# How does amplitude modulation work

1. Jul 29, 2012

### ASidd

I read on a website that in amplitude modulation the actual carrier wave does not change its amplitude but rather the sidebands.

Is this true

Last edited: Jul 29, 2012
2. Jul 29, 2012

### ehild

Amplitude modulation means that the amplitude of the carrier wave varies with the frequency of the modulating signal. If it is y(t)=Bcos(ωt) the time dependence of the whole transmitted wave can be written as
Y(t)=(A+Bcos(ωt))cos(Ωt)=Acos(Ωt)+Bcos(ωt)cos(Ωt).
Using the identity cos(a+b)+cos(a-b)=2cos(a)cos(b), the second term can be written as B/2(cos((Ω+ω)t)+B/2(cos((Ω-ω)t).

The modulated wave consist of the carrier with the original amplitude and two side-bands with half the amplitude of the modulating signal.

ehild

3. Jul 30, 2012

### Staff: Mentor

Well, if you read it on a website, then it must be true.

If you watch the waveform on an oscilloscope, you see the amplitude varying, just as the title implies. But if you watch the display on a spectrum analyzer, you see a strong line at the carrier frequency and the height of this line does not vary; there are other lines either side of the carrier, and these are at the sideband frequencies. In the first reply in your thread, ehild has shown the mathematics behind this, for the case of a sinusoidal modulating signal, demonstrating that the amplitude of that carrier frequency component is a constant.