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Answer to Question #90178 in Electrical Engineering for Shivam Nishad

Question #90178
Derive mathematical expression of an A.M. wave and indicate the sideband components. Why is the S.S.B. transmission beneficial ?
Expert's answer

Modulation is a technique which modifies waves of high frequency by the wave of low frequency.

Consider the carrier signal:


the modulating signal:


and the signal after modulation look like


Putting this all together gives


Now multiply the terms with cosines by @$V_c/V_c@$:



and substitute @$V_m/V_c@$ with @$m_a@$ - the amplitude modulation index.


The sideband components are



@$ \frac{\omega_c+\omega_m}{2\pi}=f_c+f_m.@$

The single-sideband transmission reduces the bandwidth transmitted and it allows to double the number of channels within the same frequency band.

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