# (a) Explain amplitude modulation of a sinusoidal carrier wave using a modulating signal, with the help of necessary diagrams.(b) For a given amplitude modulated wave, the maximum amplitude is 20V and minimum amplitude is 5V. Calculate the modulation index.

Amplitude modulation is the process of varying the magnitude of a carrier wave in accordance with respect to the instantaneous variation of the signal that is audio frequency signal.

Audio frequency signal $= e_{c}= E\sin \omega _{s}t;\omega _{s}=2\pi f_{s}$

fs = frequency of signal

For amplitude modulated wave $E_{max}= E_{C}+E_{S}$

$E_{min}= E_{C}-E_{S}$

(B) Given,

the maximum amplitude of the wave, $E_{max}=20V$

minimum amplitude of the wave, $E_{min}=5V$

We know that,

modulation index,

$m = \frac{E_{max}-E_{min}}{E_{max}+E_{min}}$

$m = \frac{20-5}{20+5}= \frac{15}{25}=\frac{3}{5}$

hence the modulation index of given amplitude wave is 0.6.

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