A signal Acos is transmitted using ν _ 0 sin ω _ 0 t as carrier wave. The correct amplitude modulated ( AM ) signal is:

Correct answer: D. ν _ 0 sin ω _ 0 t + (A)/(2) ( ω _ 0 - ω)t + (A)/(2) ( ω _ 0 + ω)t y _ m = Acos y _ c = V _ 0 sin ω _ 0 t Modulated signal = ( V _ 0 + Acos )sin ω _ 0 t = V _ 0 sin ω _ 0 t + Acosω tsin ω _ 0 t = V _ 0 sin ω _ 0 t + (A)/(2) ( ω _ 0 - ω)t + (A)/(2) ( ω _ 0 + ω)t

JEE Main 20199 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 9 April
Shift: Morning Shift
Subject: Physics
Chapter: Communication System

JEE Main 2019 · 9 April · Morning Shift · Physics · Communication System

A signal Acos is transmitted using ν _ 0 sin ω _ 0 t as carrier...

A signal

Acos\omegat

is transmitted using

{ν}_{0}sin{\omega}_{0}t

as carrier wave. The correct amplitude modulated

( AM )

signal is:

Options

A ${ν}_{0}sin [ {\omega}_{0}\left(1 + 0.01Asin\omegat\right)t ]$
B $\left({ν}_{0} + A\right)cos\omega tsin{\omega}_{0}t$
C ${ν}_{0}sin{\omega}_{0}t + Acos\omegat$
D ${ν}_{0}sin{\omega}_{0}t + \dfrac{A}{2}\sin \left({\omega}_{0} - \omega\right)t + \dfrac{A}{2}\sin \left({\omega}_{0} + \omega\right)t$

Correct answer

D. ${ν}_{0}sin{\omega}_{0}t + \dfrac{A}{2}\sin \left({\omega}_{0} - \omega\right)t + \dfrac{A}{2}\sin \left({\omega}_{0} + \omega\right)t$

Step-by-step solution

{y}_{m} = Acos\omegat

{y}_{c} = {V}_{0}sin{\omega}_{0}t

Modulated signal

= \left({V}_{0} + Acos\omegat\right)sin{\omega}_{0}t

= {V}_{0}sin{\omega}_{0}t + Acos\omega tsin{\omega}_{0}t

= {V}_{0}sin{\omega}_{0}t + \dfrac{A}{2}\sin \left({\omega}_{0} - \omega\right)t + \dfrac{A}{2}\sin \left({\omega}_{0} + \omega\right)t

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