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NIELIT 2022 April Scientist B | Section B | Question: 109

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A $1 \; \text{MHz}$ sinusoidal carrier is amplitude modulated by a symmetrical square wave of period $100 \; \mu \text{sec}.$ Which of the following frequencies will not be present in the modulated signal ?

  1. $990 \; \text{MHz}$
  2. $1010 \; \text{MHz}$
  3. $1020 \; \text{MHz}$
  4. $1030 \; \text{MHz}$
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C.  1020 MHz …

 

Let the baseband signal or the message signal are having frequencies f1, f2, f3, etc.

If the carrier signal having frequency fc is amplitude modulated by this signal, then the frequencies present in the amplitude modulated signal are as follows: (fc ± f1), (fc ± f2), (fc ± f3) etc.

 

Given, fc = 1000 kHz ….

The message signal is a symmetrical square wave and hence it will contain only the odd harmonics

i.e., f m, 3 fm, 5 fm, etc. f(m)= 1 / (100 μs) =10 kHz ….

The modulated signal will contain: (1000 ± 10) kHz, (1000 ± 30) kHz, etc.

We can therefore conclude that 1020 kHz will not be present in the modulated signal….

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