Unit -08

Feedback amplifier

Negative feedback amplifier and advantage

Gain stability and extension of bandwidth
Important of positive feedback amplifier on oscillation.

Negative feedback amplifier and advantage

Principle of Feedback Amplifier

A feedback amplifier generally consists of two parts. They are the amplifier and the feedback
circuit. The feedback circuit usually consists of resistors. The concept of feedback amplifier
can be understood from the following figure.

From the above figure, the gain of the amplifier is represented as A. the gain of the amplifier is
the ratio of output voltage Vo to the input voltage Vi. the feedback network extracts a voltage
Vf = β Vo from the output Vo of the amplifier.
This voltage is added for positive feedback and subtracted for negative feedback, from the
signal voltage Vs. Now,
Vi = Vs+Vf = Vs+βVo

Vi = Vs−Vf = Vs−βVo

The quantity β = Vf/Vo is called as feedback ratio or feedback fraction.

Let us consider the case of negative feedback. The output Vo must be equal to the input
voltage (Vs - βVo) multiplied by the gain A of the amplifier.
Hence,
(Vs−βVo)A=Vo

Or

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 1

 AVs−AβVo=Vo

Or
AVs=Vo(1+Aβ)

Therefore,
Vo / Vs = A / 1+Aβ

Let Af be the overall gain (gain with the feedback) of the amplifier. This is defined as the ratio of
output voltage Vo to the applied signal voltage Vs, i.e.,
Af = Output voltage / Input signal voltage=Vo/Vs

So, from the above two equations, we can understand that,

The equation of gain of the feedback amplifier, with negative feedback is given by
Af = A / 1+Aβ

The equation of gain of the feedback amplifier, with positive feedback is given by
Af = A / 1−Aβ

These are the standard equations to calculate the gain of feedback amplifiers.

Types of Feedbacks

The process of injecting a fraction of output energy of some device back to the input is known
as Feedback. It has been found that feedback is very useful in reducing noise and making the
amplifier operation stable.

Positive Feedback

The feedback in which the feedback energy i.e., either voltage or current is in phase with the
input signal and thus aids it is called as Positive feedback.
Both the input signal and feedback signal introduces a phase shift of 180o thus making a
360o resultant phase shift around the loop, to be finally in phase with the input signal.
Though the positive feedback increases the gain of the amplifier, it has the disadvantages
such as

 Increasing distortion
 Instability
It is because of these disadvantages the positive feedback is not recommended for the
amplifiers. If the positive feedback is sufficiently large, it leads to oscillations, by which
oscillator circuits are formed.

Negative Feedback

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 2

The feedback in which the feedback energy i.e., either voltage or current is out of phase with
the input and thus opposes it, is called as negative feedback.
In negative feedback, the amplifier introduces a phase shift of 180o into the circuit while the
feedback network is so designed that it produces no phase shift or zero phase shift. Thus the
resultant feedback voltage Vf is 180o out of phase with the input signal Vin.
Though the gain of negative feedback amplifier is reduced,
Negative feedback in an amplifier is the method of feeding a portion of the amplified output to
the input but in opposite phase. The phase opposition occurs as the amplifier provides
180o phase shift whereas the feedback network doesn’t.
While the output energy is being applied to the input, for the voltage energy to be taken as
feedback, the output is taken in shunt connection and for the current energy to be taken as
feedback, the output is taken in series connection.
There are two main types of negative feedback circuits. They are −

 Negative Voltage Feedback

 Negative Current Feedback

Negative Voltage Feedback

In this method, the voltage feedback to the input of amplifier is proportional to the output
voltage. This is further classified into two types −

 Voltage-series feedback
 Voltage-shunt feedback

Negative Current Feedback

In this method, the voltage feedback to the input of amplifier is proportional to the output
current. This is further classified into two types.

 Current-series feedback
 Current-shunt feedback
Let us have a brief idea on all of them.

Voltage-Series Feedback

In the voltage series feedback circuit, a fraction of the output voltage is applied in series with
the input voltage through the feedback circuit. This is also known as shunt-driven series-
fed feedback, i.e., a parallel-series circuit.
The following figure shows the block diagram of voltage series feedback, by which it is evident
that the feedback circuit is placed in shunt with the output but in series with the input.

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 3

As the feedback circuit is connected in shunt with the output, the output impedance is
decreased and due to the series connection with the input, the input impedance is increased.

Voltage-Shunt Feedback

In the voltage shunt feedback circuit, a fraction of the output voltage is applied in parallel with
the input voltage through the feedback network. This is also known as shunt-driven shunt-
fed feedback i.e., a parallel-parallel proto type.
The below figure shows the block diagram of voltage shunt feedback, by which it is evident that
the feedback circuit is placed in shunt with the output and also with the input.

As the feedback circuit is connected in shunt with the output and the input as well, both the
output impedance and the input impedance are decreased.

Current-Series Feedback

In the current series feedback circuit, a fraction of the output voltage is applied in series with
the input voltage through the feedback circuit. This is also known as series-driven series-
fed feedback i.e., a series-series circuit.
The following figure shows the block diagram of current series feedback, by which it is evident
that the feedback circuit is placed in series with the output and also with the input.

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 4

As the feedback circuit is connected in series with the output and the input as well, both the
output impedance and the input impedance are increased.

Current-Shunt Feedback

In the current shunt feedback circuit, a fraction of the output voltage is applied in series with the
input voltage through the feedback circuit. This is also known as series-driven shunt-
fed feedback i.e., a series-parallel circuit.
The below figure shows the block diagram of current shunt feedback, by which it is evident that
the feedback circuit is placed in series with the output but in parallel with the input.

As the feedback circuit is connected in series with the output, the output impedance is
increased and due to the parallel connection with the input, the input impedance is decreased.
Let us now tabulate the amplifier characteristics that get affected by different types of negative
feedbacks.

Types of Feedback
Characteristics
Voltage- Voltage- Current- Current-
Series Shunt Series Shunt

Voltage Gain Decreases Decreases Decreases Decreases

Bandwidth Increases Increases Increases Increases

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Input resistance Increases Decreases Increases Decreases

Output
Decreases Decreases Increases Increases
resistance

Harmonic
Decreases Decreases Decreases Decreases
distortion

Noise Decreases Decreases Decreases Decreases

Advantages of a negative feedback amplifier:

 The negative feedback reduces the size
 It has highly stabilized gain
 It has fewer harmonics distortion
 It has less phase distortion
 It has higher fidelity
 More linear operation
 It has less frequency distortion
 Input-output impedances can be modified as desired
 It can increase or decrease output impedances
 It can control the step response of an amplifier
 It can control the step response of an amplifier
 It has less amplitude distortion
Disadvantages of a negative feedback amplifier:
 Its reduction in gain
 It increases output resistance in the case of shunt and current series feedback amplifiers

Gain stability and extension of 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

…………………………………..(1)

Where Am denotes the midband gain and ωH 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:

…………………………………..(2)

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 6

Substituting for A (s) from Eq. (1) results after a little manipulation, in

…………………………………(3)

Thus the feedback amplifier will have a midband g

gain of Am / (1+βAm) and an upper 3-dB
3
frequency ωH given by

It follows that the upper 3-dB

dB frequency is increased by a factor equal to the amount of
feedback.

Similarly. it can be shown that if the open

open-loop
loop gam is characterized by a dominant low-
low
frequency pole giving rise to a lower 3 3-dB frequency ωL, then the feedback amplifier
amplifi will have
a lower 3-dB frequency ωLF,

Gain stability of negative feedback

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT

UNIT- 08) Page 7
Important of positive feedback amplifier on oscillation.

How does an oscillator differ from an amplifier?

Negative Feedback Example No1

A system has a gain of 80dB without feedback. If the negative feedback fraction is 1/50th.
Calculate the closed-loop gain of the system in dB with the addition of negative feedback.
Formula of gain , Af = A / 1+Aβ

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Then we can see that the system has a loop gain of 10,000 and a closed-loop gain of 34dB.

Negative Feedback Example No2

If after 5 years the loop gain of the system without negative feedback has fallen to 60dB and the
feedback fraction has remained constant at 1/50th. Calculate the new closed-loop gain value of
the system.
Formula of gain , Af = A / 1+Aβ

Er. Manish kr. Yadav (Feedback Amplifier @ UNIT- 08) Page 9