Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •

Analog IC Analysis and Design 8- Chih-Cheng Hsieh

Feedback

CHAPTER 8

1


Outline

2

1. General Consideration

2. Feedback Topologies

3. Effect of Loading

4. Effect of Feedback on Noise


General Consideration

• H(s) : Feedforward network (Represents an amplifier)

• G(s) : Feedback network (β, feedback factor, freq. independent)

• X(s) – G(s)Y(s) : The input to H(s), also called feedback error

• H(s) : open loop transfer function

• Y(s)/X(s) : closed loop transfer function

3

( ) ( )( ) ( )[ ( ) ( ) ( )],

( ) 1 ( ) ( )

Y s H sY s H s X s G s Y s

X s G s H s


General Consideration

• In a well designed negative feedback system, the error term is minimized, making the output G(s) an accurate copy of the input.

• Input of H(s) as “virtual ground”.

• Four elements in the feedback system – The feedforward amplifier.

– A means of sensing the output.

– The feedback network.

– A means of generating the feedback error.

4


Properties of Feedback Circuits

• Gain Degeneration

• Terminal Impedance Modification

• Bandwidth Modification

• Nonlinearity Reduction

5

Analog IC Analysis and Design 8- Chih-Cheng Hsieh 6

1. Desensitize the gain : • make gain less sensitive to variations.

2. Reduce nonlinear distortion : • make gain independent of signal level.

3. Reduce effect of noise : • minimize unwanted signal contribution to output.

4. Control the input and output impedance : • use feedback to control impedance.

5. Extend bandwidth of the amplifier.

Negative Feedback properties :

The basic idea of negative feedback is to trade off gain for other desirable properties, like increased input impedance, extended bandwidth… etc.

Properties of Feedback Circuits


Terminologies

7

Signal-flow diagram

1. Open-loop Gain : 2. Feedback Factor : 3. Loop Gain : 4. Amount of Feedback : 5. Closed-Loop Gain :

A

A1 A

/ (1 )fA A A

o ix Axf ox x i s fx x x

1

of

s

x AA

x A

11, fA A

1f s s

Ax x x

A

10

1i sx x

A

1. Af is almost determined by β and independent of A, that is, the process variation. 2. β can be implemented by passive component and accurate, predictable, stable. 3. xi : negative feedback reduces the input signal of the basic Amp by (1+Aβ )

Comparison circuit (Mixer)


Gain Desensitization

• Gain desensitization

Compared to gm1 ro1, this gain can be controlled with much higher accuracy

because it is given by the ratio of two capacitors – gain desensitization.

8

Poor definition of the gain : both gm1 and ro1 vary with process and temperature.

For the CS amplifier with feedback (C1 & C2)

The overall voltage gain of the circuit at low freq. such that C2 does not load the output node

1 1( ) m oA v g r

sCVVsCVV inXXout 12

1

2

2

1

111

2

11

/1

/1

111

1

sC

sC

C

C

rgC

C

rg

V

V

OmOm

in

out

X

1)( 11 om

X

out rgV

VvA


Gain Desensitization

• In a feedback system, the closed-loop gain is much less sensitive to device parameters than the open-loop gain is.

• The closed loop gain varies by a small percentage even if the open loop gain A varies a lot if the loop gain (βA) >> 1.

• The higher the loop gain (βA), the less sensitive Y/X will be to variations in A. – We begin with a high-gain amplifier and apply feedback to obtain a low, but

less sensitive closed-loop gain.

9

1 if 11

11

1

A

AA

A

X

Y


Loop Gain

• Calculation of loop gain – Set the main input to zero.

– Break the loop at some point.

– Inject a test signal in the right direction.

– Obtain the value that returns to the break point.

10

21 1

1 2

,t m O F

CV g r V

C C

2

1 1

1 2

Fm O

t

V Cg r A

V C C


• The input resistance without feedback

• Consider the input resistance with feedback, as

• The Loop gain

Input Impedance Modification

• Common gate circuit with feedback (capacitive voltage divider).

11

1 1 ,out m mb X DV g g V R 1 11 1

1 2 1 2

( ) ,P out m mb X D

C CV V g g V R

C C C C

21

11122 )(

CC

CRVgggI DXmbmmM

11 1 2 1 1

1 2

( ) ( ) ,X m mb X m m mb D X

CI g g V g g g R V

C C

,

12

1 1

1 2

1 1/

1 m D

in closed X X

m mb

RC

g Rg

C

Ig

C

V

1

, 1 1( )in open m mbR g g

12

1 2

m D

Cg R A

C C

,

1

1in open

AR


Loop Gain

• The feedforward amplifier : M1 and RD (A= )

• Output sensed by C1 and C2.

• The feedback network : C1, C2 and M2 (β= )

• The subtraction occurs in the current domain at the input terminal.

• Loop gain =

12

12

1 2

m

Cg

C C

12

1 2

, ( )outD m

t

VCA R g A

C C V

DR

A


Output Impedance Modification

• Common source stage with feedback.

• Common source stage: M1, RS and RD.

• Feedback network sense the Vout, returning a current equal to

• To find the output resistance at relatively low frequencies

13

2

21

1moutgV

CC

C

11 2 1

2 1 11 2 1

1 1 1 1 1 2

, , 1 1

11

S X X D DD X m X D

m S m mb DD XS

m mb m mb S

RC V V R RI V g I I

g R g g RC C R I ACR

g g g g R C C


Bandwidth Modification

• Suppose the feedforward amplifier has a one-pole transfer function

• The transfer function of the closed loop system is

• The -3dB bandwidth has increased by a factor , albeit at the cost of a proportional reduction in the gain.

• If A is large, the closed loop gain remains approximately equal to

14

0 0

0 0 0

00

0 0 00

1 / 1( )

1 1111 /

A A

s A AYs

A s sXA

As

0

0

( )1 /

AA s

s

01 A

1/


Bandwidth Modification Example

• Suppose we need to amplify a 20-MHz square wave by a factor of 100 and maximum bandwidth but we have only a single-pole amplifier with an open loop gain of 100 and -3 dB bandwidth of 10 MHz.

(a) With open-loop amplifier, the risetime and falltime is long:

(b) Placing two of the amplifiers with feedback in cascade to achieve the same gain. The power dissipation is doubled.

15

nsf dB

162

1

3


Types of Amplifiers • Circuits sensing a voltage must exhibit a high Zin (as a voltmeter),

circuits sensing a current must provide a low Zin ( as a current meter).

• Circuits generating a voltage must exhibit a low Zout (as a voltage source), circuits generating a current must provide a high Zout (as a current source).

16


Amplifiers with Improved Performance

• The basic circuits may not provide adequate performance in many applications.

• Use modified circuits to alter the output impedance or increase the gain.

17


Sense and Return Mechanisms

• Four type of feedback : voltage-voltage (series-shunt), voltage-current (shunt-shunt), current-current (shunt-series), and current voltage (series-series).

• The first entry in each case denotes the quantity sensed at the output and the second the type of signal returned to the input.

• To sense a current, a current meter is inserted in series with the signal.

• The addition of the feedback signal and the input signal can be performed in the voltage domain or current domain.

18

Sensing a voltage by a voltmeter

Sensing a current by a current meter

Sensing a current by a small resistor


Return Mechanisms

• To add two quantities, we place them in series if they are voltages and in parallel if they are current.

• The feedback network in reality introduces loading effects that must be taken into account.

19

Voltage mode addition

Current mode addition


Practical Examples

• Voltage can be sensed by a resistive / capacitive divider in parallel with the port.

• A current can be sensed by placing a resistor in series with the wire and sensing the voltage across it.

• To subtract two voltages, a differential pair or a single transistor can be used.

20


Sense and Return Mechanism

• Subtraction of currents can be accomplished as follows.

• In summary

– For voltage subtraction, the input and feedback signals are applied to two distinct nodes.

– For current subtraction, they are applied to a single node.

– It help to identify the type of feedback

21


Outline

22






Voltage-Voltage (V-V) Feedback

• Voltage-voltage feedback (series - shunt)

– samples the output voltage and returns the feedback signal as a voltage.

• The feedback network is connected in parallel with the output and in series with the input port.

• An ideal feedback network in this case exhibits infinite input impedance and zero output impedance.

23

outinoutFineoutF VVAVVVVVV 0 0

0

1 A

A

V

V

in

out

21

2

RR

R


Effect of V-V Feedback on Rout

• If the amplifier is loaded by a resistor RL

– Consider a voltage amplifier without feedback (open-loop configuration), the output would drop in proportional to

– Consider a feedback amplifier, if loop gain remains much greater than unity

– The circuit stabilizes the output voltage amplitude despite load variations, it behaves as a voltage source, thus exhibiting a low output impedance.

24

0

001

/ A

R

I

V RVAVIVAVVVVV out

X

XoutXXXXMXeXF

/ ( )L L outR R R

/ 1/out inV V


Effect of V-V Feedback on Rin

• For the open loop Amp, the Rin of the FF Amp sustains the entire Vin.

• For the closed loop Amp, the Rin of the FF Amp sustains only a fraction of Vin .

• The I(Rin) in the FB topology is less than that in the open-loop system.

• Returning a voltage quantity to the input increases the input impedance.

25

01 ARI

Vin

X

X

inXXFXeinXFinXe RIAVVVVRIAVRIV 00

inXXinX RIAVRI 0


Current-Voltage (I-V) Feedback

• Sense the output current to perform feedback. (series – series)

• The current is usually sensed by placing a small resistor in series with the output and using the voltage across the resistor as the feedback information.

• The feedback factor β (RF) .

• An ideal FB network in this case exhibits zero input and output impedance .

• The loop gain = Gm RF.

26

, , outF F t out m F t m F

t

IV R I I G R I G R

I

, , F F out e in F out out m in F outV R I V V R I I G V R I Fm

m

in

out

RG

G

V

I

1


Rin/Rout of I-V Feedback Amplifier

• Output resistance of a current-voltage feedback amplifier

• Input resistance of a current-voltage feedback amplifier

27

XFF IRV

outXXmXF RVIGIR /

Fmout

X

X RGRI

V 1

outmXin IGIR

inXFmXe RIRGVV

Fmin

X

X RGRI

V 1


Voltage-Current (V-I) Feedback

• The output voltage is sensed and a proportional current is returned to the summing point at the input. (shunt – shunt)

• The feedforward path incorporates a transimpedance amplifier with gain R0 .

• The feedback factor has a dimension of conductance.

• The feedback network ideally exhibiting infinite input and output impedance.

• The Loop gain : gmFR0

28

outmFineout VgIRIRV 00FineoutmFF IIIVgI 0

0

1 Rg

R

I

V

mFin

out


Rin/Rout of V-I Feedback Amplifier • Rin of a voltage-current feedback amplifier.

• The Rin of R0 is placed in series because an ideal transimpedance amplifier exhibits a zero input impedance.

• Output impedance of a voltage-current feedback amplifier.

29

/ inXXF RVII FmFinX IgRRV 0/

mF

in

X

X

gR

R

I

V

01

XmFMFemFXF VgRVIIgVI 0

/ / 0 outXmFXoutMXX RVRgVRVVI

1 0Rg

R

I

V

mF

out

X

X


Current-Current (I-I) Feedback

• The feedforward amplifier is characterized by a current gain AI . (shunt – series)

• The feedback network by a current ratio β.

• The closed loop current gain is

• The input resistance is

• The output resistance is

30

1 i

iif

A

AA

i

iif

A

RR

1

1 outiof RAR


Outline

31






Two-Port Network Models

32

For voltage-voltage feedback (G)

For voltage-current feedback (Y) For current-voltage feedback (Z)

For current-current feedback (H)

2221212

2121111

IZIZV

IZIZV

2221212

2121111

VYVYI

VYVYI

2221212

2121111

VHIHI

VHIHV

2221212

2121111

IGVGV

IGVGI


Loading in V-V Feedback

• If A0 is large, the signal amplified by A0 is much greater than the contribution of G12I2.

33

1 0211

11

1

11

22

1

11

1

11

22

0

AGZG

G

GZ

Z

ZG

G

GZ

ZA

V

V

outin

in

outin

in

in

out

out

outin

inoutin

in

inoutine

VZG

GA

GZ

ZVGV

GZ

ZVGVV

1

11

1

110

22

21

22

21

1

11 22

0 21 0

If , 0,

/ / (1 )out in

G G

V V A G A


Loading in a V-V Feedback Circuit

• If we define the open-loop gain in the presence of loading as

34

• The finite input and output impedances of the feedback network reduces the output voltage and the voltages seen by the input of the main amplifier.

01

11

1

11

22

, AZG

G

GZ

ZA

outin

inopenv

• G11 is obtained by leaving the output of the feedback network open.

• G22 is calculated by shorting the input of the feedback network.

• Consider the loading effect

2

111

1 0I

IG

V

1 21,

,

GA

A

V

V

openv

openv

in

out

1

222

2 0V

VG

I


Example of V-V Feedback

35

2

111

1 0I

IG

V

1

222

2 0V

VG

I

1

222

2 0

||S F

V

VG R R

I

2

1111

1 0

S F

I

IG R R

V

2

221

1 0

S

S FI

RVG

V R R

1, 2 2

1

{ [ || ( )]} || 1/

Dv open m D F S

F S m

RA g R R R

R R g

,

,

21 ,1

v open

v closed

v open

AA

G A


Loading in I-V Feedback

• Replacing the feedback network by a Z model, and neglect the source Z12I2

• The loaded open loop gain is equal to

36

out

out

outm

in

inoutin I

ZZ

ZG

ZZ

ZIZV

1122

21

21

1122

1122

1 ZGZZ

Z

ZZ

Z

GZZ

Z

ZZ

Z

V

I

m

out

out

in

in

m

out

out

in

in

in

out

1122

, m

out

out

in

inopenm G

ZZ

Z

ZZ

ZG


Loading in V-I Feedback

• Replacing the feedback network by a Y model, and neglect the source Y12V2


37

211

11

1

1101

22

1

22

1

11

1

1101

22

1

22

1 YZY

YR

ZY

Y

ZY

YR

ZY

Y

I

V

outin

outin

in

out

out

outin

outin VZY

YR

ZY

YVYI

1

11

1

1101

22

1

2221

01

11

1

11

1

22

1

22,0 R

ZY

Y

ZY

YR

outin

open


Example of V-I Feedabck

38

1

222

2 0

1/ ,F

V

IY R

V

2

111

1 0

1/ ,F

V

IY R

V

2

221

1 0

1/ ,F

V

IY R

V

0, ( || ) ( || ) outopen S F m F D

N open

VR R R g R R

I

0,

0,

21 0,

( || ) ( || )

1 1 ( || ) / ( )

open S F m F Dclosed

open m F D S S F

R R R g R RR

Y R g R R R R R

0, ( || ) ( || ) 1 1

1 ( || ) / ( )

closedout out S F m F D

in N S S S m F D S S F

RV V R R g R R

V I R R R g R R R R R


Loading in I-I Feedback

• Replacing feedback network by an H model. Neglecting the effect of H12 V2


39

out

out

outI

in

outin IZH

ZA

ZH

HIHI

11

1

22

1

2221

21

11

1

22

1

22

11

1

22

1

22

1 HZH

ZA

ZH

H

ZH

ZA

ZH

H

I

I

out

outI

in

out

outI

in

in

out

out

outI

in

openIZH

ZA

ZH

HA

11

1

22

1

22,


Summary of Loading Effects • The analysis is carried out in three steps

– Open the loop with proper loading and calculate the open-loop gain AOL, and the open-loop input and output impedances.

– Determine the feedback ratio β and hence the loop gain βAOL.

– Calculate the closed-loop gain and input and output impedances by scaling the open loop values by a factor of 1+ βAOL

40


Outline

41






Effect of Feedback on Noise

• Feedback does not improve the noise performance of circuits.

• Assume the open-loop voltage amplifier A1 is characterized by only an input-referred noise voltage and the feedback network is noiseless.

• In practice, the feedback network itself may contain resistors or transistors, degrading the overall noise performance.

42

1

11

1

A

AVVVVAVVV ninoutoutnoutin


Effect of Feedback on Noise

• As

43

1 , , , , ,, whereas 0Sn in closed n RD n in open

D

RA V V V

R

1

1

1

,1, , 1

1 1

1, ,

, 1

1

1 , 1

1 1

, 1

D

xin x x m

s

m in Dx o X

Sm

s

n Ro m Dn in closed S

in m S D mclosed

o m Dn in open

in m Sopen

VV V A V g

R

g AV RV V V

Rg A

R

VV g R AV A R

V g R A A R g

VV g R AV

V g R

,

1

1Dn R

S

D m

RA R g

x

Documents

Feedback - ee.nthu.edu.twVoltage-Voltage (V-V) Feedback • Voltage-voltage feedback (series - shunt) –samples the output voltage and returns the feedback signal as a voltage. •