, Chapter 10, Sections 10.1-10.4
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I. Frequency Response Review
Phasor Analysis of the Low-Pass Filter
• Example:
R
+
Vin
+
−
C
Vout
−
ω
• Replacing the capacitor by its impedance, 1 / (jωC),
we can solve for the ratio of the phasors Vout Vin
Vout
1/ jωC
=
V in R + 1/ j ωC
Vout
1
=
V in 1+ jωRC
•
Vout ≡ Phasor notation
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Magnitude Plot of LPF
•
•
Vout /Vin
Vout /Vin
--&gt; 1 for “low” frequencies
--&gt; 0 for “high” frequencies
Vout
Vin
log scale
1
Vout
Vin
Break point
0
−3dB
0.1
0.01
1 = 0.707
2
1/ω
dB
0.001
0.0001
dB
scale
−20
−40
−60
0.01
RC
0.1
RC
1
RC
10
RC
100
RC
1000
RC
−80
ω
log scale
(a)
•
•
•
•
The “break point” is when the frequency is equal to ωo =
1 / RC
The break frequency defines “low” and “high”
frequencies.
dB 20 log x ----&gt; 20dB = 10, 40dB = 100,
-40dB = .01
At ωo the ratio of phasors has a magnitude of
- 3 dB.
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≡
3
Phase Plot of LPF
• Phase (Vout / Vin ) = 0o for low frequencies
• Phase (Vout / Vin ) = -90o high frequencies.
V
∠ out
V
in
Break point
0&deg;
−45&deg;
−45&deg;
−90&deg;
−135&deg;
−180&deg;
0.01
RC
0.1
RC
1
RC
10
RC
100
RC
1000
RC
ω
log scale
• Transition region extends from ωo / 10 to 10 ωo
• At ωo Phase = -45o
Review of Frequency Domain Analysis Chap 10.1
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II. Small Signal Models for
Frequency Response
Bipolar Transistor
C&micro;
B
C
+
rπ
π
Vπ
Cπ
π−
π
gmVπ
ro
π
E
E
(a)
MOS Transistor - VSB = 0
Cgd
G
D
+
Vgs
Cgs
gmVgs
ro
−
S
S
(b)
• Replace Cgs for Cπ
• Replace Cgd for C&micro;
• Let rπ ---&gt; ∞
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III. Frequency Response of
Intrinsic CE Current Amplifier
RS ---&gt; ∞ &amp; RL = 0
Circuit analysis - Short Circuit Current Gain Io/Iin
C&micro;
Io
+
Iin
rπ
Vπ
gmVπ
Cπ
−
• KCL at the output node:
Io = gmVπ − Vπ j ωC&micro;
• KCL at the input node:
V
Iin = π + Vπ j ωC&micro;
where
Zπ
Zπ = rπ
 1 


 jω Cπ 
• After Algebra
 jω C&micro; 



jωC&micro; 
ω


1− j 
gm rπ 1−
β o 1−
gm 
gm 

ωz 
Io


=
=
= βo

ω
Iin 1+ j ωrπ (Cπ + C&micro; ) 1+ jω rπ (Cπ + C&micro; )
1+ j


ω p 
gm
ωZ =
C&micro;
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ωp =
rπ (Cπ + C&micro; )
6
Bode Plot of Short-Circuit Current Gain
Io
I
in
βo = gmrπ
1
C&micro;
Cπ + C&micro;
1
r(π Cπ + C&micro;)
gm
Cπ + C&micro;
gm
C&micro;
ω
log scale
(a)
I
∠ o
Iin
0
−45
−90
−135
−180
gm
C&micro;
1
rπ(Cπ + C&micro;)
ω
log scale
(b)
• Frequency at which current gain is reduced to 0 dB
is defined at fT:
 1 
gm
fT =  
 2π  (Cπ + C&micro; )
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Gain-Bandwidth Product
• When we increase βo we increase rπ BUT we
decrease the pole frequency---&gt; Unity Gain
Frequency remains the same
Io
Iin
βo1
βo2
1
gm
βo1(Cπ + C&micro;)
gm
βo2(Cπ + C&micro;)
ωT =
gm
Cπ + C&micro;
ω
log scale
βo1 &gt; βo2
Examine how transistor parameters affect ωT
• Recall
Cπ = C je + gmτ F
• The unity gain frequency is
I C / Vth
ωT =
(IC / Vth )τF + C je + C&micro;
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I C / Vth
ωT =
(IC / Vth )τF + C je + C&micro;
fT dominated by diffusion
capacitance
fT
1
2πτF
fT dominated by depletion
capacitances C&micro; and Cje
IC
• At low collector current fT is dominated by
depletion capacitances at the base-emitter and basecollector junctions
• As the current increases the diffusion capacitance,
•
gmτF ,becomes dominant
• Fundamental Limit for the frequency response of a
bipolar transistor is set by
WB 2
τF =
2 Dn, p
To Increase fT
• High Current - Diffusion capacitance limited Shrink basewidth
• Low Current - Depletion capacitance limited Shrink emitter area and collector area - (geometries)
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MIT OpenCourseWare
http://ocw.mit.edu
6.012 Microelectronic Devices and Circuits
Spring 2009