Question

In an amplitude modulator circuit, the carrier wave is given by, $C(t) = 4$ sin ($20000\, \pi t$) while modulating signal is given by, $m(t) = 2$ sin $(200\, \pi t$). The values of modulation index and lower side band frequency are :

• A. 0.5 and 9 kHz
• B. 0.5 and 10 kHz
• C. 0.3 and 9 kHz
• D. 0.4 and 10 kHz

Answer 1

Answer: (A)

Modulation index is given by
$m = \frac{A_m}{A_c} \, = \, \frac{2}{4} = 0.5$
& (a) carrier wave frequency is given by
$ \, \, \, = 2 \pi f_c \, = \, 2 \times \, \, 10^4 \, \pi$
(b) modulating wave frequency (f$_m$)
$2 \pi f_{m} \, = \, 2000 \pi$
$\Rightarrow \, \, f_m \, \, = \, 1 kHz$
lower side band frequency $\Rightarrow \, \, f_c - f_m$
$ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Rightarrow \, \, 10\, kHz - 1 \,kHz = 9\, kHz$