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EE 332 

DEVICES AND CIRCUITS II

Lecture 13

Small-Signal Models

and Single Transistor Amplifier (5)

(CS Amplifier) 

CS AMPLIFIER (INVERTING)/SMALL SIGNAL MODEL

RI

vS

C1

R2

R1

RD

RS

M1

C2

VDD

RL

voRI

vS

C1

R2

R1

RD

RS

M1

C2

VDD

RL

vo

vo

vs

RG

RI

RD RL

rπ→∞

ro

gmvgs

vgs

RS

1

 

CS AMPLIFIER (INVERTING)/INPUT RESISTANCE

1 2

( 1)

/ / / /

x 

b E 

x 

CE 

i b 

v r r R 

i 

R R R r  

πβ= + +

=

Recall input resistance of  CE

Common Source input resistance:

The difference between small signal models of  CE and CS is rπ→∞,  ( 1)

g S r r R 

π

 

/ /

CS 

i G g G  R R r R  

β+ + →∞

vo

vs

RG

RI

RD RLro

gmvgs

vgs

= =

RS

rgRi

1

 

Lecture Goals

Understanding of concepts related to: CS Amplifier 

(Inverting)

•  Small Signal Model

•  Input Resistance

•  Output Resistance

•  Small Signal Analysis

•  Small Signal Parameter 

•  Gain

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 CS AMPLIFIER (INVERTING)

/OUTPUT RESISTANCE

vo

vs

RG

RI

RD RLro

gmvgs

vgs

RS

rdRo

0;

; (1 ) ( )

/ /

E c o 

E th c o th  

CE 

o c C 

R r r 

R r R r r R r  

R r R 

π π

= =

>> = + + +

=

if then

if , then

Recall output resistance of  CE

Common Source output resistance:The difference between small signal models of  CE and CS is r

π→∞, 

then0;

/ /

S d o 

CS 

o d D 

R r r 

R r R 

= =

=

1

 

CS AMPLIFIER (INVERTING)/ SMALL SIGNAL ANALYSIS

Theveninizing LHS loop:

(2). RHS loop:

Assuming saturation:

1

1 2

2

(1).

(3). ( )2

(4).

th DD  

DD DS D DS DS S  

n 

DS GS TN  

S DS S  

R V V 

R R 

V I R V I R  

K I V V 

V I R 

=

+

= + +

= −

=

Substitute (4) into (3)

1. Solve for VS

2. Use (4) to solve for IDS

3. Use (2) to solve for VDS

4. Solve for VGS

R2

R1

RD

RS

M1

VDD

IDS

VDS

1

gm: small signal transconductance

ro: small signal output resistance=

CS AMPLIFIER (INVERTING)/ SMALL SIGNAL PARAMETERS

2D 

m 

GS TN  

I g 

V V =

−

2 1 2

( )

21

D 

F m o 

GS TN D GS TN  

n 

I g r 

V V I V V  

K 

μλ λ

= ≈ × =

− −

F 

D I 

μλ

⇒ ≈

1 1DS 

o 

D D 

V r 

I I 

λ

λ λ

+= ≈

vdsro

gmvgsvgs

1

 

CS AMPLIFIER (INVERTING)

/SMALL SIGNAL ANALYSIS

DC analysis

RI

vS

C1

R2

R1

RD

RS

M1

C2

VDD

RL

vo RI

C1

R2

R1

RD

RS

M1

C2

VDD

RL

vo

vS

1  

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CS AMPLIFIER (INVERTING)/GAIN

1

CE  m L

v 

m E 

g R A

g R 

−≈

+

Small Signal Equivalent Circuit

Common Source gain:

The difference between small signal models of  CE and CS is rπ→∞, which doesn’t affect 

the result of  

Terminal Voltage gain:Recall CE:

1

CS  m L

v 

m S 

g R A

g R 

−≈

+

vo

vs

RG

RI

RD RL

rogmvgs

vgs

RS

1  

End of Lecture 13

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