EE105 Fall 2007 Lecture 25, Slide 1 Prof. Liu, UC Berkeley

Lecture 25

OUTLINE• Feedback– General considerations– Benefits of negative feedback– Sense and return techniques– Voltage-voltage feedback

Reading: Chapter 12.1-12.2,12.4,12.6.1

ANNOUNCEMENTS• Reminder: Prof. Liu’s office hour is cancelled on Tuesday 12/4

EE105 Fall 2007 Lecture 25, Slide 2 Prof. Liu, UC Berkeley

Negative Feedback System• A negative feedback system consists of four components:

1) feedforward system, 2) sense mechanism, 3) feedback network, and 4) comparison mechanism.

• Closed loop transfer function:1

1

1 KA

A

V

V

X

Y

EE105 Fall 2007 Lecture 25, Slide 3 Prof. Liu, UC Berkeley

Negative Feedback Example• The amplifier is the feedforward system, R1 and R2 provide the

sensing and feedback capabilities, and comparison is provided by differential input to the amplifier.

121

2

1

1 ARR

RA

V

V

X

Y

EE105 Fall 2007 Lecture 25, Slide 4 Prof. Liu, UC Berkeley

Comparison Error• As A1K increases, the difference between the input and fed

back signal decreases, i.e. the fed back signal becomes a good replica of the input.

KA

VE X

11E

EE105 Fall 2007 Lecture 25, Slide 5 Prof. Liu, UC Berkeley

Comparison Error Example

2

11R

R

V

V

X

Y

EE105 Fall 2007 Lecture 25, Slide 6 Prof. Liu, UC Berkeley

Loop Gain

test

N

V

VKA 1

• The loop gain is the product of the gain of the feedforward system (A1) and the feedback factor (K). It can be interpreted to be the gain if a signal “goes around the loop,” i.e. if we break the loop at an arbitrary location, then apply a test voltage at one end and determine the voltage that comes out at the other end, with the input grounded:

0XV

EE105 Fall 2007 Lecture 25, Slide 7 Prof. Liu, UC Berkeley

Benefit #1: Gain Desensitization• A large loop gain is needed to achieve a precise gain, one that

does not depend on A1, which can vary by ±20%.

11 KAKV

V

X

Y 1

EE105 Fall 2007 Lecture 25, Slide 8 Prof. Liu, UC Berkeley

Ratio of Resistor Values• If two resistors are built using the same unit resistor, then the

ratio of their resistances does not change with variations in the fabrication process and the circuit operating temperature. Thus, the ratio of two resistances can be more precisely controlled than the open loop gain (A1) of an amplifier.

EE105 Fall 2007 Lecture 25, Slide 9 Prof. Liu, UC Berkeley

Example

DmRgA 1Dm

Dm

in

out

RgRR

RRg

v

v

21

21

Open Loop Gain Closed Loop Gain

EE105 Fall 2007 Lecture 25, Slide 10 Prof. Liu, UC Berkeley

Desensitization to Load Variation

3/DmDm RgRg Dm

Dm

Dm

Dm

RgRR

RRg

RgRR

RRg

21

2

21

2 31

w/o FeedbackLarge Difference

with FeedbackSmall Difference

EE105 Fall 2007 Lecture 25, Slide 11 Prof. Liu, UC Berkeley

Benefit #2: Bandwidth Enhancement• Although negative feedback lowers the gain by (1+KA1), it

increases the bandwidth by the same factor.

0

01

1jA

jA

00

0

0

11

1

KAjKAA

jV

V

X

Y

Open Loop Closed Loop

Negative Feedback

EE105 Fall 2007 Lecture 25, Slide 12 Prof. Liu, UC Berkeley

Bandwidth Enhancement Example• As the loop gain increases, the low-frequency gain decreases

and the bandwidth increases.

EE105 Fall 2007 Lecture 25, Slide 13 Prof. Liu, UC Berkeley

Benefit #3: Modification of I/O Impedances

Dmm

in RgRR

R

gR

21

211

min gR

1

Open Loop Closed Loop

EE105 Fall 2007 Lecture 25, Slide 14 Prof. Liu, UC Berkeley

Modification of I/O Impedances (cont’d)

Dm

Dout

RgRR

RR

R

21

21

Open Loop Closed Loop

Dout RR

EE105 Fall 2007 Lecture 25, Slide 15 Prof. Liu, UC Berkeley

Benefit #4: Linearity Improvement

w/o feedback

with feedback

EE105 Fall 2007 Lecture 25, Slide 16 Prof. Liu, UC Berkeley

Sensing a Voltage • In order to sense a voltage across two terminals, a voltmeter

with ideally infinite impedance is used.

EE105 Fall 2007 Lecture 25, Slide 17 Prof. Liu, UC Berkeley

Sensing and Returning a Voltage • Similarly, for a feedback network to correctly sense the output

voltage, its input impedance needs to be large.• R1 and R2 also provide a means to return the voltage.

– To return a voltage, the output impedance of an ideal feedback network should be small.

21 RR

FeedbackNetwork

EE105 Fall 2007 Lecture 25, Slide 18 Prof. Liu, UC Berkeley

Example: Sense and Return • R1 and R2 sense and return the output voltage to the

feedforward network consisting of M1, M2, M3, and M4.

• M1 and M2 also act as a voltage comparator.

EE105 Fall 2007 Lecture 25, Slide 19 Prof. Liu, UC Berkeley

Example (cont’d)

)||(1

)||(

21

2OPONmN

OPONmN

in

out

rrgRR

Rrrg

V

V

EE105 Fall 2007 Lecture 25, Slide 20 Prof. Liu, UC Berkeley

Input Impedance with Feedback • Negative feedback raises the input impedance.

)1( 0KARI

Vin

in

in

EE105 Fall 2007 Lecture 25, Slide 21 Prof. Liu, UC Berkeley

Output Impedance with Feedback• Negative feedback lowers the output impedance.

01 KA

R

I

V out

X

X

EE105 Fall 2007 Lecture 25, Slide 22 Prof. Liu, UC Berkeley

Example

mNoPoNmN

oPoNclosedout gR

R

rrgRR

Rrr

R1

11 2

1

21

2,

EE105 Fall 2007 Lecture 25, Slide 23 Prof. Liu, UC Berkeley

Summary: Benefits of Negative Feedback

1) Gain desensitizationto variations in gm, RD, RL

2) Bandwidth enhancementby the factor (1 + loop gain)

3) Modification of I/O impedances– Rin is increased by the factor (1 + loop gain)

– Rout is decreased by the factor (1 + loop gain)

4) Linearity improvement– Gain is more uniform for different signal levels.