SATHEE: communication-systems Question 32

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Question: Q. 6. A message signal of frequency $10 kHz$ and peak voltage $10 V$ is used to modulate a carrier wave of frequency $1 MHz$ and peak voltage $20 V$ . Determine :

A [Delhi Comptt. I, II, III 2013]

(i) The modulation index,

(ii) the side bands produced.

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Solution:

Ans. (i) Modulation index, $μ = \frac{A_{max} - A_{min}}{A_{max} + A_{min}}$

or $μ = \frac{A_{m}}{A_{c}}$

Given, $A_{max} - V_{min} = 10 V$

$A_{max} + A_{min} = 20 V$

Hence $μ = \frac{20 - 10}{20 + 10} = \frac{1}{3}$

(ii)

Given

sidebands $= f_{c} - f_{m}$ and $f_{c} + f_{m}$

hence sidebands

$f_{m} = 10 kHz$

$f_{c} = 1 MHz$

$\begin{aligned} (1) & f_{c} + f_{m} & = 1000 kHz + 10 kHz & = 1010 kHz f_{c} - f_{m} & = 1000 kHz - 10 kHz & = 990 kHz \end{aligned}$

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