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

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Semiconductors

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

C (t) = 4 sin (20000 π t)

while modulating signal is given by,

m (t) = 2 sin (2000 π t)

. The values of modulation index and lower side band frequency are:

Answer: (A)

The carrier has amplitude

4

and the message has amplitude

2

, so the modulation index is just their ratio,

μ = \frac{2}{4} = 0.5

. For the frequencies, match each argument against

2 π f t

: the carrier

4 sin (20000 π t)

has

2 π f_{c} = 20000 π

, giving

f_{c} = 10

kHz, and the message

2 sin (2000 π t)

gives

f_{m} = 1

kHz. The lower side band lies at

f_{c} - f_{m} = 10 - 1 = 9

kHz, so a modulation index of

0.5

with a lower side band at

9

kHz.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option