Tài liệu Circuits & Electronics P11 pdf

6.002 CIRCUITS ANDELECTRONICS Small Signal Circuits... large signal circuit model for amp We can replace large signal models with small signal circuit models.. Small Signal Circuit Analy

6.002 CIRCUITS AND

ELECTRONICS

Small Signal Circuits

„ Small signal notation

„

v A = V A + v a

total operating

point signalsmall

V v

I I

out

I OUT

v v

f dv

d v

v f v

I I

⋅

=

=

=

) (

V

L

R

o O

O V v

v = +

+

i I

I V v

v = +

Review:

I Graphical view

(using transfer function)

behaves linear for small

perturbations

I

v

O

v

Review:

II Mathematical view

L

T

I S

v

2

2

−

−

=

i

V v

L T

I S

I

R V

v

K V

dv

d v

I I

⋅







=

=

2

2

related to V I

constant for fixed

DC bias

( I T ) L i

g m

Review:

Choosing a bias point:

DS

i

O

v

L

S L T

I

KR

V KR V

v −1+ 1+ 2

+

2 O

2

K

i <

load line

L

O L

S DS

R

v R

V

i = −

How to choose the bias point,

using yet another graphical view

based on the load line

O

V

I

V

input signal response

I L

m R V

1 Gain

2 Input valid operating range for amp.

3 Bias to select gain and input swing.

III The Small Signal Circuit View

We can derive small circuit equivalent

models for our devices, and thereby conduct small signal analysis directly on circuits

T I

2

K

+ –

R

OUT

+ –

I

e.g large signal

circuit model

for amp

We can replace large signal models with

small signal circuit models

Foundations: Section 8.2.1 and also in the last slide in this lecture

Small Signal Circuit Analysis

1 Find operating point using DC bias

inputs using large signal model

Develop small signal (linearized) models for elements

Replace original elements with small signal models

2

3

Analyze resulting linearized circuit…

Key: Can use superposition and other

linear circuit tools with linearized circuit!

Small Signal Models

MOSFET

A

large

2 GS T

D

S

GS

v

Small signal?

Small Signal Models

MOSFET

A

large

2 GS T

D

S

GS

v

Small signal:

small

signal

D

S

gs

v

( GS T ) gs

gs m

ds g v

i =

2 GS T

V v

T GS

GS

v

i

GS GS

⋅







∂

∂

=

=

2

2 ( GS T ) gs

g m

i ds is linear in v gs !

DC Supply V S

B

large

signal

S

S V

v =

s I

i S

S

i

V v

S S

⋅

∂

∂

=

=

0

v s =

+ – v S =V S

S

i

+ –v s

s

i

DC source behaves

as short to small signals

Small signal

Similarly, R

C

large

signal

small signal

R

+ –R

v

R

i

R

+ –v r

r

i

R

R R i

( )

r I

i R

R

i

Ri v

R R

⋅

∂

∂

=

=

r

r R i

Large signal

2 I T

( I T ) L

S

2 −

−

=

L

R

O

v

+

– v I

+ – V S DS

i

L

R

o

v

+ – v i i ds

( I T ) i

0

=

+ o

L

ds R v i

L ds

v = −

( I T ) L i

i L

m R v

−

= Small signal

Amplifier example:

To find the relationship between the small signal parameters of

a circuit, we can replace large signal device models with

corresponding small signal device models, and then analyze the resulting small signal circuit.

Foundations: (Also see section 8.2.1 of A&L)

KVL, KCL applied to some circuit C yields:

III The Small Signal Circuit View

b B

out OUT

a

"

Replace total variables with

operating point variables plus small signal variables

Operating point variables themselves satisfy the same KVL, KCL equations

B OUT

"

so, we can cancel them out

B OUT

+ " " "

b out

"

Leaving

2

Since small signal models are linear, our linear tools will now

But is the same equation as with small signal

variables replacing total variables, so must reflect same topology as in C, except that small signal models are used

2