ISRO EC 2023 Q.41: solution and answer

Official answer: BSource: ISRO's revised and final answer key of 16 February 2024

1. An oscillator has no input signal. It must start from noise and grow into a steady sinusoid, so the loop has to be unstable at the oscillation frequency.

2. Write the closed-loop gain with positive (regenerative) feedback as $A_f=\frac{A}{1-A\beta }$. Instability, meaning a finite output with no input, appears when $A\beta =1\angle 0^{\circ }$ (the Barkhausen condition). For oscillations to build up, the loop gain must start with $|A\beta |>1$ at zero total phase shift.

3. A total loop phase shift of $0^{\circ }$ (or $360^{\circ }$) means the fed-back signal adds to the input. That is positive feedback, and it is what makes $A_f\to \infty$.

4. Option (a) is wrong. Negative feedback gives $A_f=\frac{A}{1+A\beta }$, which reduces gain and stabilises the amplifier, so no oscillation grows.

5. Option (c) is wrong. A tank circuit only fixes the frequency at which the phase condition is met. It does not by itself create the instability, and some oscillators (RC phase-shift, for example) have no tank circuit.

6. Option (d) is wrong because positive feedback is the correct answer. Hence instability in transistor (FET or BJT) oscillators is achieved by positive feedback.