spectrum of PWM

[Magnus Danielson]

From: jhaible at t-online.de (jh.)
Subject: Re: spectrum of PWM
Date: Tue, 5 Dec 2000 20:43:35 +0100

> 
> > Perhaps this has some info
> >
> > http://www.musicsynthesizer.com/Circuitry/probability.htm
> 
> Thanks for the link. That's the easy stuff (static pulse wave,
> or slow modulation).
> 
> But I am looking for the *general* case, as in audio rate PWM.
> 
> Maybe there is no analytic function for the spectrum.
> I mean you already need Bessel functios for ordinary FM. I was
> hoping for something similar for PWM.

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?

Cheers,
Magnus