Electronics Ch9

7/29/2019 Electronics Ch9

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CHAPTER 9 FEEDBACK

Chapter Outline9.1 The General Feedback Structure

9.2 Some Properties of Negative Feedback

9.3 The Four Basic Feedback Topologies

9.10 The Stability Problem9.11 Effect of Feedback on the Amplifier Poles

NTUEE Electronics L.H. Lu 9-1


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9.1 The General Feedback Structure

Feedback amplifierSignal-flow diagram of a feedback amplifier

Open-loop gain:A

Feedback factor:


Amount of feedback: 1 + A

Gain of the feedback amplifier (closed-loop gain):

Negative feedback:

The feedback signalxfis subtracted from the source signalxsNegative feedback reduces the signal that appears at the input of the basic amplifier

The gain of the feedback amplifierAfis smaller than open-loop gainAby a factor of (1+A)

The loop gainAis typically large (A>>1):

The gain of the feedback amplifier (closed-loop gain)Af 1/

The closed-loop gain is almost entirely determined by the feedback networkbetter accuracy ofAfxf=xs(A)/(1+A) xs error signalxi =xsxf

A

A

x

xA

s

of

1


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ExampleThe feedback amplifier is based on an opamp with infinite input resistance and zero output resistance

(a) Find an expression for the feedback factor.

(b) Find the condition under which the closed-loop gainAf is almost entirely determined by the feedback network.

(c) If the open-loop gainA = 10000 V/V, findR2/R1 to obtain a closed-loop gainAfof 10 V/V.

(d) What is the amount of feedback in decibel?

(e) If Vs = 1 V, findVo, VfandVi.(f) If A decreases by 20%, what is the corresponding decrease inAf?



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9.2 Some Properties of Negative Feedback

Gain desensitivityThe negative reduces the change in the closed-loop gain due to open-loop gain variation

Desensitivity factor: 1+A

Bandwidth extensionHigh-frequency response of a single-pole amplifier:

A

dA

AA

dA

A

dAdA

f

f

f

1

1

)1( 2

)1(/1

)1/()(

/1)(

MH

MMf

H

M

As

AAsA

s

AsA

- -

Negative feedback:

Reduces the gain by a factor of (1+AM)

Extends the bandwidth by a factor of (1+AM)


)1/(

)1/()()(

ML

MMf

L

M

As

AAsA

s

sAsA


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Interference reductionThe signal-to-noise ratio:

The amplifier suffers from interference introduced at the input of the amplifier

Signal-to-noise ratio: S/I= Vs/VnEnhancement of the signal-to-noise ratio:

Precede the original amplifierA1by a clean amplifierA2 Use negative feedback to keep the overall gain constant

2

21

1

21

210

11A

V

V

I

S

AA

AV

AA

AAVV

n

sns



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Reduction in nonlinear distortionThe amplifier transfer characteristic is linearized through the application of negative feedback

= 0.01

A changes from 1000 to 100


5001.01001

100

9.9001.010001

1000

1

1

f

f

A

A


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9.3 The Four Basic Feedback Topologies

Voltage amplifiersThe most suitable feedback topologies is voltage-mixing and voltage-sampling one

Known as series-shunt feedback

Example:



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Current amplifiersThe most suitable feedback topologies is current-mixing and current-sampling one

Known as shunt-series feedback

Example:



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Transconductance amplifiersThe most suitable feedback topologies is voltage-mixing and current-sampling one

Known as series-series feedback

Example:



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Transresistance amplifiersThe most suitable feedback topologies is current-mixing and voltage-sampling one

Known as shunt-shunt feedback

Example:



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9.10 The Stability Problem

Transfer function of the feedback amplifierTransfer functions:

Open-loop transfer function:A(s)

Feedback transfer function:(s)

Closed-loop transfer function:Af(s)

For physical frequencies s =j

)()(1)()(

ssAsAsAf

1

)()(

A

jAjAf

Loop gain:Stability of the closed-loop transfer function:

For loop gain smaller than unity at 180:

Becomes positive feedback

Closed-loop gain becomes larger than open-loop gain

The feedback amplifier is still stable For loop gain equal to unity at 180:

The amplifier will have an output for zero input (oscillation)

For loop gain larger than unity at 180:

Oscillation with a growing amplitude at the output


)(|)()(|)()()( jejjAjjAjL


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The Nyquist plotA plot used to evaluate the stability of a feedback amplifier

Plot the loop gain versus frequency on the complex plane

Stability:

The plot does not encircle the point (-1, 0)



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9.11 Effect of Feedback on the Amplifier Poles

Stability and pole locationConsider an amplifier with a pole pair at

The transient response contains the terms of the form )cos(2][)( 00 teeeetv nttjtjt nn

njs 0



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Poles of the feedback amplifierCharacteristic equation: 1+A(s)(s) = 0

The feedback amplifier poles are obtained by solving the characteristic equation

Amplifier with single-pole response

The feedback amplifier is still a single-pole system

)1(/1

)1/(

)(/1)( 0

000

As

AA

sAs

A

sA Pf

P

)1( 0APPf


-

The bandwidth is extended by feedback at the cost of a reduction in gainUnconditionally stable system (the pole never enters the right-half plane)


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Amplifier with two-pole responseFeedback amplifier

Still a two-pole system

Characteristic equation

The closed-loop poles are given by

)(1

)()(

)/1)(/1()(

11

0

sA

sAsA

ss

AsA f

PP

0)1()( 210212

PPPP Ass

2102

2121 )1(4)(2

1)(

2

1PPPPPP As


The plot of poles versus is called a root-locus diagramUnconditionally stable system (the pole never enters the right-half plane)


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Amplifier with three or more polesRoot-locus diagram


The feedback amplifier is stable only ifdoes not exceed a maximum value

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Electronics Ch9