Power Content In Multiple-Tone AM

Power Content In Multiple-Tone AM

A multiple-tone amplitude modulation is that type of modulation in which the modulating signal consists of more than one frequency components.

Mathematical Expression

Let us consider that a carrier signal A cos ω_ct is modulated by a baseband or modulating signal x(t) which is expressed as :

……………….(1)

As we know, the general expression for AM wave is :

………………… (2)

Now, putting the value of x(t) from equation (1) in equation (2), we get

……….. (3)

But we know that,

Therefore,

………………. (4)

Where

are  the modulation indexes of the corresponding frequency components.

The expression for AM wave in equation (4) may further be expanded as :

…… (5)

Now we know that the total power in AM is given as

P_t = carrier power + sideband power

P_t = P_c  + P_s  ……….. (6)

The carrier power P_c is given as :

……………. (7)

Similarly, the sideband power is given as :

……………. (8)

But we know that,

Putting the values of V₁, V₂ and V₃ in equation (8), we get,

…………. (9)

Now putting the value of P_c and P_s in equation (6), we get:

This expression may be extended upto to n-modulating terms i.e.,

…………… (10)