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Question

Define modulation index. Why is it's value kept, in practice, less than one?
A carrier wave of frequency 1.5 MHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced.

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Solution

The modulation index μ, can be defined as the ratio between the amplitude of the modulating signal and the amplitude of the carrier signal.
A modulation index above 1 causes over-modulation, resulting in distorted waveform envelope which will result in distorted output signal.

Given, carrier wave frequency = 1.5 MHz,
carrier wave amplitude, Vc=50V
Sinusoidal wave frequency = 10 kHz
Amplitude modulation = 50%

Now, Modulation factor =50100=0.5

and 0.5=VmVc

0.5=Vm50

Vm=0.5×50=25V

Thus, amplitude of the AM wave = 25 volt

Now, fUSB=1.5×1000+10

=1500+10=1510 kHz

fLSB=1.5×100010=1490 kHz

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