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A message signal of frequency  \(10\ {kHz}\)  and peak voltage of  \(10\ \mathit{V}\)  is used to modulate a carrier of frequency  \(1\ {Mhz}\)  and peak voltage of  \(20\ {V}\) . Determine modulation index and the side bands produced.
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Question

A message signal of frequency  \(10\ {kHz}\)  and peak voltage of  \(10\ \mathit{V}\)  is used to modulate a carrier of frequency  \(1\ {Mhz}\)  and peak voltage of  \(20\ {V}\) . Determine modulation index and the side bands produced.

Answer

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Solution

Given data,
Frequency of message signal  \(f_m=10\ \mathit{kHz}\)
Amplitude of message signal  \(A_m=10\ V\)
Frequency of carrier signal  \(f_c=1\ {MHz}\)
Amplitude of carrier signal  \(A_c=20\ V\)
Modulation index,
 \(\mu =\frac{A_m}{A_c}\) 
 \(=\frac{10}{20}\) 
 \(=0.5\)
Upper side band frequency \(=f_c+f_m\)
 \(=\left(1\times 10^6\right)+(10\times 10^3)\)
 \(=1010\ {kHz}\)
Lower side band frequency \(=f_c-f_m\)
 \(=\left(1\times 10^6\right)+(10\times 10^3)\)
 \(=990\ { kHz}\) 
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