Question

An amplitude modulated signal consists of a message signal of frequency $1\, KHz$ and peak voltage of $5\,V$, 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 1

Answer: (B)

Given,
Frequency of message signal $\left(f_{m}\right)=1 KHz$
$=1 \times 10^{3} Hz$
Peak voltage of message signal $\left(E_{m}\right)=5 V$
Carrier frequency $\left(f_{c}\right)=1 MHz =1 \times 10^{6} Hz$
Peak voltage of carrier $\left(E_{c}\right)=15 V$
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 \left(2 \pi f_{m}\right) t\right] \sin 2 \pi f_{C} t $
$=15\left[1+\frac{5}{15} \sin \left(2 \pi \times 10^{3}\right) t\right] \sin 2 \pi \times 10^{6} t $
$=15\left[1+\frac{1}{3} \sin \left(2 \pi 10^{3} t\right)\right] \sin \left(2 \pi 10^{6} t\right)$