in an amplitude modulator circuit


in an amplitude modulator circuit, the carrier wave is given by, $\mathrm{C}(t)=4 \sin (20000 \pi t)$ while modulating signal is given by, $m(t)=2 \sin (2000 \pi t)$. The values of modulation index and lower side band frequency are :

  1. (1) $0.5$ and $10 \mathrm{kHz}$

  2. (2) $0.4$ and $10 \mathrm{kHz}$

  3. (3) $0.3$ and $9 \mathrm{kHz}$

  4. (4) $0.5$ and $9 \mathrm{kHz}$

Correct Option: , 4


(4) Modulation index, $\mu=\frac{A_{m}}{A_{c}}=\frac{2}{4}=0.5$

Given, $f_{e}=\frac{20000 \pi}{2 \pi}=10000 \mathrm{~Hz}$.

and $f_{m}=\frac{2000 \pi}{2 \pi}=1000 \mathrm{~Hz}$.

$\therefore \quad L S B=f_{e}-f_{m}=10000-1000=9000 \mathrm{~Hz}$.

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