fet amplifier circuits analysis

EE2603-02 Electronic Circuit Analysis

1

2. FET Amplifier Circuits Analysis

•  FET amplifier parameter gm •  CS amplifiers •  CS with RS amplifiers •  SF amplifiers •  Bootstrap amplifier •  CG amplifiers


EE2603-02 2

Types of FET amplifiers (MOSFET)

(a) Common Source (CS) High AV and high Ri Voltage amplifications

VDD

RD

RL

CS

Ri C1C2

vi RGRS

vo

(b) Common Source (CS) with RS Low AV and high Ri Stability applications

VDD

RD

RL

Ri C1C2

vi RGRS

vo

(c) Source Follower (SF) Very low Ro and high Ri Buffer applications

VDD

RL

Ri

C1

C2

vi RGRS

vo

(d) Common Gate (CG) Very low Ri and high AV

High Frequency applications

VDD

RD

RLRi

C1CG

viRGRS

vo

C2


FET amplifier parameter gm

3

VDD

RD

RGRS

ID

IDRS

+

-

-+VGS

IG=0IDSS VP gm

nscalculatiocircuitequivalentFETforVV

1VI2

gFind

)3(Vgetand)1(inISubstituteandISolveIinequationquadraticgetandabove)2(inR,V,IgivenSubstitute

)2(VRI

1IVV

1II

)circuittheingivenarecomponentsall(RR

RVVWhere

)1()biasdividervoltage(RIVVor)biasself(RIV

P

GS

P

DSSm

GSDD

DSPDSS

2

P

SDDSS

2

P

GSDSSD

21

1DDG

SDGGSSDGS

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

−−−−

−−−−⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

+=

−−−−=−=

MOSFET-self-bias amplifier


FET amplifier parameter gm

4

RS

R2

RD

VDD

VGS

ID

+

-

+-

R1

VG

+

-IDRS

IDSS VP gm

MOSFET-voltage divider-bias amplifier

nscalculatiocircuitequivalentFETforVV

1VI2

gFind

)3(Vgetand)1(inISubstituteandISolveIinequationquadraticgetandabove)2(inR,V,IgivenSubstitute

)2(V

RIV1I

VV

1II

)circuittheingivenarecomponentsall(RR

RVVWhere

)1()biasdividervoltage(RIVV

P

GS

P

DSSm

GSDD

DSPDSS

2

P

SDGDSS

2

P

GSDSSD

21

1DDG

SDGGS

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

−−−−

−−−−⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

+=

−−−−=


EE2603-02 5

VDD

RD

RG RS=2.4k

ID

IDSS=8mAVP=8V

gm=?Example: Find gm of the given MOSFET amplifier

( )

( )

( ) ( )

mSVV

VIg

neglectedVVbeyondVVButVkmAorVkmAV

orI

IIIII

IIVVII

IRIVbutkRmAIVV

P

GS

P

DSSm

PGS

GS

D

DDDDD

DD

P

GSDSSD

DSDGSSDSSp

94.0825.41

8821

281.15

1.154.229.625.44.277.1

29.677.152.11

04.264.4652.11

6.147421534.46

0644.4676.54.3876.5648

4.28648

84.2

181

4.24.2,8,8

22

222

=⎟⎠

⎞⎜⎝

⎛−

−−

−

×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=∴

∴−=−=

−=×−−=×−=∴

=±

=−±−−

=

=+−⇒−+=

+−=⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=∴

−=−===−=


6

Example: Find gm of the given FET amplifier

( )

( )

( ) ( )( )

mS025.189.31

882

VV

1VI2

g

V9.3VisanswerCorrectneglectedisitV8VbeyondisV37.15VBut

V37.15k4.2mA8.695.0orV9.3k4.2mA04.295.0V

mA8.6ormA04.252.11

41.2796.5052.11

1845259796.50I

01.80I96.50I76.5I96.42I76.51.80I8

I4.295.08648

8I4.295.0

18VV

1II

V95.0k2000k100

k10020whereV

I4.295.0RIVVbutk4.2R,mA8I,V8V

P

GS

P

DSSm

GS

PGS

GS

D

D2DD

2DD

2D

2D

2

P

GSDSSD

G

DSDGGSSDSSp

=⎟⎠

⎞⎜⎝

⎛−

−−

−

×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=∴

−=

∴−=−=

−=×−−=×−=∴

=±

=−±−−

=

=+−⇒−+=

+−−=⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=∴

=+

×=

−=−===−=

RS=2.4kWR2=

100kW

RD=4.7kW

VDD=20V

VGS

ID

+-

R1=2MW

VG

+

-

IDSS=8mA

VP=-8V


CS amplifier analysis

7 Rin = RG

( ))R//R(g

vR//Rvg

vvA LDm

gs

LDgsm

in

ov −=

×−==

Ri

viRG

vo

Rin

Ro

vin

iin

iL

ig=0 DG

S

gmvgs

RL

vgs

RD

Ro = RD

MOSFET-self-bias CS amplifier MOSFET-voltage divider-bias CS amplifier

RS

RG

RD

RL

VDD

CS

ViVo

RS

R2

RD

RL

VDD

CS

R1

ViVo


CS with RS amplifier analysis

8

Ri

viRG

vo

Rin

Ro

vin

iin

iL

ig=0 DG

S

gmvgs

RL

vgs

RD

RS

Rin = RG Ro = RD

( )

{ }SmS

LD

SmLDm

Sgsmgs

LDgsm

ino

v

Rg1ifR

)R//R(Rg1

)R//R(gRvgv

R//RvgvvA

<<−

≈

+

−=

+

×−==

approximate

JFET-self-bias CSwithRS amplifier MOSFET-voltage divider-bias CS withRS amplifier

RS

RG

RD

RL

VDD

ViVo

RS

R2

RD

RL

VDD

R1

ViVo


SF amplifier analysis

9

( )( ) ( )

( )LSm

LSmLSm

LSgsmgs

LSgsm

ino

v

R//Rg1if1R//Rg1)R//R(g

R//RvgvR//Rvg

vvA

<<⇒≈

+=

+

×==

Ri

viRG vo

Rin Ro

vin

iin ig=0 DG

S

gmvgs

RL

vgs

RS( )( ) ( )mSgsmgsS

RSRSSogsmRSgsRSg/1//Rvg/v//R

I/V//RRvgIandvV==

=⇒==

MOSFET-v.divider-bias SF amplifier

RS

RG

RL

VDD

Vo

Vi

JFET-self-bias SF amplifier

Rin = RG Ro = RS//1/gm

R2 RS

R1

RL

VDD

Vi

Vo


EE2603-02 10

( )

( )

( ) ( )

mSVV

VIg

neglectedVVbeyondVVButVkmAorVkmAV

orI

IIIII

IIVVII

IRIVbutkRmAIVV

P

GS

P

DSSm

PGS

GS

D

DDDDD

DD

P

GSDSSD

DSDGSSDSSp

94.0825.41

8821

281.15

1.154.229.625.44.277.1

29.677.152.11

04.264.4652.11

6.147421534.46

0644.4676.54.3876.5648

4.28648

84.2

181

4.24.2,8,8

22

222

=⎟⎠

⎞⎜⎝

⎛−

−−

−

×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=∴

∴−=−=

−=×−−=×−=∴

=±

=−±−−

=

=+−⇒−+=

+−=⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=∴

−=−===−=

Example: .amplifierSFfolowingtheofvvA,

ivR,RFind

in

ov

in

inino ==

VDD

RS=2.4k

IDSS=8mAVP=8V

RL=2.4k

Vin

Vo

Ro

Rin

RG=1M

( ) Ω==== k74.0k06.1//k4.2k94.01//k4.2g/1//RR mSo

( ) 53.013.213.1

)k4.2//k4.2(94.01)k4.2//k4.2(94.0

R//Rg1)R//R(g

vvA

LSm

LSm

in

ov ==

+=

+==

Ω== 1M R R Gin


EE2603-02 11

Bootstrap Amplifier analysis Miller’s Theorem

alminteroutputatcetanresisA11

ZV

V1Z

VVZV

IVZ

V

2112

222

2M

⇐−

=

−=

−

×==

ZVVIand

ZVVI 12

221

1−

=−

=

cetanresisInputA1

Z

VV1Z

VVZV

IVZ

V1

2

211

11

1M

⇐−

=−

=

−

×==

12

V VVAWhere =

ZI1 I2

V1 V2

I1 I2

V1 V2ZM2ZM1

Rin


EE2603-02 12

RL

RS2

RG

RD

VDD

Rin

RS1

Vo

Vo2

Vo1

Vin

Miller’s Theorem applied to Bootstrap amplifier

Rin

Miller’s resistor RG is connected between Vin and Vo2

ZI1 I2

V1 V2

I1 I2

V1 V2ZM2ZM1

RL

RS2

RM1

RD

VDD

Rin

RS1

Vo

Vo2

Vo1

Vin

RM2

V

G1Min A1

RRR

−==

V

G2M3S

A11

RRR

−==


EE2603-02 13

Example: .amplifierCSBootstrapfolowingtheofRFind in

RLRG

RD

VDD

Rin 1.2kW

Vo3

Vo1

Vin

300kW

RS2

1kW RS1

Vo2

1. Find gm

2. Find Vo1/Vin=AV1

( )( ) ( )( ) 3990

72834881

22241121241

21

211 .

.

.)k.(mS.

)k.(mS.RRVgV

RVgvvA

SSgsmgs

Sgsm

in

ov ==

+=

++==

3. Find Rin = RM1

)VtofromVconnectedR(k.k

AR

RR oinGV

GMin 1

11 499

39901300

1Ω=

−

Ω=

−==

( )

( )

( ) ( )

mS..VV

VI

g

neglectedVVbeyondisV.VButV.kmA.orV.k.V

.or...

I

IIIII

II

VV

II

IRIVbutkR,mAI,VV

P

GS

P

DSSm

PGS

GS

D

DDDDD

DD

P

GSDSSD

DSDGSSDSSp

2418053

1882

12

8920

92019200531053

945200532891724

521125657624

0642416648

8648

8181

1188

22

222

1

=⎟⎠

⎞⎜⎝

⎛−

−−

−

×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=∴

∴−=−=

−=×−−=×−=∴

=±

=−±−−

=

=+−⇒−+=

+−=⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=∴

×−=−===−=

RLRG

RD

Rin 1.2kW

Vo3

Vo1

Vgs

300kW

RS2

1kW RS1Vgs

Vin gmVgs


CG Amplifier

14

R2 RS

R1

RD

RL

VDD

C1

VO

Rin

Vin

RSRG

RD

RL

VDD

C1

VO

Rin

Vin

MOSFET-voltage divider-bias CG amplifier MOSFET-self-bias CG amplifier


EE2603-02 15

gmvgsvgs

+

-

G D

S

vin+

-Rin

vo

+

-

Gate capacitor

shortRG RL

IRS

⎟⎠⎞⎜

⎝⎛=

⎟⎠

⎞⎜⎝

⎛−

−=⎟

⎠⎞

⎜⎝⎛=

−=−=

mS

gsmgs

SinSin

gsmgsin

g1//R

vgv//RI

V//RR

vgIandvV

( )( )

( )⇐=−

×−==∴

−=×−=

LDmgs

gsm

ino

V

gsinLDgsmo

R//Rgv

RL//RDvgVVA

vVbutR//RvgV

CG amplifier analysis

RSRG

RD

RL

VDD

C1

VO

Rin

Vin

fet amplifier circuits analysis

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