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. $5[1+3\sin \left(2\pi {10}^{6}t\right)]\sin \left(2\pi {10}^{3}t\right)$
• B. $15[1+\frac{1}{3}\sin \left(2\pi {10}^{3}t\right)]\sin \left(2\pi {10}^{6}t\right)$
• C. $[5+15\sin \left(2\pi {10}^{3}t\right)]\sin \left(2\pi {10}^{6}t\right)$
• D. $[15+5\sin \left(2\pi {10}^{6}t\right)]\sin \left(2\pi {10}^{3}t\right)$

Answer 1

Answer: (B)

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

message wave signal$=5\sin (20\times {10}^{3}t)$
Carrier wave signal $=15\sin (20\times {10}^{6}t)$
Modulated wave signal
$=[15+5\sin \left(2\pi {10}^{3}t\right)]\sin \left(2\pi {10}^{6}t\right)=15[1+\frac{1}{3}\sin \left(2\pi {10}^{3}t\right)]\sin \left(2\pi {10}^{6}t\right)$