Discussion Forum



1)

An amplitude modulated signal consists of a message signal of frequency 1KHz and peak voltage of 5V, modulating a carrier frequency of 1 MHz and peak voltage of 15 V  . The correct description of this signal is 


A) $5[1+3\sin(2\pi 10^{6}t)]\sin (2 \pi 10^{3}t)$

B) $15[1+\frac{1}{3}\sin(2\pi 10^{3}t)]\sin (2 \pi 10^{6}t)$

C) $[5+15\sin(2\pi 10^{3}t)]\sin (2 \pi 10^{6}t)$

D) $[15+5\sin(2\pi 10^{6}t)]\sin (2 \pi 10^{3}t)$

Answer:

Option B

Explanation:

 Given ,

 Frequency  of message signal  $(f_{m})$ =1 KHz= $1 \times 10^{3} Hz$

 Peak voltage  of messages signal ($E_{m}$)=5V

 Carrier frequency $(f_{c})$ =1 MHz= $1 \times 10^{6} Hz$

 Peak voltage of carrier $(E_{c})$=15 V

 We know that, The equation of amplitude modulated wave is given by

     $e(t)= E_{c}\left[1+\frac{E_{m}}{E_{c}}\sin \omega_{m}t\right]\sin  \omega_{c}t$

     $= E_{c}\left[1+\frac{E_{m}}{E_{c}}\sin (2 \pi f_{m})t\right]\sin  2\pi f_{c}t$

$= 15\left[1+\frac{5}{15}\sin (2 \pi \times10^{3})t\right]\sin  2\pi \times 10^{6}t$

  $= 15\left[1+\frac{1}{3}\sin (2 \pi 10^{3}t)\right]\sin ( 2\pi  10^{6})t$