spectrum of PWM

[Magnus Danielson]

From: Haible Juergen <Juergen.Haible at nbgm.siemens.de>
Subject: RE: spectrum of PWM
Date: Thu, 7 Dec 2000 14:33:18 +0100 

> 
> 	>You should be able to model it using Bessel functions.
> 	>
> 	>Consider this:
> 	>
> 	>You have two sawtooth waveforms which are at exactly the same
> 	>frequency (SHARP! THE same) which are added together 1:-1. One of these
> 	>are phase-modulated in the relation to the other. Now, as we change
> 	>the phase modulation will the resulting pulse-width change. Now, we
> 	>can handle this using Bessel functions in the frequency plane.
> 	>I think scetching something along these lines will make you arive at
> 	>an exact solution.
> 	>
> 	>Is that sufficient for you?
> 
> Excellent. I think that's the solution !

Good. This would make it such that each sine in the sawtooth would
widend with a spectra of multiples of the modulating signal and the
strength as given by the Bessel components. Naturally would the center
frequency be modulated by its the Bessel component, but consider that
it is a sum of the Bessel modulated and the carrier of the same
strength, so the center amplitude has to be modified. Only deep
modulation will kill the (over)tone.

I guess one has to feel at home with Bessel components to get all
this... also, phasemodulation is not EXACTLY the same as frequency
modulation.

Cheers,
Magnus