Question

When the negative feedback is applied to an amplifier of gain 100, the overall gain falls to 50. If the same feedback factor is maintained, the value of the amplifier gain required for the overall gain of 75 is

• A. 50
• B. 75
• C. 125
• D. 300

Hint:

Gain with negative feedback: \(A_f = A / (1 + A\beta)\).
First, use the initial conditions to find the feedback factor \(\beta\).
Then, use this \(\beta\) and the new desired closed-loop gain to find the required open-loop gain.

Answer 1

The Correct Option is D

The formula for the gain of an amplifier with negative feedback is:

\[ A_f = \frac{A}{1 + A\beta} \] 

where \(A_f\) is the gain with feedback, \(A\) is the open-loop gain (gain without feedback), and \(\beta\) is the feedback factor.

Case 1: \(A = 100\), \(A_f = 50\).

\(50 = \frac{100}{1 + 100\beta}\)

\(50(1 + 100\beta) = 100\)

\(1 + 100\beta = \frac{100}{50} = 2\)

\(100\beta = 2 - 1 = 1\)

\(\beta = \frac{1}{100} = 0.01\).

Case 2: The same feedback factor \(\beta = 0.01\) is maintained. The desired overall gain (gain with feedback) is \(A'_f = 75\). We need to find the new required open-loop gain \(A'\).

Using the formula: \(A'_f = \frac{A'}{1 + A'\beta}\)

\(75 = \frac{A'}{1 + A'(0.01)}\)

\(75(1 + 0.01A') = A'\)

\(75 + 0.75A' = A'\)

\(75 = A' - 0.75A'\)

\(75 = 0.25A'\)

\(A' = \frac{75}{0.25} = \frac{75}{1/4} = 75 \times 4 = 300\).

The required amplifier gain (open-loop gain) is 300.

\[ \boxed{300} \]