Tài liệu Circuits & Electronics P10 doc

6.002 CIRCUITS Amplifiers --Small Signal Model... Saturation discipline satisfied... v In other words, our circuit behaves like a linear amplifier for small signals... Input valid opera

6.002 CIRCUITS

Amplifiers

Small Signal Model

Review

„ MOSFET amp

S V

L

R

DS i

v O

v

„ Saturation discipline — operate

MOSFET only in saturation region

„Large signal analysis

1 Find v O vs v I under saturation discipline

2 Valid v I , v O ranges under saturation discipline

Large Signal Review

1 v O vs v I

v O = V S − K (v I −1)2

R

valid for v I ≥ V T

and

v O ≥ v I – V T

(same as i DS ≤ K v O 2 )

2 Valid operating ranges

S

O

O

v O =

v >

O

v <

v V

1V

“interesting” region

for v I Saturation discipline satisfied

But…

S

V O

v

O

v =

I

v

v I −V

v

v

Demo

V

1V

Amplifies alright, but distorts

v

v

Amp is nonlinear … /

Small Signal Model

~ 5V V S

~ 1V

Hmmm …

L

T

I

S

O V K v V R

v

2

2

−

−

= Amp all right, but nonlinear!

I

v

O

v

T

V

V

1 ~ 2V

Insight:

(V I , V O )

Focus on this line segment

So what about our linear amplifier ???

But, observe v I vs v O about some

point (V I , V O) … looks quite linear !

Trick v o

i

v

I

V

O

V ( V , I V O )

O

v

∆

looks linear

™ Operate amp at V I , V O

Æ DC “bias” (good choice: midpoint

of input operating range)

™ Superimpose small signal on top of V

™ Response to small signal seems to be

approximately linear

Trick v o

i

v

I

V

O

V ( V , I V O )

O

v

∆

looks linear

™ Operate amp at V I , V O

Æ DC “bias” (good choice: midpoint

of input operating range)

™ Superimpose small signal on top of V I

™ Response to small signal seems to be

approximately linear

Let’s look at this in more detail —

I III from a circuit viewpoint

We use a DC bias V I to “boost” interesting input

signal above V T , and in fact, well above V T

interesting

input signal

+ – + –

S

V

L

R

v O

V

Offset voltage or bias

Graphically

interesting

v O

S

V

L

R

+ – + –

input signal

V

S

V v O

O

V

operating point

O

I V

V ,

I

V

T

V

O v

v =

0

I −V

v

aka incremental model

aka linearized model

Notation —

Input:

total

v I = V I + v i

DC small

variable bias signal (like ∆v I) bias voltage aka operating point voltage

Output: v O = V O + v o

Graphically,

V I

V O

II Mathematically

(… watch my fingers)

v O = V S − R L K (v I −V T )2

V O = V S − R L K (V I −V T )

2

substituting v I = V I + v i v i << V

v O = V S − R L K ( [V I + v i ]− v T )

= V S − R L K ( [V I −V T ]2 + 2[V I − v T ]v i + v i 2

O

T

I

L

S V V

2

K

R

V − − ) − R L K (V I −V T )v

v o = −R L K ( V I −V v T )

g m related to V

Mathematically

v o = −R L K ( V I −V v T )

g m related to V

v o = −g m R L v

For a given DC operating point voltage V I

V I – V T

v o = − A v

constant w.r.t v

In other words, our circuit behaves like a linear amplifier for small signals





Another way

v O = V S − R L K (v I −V T )

v o =

dv

d

I



VS − R L 2 K (v I −V T )2







⋅ v

I

I

v

slope at V

v o = −R L K (V I −V T ) ⋅ v

g m = K (V I −V T )

A = −g m R L amp gain Also, see Figure 8.9 in the course notes

for a graphical interpretation of this result

More next lecture …

Demo

DS

i

I

V

O

v

load line

operating point

input signal response

V O

How to choose the bias point:

1 Gain component g m ∝ V I

2 v i gets big Æ distortion

So bias carefully

3 Input valid operating range

Bias at midpoint of input operating

range for maximum swing