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Chapter #10: Feedback
from Microelectronic Circuits Text
by Sedra and Smith
Oxford Publishing
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Introduction
 IN THIS CHAPTER YOU WILL LEARN
 The general structure of the negative-feedback amplifier and
the basic principle that underlies its operation.
 The advantages of negative feedback, how these come about,
and at what cost.
 The appropriate feedback topology to employ with each of the
four amplifier types: voltage, current, trans-conductance, and
trans-resistance.
 Why and how negative-feedback amplifiers may be unstable
(i.e. oscillate) and how to design the circuit to ensure stable
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Introduction
 Most physical systems incorporate some sort of
feedback.
 Although theory of negative feedback was developed by
electrical engineers.
 Harold Black with Western Electric Company
 Feedback can be negative (degenerative) or positive
(regenerative).
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Introduction
 Feedback may be used to:
 desensitize the gain
 reduce nonlinear distortion
 reduce the effect of noise
 control the input and output resistances
 extend bandwidth
 These characteristics result, however, in loss of gain.
 “The basic idea of negative feedback is to trade-off gain for
other
desirable
properties.”
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Introduction
 Under certain conditions, negative feedback can be
come positive.
 This causes oscillation.
 However, positive feedback does not always lead to
instability.
 Regenerative feedback has a number of applications –
specifically, in active filtering.
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10.1. The General
Feedback Structure
 Figure 10.1. shows the basic structure of a feedback
amplifier – signal-flow diagram.
 Open-loop amplifier has gain A (xo = Axi).
Figure
10.1:
General
the feedback amplifier. This is a signal-flow
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diagram,
and the
quantities
x represent either voltage or current signals.
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10.1. The General
Feedback Structure
 Output (xo) is fed to load as well as feedback network.
 Feedback factor (b.) defines feedback signal (xf).
 Feedback signal (xf) is subtracted from input (xi).
 This characterizes negative feedback.
 Gain of feedback amplifier is defined in (10.4).
 Note that (10.4) may be approximated at 1/b..
 As such, gain of feedback amplifier is almost entirely
determined by feedback network.
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10.1. The General
Feedback Structure
xo
A
(eq10.4) gain with feedback: Af  
xi 



1   Ab  

loop 
gain 

amount of
feedback
(eq10.5) if assumed that Ab  1: Af 
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1
b
10.1. The General
Feedback Structure
Equations (10.1) through
(10.3) may be obtained from
(10.6) and (10.7).
Ab
xs
1  Ab

Ab
(eq10.7) input signal: xi  x s  x f  x s 
xs
1  Ab
(eq10.6) feedback signal: x f 

Ab 
(eq10.6) input signal: xi   1 
 xs
 1  Ab 
 1 
(eq10.6) input signal: xi  
 xs
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 1  Ab 
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10.2. Some
Properties of
Negative Feedback
 10.2.1. Gain De-sensitivity
 Equations (10.8) and (10.9) define de-sensitivity
factor of (1+Ab.).
 10.2.2. Bandwidth Extension
 Equations (10.10) through (10.13) demonstrate how
3-dB frequencies may be shifted via negative
feedback.
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10.2. Some
Properties of
Negative Feedback
 10.2.3. Interference Reduction
 Signal-to-interference ratio (S/I = Vs/Vn)
 Equations (10.14) through (10.16) define this value.
 Power supply hum
 Pre-amplification
 10.2.4. Reduction in Nonlinear Distortion
 Negative feedback may facilitate linearization.
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to-interference ratio in amplifiers.
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10.3. The Four Basic
Feedback Topologies




10.3.1. Voltage Amplifiers
10.3.2. Current Amplifiers
10.3.3. Trans-conductance Amplifiers
10.3.4. Trans-resistance Amplifiers
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10.3.1. Voltage
Amplifiers
 voltage amplifiers – accept input voltage and yield
output voltage.
 VCVS
 Thevenin Output
 voltage-mixing / voltage-sampling – is the topology
most suitable for voltage amps.
 Is also known as series-shunt feedback.
 Provides high input resistance/low output resistance.
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Figure
10.6: Block diagram of a feedback voltage amplifier. Here the appropriate
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feedback topology is series–shunt.
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10.3.1. Voltage
Amplifiers
 Increased input resistance results because Vf subtracts
from Vs, resulting in smaller signal Vi at the input.
 Low Vi causes input current to be smaller.
 This effects higher input resistance.
 Decrease output resistance results because feedback
works to keep Vo as constant as possible.
 DVo and DIo change / vary together.
 This effects lower output resistance.
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Figure
10.7: Examples of a feedback voltage amplifier. All these circuits employ
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series–shunt
feedback. Note that the dc bias circuits are only partially shown.
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
10.3.2. Current
Amplifiers
 current amplifier – accepts input current to generate
output current.
 CCCS
 Norton Source
 current-mixing / current-sampling – topology is most
suitable for current amps.
 Is also known as shunt-series feedback.
 Provides low input resistance/high output resistance.
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Figure 10.8: (a) Block diagram of a feedback current amplifier. Here, the
appropriate
feedback topology is the shunt–series. (b) Example of a feedback
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current amplifier.
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10.3.3.
Transconductance
Amplifiers
 transconductance amplifier – accepts input voltage and
generates output current.
 VCCS
 Norton Source Output
 voltage-mixing / current-sampling – topology is most
suitable for transconductance amps.
 Is also known as series-series feedback.
 Provides high input resistance/high output resistance.
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Figure 10.10: (a) Block diagram of a feedback transconductance amplifier. Here,
theTheappropriate
feedback topology is series–series. (b) Example of a feedback
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transconductance amplifier. (c) Another example.
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10.3.4. Transresistance
Amplifiers
 transresistance amplifier – accepts input current and
generates output voltage.
 CCVS
 Thevenin Source Output
 current-mixing / voltage-sampling – topology is most
suitable for current amps.
 Is also known as shunt-shunt feedback.
 Provides low input resistance/low output resistance.
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Figure 10.11: (a) Block diagram of a feedback transresistance amplifier. Here, the
appropriate
feedback topology is shunt–shunt. (b), (c), and (d) Examples of
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feedback transresistance amplifiers.
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10.4. The Feedback
Voltage Amplifier
 Series-shunt is appropriate feedback for voltage
amplifier.
 Unilateral open-loop amplifier (circuit A).
 Ideal Voltage-Sampling, voltage-mixing feedback
network (b circuit)
 Input resistance Ri
 Open Circuit Gain A
 Output resistance Ro
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Figure
feedback amplifier: (a) ideal structure; (b)
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equivalent circuit.
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10.4.1. The Ideal
Case
Vo
A
(10.17) closed-loop gain: Af  
Vs 1  Ab
Vs
Vi
(10.18) input current: Ii  
Ri 1  Ab  Ri
(10.19) input resistance: Rif  1  Ab  Ri
Vx
(10.20) output resistance: Rof 
Ix
Vx  AVi
(10.21) current-x: Ix 
Ro
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Figure
Determining
the output
resistance of the feedback amplifier of Fig.
The 10.13:
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10.12(a):
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(0195323033) Rof = Vx /Ix.
10.4.2. The Practical
Case
 In practical case, feedback network will not be ideal
VCVS.
 Actually, it is resistive and will load the amplifier.
 Source and load resistances will affect A, Ri, and Ro.
 Source and load resistances should be lumped with basic
amplifier.
 Expressed as two-port network.
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10.4.3. Summary
 1. Ri and Ro are the input and output resistances,
respectively, of the A circuit in Figure 10.15(a).
 2. Rif and Rof are the input and output resistances,
respectively, of the feedback amplifier, including Rs and
RL (see Figure 10.14a).
 3. The actual input and output resistances of the
feedback amplifier exclude Rs and RL. These are denoted
Rin and Rout in Figure 10.14(a) and can be determined via
equations (10.25) and (10.25).
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10.5. The Feedback
Transconductance
Amplifier
Figure 10.18: The series–series
feedback amplifier: (a) ideal
structure; (b) equivalent circuit.
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10.6. The Feedback
Transresistance
Amplifier
Figure 10.24: (a) Ideal structure for
the shunt–shunt feedback amplifier.
(b) Equivalent circuit of the amplifier
in (a).
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10.7. The Feedback
Current Amplifier
Figure 10.28: (a) Ideal structure for
the shunt–series feedback amplifier.
(b) Equivalent circuit of the amplifier
in (a).
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10.8. Summary of
Feedback Analysis
Method
 Always begin analysis by determining an approximate value for
the closed-loop gain (Af).
 Assume that loop gain Ab is large.
 Af = 1/b
 This value should serve for final check on Af.
 The shunt connection at input or output will always result in
reducing the corresponding resistance.
 In utilizing negative feedback to improve the properties of an
amplifier under design, the starting point is selection of feedback
topology.
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 The
Feedback
factor (b.) may be determined as 1/Af.
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10.9. Determining
Loop Gain
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10.10 The Stability
Problem
 In a feedback amplifier, the open loop gain (A) is
generally a function of frequency.
 Therefore, it should be called open-loop transfer
function A(s).
 One big question is: What happens to gain at higher
frequencies?
 This has huge implications on stability of the
amplifier.
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10.4.1. The Ideal
Case
A s
(10.81) closed-loop gain t-function: A f  s  
1  A  s β  s 
(10.82) closed-loop gain t-function: A f  j  
A  j 
1  A  j  β  j 
angle
(10.83) loop-gain: L  j   A  j  β  j   A  j  β  j  e jφw 
magnitude of gain
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10.4.2. Nyquist Plot
Figure 10.34: The Nyquist
plot of an unstable
amplifier.
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10.11. Effect of
Feedback on the
Amplifier Poles
Figure 10.35: Relationship
between pole location and
transient response.
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10.4.1. The Ideal
Case
(10.84) instantaneous voltage: v  t   e 0t ent  ent   2e 0t cos nt 
(10.85) feedback-ampflier pole constraint: 1  A  s  β  s   0
A0
(10.86) open-loop transfer function: A  s  
1  s / P
(10.87) closed-loop transfer function: A f  s  
A0 / 1  A0 b 
1  s / P 1  A0 b 
(10.88) pole: Pf  P 1  A0 b 
(10.89) closed-loop transfer function: A f  s  
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A0P
 A  s
s
10.11. Effect of
Feedback on the
Amplifier Poles
Figure
10.36: Effect of feedback on (a) the pole location and (b) the frequency
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response
of an amplifier having a single-pole, open-loop response.
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10.12. Stability
Study Using Bode
Plots
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Summary
 Negative feedback is employed to make the amplifier gain less
sensitive to component variations; to control input and output
impedances; to extend bandwidth; to reduce nonlinear distortion;
and to enhance signal-to-interference ratio.
 The advantages above are obtained at the expense of a reduction
in gain and at the risk of the amplifier becoming unstable (that is,
oscillating). The latter problem is solved by careful design.
 For each of the four basic types of amplifier, there is an
appropriate feedback topology. The four topologies, together
with their analysis procedures, are summarized in Table 10.1.
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Summary
 The key feedback parameter are the loop gain (Ab.), which for
negative feedback must be a positive dimensionless number, and
the amount of feedback (1+Ab.). The latter directly determines
gain reduction, gain desensitivity, bandwidth extension, and
changes in input and output resistances.
 Since A and b are in general frequency dependent, the poles of
the feedback amplifier are obtained by solving the characteristic
equation 1+A(s)b(s) = 0.
 For the feedback amplifier to be stable, its poles must all be in the
left-hand side of the s-plane.
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Summary
 Stability is guaranteed if at the frequency for which the phase
angle of Ab is 180O, |Ab| is less than unity; the amount by which it
is less than unity, expressed in decibels, is the gain margin.
Alternatively, the amplifier is stable if, at the frequency at which
|Ab| = 1, the phase angle is less than 180O, the difference ifs the
phase margin.
 The stability of a feedback amplifier can be analyzed by
constructing a Bode plot for |A| and superimposing it on a plot for
1/|b|. Stability is guaranteed if the two plots intersect with a
difference in slope no greater than 6dB/decade.
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Summary
 To make a given amplifier stable for a given feedback factor b, the
open-loop frequency response is suitably modified by a process
known as frequency compensation.
 A popular method for frequency compensation involves
connecting a feedback capacitor across an inverting stage in the
amplifier. This causes the pole formed at the input of the
amplifier stage to shift to a lower frequency and thus become
dominant, while the pole formed at the output of the amplifier
stage is moved to a very high frequency and thus becomes
unimportant. This process is known as pole splitting.
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