ECE 342 – Jose Schutt‐Aine 1ECE 342 – Jose Schutt‐Aine 1
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 342Electronic Circuits
Lecture 26Frequency Response of Cascaded
Amplifiers
ECE 342 – Jose Schutt‐Aine 2ECE 342 – Jose Schutt‐Aine 2
CE Cascade Amplifier
Exact analysis too tedious use computerCE cascade has low upper‐cutoff frequency
ECE 342 – Jose Schutt‐Aine 3ECE 342 – Jose Schutt‐Aine 3
11
1o
o
Define gr
Common source amplifier, followed by common gate stage – G2 is an incremental ground
MOS Cascode Amplifier
22
1o
o
gr
LR current source impedance
1L
L
GR
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• CS cacaded with CG CascodeVery popular configurationOften considered as a single stage amplifier
• Combine high input impedance and large transconductance in CS with current buffering and superior high frequency response of CG
• Can be used to achieve equal gain but wider bandwidth than CS
• Can be used to achieve higher gain with same GBW as CS
MOS Cascode Amplifier
ECE 342 – Jose Schutt‐Aine 5ECE 342 – Jose Schutt‐Aine 5
MOS Cascode Incremental Model
Lo
L
ivG
2 2 2 2 2 2L mb s m s s o oi g v g v v v g
2 2 2 2 2 2L
L s mb m s o oL
ii v g g v g gG
ECE 342 – Jose Schutt‐Aine 6ECE 342 – Jose Schutt‐Aine 6
22 2 2 21 o
L s mb m oL
gi v g g gG
22
2 2 2
1 /L o Ls
mb m o
i g Gv
g g g
KCL at vs2
1 2 1 2 2 2 2 2 2( ) 0m gs s o m s mb s o s og v v g g v g v g v v
MOS Cascode Analysis
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1 21 1
2 2 2
1 /1 0o o L
m gs Lo m mb
g g Gg v i
g g g
1 1
1 2
2 2 2
1 /1
m gsL
o o L
o m mb
g vi
g g Gg g g
1
1 2
2 2 2
o m
in o L oL
o m mb
v gv g G g
Gg g g
Two cases
MOS Cascode Analysis
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1 2 2 2 1 2 om o m mb o o
in
v g g g g r rv
1 2 1 2 1 2 1 2 MB m o m m m mb o oA g g g g g g r r
1 1 2 2MB m o m oA g r g r
CASE 1
The voltage gain becomes
1: 0LCase If G
MOS Cascode Analysis
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1 2
2 2 2
2 :
o L o
Lo m mb
g G gCase If G
g g g
1 o m
MBin L
v gAv G
CASE 2
The voltage gain becomes
MOS Cascode Analysis
ECE 342 – Jose Schutt‐Aine 10ECE 342 – Jose Schutt‐Aine 10
MOS Cascode at High Frequency
23 2
12o
ds
fr C
The upper corner frequency of the cascode can be approximated as:
2 2 2 3 3where db gd db gdC C C C C
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• Capacitance Cgs1 sees a resistance Rsig• Capacitance Cgd1 sees a resistance Rgd1• Capacitance (Cdb1+Cgs2) sees resistance Rd1• Capacitance (CL+Cgd2) sees resistance (RL||Rout)
gd1 m1 d1 sig d1R 1 g R R R Ld1 o1
m2 mb2 vo2
R1R rg g A
H gs1 sig gd1 m1 d1 sig d1C R C 1 g R R R
db1 gs2 d1 L gds2 L outC C R C C R R
HH
1f2
MOS Cascode at High Frequency
ECE 342 – Jose Schutt‐Aine 12ECE 342 – Jose Schutt‐Aine 12
If Rsig is large, to extend the bandwidth we must lower RL. This lowers Rd1 and makes the Miller effect insignificant
If Rsig is small, there is no Miller effect. A large value of RL will give high gain
MOS Cascode at High Frequency
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Effect of Cascoding(when Rsig=0)
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Common emitter amplifier, followed by common base stage – Base of Q2 is an incremental ground
BJT Cascode Amplifier
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Cascode Amplifier
First stage is CE and second stage is CB
1 2v m LA g R
If Rs << r1, the voltage gain can be approximated by
ECE 342 – Jose Schutt‐Aine 16ECE 342 – Jose Schutt‐Aine 16
BJT Cascode Incremental Model
2 2o m Lv g R v
2 22 2
2 2 2
1x xx
x
v r rv v vr r r
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BJT Cascode Analysis
1 1 2 22 2
xm m
x
v g v g vr r
Ignoring rx2
21 1 2 2
2m m
v g v g vr
1 1 2 22
1m mg v v g
r
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BJT Cascode Analysis
11
1 1in
s x
rv vR r r
1 12
1 12
2
11
m in
s xm
g r vvR r r
gr
2 1 1
1 12
2
11
m L m ino
s xm
g R g r vvR r r
gr
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BJT Cascode Analysis
2 2 1 1
1 1 2 21o m m L
in s x m
v g r g r Rv R r r g r
1 2
1 1 2 1o L
in s x
v Rv R r r
1 2v m LA g R
If Rs << rx1+r1, the voltage gain can be approximated by
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BJT Cascode at High Frequency
Define rcs as the internal impedance of the current source. R includes generator resistance and base resistance rx1 base of Q1
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There is no Miller multiplication from the input of Q2 (emitter) to the output (collector).
BJT Cascode at High Frequency
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1 1 2 2 3
1 1 11 1 1MB
e out
A Aj C r R j r C j R C
22 2
12 e
fr C
1 1
12in highf
r R C
1 1
1 1MB
in high out high
A A f fj jf f
BJT Cascode at High Frequency
3 2 out csDefine R r r
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BJT Cascode at High Frequency
3
12out high
out
fC R
2out out outcsC C C
current source output capacitanceoutcsC
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Cascode Amplifier – High Frequency
High‐frequency incremental model
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' 's i s 1 1 1 a 1 bG V G g s C C V sC V
m1 1 a 2 m2 2 1 b 2 m2 2 d0 g sC V g g s C C V g g sC V
2 2 b x2 2 2 2 d 2 o0 g sC V g g s C C V sC V
m2 b m2 2 d L 2 o0 g V g sC V G sC V
Applying Kirchoff’s current law to each node:
Find solution using a computer
Cascode Amplifier – High Frequency
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gm=0.4 mhos =100r=250 ohms rx=20 ohmsC=100 pF C=5 pfGL=5 mmhos GS’=4.5 mmhos
sa=8.0 sd=‐0.0806sb=‐2.02 + j5.99 se=‐0.644sc=‐2.02 – j5.99 sf=‐4.05
sg=‐16.45
POLES (nsec‐1)ZEROS (nsec‐1)
As an example use:Cascode Amplifier – High Frequency
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If one pole is at a much lower frequency than the zeros and the other poles, (dominant pole) we can approximate 3dB
93dB 0.0806 10 rad / sec
3dBf 12.9 MHz
For the same gain, a single stage amplifier would yield:
93dB 0.0169 10 rad / sec
3dBf 2.7 MHz
Second stage in cascode increases bandwidth
Cascode Amplifier – High Frequency
