Small Signal Model MOS Field-Effect Transistors (MOSFETs)

1

Small Signal ModelMOS Field-Effect Transistors (MOSFETs)

Quiz No 3 DE 27 (CE)

(a) Draw small signal model (4)(b) Find expression for Rout (2) (c) Prove vo/vsig = (β1α2RC)/(Rsig+rπ) (4).

Rout.

20-03-07

Figure 4.2 The enhancement-type NMOS transistor with a positive voltage applied to the gate. An n channel is induced at the top of the substrate beneath the gate.

Enhancement-type NMOS transistor:

MOSFET Analysis

iD = iS, iG = 0

Large-signal equivalent-circuit model of an n-channel MOSFET : Operating in the saturation region.

Large-signal equivalent-circuit model of an p-channel MOSFET : Operating in the saturation region.

Large Signal Model : MOSFET

Transfer characteristic of an amplifier

Conceptual circuit utilized to study the operation of the MOSFET as a small-signal amplifier.

The DC BIAS POINT

To Ensure Saturation-region Operation

Signal Current in Drain Terminal

Total instantaneous voltages vGS and vD

Small-signal ‘π’ models for the MOSFET

Common Source amplifier circuitExample 4-10

Small Signal ‘T’ Model : NMOSFET

Small Signal Models

‘T’ Model

Single Stage MOS Amplifier

Amplifiers Configurations

Common Source Amplifier (CS) :Configuration

Common Source Amplifier (CS)• Most widely used

• Signal ground or an ac earth is at the source through a bypass capacitor

• Not to disturb dc bias current & voltages coupling capacitors are used to pass the signal voltages to the input terminal of the amplifier or to the Load Resistance

• CS circuit is unilateral – – Rin does not depend on RL and vice versa

Small Signal Hybrid “π” Model (CS)

Small Signal Hybrid “π” Model : (CS)

Gin RR sig

sigG

Ggs v

RR

Rv

LDogsmo RRrvgv ||||

sigG

GLDom

gs

ov RR

RRRrg

v

vG ||||

Doo Rr ||R

sig

gs

gs

o

sig

ov v

v

v

v

v

vG

Small-signal analysis performed directly on the amplifier circuit with the MOSFET model implicitly utilized.

Gin RR

sigG

GLDom

gs

o

RR

RRRrg

v

v||||

Doo Rr ||R

• Input Resistance is infinite (Ri=∞)

• Output Resistance = RD

• Voltage Gain is substantial

Common Source Amplifier (CS) Summary

Gin RR

sigG

GLDom

gs

o

RR

RRRrg

v

v||||

Doo Rr ||R

Common-source amplifier with a resistance RS in the source lead

The Common Source Amplifier with a Source Resistance

• The ‘T’ Model is preferred, whenever a resistance is connected to the source terminal.

• ro (output resistance due to Early Effect) is not included, as it would make the amplifier non unilateral & effect of using ro in model would be studied in Chapter ‘6’

Small-signal equivalent circuit with ro neglected.

Sm

g

Rg

vi

1

Do

Gin

RR

RR

Small-signal Analysis.

sig

i

i

gs

gs

o

sig

ov v

v

v

v

v

v

v

vG

Sm

LDm

sigG

Gv

sig

o

sigsigG

Gi

Sm

ii

Sm

mgs

LDgsmo

Rg

RRg

RR

RG

v

v

vRR

Rv

Rg

vv

Rg

gv

RRvgv

1

||

11

1

||

Voltage Gain : CS with RS

Common Source Configuration with Rs

• Rs causes a negative feedback thus improving the stability of drain current of the circuit but at the cost of voltage gain

• Rs reduces id by the factor

– (1+gmRs) = Amount of feedback

• Rs is called Source degeneration resistance as it reduces the gain

Small-signal equivalent circuit directly on Circuit

A common-gate amplifier based on the circuit

Common Gate (CG) Amplifier• The input signal is applied to the source

• Output is taken from the drain

• The gate is formed as a common input & output port.

• ‘T’ Model is more Convenient

• ro is neglected

A small-signal equivalent circuit

A small-signal Analusis : CG

mim

i

i

iin gvg

v

i

vR

1

Dout RR

A small-signal Analusis : CG

sigm

LDm

sig

ov

sigm

sigsig

sigm

msig

sigin

ini

LDimo

sig

i

i

o

sig

ov

Rg

RRg

v

vG

Rg

vv

Rg

gv

RR

Rv

RRvgv

v

v

v

v

v

vG

1

||

11

1

||

Small signal analysis directly on circuit

The common-gate amplifier fed with a current-signal input.

Summary : CG

4. CG has much higher output Resistance5. CG is unity current Gain amplifier or a Current Buffer6. CG has superior High Frequency Response.

A common-drain or source-follower amplifier.

Small-signal equivalent-circuit model

Small-signal Analysis : CD

(a) A common-drain or source-follower amplifier :output resistance Rout of the source follower.

mmoout gg

rR11

||

(a) A common-drain or source-follower amplifier. : Small-signal analysis performed directly on the circuit.

Common Source Circuit (CS)

Common Source Circuit (CS) With RS

Common Gate Circuit (CG)Current Follower

Common Drain Circuit (CD) Source Follower

Summary & Comparison

Quiz No 4• Draw/Write the Following:

27-03-07

BJT MOSFET

Types npn pnp nMOS pMOS

Symbols

‘π’ Model

T Model

gm

Re/rs

rπ/rg

Problem 5-44

SOLUTION : DC Analysis

SOLUTION : DC Analysis

IE

Check for Active Mode

mAI

II

II

E

EE

BE

1

101100

3.3

7.05

0100)1(

7.03.35

01007.03.35

250.1

25

E

te I

Vr

IB

Solution Small Signal Analysis

Solution Small Signal Analysis : Input Resistance

Rin

ib

LCee

b

b

bin RRr

i

v

i

vR ||)1(

)1(

+

vb

-

Solution Small Signal Analysis : Output ResistanceItest

IE

IE/(1+ß)

IRC

Rout

test

testout I

VR

)1(||

)1(

)1(

)1(

sigeC

sigeC

sigeC

sige

test

C

test

testout

RrR

RrR

RrR

Rr

VR

VV

R

ERtest IIIC

)1(

sig

e

testE R

r

VI

C

testR R

VI

C

Solution Small Signal Analysis : Voltage Gain

+

-

LCmeb

o RRgv

v||+

-

vi

+

-

veb

sig

i

i

eb

eb

o

sig

o

v

v

v

v

v

v

v

v

Vo

Solution Small Signal Analysis : Voltage gain

sig

i

i

eb

eb

o

sig

o

v

v

v

v

v

v

v

v

LCmeb

o RRgv

v||+

-

vi

+

-

veb

LCe

e

i

eb

RRr

r

v

v

||


sig

i

i

eb

eb

o

sig

o

v

v

v

v

v

v

v

v

LCmeb

o RRgv

v||

+

-

vi LCe

e

i

eb

RRr

r

v

v

||

LCein RRrR ||)1(

sigLCe

LCe

sigin

in

sig

i

RRRr

RRr

RR

R

v

v

||)1(

||)1(


sig

i

i

eb

eb

o

sig

o

v

v

v

v

v

v

v

v LCm

eb

o RRgv

v||

LCe

e

i

eb

RRr

r

v

v

||

sigin

in

LCe

eLCm

sig

o

RR

R

)R(Rr

r)||R(Rg

v

v

||

sigin

in

sig

i

RR

R

v

v

sigin

in

LCe

LC

sig

o

RR

R

)R(Rr

)||R(R

v

v

||

sigin

in

LCe

LCem

sig

o

RR

R

)R(Rr

)||R(Rrg

v

v

||


+

-

LCe

LC

i

o

RRr

RR

v

v

||

||

+

-

vi

sig

i

i

o

sig

o

v

v

v

v

v

v

sigin

in

sig

i

RR

R

v

v

sigin

in

LCe

LC

sig

o

RR

R

)R(Rr

)||R(R

v

v

||

Vo

Problem

Small Signal Model MOSFET : CD


1/gm

gmvsg

D

1/gm

gmvsg

D

Solution Small Signal Analysis : Input Resistance

Rin

Ig=0

inR

1/gm

gmvsg

D

Solution Small Signal Analysis : Output ResistanceItest

ID

IG=0

IRD

Rout

test

testout I

VR

mD

m

test

D

test

testout g

R

gV

RV

VR

1||

/1

DRtest IIIC

m

testD

g

VI

1

D

testR R

VI

D

Vtest

1/gm

gmvsg

D


+

-

LDmsg

o RRgv

v||+

-

vi

+

-

vsg

sig

i

i

sg

sg

o

sig

o

v

v

v

v

v

v

v

v

1/gm

gmvsg

D

Solution Small Signal Analysis : Voltage gain

+

-

vi

+

-

vsg

LDm

m

i

sg

RRg

g

v

v

||1

1

LDmsg

o RRgv

v||

sig

i

i

sg

sg

o

sig

o

v

v

v

v

v

v

v

v


+

-

vi

inR

sigi vv

LDmsg

o RRgv

v||

sig

i

i

sg

sg

o

sig

o

v

v

v

v

v

v

v

v

LDm

m

i

sg

RRg

g

v

v

||1

1


)R(Rg

g)||R(Rg

v

v

LDm

mLDm

sig

o

||1

1

sigi vv LDmsg

o RRgv

v||

sig

i

i

sg

sg

o

sig

o

v

v

v

v

v

v

v

v

LDm

m

i

sg

RRg

g

v

v

||1

1

)R(Rg

)||R(R

v

v

LDm

LD

sig

o

||1


+

- LC

m

LD

i

o

RRg

RR

v

v

||1||

+

-

vi

sig

i

i

o

sig

o

v

v

v

v

v

v

sigi vv

LC

m

LD

sig

o

RRg

RR

v

v

||1||


LCein RRrR ||)1(

)1(

||

sigeCout

RrRR

sigin

in

LCe

LC

sig

o

RR

R

)R(Rr

)||R(R

v

v

||

1

inR

mDout g

RR1

||

LC

m

LD

sig

o

RRg

RR

v

v

||1||

Problem 6-127(e)

DC Analysis 6-127(e)

mAI

AI

mAI

C

B

E

5.0

05101/5.0

5.0

100

1

1

1

mAI

AI

mAI

C

B

E

5.0

05101/5.0

5.0

100

2

2

2

eActiveinQ

VVVVV

VV

BC

C

mod

6.44.054.0

5105.010

2

22

2

eActiveinQ

VVVV

VV

BC

C

mod

4.04.0)10(5104.0

3.47.05

1

311

1

Small Signal Model

Small Signal Model

Rin

1rRin Rout

0 sigCout VRR

sigsig

be

Rr

r

v

v

1

11

sig

be

be

eb

eb

o

sig

o

v

v

v

v

v

v

v

v 1

1

2

2

21

1

2em

be

eb rgv

vCm

eb

o Rgv

v2

2

11211212

rR

R

rR

rrgRg

v

v

sig

C

sig

emCm

sig

o

Problem6-127(f)Replacing BJT with MOSFET

Small Signal Model

Small Signal Model

Rin

inR Rout

0 sigDout VRR

sigsg vv 1sig

gs

gs

sg

sg

o

sig

o

v

v

v

v

v

v

v

v 1

1

2

2

2

1

1

2

m

m

gs

sg

g

g

v

vDm

sg

o Rgv

v2

2

Dmm

mDm

sig

o Rgg

gRg

v

v1

2

12

1rRin

Cout RR

121

rR

R

v

v

sig

C

sig

o

1

inR

Dout RR

Dmsig

o Rgv

v1

11

2

1

m

sig

C

sig

o

g

RR

v

v

Problem 6-127(f)

Solution P6-127(f)

+

+

-

-

vbe2

veb1

+

+

-

-

vbe2

veb1

+

vi

-

Solution P6-127(f)))(1( 211

1

1ee

b

bin rr

i

vR

Lout RR

sig

i

i

be

be

O

sig

O

v

v

v

v

v

v

v

v 2

2

Lmbe

O Rgv

v

2

sige

L

sigee

Lem

sigeeee

eeeLm

sig

o

Rr

R

Rrr

Rrg

Rrrrr

rrrRg

v

v

)2)(1(

)1(

))(1(

)1(

))(1(

))(1(

1

21

211

122

21121

21122

21

22

ee

e

i

be

rr

r

v

v

sigee

ee

sigin

in

sig

i

Rrr

rr

RR

R

v

v

))(1(

))(1(

211

211

Problem 6-127(f) with MOSFET

-

-

vgs2

vsg1

+

+

Solution P6-127(f)

-

-

vgs2

vsg1

+

+

Solution P6-127(f)

+vi

-

1g

iin i

vR

Lout RR

sig

i

i

gs

gs

O

sig

O

v

v

v

v

v

v

v

v 2

2

Lmgs

O Rgv

v

2

221

12 Lm

mm

Lmm

sig

o Rg

gg

Rgg

v

v

21

1

21

22

11

1

mm

m

mm

m

i

gs

gg

g

gg

g

v

v

sigi vv

ig1=0

Comparison BJT/MOSFET Cct

inR

Lout RR

2Lm

sig

o Rg

v

v

))(1( 211 eein rrR

Lout RR

sige

L

sig

o

Rr

R

v

v

)2)(1(

)1(

1

21

1

Small Signal Model

Figure P6.123

Problem 6-123

VBE=0.7 Vβ =200K’n(W/L)=2mA/V2

Vt=1V

Figure P6.123

DC Analysis

DC AnalysisVBE=0.7 Vβ =200K’n(W/L)=2mA/V2

Vt1=1VVt2=25mV

0.7V

I=0.7/6.8=0.1mA

0 ,1. 211 BSD ImAoII

VVV GSGS 316.112211.0 2

21 '2

1tGSnD VV

L

WKI

IG=0

2V

VVVV BEGSC 22

1mA

mAII C 13

252

VmAV

Ig

VOV

Dm /63.0

2 11

kg

rVmAV

Ig

mt

Cm 5,/40

22

22

Small Signal Model

Small Signal Model : Voltage Gain

ig=0+

vi

-

+vbe2

-

1

2

2 gs

i

i

be

be

o

sig

o

v

v

v

v

v

v

v

v

MRofeffectgNegelectin

RRgv

v

G

C Lmbe

o

10

-30V/V )||(22

VVrR

g

rR

v

v

Sm

S

i

be /64.0)||(

1)||(

211

212

VVRR

R

v

v

sigin

in

sig

i /83.0

VVgRR

R

rRg

rRRRg

v

v

siin

ni

Sm

SCLm

sig

/16)||(

1)||(

)||(

211

212

0

Small Signal Model : Input Resistance

ig=0

Rin

+

vi

-

ii

k

vv

R

Rvv

v

i

vR

i

o

G

Goi

i

i

iin 495

1/

VVrR

g

rRRRg

v

v

Sm

SCLm

i

/2.19)||(

1)||(

)||(

211

212

0

Small Signal Model MOS Field-Effect Transistors (MOSFETs)

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Transcript of Small Signal Model MOS Field-Effect Transistors (MOSFETs)