Question: Q. 6. A message signal of frequency $10 \mathrm{kHz}$ and peak voltage $10 \mathrm{~V}$ is used to modulate a carrier wave of frequency $1 \mathrm{MHz}$ and peak voltage $20 \mathrm{~V}$. 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, $\mu=\frac{A_{\text {max }}-A_{\text {min }}}{A_{\text {max }}+A_{\text {min }}}$
or $\quad \mu=\frac{A_{m}}{A_{c}}$
Given, $A_{\max }-V_{\text {min }}=10 \mathrm{~V}$
$A_{\max }+A_{\min }=20 \mathrm{~V}$
Hence $\quad \mu=\frac{20-10}{20+10}=\frac{1}{3}$
1
(ii)
Given
sidebands $=f_{c}-f_{m}$ and $f_{c}+f_{m}$
hence sidebands
$$ f_{m}=10 \mathrm{kHz} $$
$$ f_{c}=1 \mathrm{MHz} $$
$$ \begin{align*} f_{c}+f_{m} & =1000 \mathrm{kHz}+10 \mathrm{kHz} \ & =1010 \mathrm{kHz} \ f_{c}-f_{m} & =1000 \mathrm{kHz}-10 \mathrm{kHz} \ & =990 \mathrm{kHz} \tag{1} \end{align*} $$
