ECE 442 – Jose Schutt-Aine 1 ECE 342 Solid-State Devices & Circuits 14. CB and CG Amplifiers...

ECE 442 – Jose Schutt-Aine 1

ECE 342Solid-State Devices & Circuits

14. CB and CG Amplifiers

Jose E. Schutt-AineElectrical & Computer Engineering

University of Illinoisjschutt@emlab.uiuc.edu

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