AMU 2026 — science PYQ

1. Concept of Feedback Amplifiers

When a fraction of the output signal is fed back to the input of an amplifier, it forms a closed-loop system.

Let:

• $A$ = Open-loop gain of the internal amplifier (gain without feedback)

• $\beta$ = Feedback factor or feedback ratio (fraction of the output voltage fed back to the input)

• $A_f$ = Closed-loop gain (gain of the system with feedback)

The general expression for the closed-loop gain ($A_f$) of a negative feedback amplifier is given by the standard equation:

$$A_f=\frac{A}{1+A\beta }$$

2. Step-by-Step Derivation for Ideal Infinite Gain

We are given that the open-loop gain of the amplifier is extremely large, approaching infinity ($A\to \infty$). To find the limiting value of the closed-loop gain under this condition, we can divide both the numerator and the denominator of our formula by $A$:

$$A_f=\frac{\frac{A}{A}}{\frac{1}{A}+\frac{A\beta }{A}}$$

$$A_f=\frac{1}{\frac{1}{A}+\beta }$$

Now, let's take the mathematical limit as $A$ approaches infinity ($A\to \infty$):

$$\underset{A\to \infty }{\lim }{A}_f=\frac{1}{{\lim }_{A\to \infty }\left(\frac{1}{A}\right)+\beta }$$

Since $\frac{1}{\infty }=0$, the expression simplifies directly to:

$$A_f=\frac{1}{0+\beta }=\frac{1}{\beta }$$

3. Conclusion

When the open-loop gain ($A$) of an amplifier becomes infinitely large, the overall closed-loop gain ($A_f$) becomes entirely independent of the internal amplifier components. Instead, it depends solely on the feedback network factor ($\beta$). This is a fundamental principle utilized in ideal Operational Amplifiers (Op-Amps).

Correct Answer

The correct option is (b) $1/\beta$.