ece 442 – jose schutt-aine 1 ece 342 solid-state devices & circuits 14. cb and cg amplifiers...
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ECE 442 – Jose Schutt-Aine 1
ECE 342Solid-State Devices & Circuits
14. CB and CG Amplifiers
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
1
Common Gate Amplifier
Substrate is not connected to the source must account for body effect
Drain signal current becomes
D m gs mb bsi g v g v
And since gs bsv v
Body effect is fully accounted for by using m m mbg g g
ECE 442 – Jose Schutt-Aine 3
i m mb i roi g g v i
m mb ioi o i i L
ro io o L
o
1g g v
rv v v i Ri i
r r R1
r
with i sv v
Common Gate Amplifier
ECE 442 – Jose Schutt-Aine 4
i o L
ini m mb o
v r RR
i 1 g g r
As o inm mb
1r , R
g g
If L iR , R
o ro i m mb o i iv i v g g r v v
vo m mb oA 1 g g r
Common Gate Amplifier
ECE 442 – Jose Schutt-Aine 5
whereo L Lin o m mb o
vo m mb o
r R R1R , A g g r
A g g A
Taking ro into account adds a component (RL/Ao) to the input resistance.
vo m mb oA 1 g g r
The open-circuit voltage gain is:
The voltage gain of the loaded CG amplifier is:
Lv vo
L o vo s
RG A
R r A R
Common Gate Amplifier
ECE 442 – Jose Schutt-Aine 6
x x m mb ov i g g v r v with x sv i R
orout o m mb o s out o vo sR r 1 g g r R R r A R
CG Output Resistance
CG Amplifier as Current Buffer
sis vo
out
RG G 1
R
Gis is the short-circuit current gain
- Include CL to represent capacitance of load- Cgd is grounded- No Miller effect
High-Frequency Response of CG
ECE 442 – Jose Schutt-Aine 9
P1
gs sm mb
1f
12 C R ||
g g
P2
gd L L
1f
2 C C R
• fP2 is usually lower than fp1• fP2 can be dominant• Both fP1 and fP2 are usually much higher than fP in CS case
2 poles:
High-Frequency Response of CG
o Lin
o L
e e
r RR
r R1
r 1 r
vo m oA 1 g r 'out o m o eR r 1 g r R
'e eR R || re
rr
1
CB Amplifier
ECE 442 – Jose Schutt-Aine 11
High-Frequency Analysis of CB Amplifier
in 3dBx
S E
1
r rC R || R ||
1 1
out 3dBL
1
C R
The amplifier’s upper cutoff frequency will be the lower of these two poles.
From current gain analysis
ECE 442 – Jose Schutt-Aine 12
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
ECE 442 – Jose Schutt-Aine 13
• 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 442 – Jose Schutt-Aine 14
MOS Cascode Incremental Model
Lo
L
iv
G
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 g
G
ECE 442 – Jose Schutt-Aine 15
22 2 2 21 o
L s mb m oL
gi v g g g
G
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
ECE 442 – Jose Schutt-Aine 16
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 G
g g g
1
1 2
2 2 2
o m
in o L oL
o m mb
v g
v g G gG
g g g
Two cases
MOS Cascode Analysis
ECE 442 – Jose Schutt-Aine 17
1 2 2 2 1 2 om o m mb o o
in
vg g g g r r
v
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
ECE 442 – Jose Schutt-Aine 18
1 2
2 2 2
2 : o L oL
o m mb
g G gCase If G
g g g
1 o m
MBin L
v gA
v G
CASE 2
The voltage gain becomes
MOS Cascode Analysis
ECE 442 – Jose Schutt-Aine 19
MOS Cascode at High Frequency
23 2
1
2ods
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
ECE 442 – Jose Schutt-Aine 20
• 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) gd 1 m1 d 1 sig d 1R 1 g R R R L
d 1 o1m2 mb2 vo2
R1R r ||
g g A
H gs1 sig gd 1 m1 d 1 sig d 1C R C 1 g R R R
db1 gs2 d 1 L gds2 L outC C R C C R || R
HH
1f
2
MOS Cascode at High Frequency
ECE 442 – Jose Schutt-Aine 21
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
Effect of Cascoding(when Rsig=0)
ECE 442 – Jose Schutt-Aine 23
Cascode Example
ECE 442 – Jose Schutt-Aine 24
Cascode Example
The cascode circuit has a dc drain current of 50 mA for all transistors supplied by current mirror M3. Parameters are gm1=181 mA/V, gm2=195 mA/V, gds1= 5.87 mA/V, gmb2=57.1 mA/V, gds2= 0.939 mA, gds3= 3.76 mA/V, Cdb2 = 9.8 fF, Cgd2 = 1.5 fF, Cdb3=40.9 fF, Cgd3= 4.5 fF. Find midband gain and approximate upper corner frequency
1 2
2 2 2
5.87 3.76 0.9390.109 /
0.939 195 57.1o L o
Lo m mb
g G gA V G
g g g
3 3.76 / L dsG g A V
Therefore, we use Case 2 to compute the gain
The internal conductance of the current source is:
ECE 442 – Jose Schutt-Aine 25
Cascode Example
1 1
3
18148.1 /
3.76 m m
MBL ds
g gA V V
G g
Gain can be approximated by
Upper corner frequency is approximated by
2 15 33 2
1 110.6
2 2 56.7 10 266 10ods
f MHzr C
ECE 442 – Jose Schutt-Aine 26
Common emitter amplifier, followed by common base stage – Base of Q2 is an incremental ground
BJT Cascode Amplifier
ECE 442 – Jose Schutt-Aine 27
BJT Cascode Incremental Model
2 2o m Lv g R v
2 22 2
2 2 2
1x xx
x
v r rv v v
r r r
ECE 442 – Jose Schutt-Aine 28
BJT Cascode Analysis
1 1 2 22 2
xm m
x
vg v g v
r r
Ignoring rx2
21 1 2 2
2m m
vg v g v
r
1 1 2 22
1m mg v v g
r
ECE 442 – Jose Schutt-Aine 29
BJT Cascode Analysis
11
1 1in
s x
rv v
R r r
1 12
1 12
2
1
1m in
s xm
g r vv
R r rg
r
2 1 1
1 12
2
1
1m L m in
os x
m
g R g r vv
R r rg
r
ECE 442 – Jose Schutt-Aine 30
BJT Cascode Analysis
2 2 1 1
1 1 2 21o m m L
in s x m
v g r g r R
v R r r g r
1 2
1 1 2 1o L
in s x
v R
v R r r
1 2v m LA g R
If Rs << rx1+rp1, the voltage gain can be approximated by
ECE 442 – Jose Schutt-Aine 31
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
ECE 442 – Jose Schutt-Aine 32
There is no Miller multiplication from the input of Q2 (emitter) to the output (collector).
BJT Cascode at High Frequency
ECE 442 – Jose Schutt-Aine 33
1 1 2 2 3
1 1 1
1 || 1 1MBe out
A Aj C r R j r C j R C
22 2
1
2 e
fr C
1 1
1
2in highfr R C
1 1
1 1MB
in high out high
A Af f
j jf f
BJT Cascode at High Frequency
3 2 ||out csDefine R r r
ECE 442 – Jose Schutt-Aine 34
BJT Cascode at High Frequency
3
1
2out highout
fC R
2out out outcsC C C
current source output capacitanceoutcsC
ECE 442 – Jose Schutt-Aine 35
Cascode Amplifier – High Frequency
High-frequency incremental model
ECE 442 – Jose Schutt-Aine 36
' '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
ECE 442 – Jose Schutt-Aine 37
gm=0.4 mhos b=100rp=250 ohms rx=20 ohmsCp=100 pF Cm=5 pfGL=5 mmhos GS’=4.5 mmhossa=8.0 ns-1 sd=-0.0806 nsec-1sb=-2.02 + j5.99 se=-0.644sc=-2.02 – j5.99 sf=-4.05 sg=-16.45
POLES
ZEROS
As an example use:
Cascode Amplifier – High Frequency
ECE 442 – Jose Schutt-Aine 38
If one pole is at a much lower frequency than the zeros and the other poles, (dominant pole) we can approximate w3dB
3dB 0.0806 Grad / sec
3dBf 12.9 MHz
For the same gain, a single stage amplifier would yield:
3dB 0.0169 Grad / sec
3dBf 2.7 MHz
Second stage in cascode increases bandwidth
Cascode Amplifier – High Frequency
ECE 442 – Jose Schutt-Aine 39
CE Cascade Amplifier
Exact analysis too tedious use computer
CE cascade has low upper-cutoff frequency
ECE 442 – Jose Schutt-Aine 40
Cascode Amplifier
First stage is CE and second stage is CB
1 2v m LA g R
If Rs << rp1, the voltage gain can be approximated by
ECE 442 – Jose Schutt-Aine 41
Cascode Amplifier – High Frequency
High-frequency incremental model
ECE 442 – Jose Schutt-Aine 42
' '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
ECE 442 – Jose Schutt-Aine 43
gm=0.4 mhos b=100rp=250 ohms rx=20 ohmsCp=100 pF Cm=5 pfGL=5 mmhos GS’=4.5 mmhossa=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
ECE 442 – Jose Schutt-Aine 44
If one pole is at a much lower frequency than the zeros and the other poles, (dominant pole) we can approximate w3dB 9
3dB 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