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Q.

(a) If A and B represent the maximum and minimum amplitudes of an amplitude modulated wave, write the expression for the modulation index in terms of A & B.
(b) A message signal of frequency 20 kHz and peak voltage 10 V is used to modulate a carrier of frequency 2 MHz and peak voltage of 15 V. Calculate the modulation index.
Why the modulation index is generally kept less than one?

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Detailed Solution

We are given that A = Ac + Am and B = Ac - Am
Ac = (A + B) /2
Am = (A - B) /2
$\begin{array}{l} ∴ μ = \frac{A_{m}}{A_{v}} \\ = \frac{A - B}{A + B} \end{array}$
We have
$\begin{array}{l} μ = \frac{A_{m}}{A_{c}} \\ = \frac{10}{15} = 2 / 3 \end{array}$
$μ$ is kept less than one to avoid distortion

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