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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
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9.1 The General Feedback Structure
Feedback amplifierSignal-flow diagram of a feedback amplifier
Open-loop gain:A
Feedback factor:
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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)
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)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
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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
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)(|)()(|)()()( 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
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-
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
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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
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The feedback amplifier is stable only ifdoes not exceed a maximum value