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Question 30

The maximum and minimum amplitude of an amplitude modulated wave is 16 V and 8 V respectively. The modulation index for this amplitude modulated wave is $$x \times 10^{-2}$$. The value of $$x$$ is ______ (Round off your answer to the nearest integer)


Correct Answer: 33

Solution

For an amplitude modulated wave, the modulation index is defined as $$\mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}}$$, where $$A_{max}$$ and $$A_{min}$$ are the maximum and minimum amplitudes of the modulated wave.

Given $$A_{max} = 16$$ V and $$A_{min} = 8$$ V:

$$\mu = \frac{16 - 8}{16 + 8} = \frac{8}{24} = \frac{1}{3} = 0.333$$

Expressing as $$x \times 10^{-2}$$: $$0.333 = 33.3 \times 10^{-2}$$, so $$x \approx \mathbf{33}$$.

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