Lect 12 FeedbackII

7/17/2019 Lect 12 FeedbackII

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EE4340 / EECT 5340

Analog IC Analysis and Design– Fall 2014

Topic 12. Feedback II

Jin Liu Ph.D.

ProfessorUT Dallas





Page 3

Feedback Topologies

vs

vo

Here shows some examples on the four configurations.

1. Series-Shunt Feedback (V-to-V Feedback)

vS

vfb

ve

RS

RL vOForward

Amplifier

Feedback

NetworkSeries- Shunt Feedback

(V-to-V Feedback)



Page 4

Feedback Topologies

iSvO

2. Shunt-Shunt Feedback (V-to-I Feedback)

iS ifb

ie

RSRL vO

Forward Amplifier

FeedbackNetwork

Shunt - Shunt Feedback

(V-to-I Feedback)





Page 6

Feedback Topologies

iS

vO

iO

4. Shunt-Series Feedback (I-to-I Feedback)

The classification can be easily done by observing the feedback network.

iSifb

ie

RS RL vOForward

Amplifier

FeedbackNetwork

Shunt-Series Feedback

(I-to-I Feedback)

iO

iO



Page 7

Ideal Feedback

Ideal Feedback

The ideal feedback, which means that the feedback network

does not load the forward amplifier (no loading effect),

is introduced in this section.



Page 8

Series-Shunt Feedback

Voltage Voltage

Forward Amplifier

Feedback Network

vi ve

fvo

Ro

Ave

RL vo

vo

Rin

A series-shunt feedback network senses output vol tage

signal and feeds back vol tage signal . Thus, f is a voltage-

to-vol tage parameter . In addition, it is noted that A is voltage

gain (i.e. voltage-to-voltage gain).

0

O

L

R

or

R

F d A lifi



Page 9


f A

A

v

v

A

v Av )f A(

)v f v ( Av Av

i

o

cl

i o

oi eo

1

1

f A

R R

)f A( R R

f A

A

v

v

A

oocl

inincl

i

o

cl

1

1

1:Summary

f A

R R

R

)v f ( Av

v

R / )v Av (

v

i

v R

oocl

o

oo

o

oeo

ov

o

oocl i

1

0

1. Closed-Loop Gain

2. Closed-Loop Input Resistance

)f A( R R

)f A /( f A

R

R / )v f v (

v

i

v

R

inincl

in

inoi

i

i

i

incl

1

11

3. Closed-Loop Output Resistance

Voltage Voltage

Forward Amplifier

Feedback Network

vi ve

fvo

Ro

Ave

RL vo

vo

Rin



Page 10

Shunt-Shunt Feedback

Current Voltage

Forward Amplifier

Feedback Network

ii

i e

fvo

Rin Ro

AieRL vo

vo

RS

A shunt-shunt feedback network senses output vol tagesignal and feeds back current signal . Thus, f is a

vo ltage-to-current parameter . In addition, it is noted

that A is transresistance (i.e. current-to-voltage gain).

0

O

L

R

or

R

Forward Amplifier



Page 11


f A

A

i

v

A

v f Ai A

)v f i ( Ai Av

i

o

cl

oi

oi eo

1

f A

R R

)v f ( Av

v R R

R / )i Av (

v

i

v R

oocl

oo

ooocl

oeo

oi

o

oocl i

1

0

1. Closed-Loop Gain



f A

R R

f A

A

A

R

i A

R v R

i

R i

i

v

R

in

in

i

inoincl

i

ine

i

i incl

incl

1

1

f A

R R

)f A(

R R

f A

A

i

v A

oocl

inincl

i

ocl

1

1

1

:Summary

Current Voltage

Forward Amplifier

Feedback Network

ii

i e

fvo

Rin Ro

AieRL vo

vo

RS



Page 12

Series-Series Feedback

Voltage Current

Forward Amplifier

Feedback Network

vi

ve

fio

RinRo

Ave

RL vo

io

io

A series-series feedback network senses output current

signal and feeds back vol tage signal . Thus, f is a current-

to-vol tage parameter . In addition, it is noted that A is

transconductance (i.e. voltage-to-current gain).

O

L

R

or

R 0





Page 14


Current Current

Forward Amplifier

Feedback Network

ii

ie

fio

RinRo

Aie

RL vo

io

io

io

A shunt-series feedback network senses outpu t current

signal and feeds back current signal . Thus, f is a

cu rrent-to-current parameter . In addition, it is noted that A

is current gain (i.e. current-to-current gain).

O

L

R

or

R 0

Forward Amplifieri i



Page 15


f A

R

f Ai

v

i Af i v R

R

i f i

v

i

v R

in

e

i

ee

i incl

o

oe

i

i

i incl

11

1

For oi

o

oocl

ooo

ooo

ooeo

i

o

oocl

R )f A( i

v R

R / v i )f A( R / v )i f ( A

R / v i Ai

i

v R

i

i

1

1

0

0

1. Closed-Loop Gain



f A

A

i

i A

i f A / i i f i i

i Ai

i

ocl

oooei

eo

1

and

oocl

inincl

i

ocl

R )f A( R

f A

R R

f A A

i i A

1

1

1:Summary

Current Current

Forward Amplifier

Feedback Network

ii

ie

fio

RinRo

Aie

RL vo

io

io

io



Page 16

Extra Knowledge of Shunt and Series toResistance

A series connection increases the total resistance while a

shunt (parallel) connection decreases the total resistance.

RB

R A

R A RB

R A

RB

Series

Shunt



Page 17

Loading Effect

In the previous section, the four configurations are derived in

ideal case. In reality, the feedback network is resistive (or

capacitive/inductive), and it will load the forward amplifier at

both input and output. This is known as loading effect. Although the feedback network considered in these lecture

notes is resistive, it is still tedious to evaluate the closed-loop

gain, input resistance, and output resistance by nodal

analysis. Instead, in this section, shortcuts for the fourfeedback configurations are introduced. In addition, an

example for each feedback configuration will be given.



Page 18


The h-parameter

representation of a two-port



Page 19




Page 20


Rf Short!Output of

Feedback

Network

Input of

Feedback

Network

Feedback

Network

1. Input Loading R f (h 11f )

Shor t the input of the feedback network and calculate

the output resistance of the feedback network (series

loading ).



Page 21


2. Output Loading R L f (h 22 f )

Open the output of the feedback network and calculate

the input resistance of the feedback network (parallel

loading ).

RLf Open!

Output of

Feedback

Network

Input of

Feedback

Network

Feedback

Network



Page 22


Vf 'Open!

Output of

Feedback

Network

Input of

Feedback

Network

FeedbackNetwork

Vo'

i = 0

3. Feedback Factor f (h 12f )

The feedback factor f can be obtain by applying a test

voltage vo’ at the input of the feedback network and

measuring the open circuit voltage vf ’ at the output of

the feedback network.

' v

' v f

o

f



Page 23


4. Open-Loop Small Signal Parameters with Loading

With the loading Rf in series with the input and RLf in

parallel with the output of the forward amplifier, the open-

loop small-signal parameters including A’ (open-loop gain),

Rin’ (open-loop input resistance), and Ro’ (open-loop

output resistance) with loading can be determined.

Forward

Amplifier Vi'

Rin'Rf

Ro'

RLf RL

Vo'



Page 24


f ' A

' R R

)f ' A( ' R R f ' A

' A

v

v A

o

ocl

inincl

i

ocl

1(3)

1(2)1

(1)

5. Closed-Loop Small Signal Parameters with Loading

Finally, the closed-loop small-signal parameters including

Acl (close-loop gain), Rincl (closed-loop input resistance),

and Rocl (closed-loop output resistance) with loading can

be obtained by the following equations.



Page 25

Series-Shunt Feedback-Example

vi

vov1

RoRin

R1R2

RL Av1

Forward Amplifer

Feedback

Network

The amplifier is now with a resistive feedback network and

the feedback network is the loading of both the input and

output. Since it is a series-shunt feedback (sense voltage

signal and feed back voltage signal), the loadings of the

input an output can be found as shown below.

vs

vo



Page 26


Rf

R1

R2Short!

Feedback Network

Rf = R1 // R2

RLf

R1

R2Open!

Feedback Network

RLf = R1 + R2

Vo'R1

R2

Open!

Feedback Network

Vf '

i=0

21

2

R R

R

' v

' v f

o

f

The feedback factor f can be found as shown below.



Page 27


With the loading to the input (series) and the output (parallel), theopen-loop parameters can be obtained from the following figure.

Av1

Forward Amplifier

Vi'Rf

Rin'

V1

Rin

RLRLf

Ro

Ro'

Vo'

2121

21

R // R R

R

R )R R //( R

)R R //( R A

R R

R

R R // R

R // R A

' v

' v ' A

in

in

oL

L

f in

in

oLf L

Lf L

i

o

The open-loop gain is



Page 28

While the open-loop input resistance is


21 R // R R R R ' R inf inin

)R R ( // R // R R // R // R ' R LoLf Loo 21

And the open-loop output resistance is

Finally, the closed-loop gain is

21

2

2121

21

2121

21

1

1

R R

R

R // R R

R

R )R R //( R

)R R //( R A

R // R R R

R )R R //( R )R R //( R A

f ' A

' A

v

v A

in

in

oL

L

in

in

oL

L

i

ocl



Page 29

While the closed-loop input resistance is


21

2

2121

2121 1

1

R R

R

R // R R

R

R )R R ( // R

)R R ( // R AR // R R

)f ' A( ' R R

in

in

oL

Lin

inincl

21

2

2121

21

21

11R R

R R // R R

R R )R R ( // R )R R ( // R A

)R R ( // R // R

f ' A

' R R

in

in

oL

L

Looocl

And the closed-loop output resistance is



Page 30


The y-parameter

representation of a two-port



Page 31




Page 32


Rf Short!Output of

FeedbackNetwork

Input of

FeedbackNetwork

FeedbackNetwork

1. Input Loading R f (1/y 11f )

Short the input of the feedback network and calculate the

output resistance of the feedback network (paral lel

loading ).



Page 33


2. Output Loading R L f (1/y 22 f )

Short the output of the feedback network and calculate the

input resistance of the feedback network (paral lel

loading ).

RLf Short!

Output of

FeedbackNetwork

Input ofFeedback

Network

FeedbackNetwork



Page 34


' v

' i f

o

f

3. Feedback Factor f (y 12 f )


voltage vo’ at the input of the feedback network and

measuring the open circuit voltage if ’ at the output of the

feedback network.

Vf ’=0Short!

Output of

Feedback

Network

Input of

Feedback

Network

Feedback

NetworkVo’

If '



Page 35



With the loading Rf in parallel with the input and RLf in

parallel with the output of the forward amplifier, the open-

loop small-signal parameters including A’ (open-loop gain),

Rin’ (open-loop input resistance), and Ro’ (open-loop output

resistance) with loading can be determined.

Forward Amplifier Vi’

Rin’

Rf

Ro’

RLf RL

Vo’Iin’



Page 36


f ' A

' R R )(

)f ' A(

' R R )(

f ' A

' A

i

v A )(

oocl

in

incl in

o

cl

13

12

11



Acl (closed-loop gain), Rincl (closed-loop input resistance),

and Rocl

(closed-loop output resistance) with loading can




Page 37

Shunt-Shunt Feedback-Example

VCC VCC

RCRC

RF RF

RS

RS

vo vo

vi

iin = vi/RS

The amplifier is now with a resistive feedback network and thefeedback network is the loading of both the input and the

output. Since it is a shunt-shunt feedback (sense voltage

signal and feed back current signal), the input voltage vi is

Nortonized to a current signal iin, where iin = vi / RS.



Page 38


The loadings of the input and output can be found as shownbelow.

Short! vo'RF

if '

F o

f

R v

i f

1

'

'


Short!

Rf

RF

Rf = RF

Short!

RLf

RF

RLf = RF

Feedback NetworkFeedback Network



Page 39


With the loadings to the input (parallel) and the output (parallel),the open-loop parameters can be obtained by the following

figure.

RS Rf

RLf RCiin'

vo'


)R // R // r ( )r // R // R ( g

)R // R // r ( )r // R // R ( g ' i ' v ' A

F C of Sm

Lf C of Sm

in

o

while the open-loop input resistance is

r // R // R r // R // R ' R F Sf Sin



Page 40


F C oLf C oo R // R // r R // R // r ' R and the open-loop output resistance is

Finally, the closed-loop gain is

F F C oF Sm

F C oF Sm

in

o

cl R / )R // R // r ( )r // R // R ( g

)R // R // r ( )r // R // R ( g

f ' A

' A

i

v

A

11

F F C oF Sm

F S

incl R / )R // R // r ( )r // R // R ( g

r // R // R R

1

F F C oF Sm

F C oocl

R / )R // R // r ( )r // R // R ( g

R // R // r R

1

while the closed-loop input resistance is

and the closed-loop output resistance is



Page 41


The z-parameter

representation of a two-

port





Page 43


Feedback

Network

Rf Open!

Output of

FeedbackNetwork

Input of

FeedbackNetwork

1. Input Loading R f (z 11f )

Open the input of the feedback network and calculate the

output resistance of the feedback network (series

loading ).



Page 44


2. Output Loading R L f (z 22f )

Open the output of the feedback network and calculate

the input resistance of the feedback network (series

loading ).

Feedback

NetworkRLf Open!

Output of

Feedback

Network

Input of

Feedback

Network



Page 45


' i

' v f

o

f

3. Feedback Factor f (z 12f )


voltage io’ at the input of the feedback network and

measuring the open circuit voltage vf ’ at the output of the

feedback network.

Feedback

Networkv f ’Open!

Output of

Feedback

Network

Input of

Feedback

Network

i o’

i = 0



Page 46



With the loading Rf in series with the input and RLf in series

with the output of the forward amplifier, the open-loop

small-signal parameters including A’ (open-loop gain), Rin’

(open-loop input resistance), and Ro’ (open-loop output


Forward

Amplifier

Rin’

Rf

Ro'

RLf

RL

vo’v i’

io



Page 47


)'1(')3(

)'1(')2('1

')1(

f AR R

f AR R f A

Av i A

oocl

inincl inocl



Acl (open-loop gain), R

incl (closed-loop input resistance),

and Rocl (closed-loop output resistance) with loading can




Page 48

Series-Series Feedback-Example

VCC

RC1 RC3RC2

vo

vi RoclQ1 Q3Q2

io

RE1 RE2

RF

The amplifier is now with a

resistive feedback network

and the feedback network is

the loading of both the inputand output. It is a series-

series feedback (sense

current signal and feed back

voltage signal).



Page 49


Rf RLf

RE1 RE2

RF

RE1RE2

RFOpen!Open!

Rf = RE1 // (RE2+RF) RLf = RE2 // (RE1+RF)

RE1RE2

RFOpen!Vf ’

i = 0

io’

The loadings of the input and output can be found as shownbelow.


F E E

E E

o

f

R R R

R R

' i

' v f

21

21



Page 50


With the loadings to the input

(series) and the output (series),

the open-loop parameters can

be obtained by the figure to the

right.

VCC

RC1 RC3RC2

vo’

vi’ Ro’

Q1 Q3Q2

io’

Rf RLf



Page 51

Finally, the closed-loop small-signal parameters are


Lf m

mLf C m

f m

C m

i

o

R g

g R )( r // R g

R g

)r // R ( g

' v

' i ' A

3

3322

1

211

11

1

f in R )( r ' R 11

)R // r ( R r

R r g

r ' R C oLf

Lf m

oo223

33

3 1

)f ' A( ' R R

)f ' A( ' R R f ' A

' A

v

i A

oocl

inincl

in

ocl

1

11


where r o is assumed to be large and is neglected, while

the open-loop input resistance is

and the open-loop output resistance is



Page 52


The g-parameter

representation of a two-

port



Page 53




Page 54


Feedback

Network

Rf Open!

Output of

Feedback

Network

Input of

Feedback

Network

1. Input Loading R f (1/g 11f )

Open the input of the feedback network and calculate the

output resistance of the feedback network (paral lel

loading ).



Page 55


2. Output Loading R Lf (g 22f )

Short the output of the feedback network and calculate the

input resistance of the feedback network (series loading).

FeedbackNetwork

RLf Short!Output ofFeedbackNetwork

Input ofFeedback

Network





Page 57



With the loading Rf in parallel with the input and RLf in

series with the output of the forward amplifier, the open-loop

small-signal parameters including A’ (open-loop gain), Rin’

(open-loop input resistance), and Ro’ (open-loop output


Forward Amplifier

Rin’

Rf

Ro’

RLf RL vo’vi’

io

iin'



Page 58


)f ' A( ' R R )(

f ' A

' R R )(

f ' A

' A

i

i A )(

oocl

in

incl in

o

cl

13

12

11

5. Closed-Loop Small Signal Parameters with Loading Finally, the closed-loop small-signal parameters including

Acl (open-loop gain), Rincl (closed-loop input resistance), and

Rocl (closed-loop output resistance) with loading can be

obtained by the following equations.



Page 59

Shunt-Series Feedback-Example

VCC

RC1 RC2

vo

Rocl

Q1

Q2

io

RE

RF

RSiin

The amplifier is now with aresistive feedback network

and the feedback network is

loading of both the input and

output. It is a shunt-series

feedback (sense current

signal and feed back current

signal).



Page 60


The loadings of the input and output can be found asshown below.

Short!

RLf RLf = RE // RF

RF

RE

Open!

Rf Rf = RE + RF

RF

RE


F E

E

o

f

R R

R

' i

' i f

io’

if ’

RF

RE

Short!



Page 61


With the loadings to the

input (shunt) and the output

(series), the open-loop

parameters can be obtainedby the figure to the right.

VCC

RC1 RC2

vo’

Q1

Q2

io’

RERSiin’ Rf



Page 62



Lf m

mLf oC F Sm

in

o

R g

g R )( r // r // R )R // R // r ( g

' i

' i ' A

2

221111

11

F Sin R // R // r ' R 1

)r // R ( R r

R r g r ' R

oC Lf

Lf moo

112

222 1

)f ' A( ' R R

f ' A

' R R

f ' A

' A

i

i A

oocl

inincl

in

ocl

1

11

Finally, the closed-loop small-signal parameters are

and the open-loop output resistance is

while the open-loop input resistance is



Input Resistance of a Voltage Source of Shunt-



For the current source, and so .

Thus, for voltage source, the closed – loop input resistance is

VCC

RC

RF voRincl R1

RSiin

VCC

RC

RF vo

RSvin

R = RS+R1

p gSeries/Shunt-Shunt Feedback

1R // R R Sincl

In either shunt-series or shunt-shunt feedback, the input resistance is

with respect to a current source. When the input source is reversal

Nortonized to a voltage source, the input resistance is different.

incl S

incl S

R R

R R R

1

RR

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