Question

What is meant by feedback? Derive an expression for voltage gain of an amplifier with negative feedback.

Answer 1

In this question, we are going to apply the concept of feedback according to which it is the layout process where the portion of the output of the amplifier feeds back to the input of the amplifier. The overall result produces a very steady gain determined by the resistance ratio.

Complete step by step answer:
Feedback happens when a portion of the output signal is returned or given back to the input and coupled with the input signal.
Feedback amplifier principle: For a regular amplifier, one which does not have a feedback, let ${V_o}$ be the output voltage and ${V_i}$ be the input voltage and also if $A$ is the voltage gain of the amplifier, then gain $A = \dfrac{{{V_o}}}{{{V_i}}}$.
$A$ is also referred to as the open loop gain.
The feedback amplifier has two parts- the amplifier part and the feedback circuit. The feedback part is typically composed of passive components like resistor, capacitor and inductor. The feedback circuit gives back the fraction of the output voltage (say $\beta$ ) back to the input. Let ${V_o}'$ be a feedback output voltage.
Therefore, the input voltage ${V_1}'$ becomes,
${V_1}' = {V_1} + \beta {V_O}$ ...... (i)
$\beta$ is taken as positive for positive feedback and negative for negative feedback.
The output voltage amplified $A$ times by the amplifier is:
${V_O}' = A\left( {{V_1} + \beta {V_O}'} \right)$ ...... (ii)
$\Rightarrow{V_o}'\left( {1 - \beta A} \right) = A{V_1}$ ...... (iii)
The voltage gain of the feedback amplifier is thus given by:
${A_f} = \dfrac{{{V_O}}}{{{V_i}}} = \dfrac{A}{{1 - A\beta }}$ ...... (iv)
Since, $\left| {1 - A\beta } \right| < 1,{A_f} > A$. The amplifier gain increases when there is positive feedback.
So, the voltage gain for negative feedback is given by:
$\therefore{A_f} = \dfrac{A}{{1 - \left( { - A\beta } \right)}} = \dfrac{A}{{1 + A\beta }}$

Negative feedback reduces the amplifier gain.

Note: While using an amplifier we have to see if it is feedback or not. If a feedback amplifier is used then whether negative or positive feedback is used.