(i) Draw the plot of amplitude versus ‘ω’ for an amplitude modulated wave whose carrier wave (ω_c) is carrying two modulating signals, ω₁ and ω₂ (ω₂ > ω₁). [Hint: Follow derivation from Eq 15.6 of NCERT Textbook of XII]

Question

(i) Draw the plot of amplitude versus ‘ω’ for an amplitude modulated wave whose carrier wave (ω c ) is carrying two modulating signals, ω 1 and ω 2 (ω 2 > ω 1 ). [Hint: Follow derivation from Eq 15.6 of NCERT Textbook of XII] (ii) Is the plot symmetrical about ω c ? Comment especially about plot in region ω < ω c . (iii) Extrapolate and predict the problems one can expect if more waves are to be modulated. (iv) Suggest solutions to the above problem. In the process can one understand another advantage of modulation in terms of bandwidth?

Philoid · Accepted Answer

(i)

Let the carrier signal be and the two message signals be and .

We need to simply add them.

Now, we use the equation (15.6) in NCERT

Using the identity ,

Note that and

The frequencies present are , , ,,, , , , .

The frequencies are plotted below:

(ii)

The graph is not symmetrical around . There is crowding of frequencies for .

(iii)

There would be more crowding of waves for . As a result, it would be difficult to distinguish frequencies because of crowding.

(iv)

The above problem can be solved by increasing the frequency of carrier signal and, hence, the bandwidth. This will result in more spreading out of the frequencies.