lecture15(20-3-11)

7/27/2019 Lecture15(20-3-11)

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EE 332

DEVICES AND CIRCUITS II

Lecture 15

Small-Signal Models

and Single Transistor Amplifier (7)

(CD Amplifier)

CD AMPLIFIER (VOLTAGE FOLLOWER)/SMALL SIGNAL MODEL

Small signal model

RI

vS

C1

R2

R1

RD

RS

M1 C2

VDD

RL

vo

vo

vs

RG

RI

RD

RL

rπ→∞

rogmvgs

vgs

RS

vo

vs

RG

RI

RD

RL

rπ→∞

rogmvgs

vgs

RS

CD AMPLIFIER (VOLTAGE FOLLOWER)/INPUT RESISTANCE

vo

vs

RG

RI

RD

RL

ro

gmvgs

vgs

RS

rgRi

Input Resistance:Recall output resistance of CC

Common drain input resistance:

The difference between small signal models of CC and CD is rπ→∞, / /

CD

i g G G R r R R =

1 2/ / / /( 1)( / / )

CC

i b

b E L

R R R r r r R R

πβ

=

= + +

Lecture Goals

Understanding of concepts related to: CD Amplifier

• Small Signal Model

• Input Resistance

• Output Resistance

• Small Signal Analysis

• Small Signal Parameter

• Gain

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7/27/2019 Lecture15(20-3-11)


CD AMPLIFIER (VOLTAGE FOLLOWER)

/OUTPUT RESISTANCE

vo

vs

RG

RI

RD

RL

ro

gmvgs

vgs

RS

rs

Ro

Output Resistance:CC output resistance

/ /

1

CD

o S s

s

m

R R r

r g

=

=

Common drain input resistance:

The difference between small signal models of CC and CD is rπ→∞,

/ /

1

CC

o E e

e

m

R R r

r g

=

≈

CD AMPLIFIER (VOLTAGE FOLLOWER)/ 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

gm: small signal transconductance

rO: small signal output resistance=

CD AMPLIFIER (VOLTAGE FOLLOWER)/ 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

+= ≈

vds

rogmvgs

vgs


/SMALL SIGNAL ANALYSIS

DC analysis

RI

vS

C1

R2

R1

RD

RS

M1 C2

VDD

RL

vo

RI

C1

R2

R1

RD

RS

M1C2

VDD

RL

vo

vS

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7/27/2019 Lecture15(20-3-11)



/GAIN

vo

vs

RG

RI

RD

RL

ro

gmvgs

vgs

RS

Small Signal Equivalent Circuit

11

CD m L

vt

m L

g R A

g R ⇒ = ≈

+

Common Drain gain:The difference between small signal models of CC and CD is rπ→∞, which doesn’t affect

the result of

Terminal Voltage gain:

Recall CC:1

1

CC m LL

vt

m LL

m

g R R A

g R R

g

β

ββ

≈ = ≈

++

TERMINAL CURRENT GAIN

vo

vs

RG

RI

RD RL

gmvgs

vgs

RS

ig‐id

1

CS d

i

g

CG d

i

s

CD s

i

i

A i

i A

i

i A

g i

−

= →∞

−= ≈

−

= →∞

SUMMARY/SIGNAL-TRANSISTOR BIPOLAR AMPLIFIERS

E m

Lm

R g R g

+

−

≅

11

1≅

+

≅

Lm

Lm

R g R g Lm R g ≅

E

CE

b Rr r )1( ++= β π L

CC

b Rr r )1( ++≅ β π

m

CC

e g

r 1

≅o

CE

c r r ≅o

CB

c r r ≅

m

CB

e g

r 1

≅

1+ β β 1≅

TERMINAL CURRENT GAIN

vo

vs

RB

Rs

RC

RL

rog

m

vbe

vbe

RE

( )

1( 1)( )

( 1)1

CE c b

i

b b

CB c b

i

e b

CC e b

i

b b

i i A

i i

i i

A i i

i i A

i i

ββ

β

β

ββ

− −= = =−

− − −

= = ≈− − + −

+= = = +

ib

‐ic

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7/27/2019 Lecture15(20-3-11)


SUMMARY/SIGNAL-TRANSISTOR MOSFET AMPLIFIERS

S m

Lm

R g

R g

+

−≅

11

1≅

+

≅

Lm

Lm

R g

R g Lm R g ≅

∞=CS

g r ∞=CD

g r

m

CD

s g

r 1

≅o

CS

d r r ≅o

CG

d r r ≅

m

CG

s g

r 1

≅

∞ ∞ 1≅

End of Lecture 15

67

lecture15(20-3-11)

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