Answer to Question #90178 in Electrical Engineering for Shivam Nishad

Question

Derive mathematical expression of an A.M. wave and indicate the sideband components. Why is the S.S.B. transmission beneficial ?

Answer 1

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 :

and substitute with - the amplitude modulation index.

The sideband components are

and

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