E ② chapter one - feedback amplifier

COLLEGE OF ENGINEERING AND TECHNOLOGY
Department of Electrical and Computer Engineering
Target Group: 2nd Year ECEg Students
Prepared By:- Ashenafi Paulos (MSc.)
March, 2016
Program: Regular
Course Code: ECEg 2113
Course Title: Applied Electronics II
WOLKITE UNIVERSITY

Chapter-One
Feedback amplifiers
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Preview
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In this chapter, we will:
 Introduce feedback concepts and discuss, in general terms,
advantages and disadvantages of using feedback in electronic
circuits.
 Derive the transfer function of the ideal feedback system and
determine a few characteristics of the feedback system.
 Analyze the four ideal feedback circuit configurations and
determine circuit characteristics including input and output
resistances.
 Derive the loop-gain stability of ideal and practical feedback
circuits.

1.1 INTRODUCTION TO FEEDBACK
Objective: Introduce feedback concepts and discuss, in
general terms, a few advantages and disadvantages of
using feedback in electronic circuits.
 In a feedback system, a signal that is proportional to the
output is fed back to the input and combined with the input
signal to produce a desired system response.
 Feedback can be either negative or positive.
In negative feedback, a portion of the output signal is
subtracted from the input signal; and used for applications
include amplifiers, linear voltage regulators and filters.
For example, tends to maintain a constant value of amplifier
voltage gain against variations in transistor parameters, supply
voltages, and temperature.
In positive feedback, a portion of the output signal is added
to the input signal.
Positive feedback is used in the design of oscillators and in a
number of other applications include voltage comparators, flip-
flops, and timing circuits. 4

1.1.1 Advantages and Disadvantages of Negative Feedback
 Advantages:
Gain sensitivity.
Bandwidth extension.
Noise sensitivity.
Reduction of nonlinear distortion.
Control of impedance levels.
 Disadvantages:
 Circuit gain.
 Stability.
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1.2 BASIC FEEDBACK CONCEPTS
Objective: Analyze and obtain the transfer function of the ideal
feedback system, and determine a few characteristics (advantages)
of the feedback system.
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Figure 1.1 Basic configuration
of a feedback amplifier
• The circuit contains a basic amplifier
with an open-loop gain A and a
feedback circuit that samples the output
signal and produces a feedback signal
Sfb.
• The feedback signal is subtracted from
the input source signal, which produces
an error signal Sε.
• The error signal is the input to the basic
amplifier and is the signal that is
amplified to produce the output signal.
In the diagram,
• The various signals S can be either
currents or voltages.

1.2.1 Ideal Closed-Loop Signal Gain
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From the above figure, the output signal is
where A is the amplification factor, and the
feedback signal is
where β in this case is the feedback transfer
function.1 At the summing node, we have
where Si is the input signal. The first equation
then becomes
So, it can be rearranged to yield the closed-
loop transfer function, or gain, which is
The above equation can be written
where T = β A is the loop gain.
For negative feedback, we assume T to be a
positive real factor.
Combining the first two equations, we
obtain the loop gain relationship
Normally, the error signal is small, so
the expected loop gain is large. If the
loop gain is large so that β A>>1,
then,

Cont’d
 The feedback circuit is usually composed of passive
elements, which means that the feedback amplifier gain is
almost completely independent of the basic amplifier
properties, including individual transistor parameters.
 Since the feedback amplifier gain is a function of the
feedback elements only, the closed-loop gain can be
designed to be a given value.
 The individual transistor parameters may vary widely, and
may depend on temperature and frequency, but the
feedback amplifier gain is constant.
 The net results of negative feedback is stability in the
amplifier characteristics.
 In general, the magnitude and phase of the loop gain are
functions of frequency, and they become important when
we discuss the stability of feedback circuits.
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Problems Associated With Positive Feedback
 Positive feedback:
 Let A= -10; β= 0.099. Af= -104.
 Let A= -9.9; β= 0.099. Af= -901.
 1% change of A causes 91% change of Af.
 Negative feedback:
 Let A= 104; β= 0.01. Af= 100.
 Let A= 9000; β= 0.01.Af= 98.9.
 10% change of A causes 1% change of Af.
 Conclusion: Positive feedback increases the gain, but the gain
is unstable. In contrast negative feedback decreases the gain
and stabilizes it.
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Af–closed-loop gain;
A–open-loop gain;
Aβ–loop gain;
If Aβ> 0 –negative feedback;
if Aβ< 0 –positive feedback.

Quize
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Q_1
Two feedback configurations are shown in Figures (a) and (b) below. The closed-loop
gain in each case is Av f = vo/vi = 50. (a) Determine β1 and β2 for the two circuits. (b)
The gain A2 decreases by 10 percent in both circuits. Using the results of part (a),
determine the percent change in the closed-loop gain for each circuit. (c) What
conclusion can be made as to the “better” feedback configuration?
(a) (b)

Cont’d
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Q-2
The noninverting op-amp configuration shown in Fig. (a) below provides a direct
implementation of basic configuration of a feedback amplifier.
(a) Assume that the op amp has infinite input resistance and zero output resistance.
Find an expression for the feedback factor β. Ans.
(b) Find the condition under which the closed-loop gain is almost entirely determined
by the feedback network.
(c) If the open-loop gain A = 10000V/V, find β to obtain a closed-loop gain Af of 10
V/V.
(d) What is the amount of feedback in decibels?
(a) A non-inverting op-amp circuit
for basic configuration of a
feedback amplifier.
(b) The circuit in (a) with the amp replaced
with its equivalent circuit.

1.2.2 Some Properties of Negative Feedback
Gain Sensitivity
 If the loop gain T = β A is very large, the overall gain of the feedback
amplifier is essentially a function of the feedback network only.
 If the feedback transfer function β is a constant, then taking the
derivative of Af with respect to A:
 Or
 Dividing both sides of the above equation by the closed-loop gain
yields:
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Cont’d
 The above equation shows that the percent change in the closed-loop
gain Af is less than the corresponding percent change in the open-loop
gain A by the factor (1 + β A).
 The change in open-loop gain may result from variations in individual
transistor parameters in the basic amplifier.
 The fractional change in amplification with feedback is divided by the
fractional change without feedback is called the sensitivity of the
transfer gain. The reciprocal of the sensitivity is called the desensitivity.
 Therefore, stability of the amplifier increases with increase in
desensitivity.
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= Fractional change in amplification with feedback
= Fractional change in amplification without feedback.
Where

Bandwidth Extension
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• It has been shown already that AVf = 1/ β , the gain of the amplifier with
feedback depends upon the feedback factor, β and independent of signal
frequency.
• Therefore, the voltage gain of the amplifier will be substantially constant
over a wide range of signal frequency.
• The negative feedback, thus improves the frequency response of the
amplifier. It can be proved mathematically that:
• It is clear that by applying negative feedback to an amplifier, bandwidth is
increased by a factor (1+βA).
Where BWf = bandwidth of amplifier with feedback
BW= bandwidth of amplifier without feedback

Noise Sensitivity
 In any electronic system, unwanted random and extraneous signals
may be present in addition to the desired signal. These random signals
are called noise.
 Electronic noise can be generated within an amplifier, or may enter the
amplifier along with the input signal.
 More precisely, feedback can help reduce the effect of noise generated
in an amplifier, but it cannot reduce the effect when the noise is part of
the input signal.
 It ca be proved mathematically that:
 It is clear that by applying negative feedback to an amplifier, noise is
reduced by a factor (1+βA).
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Where Nf = noise in amplifier with feedback
N= noise in amplifier without feedback

Reduction of Nonlinear Distortion
 Distortion in an output signal is caused by a change in the basic
amplifier gain or a change in the slope of the basic amplifier transfer
function.
 The change in gain is a function of the nonlinear properties of bipolar
and MOS transistors used in the basic amplifier.
 A smaller change in gain means less distortion in the output signal of
the negative feedback amplifier.
 Since transistors have nonlinear characteristics, distortion may appear
in the output signals, especially at large signal levels, such as
amplitude distortion, harmonic distortion and intermodulation
distortions.
 Negative feedback reduces this distortion.
 It is clear that by applying negative feedback to an amplifier distortion is
reduced by a factor (1+βA). 16
Where Df = distortion in amplifiers with feedback
D = distortion in amplifier without feedback

Control of Impedance Levels
 With the proper type of negative feedback circuit, the input and output
impedances can be increased or decreased.
 The effect of negative feedback on the input resistance depends upon the way in
which the output is feedback to the input.
 Of the out put voltage (or, current) is feedback in series with the input, the input
resistance increases. It can be proved mathematically that
 It is clear that by applying negative feedback to an amplifier, the input resistance
is increased by a factor (1+βA).
 As with the input resistance, the effect of negative feedback on the out put
resistance depends upon the way in which the output is feedback to input.
 If the output voltage is feedback to the input (either in series or shunt), the output
resistance decreases. It can be proved mathematically that:
 It is clear that by applying negative feedback to an amplifier, the output resistance
is decreased by a factor (1+βA).
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Where Rif = input resistance of amplifier with feedback and
Ri= input resistance of amplifier without feedback
Where ROf = output resistance of amplifier with feedback
RO= output resistance of amplifier without feedback

1.3 IDEAL FEEDBACK TOPOLOGIES
 Objective: Analyze the four ideal feedback circuit configurations
and determine circuit characteristics including input and output
resistances.
 There are four basic ways of connecting the feedback signal. Both voltage and
current can be fed back to the input either in series or parallel. Specifically, there
can be:
1. Voltage-series feedback (Fig. a).
2. Voltage-shunt feedback ( Fig. b).
3. Current-series feedback ( Fig. c).
4. Current-shunt feedback ( Fig. d).
 In the list above, voltage refers to connecting the output voltage as input to the
feedback network; current refers to tapping off some output current through the
feedback network.
 Series refers to connecting the feedback signal in series with the input signal
voltage;
 Shunt refers to connecting the feedback signal in shunt (parallel) with an input
current source.
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Cont’d
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Fig 1.2 Feedback amplifier types: (a) voltage-series feedback, Af = Vo/Vs; (b) voltage-
shun feedback, Af = Vo/Is; (c) current-series feedback, Af = Io/Vs; (d) current-shunt
feedback, Af = Io/Is.

Cont’d
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• Series feedback connections tend to increase the input resistance,
whereas shunt feedback connections tend to decrease the input
resistance.
• Voltage feedback tends to decrease the output impedance, whereas
current feedback tends to increase the output impedance.
• Typically, higher input and lower output impedances are desired for most
cascade amplifiers.
• Both of these are provided using the voltage-series feedback connection.

1.3.1 Gain with Feedback
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Table 1.1
The gain without feedback, A , is that of the amplifier stage. With feedback b, the
overall gain of the circuit is reduced by a factor (1+ βA ), as detailed below. A
summary of the gain, feedback factor, and gain with feedback of Fig. above is
provided for reference in Table below .

Voltage-Series Feedback
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• Figure a shows the voltage-series feedback connection with a part of the
output voltage fed back in series with the input signal, resulting in an
overall gain reduction.
• If there is no feedback (Vf = 0), the voltage gain of the amplifier stage is:
If a feedback signal V f is connected in series with the
input, then
Since
then
So that the overall voltage gain with feedback is:
• The above equation shows that the gain with feedback is the amplifier gain
reduced by the factor (1 + βA ).
• This factor will be seen also to affect input and output impedance among other
circuit features.

Voltage-Shunt Feedback
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• The gain with feedback for the network of Fig. b is:

1.3.2 Input Impedance with Feedback
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• The input impedance can be determined as follows:
• The input impedance with series feedback is seen to be the value of the
input impedance without feedback multiplied by the factor (1 + βA ), and
applies to both voltage-series and current-series configurations.

1.3.2 Input Impedance with Feedback
Voltage-Shunt Feedback
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• The input impedance can be determined as follows:
• This reduced input impedance applies to the voltage-shunt connection of
and the current-shunt connection.

1.3.3 Output Impedance with Feedback
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• The output impedance for the connections of any feedback amplifier
is dependent on whether voltage or current feedback is used.
• For voltage feedback, the output impedance is decreased, whereas
current feedback increases the output impedance.

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• The voltage-series feedback circuit of Fig. 14.3 provides sufficient circuit
detail to determine the output impedance with feedback.
• The output impedance is determined by applying a voltage V , resulting in
a current I , with V s shorted out (Vs = 0). The voltage V is then
For Vs = 0,
• The above equation shows that with voltage-series feedback the output impedance
is reduced from that without feedback by the factor (1 b A ).

Current-Series Feedback
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• The output impedance with current-series feedback can be determined by applying
a signal V to the output with Vs shorted out, resulting in a current I , the ratio of V to
I being the output impedance.
• The resulting output impedance is
determined as follows. With Vs 0,

Summary Of The Effect Of Feedback On Input And Output Impedance
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Table 1.2 Effect of Feedback Connection on Input and Output Impedance
• A summary of the effect of feedback on input and output impedance is provided
in Table 1.2 .

Cont’d
EXAMPLE 1.1 Determine the voltage gain, input, and
output impedance with feedback for voltage-series
feedback having A = -100, Ri = 10 k, and Ro = 20 k for
feedback of
(a) β=-0.1
(b) β=-0.5 and
(c) Give some conclusion standing from the results?
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E ② chapter one - feedback amplifier

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