Question

An amplitude modulated signal consists of a message signal of frequency $1KHz$ and peak voltage of $5V$, modulating a carrier frequency of $1MHz$ and peak voltage of $15V$. 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 $\left(f_m\right)=1KHz$
$=1\times 10^{3}Hz$
Peak voltage of message signal $\left(E_m\right)=5V$
Carrier frequency $\left(f_c\right)=1MHz=1\times 10^{6}Hz$
Peak voltage of carrier $\left(E_c\right)=15V$
We know that, The equation of amplitude modulated wave is given by
$e(t)=E_c\left[1+\frac{E_m}{E_c}\sin {\omega }_{m}t\right]\sin {\omega }_{c}t$
$=E_c\left[1+\frac{E_m}{E_c}\sin \left(2\pi f_m\right)t\right]\sin 2\pi f_{C}t$
$=15\left[1+\frac{5}{15}\sin \left(2\pi \times 10^3\right)t\right]\sin 2\pi \times 10^{6}t$
$=15\left[1+\frac{1}{3}\sin \left(2\pi 10^{3}t\right)\right]\sin \left(2\pi 10^{6}t\right)$