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6.002x CIRCUITS AND ELECTRONICS

MOSFET SCS Model MOSFET Amplifier

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n Superposition with dependent sources. One approach: - leave all dependent sources in; - solve for one independent source at a time - [section 3.5.1 of the text]

+ –

+

– aʹ′v

bʹ′)(vfi =

n Dependent source in a circuit

Review

a b

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Review

LDSO RiVv −=

( )2I 1v2K

−

for vI ≥ 1V

= 0 otherwise + –

( )2ID 1v2Ki −=VCCS

Vs

RL

vO

vI

Next, quick review of amp. Reading: Chapter 7.3–7.7

iD

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The i-v relation for a current source

i

v

Hold the thought

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Key device Needed

+ –

VCCS

Vs

vO

vI

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Key device Needed

Let’s look at our old friend, the MOSFET …

B

C

VCCS

i = f(v)

+ –

VCCS

Vs

vO

vI

A

vD + –

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Our old friend, the MOSFET First, we sort of lied. The on-state behavior of the MOSFET is quite a bit more complex than either the ideal switch or the resistor model would have you believe.

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Let’s Look at the MOSFET Behavior Graphically

D

S

G

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Graphically Demo

SR MODEL

iDS

vDS

S MODEL

iDS

vDS

+ – +

– vGS

iDS vDS

D

SG

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Graphically Demo

vDS

iDS

+ – +

– vGS

iDS vDS

D

SG

TGS Vv ≥

TGS Vv <

TGS Vv ≥

S MODEL SR MODEL

TGS Vv <

iDS iDS

vDS vDS

TGS Vv ≥

TGSDS Vvv −≥

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Graphically

TGS Vv ≥

TGS Vv <

TGS Vv ≥

1GSvSaturation region

Trio

de r

egio

n

S MODEL SR MODEL

TGS Vv <

TGS Vv <

2GSv

3GSv

. . .

TGSDS Vvv −=

Cutoff region

vDS

iDS iDS iDS

vDS vDS

+ – +

– vGS

iDS vDS

D

SG

Notice that MOSFET behaves like a current source

when TGSDS Vvv −≥

TGSDS Vvv −<

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MOSFET SCS Model When and the MOSFET is in its saturation region, and the switch current source (SCS) model of the MOSFET is more accurate than the S or SR model

TGSDS Vvv −≥ TGS Vv ≥

D

G

S

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When to use which model

S MODEL SR MODEL SCS MODEL

for fun! for digital designs for analog designs

When to use each model in 6.002?

TGS Vv ≥

TGS Vv <

TGS Vv ≥

Saturation region

Trio

de r

egio

n

TGS Vv <

TGS Vv <

. . .

TGSDS Vvv −=iDS iDS iDS

vDS vDS vDS

vGS3

vGS2

vGS1

TGS Vv ≥

TGSDS Vvv −≥

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TGSDS Vvv −≥TGSDS Vvv −<

use SCS model use SR model

Note: alternatively (in more advanced courses)

In More Advanced Courses…

or, use SU (Switch Unified) Model (Section 7.8 of A&L)  

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Back to Amplifier

To ensure the MOSFET operates as a VCCS, we must operate it in its saturation region only. To do so, we promise to adhere to the

“saturation discipline”

A

VS

vO vI

vI vO AMP

( )212

−= ID vKi

VS

RL

vI

vO

iD

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MOSFET Amplifier

“Saturation discipline”

In other words, we will operate the amp circuit such that:

in saturation region

( )22 TIDS VvKi −=

VS

D

RL

G

S

vI

vO

TGSDS Vvv −≥

TGS Vv ≥

1GSvSaturation region

Trio

de r

egio

n

TGS Vv <

2GSv

3GSv

. . .

TGSDS Vvv −=

Cutoff region

vDS

iDS

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MOSFET Amplifier

“Saturation discipline”

In other words, we will operate the amp circuit such that

in saturation region

( )22 TIDS VvKi −=

VS

D

RL

G

S

vI

vO

TGSDS Vvv −≥

TGS Vv ≥

1GSvSaturation region

Trio

de r

egio

n

TGS Vv <

2GSv

3GSv

. . .

TGSDS Vvv −=

Cutoff region

vDS

iDS

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Let’s analyze the circuit

in saturation region

( )22 TIDS VvKi −=

VS

D

RL

G

S

vI

vO

First, replace the MOSFET with its SCS model

Two methods: 1.  Analytical 2.  Graphical

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Let’s analyze the circuit

1 Analytical method:

(vO = vDS in our example) Find

for TIO Vvv −≥

IGS vv =+

– + – S

A

( )22 TIDS VvKi −=

VS

D

vO

RL

G

vI

vO vs vI

vO vs vI

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: B From

2 Graphical method From A ( )2

2 TIDS VvKi −=: Saturation region

Trio

de

regi

on

TGS Vv <

. . .

TGSDS Vvv −=

iDS

vDS

vGS3

vGS2

iDS

vDS 0

2

2 ODS vKi =

LDSSO RiVv −=

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Constraints and must be met A B

A

2

2 ODS vKi ≤

iDS

vO VS

= vGS vI

: B

A ( ) ,2

2TIDS VvKi −=: 2

2 ODS vKi ≤for

vO vS vI Remember, superimpose “loadline due to rest of circuit (B)” over device relation (A)

2 Graphical method

L

O

L

SDS R

vRVi −=

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Constraints and must be met A B

L

S

RV

A

2

2 ODS vKi ≤

iDS

vO VS

= vGS vI

: B A ( ) ,

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TIDS VvKi −=: 2

2 ODS vKi ≤for

vO vS vI 2 Graphical method

L

O

L

SDS R

vRVi −=

B

Then, given VI, we can find VO, IDS

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Large Signal Analysis of Amplifier (under “saturation discipline”)

vO versus vI 1

2 Valid input operating range and valid output operating range (to guarantee saturation region operation)

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Large Signal Analysis 1 vO versus vI

Demo

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A Curious Aside

( ) LTIS RVvKV 2

2−−

gets into triode region

TIO Vvv −=

Cutoff region

VS

vO

VT

vI

VS

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2 What are the valid operating ranges under the saturation discipline?

Large Signal Analysis

Our Constraints

Iv

iDS

vO

VS

D

RL

G

S

vI

vO

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2 What are the valid operating ranges under the saturation discipline?

Large Signal Analysis

TIO

TI

VvvVv

−≥

≥

2

2 ODS vKi ≤

Our Constraints

Z 2

2 ODS vKi ≤

L

S

RV

L

O

L

SDS R

vRVi −=

Iv( )2

2 TIDS VvKi −=

iDS

VS

vO vI=VT vO=VS and iDS=0

VS

D

RL

G

S

vI

vO

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2 What are the valid operating ranges under the saturation discipline?

Large Signal Analysis

2

2 ODS vKi ≤

L

S

RV

L

O

L

SDS R

vRVi −=

( )22 TIDS VvKi −=

iDS

VS

vO vI=VT vO=VS and iDS=0

Iv

L

SLO KR

VKRv 211 ++−=

TIO

TI

VvvVv

−≥

≥

2

2 ODS vKi ≤

Our Constraints

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Corresponding output range:

Valid input range:

2 Valid operating ranges under the saturation discipline?

Large Signal Analysis Summary 1 vO versus vI

We will look at another way of obtaining (2) shortly

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Another Way of Obtaining (2) Valid Op Range

V5

V1

Vs

vI

vO

VT

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TVV1 V2~

V1~

~ 5V VS

vO

vI

Another Way of Obtaining (2) Valid Op Range

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( )L

TISO RVvKVv

2

2−−=

TVV1 V2~

V1~

~ 5V VS

vO

Another Way of Obtaining (2) Valid Op Range

TIO Vvv −=

IO vv =

TIO Vvv −>

TIO Vvv −<

TIO Vvv −=