Q22 of 805 Page 1

A message signal of frequency 20 KHz and a peak voltage of 20 volts is used to modulate a carrier signal of frequency 2 MHz and a peak voltage of 40 volts. Determine (i) modulation index, (ii) the side bands produced. Draw the corresponding frequency spectrum of the amplitude modulated signal.

In order to transmit some message over a long distance, amplitude modulation is used, where an initially low-frequency message signal is superimposed on a high-frequency carrier wave. As a result a new wave is formed having high frequency whose amplitude is varying by the message signal


As shown in figure



The equation of waveform of the message signal is


m(t) = Amsinωmt


where Amis the amplitude of the message signal, ωm is the angular frequency of the message signal


ωm = 2πfm


where fm is the frequency of the message signal or modulating signal.


Here,


Am = 20 V


fm = 20 KHz = 2 × 103 Hz = 2000 Hz


The equation of waveform of the Carrier wave is


c(t) = Acsinωct


where Ac is the amplitude of Carrier wave, ωc is the angular frequency of the Carrier wave


ωc = 2πfc


where fc is the frequency of the Carrier Wave


Here,


Ac = 40 V


fc = 2 MHz = 2 × 106 Hz = 2000 × 103 Hz = 2000 KHz


(i) The ratio of the amplitude of the original message signal to the amplitude of carrier wave is called modulation index


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