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EE 332

DEVICES AND CIRCUITS II

Lecture 12

Small-Signal Models

and Single Transistor Amplifier (4)

(CC Amplifier)

CC AMPLIFIER (FOLLOWER)/INPUT RESISTANCE

vx ix

rb

RL//RE

rix

ie=(+1)ix

vb

ve

: ( 1)

( 1)

x x x L

x

b L

x

K V L v i r i R

vr r R

i

= + += = + +

InputResistance

Withtestsourceapplied:/ /

C C

i B bR R r

Ingeneral,RE>>RL

RiRB

rb

CC AMPLIFIER (FOLLOWER)/OUTPUT RESISTANCE

vx

ix

Rthr i

vbe

Ro

vb

ve

RE

( 1)

,

( 1)

1

1 1

x

x

th

x

x

th

x th

e

x

th

e

i i i i

va n d i

r R

vi

r R

v r Rr

i

r Rr

1

1

th

e

m

Rr

g

= = + = +

= + ++= = +

= ++ +

Outputresistance:Withtestsourceapplied:

/ /C Co E e

= + +Usuallyverysmall

R R rre

re

i

CC AMPLIFIER (FOLLOWER)

/SMALL SIGNAL MODEL

Rs

vS

C1

R2

R1 RC

RE

Q1C2

VCC

RL

vo

R

s

vS

C1

R2

R1 RC

RE

Q1C2

VCC

RL

vovo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

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CC AMPLIFIER (FOLLOWER)/GAIN

Problem:FindthegainofCB

amplifier

Given:

, ,0.8 , 0.1 , 1001 :1.5, 100

B E ON CE sat F

R A

v V V V QV V

= = = = =

1 2

1 2

10 ; 30 ; 5.1 ; 2.2 ;

1 ; 10 ; 12 ; 10

C E

s L CC

R k R k R k R k

R k R k V V C C F

= = = = = = = = =

Rs

vS

C1

R2

R1 RC

RE

Q1C2

VCC

RL

vo

CC AMPLIFIER (FOLLOWER)/GAIN

REQ

VEQ

RC

RE

Q1

VCC

vo

ANSWER

ANSWERAssumingBJToperatinginforwardactivemodeTheveninizingLHScircuit

1

1 2

1 2

3

( / / ) 7.5

EQ CC

EQ

RV V V

R R

R R R k

= =+= =

Solvetheloop,

,

( 1)

2.3

EQ E E BE ON B EQ

E B

EQ BE ON

V I R V I R

I I

V V

10.0( 1) 7.5 101 2.2

B

EQ E

I AR R k k

= = =+ + +

= + + = +

IC

IE

IB

CC AMPLIFIER (FOLLOWER)/GAIN

REQ

VEQ

RC

RE

Q1

VCC

vo

ANSWER

ANSWER

IC

IE

IB

and

10.0

,

1 1.01

B

C E

I A

then

I mA I m A

= =SolveRHSloop

5.1

2.22

4.67

RC C C

RE E E

CE CC RC RE

V R I V

V R I V

V V V V V

= == == =

SinceVCE=4.67>VCE,sat=0.1V

TheBJToperatesinForwardActive

region

CC AMPLIFIER (FOLLOWER)/GAIN

Rs

vS

C1

R2

R1

RC

RE

Q1

C2

VCC

RL

vo

ANSWER

ANSWER

Step1:DCanalysis DCeffectsonthedashbox 4resistorBJTcircuit

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CC AMPLIFIER (FOLLOWER)/GAIN

ANSWER

ANSWER Step2:SmallSignalParameters:1

4025

100 2.540

104.67105

1

C

m

T

m

A CE

o

C

I mAg mS

V mV

r kg mS

V V Vr k

I mA

= = == = =

+= = =

CC AMPLIFIER (FOLLOWER)/GAIN

ANSWER

ANSWER

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

( 1) [ / / ]

[ ( 1) [ / / ]]

( 1) [ / / ]

[ ( 1) [ / / ]]

( 1) [ / / ]

( 1) [ / / ]

101 1803

CC o

v

b

o b E L

b b b b E L

CC o b E L

v

b b E L

E L

E L

vA

v

v i R R

v i r i r R R

v i R R A

v i r R R

R R

r R R

== + = = + +

+ = = + + + = + +

0.9862.5 101 1803k

= =

CC AMPLIFIER (FOLLOWER)/GAIN

ANSWER

ANSWER

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

(1 )[ / / ] 173

/ / 173 / /7.5 7.2

7.2

7.2 1

CC o o b

vss b s

i

b s

i s

b E L

i b B

b

s

v v vA

v v v

Rv v

R R

r r R R k

0.986 0.878 0.866CBvs

R r R k k k

v k

v k k

= = = +

A

= + + = = = = = +

Q

= =

CC AMPLIFIER (FOLLOWER)/GAIN

ANSWER

ANSWER

Rs

vS

C1

R2

R1 RC

RE

Q1C2

VCC

RL

vovo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

+

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CC AMPLIFIER (FOLLOWER)/GAIN

ANSWERANSWER

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

( )( 1)( )

0.710

= =

= +

+ +

=

CC o b e o

i

i i b e

B E

B b E L

i i i iA

i i i i

R R

R r R R

,

7.20.986 0.710

10

i L v i

i

i v

L

Use

A R A R

RA A

R

k

k

= == =

End of Lecture 12

CC AMPLIFIER (FOLLOWER)/GAIN

ANSWERANSWER

vo

vs

RBRC

RL

rro

gmvbe

vbe

Rs

RE

( 1)

( 1)

[ ( 1) ]

o L

b L

L

v i R

and

v ir i R

i r R

= += + += + +

( 1)

[ ( 1) ]

11

CC o L

vt

b L

CC m LL

vt

m LL

m

v RA

v r Rg RR

Ag R

Rg

+ = = + + = ++

AsgmRL>>1Voltagefollowerorbufferamp

TerminalVoltagegain:

RE//RLRL sinceRL