SATHEE: communication-systems Question 41

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Question: Q. 10. A sinusoidal carrier wave of amplitude $A_{c}$ and angular frequency $ω_{c}$ is modulated in accordance with a sinusoidal information signal of amplitude $A_{m}$ and angular frequency $ω_{m}$ . Show that the amplitude modulated signal contains three frequencies centered around $ω_{c}$ . Draw the frequency spectrum of the resulting modulated signal.

[CBSE -SQP-2018]

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Solution:

Ans. The modulated signal :

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

Frequency Spectrum :

[CBSE Marking Scheme, 2018]

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