Chapter 8 - Feedback

1 - Desensitize The Gain

2 - Reduce Nonlinear Distortions

3 - Reduce The Effect of Noise

4 – Control The Input And Output Impedances

5 – Extend The Bandwidth Of The Amplifier

The General Feedback Structure

xs xi xf xo

A

xo A xi

xi xs xf

xf xo

Af

xo

xs

A

1 A

A 1 A

feedabck factor loop gain amount of feedabck

x fA

1 A x s

The General Feedback Structure

MATLAB / SIMULINK

Anyone interested to put together an Introduction to MATLAB / Simulink PowerPoint Presentation plus some examples?

The General Feedback Structure

Exercise 8.1

Af 10 A 104

a ) R1

R1 R2

b ) AfA

1 A

1

given

AfA

1 A

Find 0.1

R1

R1 R20.1

R2

R19

Amount_Feedback 20 log 1 A c )

Amount_Feedback 60

Vs 1 Vo Af Vs Vo 10d )

Vf Vo Vf 0.999

Vi Vs Vf Vi 10 104

e ) A 0.8 104

AfA

1 A Af 9.998

10 9.99810

100 0.02

The General Feedback Structure

Exercise 8.1

Some Properties of Negative Feedback

Gain Desensitivity

AfA

1 A

deriving

dAfdA

1 A ( )2

dividing by AfA

1 A

dAf

Af

1

1 A ( )

dA

A

The percentage change in Af (due to variations in some circuit parameter) is smaller than the pecentage cahnge in A by the amount of feedback. For this reason the amount of feedback

1 A

is also known as the desensitivity factor.

Some Properties of Negative Feedback

Bandwidth Extension

High frequency response with a single pole

A s( )AM

1s

H

AM denotes the midband gain and H the upper 3-dB frequency

Af s( )A s( )

1 A s( )

Af s( )

AM

1 AM

1s

H 1 AM

Hf H 1 AM Lf

L

1 AM

Some Properties of Negative Feedback

Noise Reduction, Reduction of Nonlinear Distortion

Read and discuss in class

The Four Basic Feedback Topologies

Voltage Amplifiers (V/V)

Current Amplifiers (I/I)

Transconductance Amplifiers (I/V)

Transresistance Amplifiers (V/I)

The four basic feedback topologies:

(a) voltage-sampling series-mixing (series-shunt) topology;

(b) current-sampling shunt-mixing (shunt-series) topology;

(c) current-sampling series-mixing (series-series) topology;

(d) voltage-sampling shunt-mixing (shunt-shunt) topology.

The Four Basic Feedback Topologies

The Four Basic Feedback Topologies

Voltage AmplifiersVCVSInput Resistance HighOutput Resistance LowFeedback sample the output voltageVoltage-sampling series-mixing

Current Amplifiers

Transconductance Amplifiers

Transresistance Amplifiers

The Shunt-Series Feedback Amplifier

The Ideal Situation

The series-shunt feedback amplifier:

(a) ideal structure; (b) equivalent circuit.

AfVo

Vs

A

1 A

RifVs

Ii

Vs

Vi

Ri

RiVs

Vi Ri

Vi A Vi

Vi

Rif Ri 1 A

Zif s( ) Zi s( ) 1 A s( ) s( )

Z of s( )Z o s( )

1 A s( ) s( )

The Shunt-Series Feedback Amplifier

The Practical Situation

Derivation of the A circuit and circuit for the series-shunt feedback amplifier.

(a) Block diagram of a practical series-shunt feedback amplifier.

(b) The circuit in (a) with the feedback network represented by its h parameters.

(c) (c) The circuit in (b) after neglecting h21.

The Shunt-Series Feedback Amplifier

Summary

For Finding the A Circuit for a given series-shunt feedback amplifier.

The Shunt-Series Feedback Amplifier

Example 8.1

AVo'

Vi'

RL R1 R2( )[ ]

RL R1 R2

RL R1 R2( )[ ]

RL R1 R2ro

Rid

Rid RsR1 R2

R1 R2

Rif Ri 1 A Vf

Vo''

R1

R1 R2Ri Rs Rid

R1 R2R1 R2

Rin Rif RsAf

Vo

Vf

A

1 A

RofRo

1 A

Ro

roRL R1 R2( )RL R1 R2

roRL R1 R2( )RL R1 R2

The Shunt-Series Feedback Amplifier

Exercise 8.4

The Series-Series Feedback Amplifier

The Ideal Case

The Series-Series Feedback Amplifier

The Ideal Practical Case

The Series-Series Feedback Amplifier

For Finding the A Circuit for a given series-series feedback amplifier

The Series-Series Feedback Amplifier

Example 8.2

The Series-Series Feedback Amplifier

Example 8.2

The Series-Series Feedback Amplifier

Example 8.2Gain of the first stage

Vc1

Vi1

1RC1 r2

RC1 r2

re1

RE1 RF RE2

RE1 RF RE2

Since Q1 is biased at 0.6mA, re1=41.7ohms

Q2 is biased at 1mA

r2

hfe

gm2

100

402.5kohms

substituting

1 0.99 RC1 9kohms RE1 100ohms

RF 640ohms RE2 100ohms

Vc1

Vi114.92

V

V

The Series-Series Feedback Amplifier

Example 8.2

The Shunt-Shunt and Shunt-Series Feedback Amplifiers

Shunt Configuration

The Shunt-Shunt and Shunt-Series Feedback Amplifiers

The Shunt-Shunt and Shunt-Series Feedback Amplifiers

Example 8.3

The Shunt-Series Feedback Amplifier

The Shunt-Series Feedback Amplifier

The Shunt-Series Feedback Amplifier

Example 8.4

The Shunt-Series Feedback Amplifier

Example 8.4

Determining Loop Gain

The Stability Problem and Margins

Closed-LoopTransfer Function

Nyquist

Root-Locus

Bode

Polar Plot

Af s( )A s( )

1 A s( ) s( )The Nyquist Plot intersects the negative real axis at 180. If this intersection occurs to the left of the point (-1, 0), we know that the magnitude of the loop gain at this frequency is greater than the unity and the system will be unstable. If the intersection occurs to the right of the point (-1,0) the system will be stable.It follows that if the Nyquist encircles the point (-1,0) the amplifier will be unstable.

The Stability Problem and Margins

Closed-LoopTransfer Function

Nyquist

Root-Locus

BodeMagnitude and Phase

Gain MarginPhase Margin - If at the frequency of unity loop-gain magnitude, the phase lag is in excess of 180 degrees, the amplifier is unstable.

The Nyquist Plot

w 100 99.9 100 j 1 s w( ) j w f w( ) 1

G w( )50 4.6

s w( )3

9 s w( )2 30 s w( ) 40

2 1 0 1 2 3 4 5 65

0

5

Im G w( )( )

0

Re G w( )( )

Effect of Feedback On The Amplifier Poles

Stability Study Using Bode Plots

w .1 .11 2 K 2 j 1

G w( )K

j w j w 1( ) j w 2( )

Bode1 w( ) 20 log G w( )

0 0.5 1 1.5 220

0

20

Bode1 w( )

w

Open Loop Bode Diagram

T w( )G w( )

1 G w( )

0 0.5 1 1.5 220

0

20

Bode1 w( )

w

T w( )G w( )

1 G w( )

Bode2 w( ) 20 log T w( )

0.5 1 1.5 220

10

0

10

Bode2 w( )

w

Closed-Loop Bode Diagram

Frequency Compensation

Spice Simulation Examples