In an amplitude modulator circuit, the carrier wave is given by, C(t) = 4 , sin , (2000 , t) while modulating signal is given by, m(t) = 2 , sin , (2000 , t). The values of modulation index and lower side band frequency are

In an amplitude modulator circuit, the carrier wave is given by, …

MCQ

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

✓
$0.5$ and $9\, kHz$
B
$0.3$ and $9\, kHz$
C
$0.5$ and $10\, kHz$
D
$0.4$ and $10\, kHz$

✓

Answer

Correct option: A.

$0.5$ and $9\, kHz$

a
Modulation index is given by

$m=\frac{A_{m}}{A_{c}}=\frac{2}{4}=0.5$

and $(a)$ carrier wave frequency is given by

$=2 \pi \mathrm{f}_{\mathrm{c}}=2 \times 10^{4} \pi$

$\mathrm{f}_{\mathrm{c}}=1 \mathrm{kHz}$

lower side band frequency $\Rightarrow \mathrm{f}_{\mathrm{c}}-\mathrm{f}_{\mathrm{m}}$

$\Rightarrow 10 \mathrm{kHz}-1 \mathrm{kHz}=9 \mathrm{kHz}$

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