SATHEE: communication-systems Question 40

communication-systems Question 40

Question: Q. 9. A (sinusoidal) carrier wave

$C (t) = A_{c} \sin ω_{c} t$

is amplitude modulated by a (sinusoidal) message signal

$m (t) = A_{m} \sin ω_{m} t$

Write the equation of the (amplitude) modulated signal. Use this equation to obtain the values of the frequencies of all the sinusoidal waves present in the modulated signal.

U] [CBSE SQP 2014]

Show Answer

Solution:

Ans. The equation of the (amplitude) modulated signal is

$C_{m} (t) = [(A_{c} + A_{m} \sin ω_{m} t)] \sin ω_{c} t 1$

This can be rewritten as

$C_{m} (t) = [A_{c} (1 + μ \sin ω_{m} t)] \sin ω_{c} t$

where, $μ = A_{m} / A_{c} =$ modulation index

$\begin{aligned} ∴ C_{m} (t) & = A_{c} \sin ω_{c} t + \frac{μ A_{c}}{2} 2 \sin ω_{m} t \cdot \sin ω_{c} t 1 / 2 & = A_{c} \sin ω_{c} t + \frac{μ A_{c}}{2} [\cos (ω_{c} - ω_{m}) t \end{aligned}$

${- \cos (ω_{c} + ω_{m}) t]}_{1 / 2}^{1 / 2}$

There are the three sinusoidal waves present in the amplitude modulated signal.

The frequencies of these three waves are

and

$Missing or unrecognized delimiter for \right$

[CBSE Marking Scheme, 2014] 1/2

Communication Systems

communication-systems Question 40

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Communication Systems

communication-systems Question 40

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu