Microelectric Circuits by Meiling CHEN 1 Lecture 14 Feedback.

Microelectric Circuits by Meiling CHEN

1

Lecture 14Lecture 14

FeedbackFeedback

National United University Department of Electrical Engineering ~ Meiling CHEN

topicstopics

• The series-shunt feedback• The series-series feedback• The shunt-shunt feedback• The shunt-series feedback


Two port networks

Two port Network

1v

2v

1i 2i

Type I: Impedance z-parameters

222121212

212111211

),(

),(

iziziifv

iziziifv

2

1

2221

1211

2

1

i

i

zz

zz

v

v

1i 2i

11z 22z

212iz 121iz

1v

2v


Type II: Admittance y-parameters

222121212

212111211

),(

),(

vyvyvvfi

vyvyvvfi

2

1

2221

1211

2

1

v

v

yy

yy

i

i

Type III: hybrid h-parameters

222121212

212111211

),(

),(

vhihvifi

vhihvifv

2

1

2221

1211

2

1

v

i

hh

hh

i

v

2i

22

1

h

121ih

2v1i

11h

212vh

1v

ce

b

oefe

reie

c

be

v

i

hh

hh

i

v

1i 2i

212vy 121vy

1v

2v22

1

y11

1

y


Type IV: Inverse-hybrid g-parameters

222121212

212111211

),(

),(

igvgivfv

igvgivfi

2

1

2221

1211

2

1

i

v

gg

gg

v

i

1i

11

1

g

212ig

1v 2i

22g

121vg

2v

Type V: transmission ABCD parameters

)(),(

)(),(

22221

22221

iDCvivfi

iBAvivfv

2

2

1

1

i

v

DC

BA

i

v


Type VI: Inverse transmission parameters

)(),(

)(),(

11112

11112

iDvCivfi

iBvAivfv

1

1

2

2

i

v

DC

BA

i

v

Two port Network combination: I. Cascade : ABCD parameters

1v

32 vv

11

11

DC

BA1i 32 ii

4v

22

22

DC

BA3i 4i

2

2

11

11

1

1

i

v

DC

BA

i

v

4

4

22

22

3

3

i

v

DC

BA

i

v

4

4

22

22

11

11

1

1

i

v

DC

BA

DC

BA

i

v


II: series-shunt

1v

2v

1i 2i

1v

2v

1i 2i

2

1

2221

1211

2

1

v

i

hh

hh

i

v

222

222

111

111

vvv

iii

vvv

iii

2

1

2221

1211

2

1

v

i

hh

hh

i

v

2221

1211

hh

hh

2221

1211

hh

hh

2

1

2221

1211

2221

1211

2

1

2

1

2

1 }{v

i

hh

hh

hh

hh

i

v

i

v

i

v

1i 2i

1v

2v


n

A2

1i

1v

2i

2v

1

1

1

1

2

Ex:

31

12h

Find v2=?

1

1

1

1i

1v

2i

2v

21212

212122

2

211211

1

2

3

2

12

211

2

1

2

1

11

vivvi

vvivvv

i

vivvvv

i

23

21

21

21

h

29

21

23

25

totalh

212

211

2

9

2

12

3

2

5

vii

viv

9

2

0,2

2

21

v

ii


III: series-series

1v

2v

1i 2i

222

222

111

111

vvv

iii

vvv

iii

2

1

2221

1211

2

1

i

i

zz

zz

v

v

2

1

2221

1211

2

1

i

i

zz

zz

v

v

2221

1211

zz

zz

2221

1211

zz

zz

2

1

2221

1211

2221

1211

2

1

2

1

2

1 }{i

i

zz

zz

zz

zz

v

v

v

v

v

v

1v

2v

1i 2i

1i 2i

1v

2v


IV: Shunt-shunt

222

222

111

111

vvv

iii

vvv

iii

2

1

2221

1211

2

1

v

v

yy

yy

i

i

2

1

2221

1211

2

1

v

v

yy

yy

i

i

2

1

2221

1211

2221

1211

2

1

2

1

2

1 }{v

v

yy

yy

yy

yy

i

i

i

i

i

i

1i 2i

1v

2v

1v

2v

1i 2i

1v

2v

1i 2i

2221

1211

yy

yy

2221

1211

yy

yy


V: shunt-series

1i 2i

1v

2v

1i 2i

1v

2v

1i 2i

1v

2v

222

222

111

111

vvv

iii

vvv

iii

2

1

2221

1211

2

1

i

v

gg

gg

v

i

2

1

2221

1211

2

1

i

v

gg

gg

v

i

2221

1211

gg

gg

2221

1211

gg

gg

2

1

2221

1211

2221

1211

2

1

2

1

2

1 }{i

v

gg

gg

gg

gg

v

i

v

i

v

i


General feedback structure

A

A

x

xA

xxx

xx

Axx

s

of

fsi

of

io

1

Open loop gain

ALoop gain

Closed-loop gain

Mixer networkVoltage seriesCurrent shunt

Sampling networkVoltage shuntCurrent Series


Negative feedback Negative feedback propertiesproperties

• Gain desensitivity • Bandwidth extension• Noise reduction• Nonlinear distortion reduction


1.Gain desensitivity

A

dA

AA

dA

A

dAdA

A

A

x

xA

f

f

f

s

of

1

1

)1(

1

2

2.Bandwidth extension

A

dA

A

dA

f

f

)1(

)1(/1

)1/(

)(1

)()(

/1)(

MHHf

MH

MMf

H

M

H

HM

A

As

AA

sA

sAsA

s

A

s

AsA

)1/(

)(1

)()(

/1)(

MLLf

f

L

M

L

M

A

sA

sAsA

s

A

s

sAsA

LfHfBW


3.Noise reduction

)Ratio Noise toS( ignalN

SSNR

N

S

V

V

N

S

VVV

n

s

nso

1010

100

10)10(


N

S1000

N

S

100V0.1V 1001

10000

1001

10

sn

sno VVV

N

S1

N

S

100100

)01.0(10000

nso

noso

VVV

VVVV


Figure 8.3 Illustrating the application of negative feedback to reduce the nonlinear distortion in amplifiers. Curve (a) shows the amplifier transfer characteristic without feedback. Curve (b) shows the characteristic with negative feedback ( 0.01) applied.

4.Nonlinear distortion reduction

9.901

A

A

1000A

(a) without feedback

(b) with feedback 01.0100A

501

A

A


Mixer network: Voltage series Current shunt

Sampling

Feedback Topology


Sampling network : Voltage shunt Current Series


series

series

shunt voltage

current

voltage

voltage

shunt


voltage

shunt

series

current

series

voltage


shunt

current

Shunt series


Series- shunt


voltage-mixing voltage-sampling (series–shunt) topology


current-mixing current-sampling (shunt–series) topology


voltage-mixing current-sampling (series–series) topology


current-mixing voltage-sampling (shunt–shunt) topology


The series–shunt feedback amplifier

A

RR

R

AVVI

VV

R

AVVI

I

VR

ARR

AR

RV

AVV

RV

VV

I

VR

A

A

V

VA

oof

o

oo

oVi

o

ioo

Vo

oof

iif

i

i

i

ii

i

i

oi

i

sif

s

of

s

s

1

)1(

)1(

1

0

0


2

1

2221

1211

2

1

2221212

2121111

V

I

hh

hh

I

V

VhIhI

VhIhV

Passive network h21 tends to zero


Louto

of

insiif

RRA

RR

RRRAR

//)1(

)1(

vA

sv

sR outR

inR

iv

ovif vA

LR

Series -Shunt


The series–series feedback amplifier

oof

oooooiooVo

oof

i

i

i

ii

i

i

oiVif

RAR

IRARIAIRAVIVI

VR

AR

RV

AvV

RV

IV

I

VR

S

o

)1(

)1()]([)(

)1(

0

0


2

1

2221

1211

2

1

2221212

2121111

I

I

zz

zz

V

V

IzIzV

IzIzV


Figure 8.15 (Continued) (c) A redrawing of the circuit in (b) with z21 neglected.

A

AA

RRzRRAR

RRzRRAR

f

LoutoLof

insisif

1

))(1(

))(1(

22

11

2211 zRR

R

zRR

RAA

Lo

o

is

iB

sv

sR

outRinR

iv

ovif iA

LR

Loutof

insif

RRR

RRR

Series -Series


the shunt–shunt feedback amplifier

A

RR

AII

RI

AII

V

VI

V

I

VR

I

VRA

iif

ii

ii

ii

s

oi

s

s

sif

i

om

1A

RA

AR

IARI

ARI

I

VR

A

RII

AIRIVI

I

AIRI

I

VR

oo

o

oooo

o

oof

ooi

ioooIi

o

ioo

o

oof

s

1

1)

11(

1

1

)(0


2

1

2221

1211

2

1

v

v

yy

yy

i

i

1i 2i

11y 22y

212vy 121vy

ivv1

ovv2


outR

ovif iA

LRsR inRsI

ii

LRsR

11

1

y 22

1

y

A

AA

RRA

RRR

RRA

yRR

R

f

LoutLyo

of

ins

is

if

1

//)1(

////

//)1(

)1

////(

22

1

11

)//(2211

11

11

1

yLo

o

yis

ysB RR

R

RR

RAA

Shunt -Shunt


The shunt–series feedback amplifier

A

RR

R

VA

R

VAI

R

VIAII

IR

VI

iif

i

s

i

si

i

ssiVo

oi

ss

o

1

0

oIo

oof

oo

ooooioo

Io

oof

RAI

VR

IRA

RIAIRAIIV

I

VR

s

s

)1(

)1(

)]([)(

0

0


2

1

2221

1211

2

1

i

v

gg

gg

v

i

1i

11g

212ig

ivv1 oii 2

22g

121vg

2v


LRsR

11

1

g

22g

A

AA

RRRgRAR

RRA

yRR

R

f

LoutLoof

ins

is

if

1

))(1(

//)1(

)1

////(

22

11

221

1

11

11

gRR

R

RR

RAA

Lo

o

gis

gSB

outRinR

ovif iA LRsR

sI

ii

Shunt -Series


Type Amplifier Feedback parameter

Series-Shunt(voltage-voltage)

Series-Series(voltage-current)

Shunt-Shunt(current-voltage)

shunt-series(current-current)

)1()1(1 12

ARRARRGz

GG oofiif

m

mmf

ifR ofR

i

ov v

vA

i

om v

iG

i

om i

vR

i

oI i

iA

hi

v

2

1

zv

v

2

1

yi

i

2

1

gv

i

2

1

A

RRRAR

Ah

AA o

ofiifv

vf

1

)1(1 12

)1()1(1 12 A

RR

A

RR

Ry

RR o

ofi

ifm

mmf

oofi

ifI

IIf RAR

A

RR

Ag

AA )1(

11 12

A

AAf

1

insif RRR

insif RRR

insif RRR //

insif RRR //

outLof RRR //

outLof RRR //

outLof RRR

outLof RRR


Example 8.1

Step 0 : Series-shunt feedback amplifier

Step 1 : Amplifier analysis

oo

idi

rR

RR

Amplifier Voltage amplifierFeedback h parameters

1122

22

)//(

)//(

hRR

R

rhR

hR

V

VA

sid

id

oL

L

i

o

BA


Step 2 : Feedback network analysis

2221212

2121111

VhIhI

VhIhV

21

10

2

112

2102

122

2101

111

1

1

2//

RR

R

V

Vh

RRV

Ih

RRI

Vh

I

I

V


Step 3 : Amp+Feedback analysis

A

AA

findR

RRA

RRRr

A

RRR

RRR

RRRRRRAhRRAR

f

out

LoutLoLho

of

ifsin

insidsisif

1

//)1(

//)//(

)1(

////

))//()(1())(1(

211

2111

22 Feedback AMP


Example 8.2

Step 0 : Series-series feedback amplifier

Amplifier Transconductance amplifierFeedback z parameters


Step 1 : Amplifier analysis


)//(

)//(

21322

32111

RRRZ

RRRZ

Step 2 : Analysis feedback Amp

The equivalent circuit

iV

oV

1ei3ei

11Z

1er

1cR

22Z

Vgm

V r 2cR 3er

3cRAV

oI

iR

oR1ei


Step 3 : Amp+Feedback analysis

m

mf

i

om

ec

ic

e

e

efecm

e

Ao

efecmA

eei

G

GA

V

IGA

ZrrR

vV

rR

vi

Zr

ZrhRvg

Zr

VI

ZrhRvgV

ZriV

1

)()//(//

)])(1//([

)])(1//([

)(

11111

1

222

2232

222

2232

1111

oof

iif

fe

ceo

feei

RAR

RAR

h

RZrR

hZrR

)1(

)1(

1

)1)((

2223

111


Example 8.3

Shunt-shunt: Rm amplifier + y parameter

2

1

2221

1211

2

1

v

v

yy

yy

i

i


02

2220

1

111 12 vv v

iy

v

iy


fv

o

f

cfo

sfi

sf

cfm

i

om

Rv

iy

kRRR

krRRR

k

rRRv

RRvg

i

vR

s

1

27.4//

4.1////

7.358

)////(

)//(

012

4951

//2.1621

6.411

12

12

12

m

oof

insm

iif

m

mmf

s

of

Ry

RR

RRRy

RR

kRy

RR

i

vA


Example 8.4

1.DC analysis

mAk

I

VkV

mAI

mAI

IIkkVkk

k

E

C

C

B

BB

765.04.3

7.03.3

3.31087.012

87.0

0087.0

87.0)1(7.0)15//100(1210015

15

2

1

1

1

11

22

12

2

22

75

030.0

Co

B

T

T

Cm

Ir

rI

Vr

V

Ig

11

11

11

75

9.2

0344.0

Co

B

T

T

Cm

Ir

kI

Vr

V

Ig


Shunt-seriescurrent Mixing – current samplingAmplifier: Current Amplifier Feedback network: hybrid parameters

02

222

01

111

2

1

2221

1211

2

1

1

2

v

i

i

vg

v

ig

i

v

gg

gg

v

i

LRsR

11

1

g

22g


1

1

111

//4.13//13//

)10//4.3(

)]10//4.3)(1//(//10[

)10//4.3(

rkkR

vi

kkr

kkrhrkvg

kkr

vi

i

iA

si

e

efeom

e

co

i

o

fE

E

o

fv RR

R

i

i

i

ig

2

20

2

112 1

1cv


oof

fe

oeo

iif

si

RAR

h

krkkrR

A

RR

rkkRR

)1(

1

10//)10//4.3(

1

)//4.13//13//(

12

1

neglect

Microelectric Circuits by Meiling CHEN 1 Lecture 14 Feedback.

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Transcript of Microelectric Circuits by Meiling CHEN 1 Lecture 14 Feedback.