Modern Physics 7 Question 59
7. A message signal of frequency $100 MHz$ and peak voltage $100 V$ is used to execute amplitude modulation on a carrier wave of frequency $300 GHz$ and peak voltage $400 V$. The modulation index and difference between the two side band frequencies are
(Main 2019, 10 April I)
(a) $0.25 ; 1 \times 10^{8} Hz$
(b) $4 ; 1 \times 10^{8} Hz$
(c) $0.25 ; 2 \times 10^{8} Hz$
(d) $4 ; 2 \times 10^{8} Hz$
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Solution:
- Given, $f _m=100 MHz=100 \times 10^{6} Hz$,
$$ \begin{aligned} A _m & =100 V \\ A _c & =400 V \end{aligned} $$
Range of frequency in case of amplitude modulation is $\left(f _c-f _m\right)$ to $\left(f _c+f _m\right)$.
$$ \begin{aligned} \therefore \text { Bandwidth }=2 f _m & =2 \times 100 \times 10^{6} Hz \\ & =2 \times 10^{8} Hz \end{aligned} $$
and modulation index,
$$ MI=\frac{A _m}{A _c}=\frac{100}{400}=0.25 $$
