A signal $A \cos \omega t$ is transmitted using $v_{0} \sin \omega_{0} t$ as carrier wave. The correct amplitude modulated (AM) signal is:

(B) $v_{0} \sin \omega_{0} t+\frac{A}{2} \sin \left(\omega_{0}-\omega\right) t+\frac{A}{2} \sin \left(\omega_{0}+\omega\right) t$

(A) $v_{0} \sin \left[\omega_{0}(1+0.01 A \sin \omega t) t\right]$

(C) $v_{0} \sin \omega_{0} t+A \cos \omega t$

(D) $\left(v_{0}+A\right) \cos \omega t \sin \omega_{0} t$

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Semiconductors

A signal

A cos ω t

is transmitted using

v_{0} sin ω_{0} t

as carrier wave. The correct amplitude modulated (AM) signal is:

(A) $v_{0} sin [ω_{0} (1 + 0.01 A sin ω t) t]$
(B) $v_{0} sin ω_{0} t + \frac{A}{2} sin (ω_{0} - ω) t + \frac{A}{2} sin (ω_{0} + ω) t$ ✓ Correct
(C) $v_{0} sin ω_{0} t + A cos ω t$
(D) $(v_{0} + A) cos ω t sin ω_{0} t$

Answer: (B)

An amplitude-modulated wave rides the message on the carrier's amplitude:

s (t) = [v_{0} + A cos ω t] sin ω_{0} t = v_{0} sin ω_{0} t + A cos ω t sin ω_{0} t

. Turning the product into a sum,

A cos ω t sin ω_{0} t = \frac{A}{2} sin (ω_{0} + ω) t + \frac{A}{2} sin (ω_{0} - ω) t

, so

s (t) = v_{0} sin ω_{0} t + \frac{A}{2} sin (ω_{0} - ω) t + \frac{A}{2} sin (ω_{0} + ω) t

, the carrier flanked by its two sidebands.

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option