FEEDBACK PRINCIPLES

The notes have been taken from the text books below
1. Robert Boylestad and Louis Nashlesky, Electronic Devices
and Circuit Theory, 11th ed. Pearson Education, Inc., 2011.
chapter 14
2. Adel S. Sedra and Kenneth C. Smith, Microlectronic
circuits, 6th ed. Ney York: Oxford University Press, 2010.
chapter 10
INTRODUCTION
• A feedback amplifier is one in which a fraction of the amplifier
output is fed back to the input circuit. This partial dependence of
amplifier input on its output helps to control the output. A
feedback amplifier consists of two parts: an amplifier and a
feedback circuit.
• Depending on the relative polarity of the signal being fed back
into a circuit, one may have negative or positive feedback.
Positive feedback
If the feedback voltage (or current) is so applied so as to increase
the input voltage (i.e. it is in phase with it), then it is called positive
feedback (regenerative or direct feedback). Since positive feedback
produces excessive distortion, it is seldom used in amplifiers.
However, because it increases the power of the original signal, it is
used in oscillator circuits.
Negative feedback
• If the feedback voltage (or current) is so applied so as to reduce
the amplifier input (i.e. it is 180° out of phase with it), then it is
called negative feedback (degenerative or inverse feedback).
Negative feedback is frequently used in amplifier circuits.
• Negative feedback results in decreased voltage gain, for which a
number of circuit features are improved as summarized on slide
5.
• A typical feedback connection is shown in Fig. 14.1 . The input
signal Vs is applied to a mixer network, where it is combined
with a feedback signal Vf . The difference of these signals Vi is
then the input voltage to the amplifier. A portion of the amplifier
output Vo is connected to the feedback network (𝛽), which
provides a reduced portion of the output as feedback signal to
the input mixer network.
If the feedback signal is of opposite polarity to the input signal, as
shown in Fig. 14.1, negative feedback results. Although negative
feedback results in reduced overall voltage gain, a number of
improvements are obtained, among them being:
1. Higher input impedance.
2. Better stabilized voltage gain.
3. Improved frequency response.
4. Lower output impedance.
5. Reduced noise.
6. More linear operation.
FEEDBACK CONNECTION TYPES
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. 14.2 a).
2. Voltage-shunt feedback ( Fig. 14.2 b).
3. Current-series feedback ( Fig. 14.2 c).
4. Current-shunt feedback ( Fig. 14.2 d).
• In the previous list, 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.
• 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. We shall therefore concentrate first on this
amplifier connection.
Gain with Feedback
• In this section we examine the gain of each of the feedback
circuit connections of Fig.14.2 . The gain without feedback, A ,
is that of the amplifier stage. With feedback 𝛽, 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. 14.2 is provided for reference in Table 14.1 .
Examples
• Example 14.1 demonstrates the trade-off of gain for
desired input and output resistance. Reducing the gain by
a factor of 11 (from 100 to 9.09) is complemented by a
reduced output resistance and increased input resistance
by the same factor of 11.
• Reducing the gain by a factor of 51 provides a gain of only
2 but with input resistance increased by the factor of 51
(to over 500 k) and output resistance reduced from 20 k to
under 400 .
• Feedback offers the designer the choice of trading away
some of the available amplifier gain for other desired
circuit features.
Reduction in Frequency Distortion
• For a negative-feedback amplifier having 𝛽𝐴 ≫ 1, the gain with
feedback is 𝐴𝑓 ≅ 1/𝛽. It follows from this that if the feedback
network is purely resistive, the gain with feedback is not
dependent on frequency even though the basic amplifier gain
is frequency dependent.
• Practically, the frequency distortion arising because of varying
amplifier gain with frequency is considerably reduced in a
negative-voltage feedback amplifier circuit.
Reduction in Noise and Nonlinear Distortion
• Signal feedback tends to hold down the amount of noise signal
(such as power-supply hum) and nonlinear distortion. The
factor ( 1 + 𝛽𝐴 ) reduces both input noise and resulting
nonlinear distortion for considerable improvement. However,
there is a reduction in overall gain (the price required for the
improvement in circuit performance).
Noise Reduction
Consider the open loop system below

𝑉𝑛

𝑉𝑠 𝑉𝑜
𝐴1 + 𝐴2

𝑉𝑜 = 𝑉𝑠 𝐴1 𝐴2 + 𝑉𝑛 𝐴2
Now let us consider a closed loop system
𝑉𝑛

𝑉𝑠 𝑉𝑜
+ 𝐴1 + 𝐴2
_

𝛽
Noise Reduction
𝑉𝑠 𝐴1 𝐴2 𝑉𝑛 𝐴2
𝑉𝑜 = 1+𝐴1 𝐴2 𝛽
+ 1+𝐴 𝐴 𝛽
1 2

When compared to the open loop system, noise 𝑉𝑛 in the feedback

1
loop system is modified by a factor 1+𝐴 𝐴 𝛽 This is called the
1 2
disturbance rejection.
Whenever a disturbance occurs in a closed loop control system, it is
reduced by a factor 1 + 𝐴𝛽 where A is the forward path transfer
function (gain) and 𝛽 is the feedback function. This is an advantage
of closed loop/feedback systems over open loop control systems in
modifying the effect of disturbances. Disturbances in the system can
originate from various causes e.g. defects within components of the
system, noise, external sources, friction, defects in measurement
systems.
Gain desensitivity/stability with feedback
Recall the equation of the feedback gain:
𝐴
𝐴𝑓 = 1+𝐴𝛽
(1)

Assume that β is constant. Taking differentials of both sides of

Eq. (1) with respect to A results in:

𝑑𝐴
𝑑𝐴𝑓 = (2)
(1+𝐴𝛽)2

Dividing equation (2) by equation (1) (i.e) dividing both sides by

𝐴𝑓 gives
dAf 1 dA

Af (1  A ) A (3)
• Equation 3 says that the percentage change in Af (due to variations in some circuit
parameter) is smaller than the percentage change in A by the amount of feedback. For
this reason the amount of feedback, is also known as the desensitivity factor.
• The quantity 𝛃𝐀 in all derived equations is called the loop gain while the quantity 1
+ 𝐴𝛽, is called the amount of feedback
Example
If an amplifier with gain of −1000 and feedback of 𝛽 = −0.1 has a gain change of 20%
due to temperature, calculate the change in gain of the feedback amplifier.
𝑑𝐴𝑓 1 𝑑𝐴 1
= = ∗ 0.2 = 0.00198 ≈ 0.2%
𝐴𝑓 1 + 𝛽𝐴 𝐴 1 + (−0.1 ∗ −1000)

Thus, whereas the amplifier gain changes from 𝐴 = 1000 by 20%, the gain with
feedback changes from 𝐴𝑓 = 10 by only 0.2%.
Effect of Negative Feedback on Bandwidth
Bandwidth. The range of frequency over which
the voltage gain is equal to or greater than
*70.7% of the maximum gain is known as
bandwidth.
* The human ear is not a very sensitive hearing
device. It has been found that if the gain falls to
70.7% of maximum gain, the ear cannot detect
the change. For instance, if the gain of an
amplifier is 100, then even if the gain falls to
70.7, the ear cannot detect the change in
intensity of sound and hence no distortion will
be heard. However, if the gain falls below 70.7,
the ear will hear clear distortion.
Effect of Negative Feedback on Bandwidth
Consider an amplifier whose high frequency response is characterized
by a single pole. Its gain at mid and high frequencies can be expressed
as AM
A( s )  (4)
s
1
wH
where 𝐴𝑀 denotes the midband gain and wH is the upper 3-dB
frequency. Application of negative feedback, with a frequency-
independent factor 𝛽, around this amplifier results in a closed-loop gain
𝐴𝑓 (𝑠) given by
A( s )
Af ( s )  (5)
1   A( s )

Substituting for A(s) in eq. (5) using Eq. (4) results,

AM / (1  AM  )
Af ( s ) 
1  s / wH (1  AM  ) (6)
Thus the feedback amplifier will have a midband gain of
AM / (1  AM  ) (7)
and an upper 3-dB frequency wHf given by
wHF  wH (1  AM  ) (8)
It follows that the upper 3-dB frequency is increased by a factor
equal to the amount of Feedback.
Similarly, it can be shown that if the open-loop gain is
characterized by a dominant low frequency pole giving rise to a
lower 3-dB frequency 𝑤𝐿 then the feedback amplifier will have a
lower 3-dB frequency 𝑤𝐿𝐹 ,
𝑤𝐿
𝑤𝐿𝐹 = (9)
1+𝐴𝑀 𝛽
Note that the amplifier bandwidth is increased by the same factor
by which its midband gain is decreased, maintaining the gain–
bandwidth product at a constant value.
EXAMPLES OF VOLTAGE SERIES FEEDBACK CIRCUITS
Figure 14.7 shows a FET amplifier stage with voltage-series
feedback. A part of the output signal (Vo) is obtained using a
feedback network of resistors R 1 and R 2 . The feedback voltage Vf
is connected in series with the source signal Vs , their difference
being the input signal Vi . Without feedback the amplifier gain is
Voltage-Series Feedback cont…
Voltage-Series Feedback cont…
Voltage-Series Feedback cont…
Figure 14.8 shows a voltage-series feedback connection using
an op-amp. It can be shown that the feedback gain is given
by:
Voltage-Series Feedback cont…
The emitter-follower circuit of Fig. 14.9 provides voltage-
series feedback. The signal voltage Vs is the input voltage Vi .
The output voltage Vo is also the feedback voltage in series
with the input voltage. The amplifier, as shown in Fig. 14.9 ,
provides the operation with feedback. The operation of the
circuit without feedback provides Vf = 0, so that