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# Define modulation index. Why is its value kept, in practice, less than one?A carrier wave 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

## Modulation index is a measure of extent of modulation done on a carrier signal. In Amplitude modulation, it is defined as the ratio of the amplitude of modulating signal to that of the carrier signal.m=AmAc Its value is kept less than 1 to avoid overmodulation which leads to distortions in the modulated signal and makes it very hard to demodulate and extract the modulating signal.From the given data,m=AmAc=Am500.5=Am50Am=25VAM wave is given by,x(t)=Ac(1+mcos(ωmt))cos(ωct)Hence, amplitude is given by:Ax=Ac(1+mcos(ωmt)) =50(1+0.5cos(2π×104t))Maximum value of AM wave is xmax=50×1.5=75VFrequency of lower sideband, f1=fc−fm=1.5×106−104=1.49 MHz Frequency of upper sideband, f1=fc+fm=1.5×106+104=1.51 MHz  Suggest Corrections  1      Similar questions  Related Videos   Modulation
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