� �

Chapter 10 Transistor amplifier design

10.1 Stability considerations

unconditionally stable, conditionally stable, stability factor, source stability circle,

load stability circle

10.2 Amplifier design for maximum gain

unilateral case, bilateral case, simultaneously conjugate match, unilateral figure

of merit

10.3 Constant gain circles

unilateral case, bilateral case

10.4 Constant noise figure circles

10.5 Broadband amplifiers

negative feedback amplifier, balanced amplifier, traveling wave amplifier

10.6 Small signal equivalent circuit models of transistors

BJT, MESFET

10.7 DC bias circuits for transistors

� � � �

10.1 Stability considerations

Basics

1. Unconditionally stable

1

12

1

11

11

1,1allfor

12212211

1221

22

22

2

11

11

122122out

22

122111in

Ls

SSSS

SS

SSk

S

SSS

S

SSS

s

s

L

L

2. Conditionally stable: there exists some s and L, such that one or both of these

conditions violated.

� � �

Discussion

1. Stability circles

22

11

2112

22

11

*

2211s

s

11

211222out

22

22

2112

22

22

*

1122L

L

22

122111in

,)(

with plane-in

circlestability11

,)(

with plane-in

circlestability11

S

SSr

S

SSC

rCloadS

SSS

S

SSr

S

SSC

rCloadS

SSS

ss

ss

s

s

LL

LL

L

L

� �

2. If L=0 in=S11, the center of Smith chart represent a stable point if S11

� � � �

4. Ex.10.1 A transistor has S11=0.894 -60.6 , S12=0.02 62.4, S21=3.122 123.6 ,

S22=0.781 -27.6 at 2GHz

2.0,7.4636.1

5.0,7.4636.1

1607.02

1,16964.0

1221

22

22

2

11

12212211

Ls

LL

rC

rC

SS

SSkSSSS

� � � �

10.2 Amplifier design for maximum gain

Basics

1.Unilateral case: S12=0

stability condition: S11

� � � �

2. Bilateral case (simultaneously conjugate match)

*

11222

*

22111

22

11

2

222

22

22

2

111

1

2

1

2

11

11

122122out

*

L

2

2

2

2

22

22

122111in

*

s

12

212

12

21

2

s11

2

2

2122

L22

2

2

212

*

Lo

*

in

,

1,1

2

4

1

2

4

1

1kasgainstablemaximum:),1(

1

1

1

1

1

1

1

1

,smatchconjugateuslysimultaneooutputandinput

1,1

SSCSSC

SSBSSB

C

CBB

S

SSS

C

CBB

S

SSS

S

SGKK

S

S

SS

SSGG

Kif

Ms

s

s

ML

L

L

MSG

s

L

L

s

TMaxT

ut

� � � �

3. Unilateral figure of merit

)1)(1(

)1(

1

)1(

1

2

22

2

11

22122111

22

SS

SSSSU

UG

G

U U

T

Discussion

1. Linear amplifier design procedure

(1) if | 1, use input and output simultaneously conjugate matches for GTmax

(2) if K

� ! " #

2. Ex.10.2, A transistor has (Zo=50 ), S11=0.606 -155 , S12=0, S21=6 180 ,

S22=0.48 -20 at 1GHz design an amplifier to give GTUmax.

dB

SS

SG

SS

SS

TU

Ls

69.189.733.13658.1

48.01

16

606.01

1

1

1

1

1

2048.0,155606.0

148.0,1606.0

2

2

22

22

2

212

11

max

*

22

*

11

2211

1: y=j1.7, or z=-j0.45

2: z=j0.2

3: z=-j1.38, or y=j0.48

4: y=-j0.16

$ % & $ %

3. Ex.10.2 A transistor has (Zo=50 ), S11=0.614 -167.4 , S12=0.046 65 ,

S21=2.187 32.4 , S22=0.716 -83 at 6GHz design an amplifier to give Gtmax

| 1

dBKKS

SG

C

CBB

C

CBB

TMax

Ms

ML

58.14728.28)1(

48.849011.02

4

4.1678673.02

4

2

12

21

1

2

1

2

11*

Lout

2

2

2

2

22*

sin

' ( ) ' '

1: MS=0.8673 169.76

2: y=-j2.7

3: ML=0.9011 84.48

4: z=j3.4

* + , * -

4. Ex.10.4 transistor A: S11=0.45 150 , S12=0.01 -10 , S21=2.05 10 , S22=0.4

-10 transistor B: S11=0.641 -171.3 , S12=0.057 16.3 , S21=2.058 28.5 ,

S22=0.572 -95.7 compare their Us

dBG

GdB

dBG

GdB

G

G

G

G

UG

G

U

U

U

SS

SSSSU

B

U

T

A

U

T

B

U

T

A

U

T

U

T

A

9976.08948.0

0238.0476.0

2582.18238.0

0055.19891.0

)1(

1

)1(

1

1085.0

00551.0

)1)(1(

22

2

22

2

11

22122111

B

. / 0 . 1

10.3 Constant gain circles

Basics

1. Unilateral case (S12=0)

2

22

2

22

2

22

*

22

LL

max

2

11

2

11

2

11

*

11

ss

max

2

22

max2

22

2

2

11

max2

11

2

02

22

2

2

212

11

2

)1(1

)1(1,

)1(1

incirclesgainconstant

)1(1

)1(1,

)1(1

incirclesgainconstant

1

1,

1

1,

1

1,

1

1

1

1

1

1

Sg

SgR

Sg

Sgd

RdplaneG

Gg

Sgs

SgsRs

Sgs

Sgds

RsdsplaneG

Ggs

SG

SG

SG

SG

GGGS

SS

G

L

L

L

L

LL

LL

L

LL

s

s

s

L

L

L

Ls

s

s

s

Ls

L

L

s

s

TU

3 4 5 3 6

2. Bilateral case (S12 0)

(1) Unconditionally stable case, use GP or GA

max

2

12

21

max

2

2112

max

*

1122222

22

22

21122112

22

22

*

2

LL2

L11

2

L22

2

2

21

22

11

22

1221112

L22

2

2

212

)1(

)1(1

,)(1

21,

)(1

incirclesgainconstant1

1

11,

1

1

1

1

TPP

PP

P

P

PP

P

P

PP

PP

L

P

PP

L

L

L

Lim

L

im

P

GKKS

SGG

KKSS

gg

R

SSCSg

gSSgSSKR

Sg

Ccc

RcplaneSS

g

gSG

S

S

S

SSS

SSG

7 8 9 7 :max

2

12

21

max

2

2112

max

*

2211122

11

22

21122112

22

11

*

1

ss2

s22

2

s11

2

2

21

11

22

11

1221222

2

212

S11

2

)1(

)1(1

,)(1

21,

)(1

incirclesgainconstant1

1

11,

1

1

1

1

TAA

AA

s

A

AA

s

A

As

ss

S

A

AP

s

s

s

sout

out

S

A

GKKS

SGG

KKSS

gg

R

SSCSg

gSSgSSKR

Sg

Cgc

RcplaneSS

g

gSG

S

S

S

SSSS

SG

; < = ; >

(2) Potentially unstable case

use GP to plot constant gain circles in L-plane and plot load stability circles

properly select L, calculate s= in

use GA to plot constant gain circles in s-plane and plot source stability circles

properly select s, calculate L= out

Discussion

1. Ex. 10.5 A MESFET with S-parameters (Zo=50 )

S11 S21 S12 S22

3GHz 0.8 -90 2.8 100 0 0.66 -50

4GHz 0.75 -120 2.5 80 0 0.6 -70

5GHz 0.71 -140 2.3 60 0 0.68 -85

plot constant gain circles @4GHz for GL=0, 1dB, and Gs=2, 3dB design an

amplifier of 11dB gain

dBGdBSG

dBS

GdBS

G

GGGS

SS

G

TU

Ls

Ls

L

L

s

s

TU

47.1392.196.759.3,96.725.6

92.15625.11

1,59.3228.2

1

1GHz,4@

1

1

1

1

max

2

210

2

22

max2

11

max

02

22

2

2

212

11

2

? @ A ? B

chose GTU(4GHz) 11dB=2dB+8dB+1dB to design the circuit

GTU(3GHz)=7.3GTU(5GHz)=6.96dB

44.0

303.0,

7064.0

7052.0

64.0

8064.0

10

26.11

294.0

166.0,

120627.0

120706.0

691.0

785.0

58.12

23

LLLL

s

RdgdB

dBG

RdsgsdB

dBGs

C D E C F

2. Ex. 10.6 A GaAs FET with S-parameters (Zo=50 , 1GHz) S11=2.27 -120 , S21=4

50 , S12=0, S22=0.6 -80

(1) calculate Zin, plot unstable region in s-plane

(2) plot constant gain circles for Gs=3, 5dB

(3) find Zs for Gs=3dB with maximum degree of stable, determine ZL to give maximum

GL, then design the amplifier

(4) calculate GTU

unstablebe to5.24

235.240

012027.2)1( 11

Rs

jZinZZin

ZZinS in

G H I G J

(2)

dBGS

G

jZSFor

jZssA

TULMAX

LL

175056.142,56.11

1

5.5127806.0:CselectGL,maximum

25507624.0:

Rspossiblemaximumagivetofor ZsASelect(3)

2

2

22

*

22

2698.0

2174.0,

1204.0

12045.0

3.8

13.13

23

16.35sRdsgs

dB

dBGs

K L M N L

3. Ex. 10.7 A GaAs FET with S-parameters (Zo=50 , 6GHz) S11=0.641 -171.3 ,

S21=2.058 28.5 , S12=0.057 16.3 ,S22=0.572 -95.7 design an amplifier to

give GP=9dB

6.17563.0:6.17563.05036.0:Cselect

43.0,1045.0

planeincirclesgainconstant9

38.11)1(3.01.5K

sL

LL

2

12

21

A

Rc

RcdBG

dBKKS

SGG

in

pp

ppP

PMaxP

O P Q R O

4. Ex. 10.8 A GaAs FET with S-parameters (Zo=50 , 8GHz) S11=0.5 -180 ,

S21=2.5 70 , S12=0.08 30 , S22=0.8 -100 design an amplifier to give

GP=10dB

3.17952.0:3.17952.0971.0:Cselect

4733.0,2.9757.0

planeincirclesgainconstant10

3388.0,9717.1Ccirclestabilityload

998.0,6.17067.1Cscirclestabilitysource2228.0.3990K

sL

LL

L

A

Rc

RcdBG

r

rs

in

pp

ppP

L

S T U V V

5. Ex. 10.9 A BJT with S-parameters (Zo=50 , 750MHz) S11=0.277 - 59 , S21=1.92

64 , S12=0.078 93 , S22=0.848 -31 design an amplifier to give GTmax

6. Ex. 10.10 use the BJT in Ex.10.9 design an amplifier to give GP=10dB,

determine Gs, GL for GPmax

°3.8530.9511=?3510.7298=

matchconjugateuslysimultaneo3242.0,0325.1|G|

MLMS

Ss

LL

s

L

LL

1357298.0

84.339511.08.12

45.563455.0:

4.563455.03456.0:Cselect

2142.0,8.3378.0

planeincirclesgainconstant10

M

MMAXP

in

pp

ppP

dBG

A

Rc

RcdBG

W X Y Z [

10.4 Constant noise figure circles

Basics

amplifier port - two a For

1

)1(,

1

circlefigurenoiseconstant

parameterfigurenoise:1/41

N

r transistoofresistancenoiseequivalent,,:parameternoise

1)1(

4

2

2

0

min

2

2

min

22

2

0

min

2

min

N

NNNR

NC

RC

ZR

FF

RYF

Z

RFYY

G

RFF

opt

NF

opt

NF

NFNFs

opt

ns

opts

nopt

opts

optsnopts

s

n

\ ] ^ _ `

Discussion

1. Ex. 10.11 A BJT with S-parameters (Zo=50 , 1GHz) S11=0.707 -155 , S21=5

180 , S12=0, S22=0.51 -20 , Fmin=3dB, Rn=4 , opt= 0.45 180 design an

amplifier to give GT=16dB, F

a b c d e

2. Ex. 10.12 A GaAs FET with S-parameters (Zo=50 , 4GHz) S11=0.6 -60 ,

S21=1.9 81 , S12=0.05 26 , S22=0.5 -60 , Fmin=1.6dB, Rn=20 , opt= =0.62

100 (1) assume S12=0, design an amplifier to give GTUmax, F

f g h i j

8.67504.08.67504.090535.0

234.0,7.64527.08G

planeincirclesgainconstantGuse)2(

A

ssA

Louts

ss

ss

select

RcdB

Rc

3. Low noise amplifier design procedure:

if unconditionally stable, use GA constant gain circles and constant noise figure

circles to determine s , and L= *out.

if potentially unstable, consider source and load stability circles in addition.

k l m n op , 1GHz) S11=0.6 -130 , S21=7.12

86 , S12=0.039 35 , S22=0.5 -38 , Fmin=1.3dB, Rn=8 , opt= =0.06 49

design an amplifier to give 16dB power gain, F

q r s t u

10.5 Broadband amplifiers

Basics

1. Negative feedback amplifier

''

1'),1('

)1(1

1

1

1

00

0

000

0

0

0

0

0

cc

cc

c

V

v

v

i

V

fAfA

A

AAAff

Af

fj

A

A

G

fc

fj

AAv

A

A

V

VG

v w x y z

2. Balanced amplifier

{ hybrids and amplifier gain.

| } ~ }

2. Traveling wave amplifier (distributed amplifier) TEM line “extreme wide operation

bandwidth”

10.6 Small-signal equivalent circuit models of transistor

Basics

1. BJT

2. MESFET

powergate

fgate

10.7 DC bias circuits for transistors

Discussion

1. Resistive bias with voltage feedback for BJT,inchanges tosensitivelesshave

1,

1

,

,

BEE

BBEcc

B

BEccE

CBEE

BEBBE

VIto

RRcVV

RRc

VVI

IIIIIc

VRIRcIVcc

2. Bias circuit with emitter bypassed resistor for BJT

inth

cc

cECBth

BEE

thEBEth

thE

BEccE

BEEEth

EEBEBthTh

THCCTH

RR

V

VVV

VIto

RRVV

RR

VVI

VIRR

RIVIRV

RR

RRRV

RR

RV

20%~15%Vthusually

swingoutputitedlim,

,inchanges tosensitivelesshave

1,

1

,)1

(

,21

21

21

2

3. Unipolar bias circuits for MESFET