6.002x CIRCUITS AND ELECTRONICS€¦ · 6.002x CIRCUITS AND ELECTRONICS Amplifiers – Revisit Small Signal Trick Reading: Amplifier small signal model -- Chapter 8 of A&L . 2 ! ...

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6.002x CIRCUITS AND ELECTRONICS

Amplifiers – Revisit Small Signal Trick

Reading: Amplifier small signal model -- Chapter 8 of A&L

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n MOSFET amp

n Saturation discipline — operate MOSFET only in saturation region

n  Large signal analysis 1. Find vO vs vI under saturation discipline. 2. Valid vI , vO ranges under saturation discipline.

Review Vs RL

vO

vI iDS

3  

Large Signal Analysis Review Review ( )

LTI

SO RVvKVv2

2−−=

“interesting” region for vI .

Saturation discipline satisfied.

corresponding interesting region for vO

2 Valid operating ranges

TIO Vvv −=TIO Vvv −>

TIO Vvv −<

Vge 5 .,.

V1

V1

Vs

vI

vO

VT

V2

1 vO vs vI  

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Operating in the saturation region

Iv

SV

TV

TIO Vvv −=

vO

Vs RL

vO vI iDS

( )L

TISO RVvKVv

2

2−−=

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But…

Iv

SV

TV

TIO Vvv −=

vO

Demo

( )L

TISO RVvKVv

2

2−−=

Amp is nonlinear … L How do we get a linear amplifier?

Vs RL

vO vI iDS + –

+ – VI

vA

VI vA

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Small Signal Trick

TV

VS

vO

vI

Vs RL

vO

vI iDS

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Small Signal Trick

v Operate amp at VI , VO à DC “bias” (possible choice: midpoint of valid input operating range)

v Superimpose small signal of interest on top of VI

v Response to small signal seems to be approximately linear

Remember “Boost and Shrink”

Vs RL

vO

vI iDS + –

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We use a DC bias VI to “boost” interesting input signal above VT (and in fact, well above VT )

Boost – Use DC Bias Vs RL

vO

vI iDS + –

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Let’s look at this in more detail — I graphically II mathematically III from a circuit viewpoint

In the next sequence

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I Graphically interesting input signal

+– +–

IvΔ

Vs

RL

vO

VI

TIO Vvv −=

vO

VS

0 VT

vI

vI

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Recall Small Signal Model Notation aka incremental model aka linearized model

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Small Signal Model Input: vI = VI + vi

Output: vO = VO + vo

0 0

vI vO

t t

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II Mathematically

… watch my fingers!

( )22 TIL

SO VvKRVv −−=

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II Mathematically

… watch my fingers!

( )22 TIL

SO VvKRVv −−=

Transconductance related to MOSFET parameters and VI

We will see why this is called transconductance in the next sequence  

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Mathematically ( ) iTILo vVVKRv −−=

gm related to VI

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

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Also, see Figure

8.9 in the text

for a graphical

interpretation

of this result

Another way ( )2

2 TIL

SO VvKRVv −−=

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Small Signal Demo interesting input signal

+ – + –

Iv

SV

TVTIO Vvv −=

0

Demo

Vs

RL

vO vi

VI

vO

Iv