We know, the instantaneous voltage of AM wave is:
e_AM = Ec * cos(2*pi*fc*t) + ((m * Ec) / 2) * cos(2*pi*(fc + fs)*t) + ((m * Ec) / 2) * cos(2*pi*(fc - fs)*t) Here: Ec = Amplitude of the carrier fc = frequency of the carrier Es = Amplitude of the message signal fs = frequency of the message signal m = modulation index
Here we get the bandwidth =
(fc + fs) - (fc - fs) = 2*fs
But in the equation in the lower side-band's term if we take
cos(2*pi*(fs - fc)*t) instead of
cos(2*pi*(fc - fs)*t) therefore the bandwidth becomes =
(fc + fs) - (fs - fc) that is
That is instead of getting the 2 times of the frequency of the message signal (
fs) we are getting the 2 times of the frequency of carrier signal (
cos(-x) = cos(x) hence if we swap the position of
fs inside the lower side-band term as the equation is mathematically valid. But it is clear that
fs are not the same thing. Hence we are getting two possible values of bandwidth. Although so far I've only seen
2*fs to be used as the value of the bandwidth. So why
2*fc is not used? Isn't it valid? If not, then why mathematically we are getting it to be an alternate solution?
Again if the alternate one is also a valid solution then what is the significance of it?