AIIMS 2006 Physics AM Demodulation MCQ Question

To understand the requirement for the time constant $RC$ in an AM demodulator circuit, we need to delve into the principles of amplitude modulation and demodulation.

Explanation of the Correct Answer: D) $RC \gg \frac{1}{f}$

When demodulating an amplitude modulated (AM) signal, it is crucial that the time constant $RC$ of the circuit is much greater than the period of the carrier wave. The carrier frequency $f$ is related to its period $T$ by the relation:

$$T = \frac{1}{f}$$

For effective demodulation, the time constant $\tau$ (which is equal to $RC$ in the context of RC circuits) must be large enough to ensure that the circuit can respond to the variations in the envelope of the AM signal but not too slow that it fails to track the rapid changes of the carrier signal. Thus, we require:

$$RC \gg T = \frac{1}{f}$$

This condition ensures that the circuit can efficiently filter the high-frequency carrier signal while allowing the lower frequency envelope (the modulating signal) to pass through effectively. In practical terms, this means the circuit should have a time constant that is sufficiently larger than the period of the carrier wave.

Why Other Options are Incorrect

1. A) $RC = \frac{1}{f}$: This condition implies that the time constant is equal to the period of the carrier wave. While this could allow the circuit to respond to the signal, it would not provide adequate filtering of the carrier, which could lead to distortion in the demodulated signal. A time constant equal to the period would typically allow for insufficient response to the envelope variations.

2. B) $RC < \frac{1}{f}$: Choosing a time constant that is less than the period of the carrier wave would result in the circuit being unable to follow the envelope of the AM signal accurately. This would cause the demodulated output to be distorted due to the inability to integrate the variations in amplitude effectively.

3. C) $RC \geq \frac{1}{f}$: Although this option allows for better tracking of the envelope than $RC < \frac{1}{f}$, it still does not ensure sufficient filtering of the high-frequency carrier. Merely being greater than or equal to the time period may still lead to incomplete signal recovery and potential distortion.

Summary

In summary, for effective demodulation of an AM signal, the time constant $RC$ must be much greater than the period of the carrier frequency $f$:

$$RC \gg \frac{1}{f}$$

This ensures that the circuit can adequately filter the carrier frequency while accurately following the modulating signal's envelope, leading to a clear and accurate demodulated output. Hence, the correct answer is D) $RC \gg \frac{1}{f}$.