[sdiy] PWM audio distortion explanation

[ASSI]

On Dienstag, 28. Juni 2016 17:13:36 CEST Tom Wiltshire wrote:
> That's very interesting and right up my street, but unfortunately I don't
> get past the first sentence:
> 
> "At its most basic level, PWM is amplitude modulation (AM) of a carrier
> frequency (the PWM frequency)."

Well, I'd have to agree that explaining the first thing with a probably 
equally unknown second thing isn't quite helpful.  But maybe somewhere else on 
that site they've explained what AM is and expected the reader to know that 
part already.  Obviously the authors of the article thought fondly of the 
idea.

> Why? PWM doesn't change the amplitude at all, as far as I can see. The
> *average* amplitude, maybe, but that's not the same thing, and it seems
> like a bit of a jump from this initial claim to then go "…so then this
> maths applies!". Does it? Why?

You have a pulse every period, so that's your carrier at f=1/T.  If you make 
that pulse narrow, you have less energy (equivalently lower amplitude) at the 
carrier and with a wider pulse you have more energy (higher amplitude).  Of 
course you also have energy at each harmonic and it's changing with the 
pulsewidth too, which they start to explain in the third paragraph.  So, you 
can indeed think of PWM as simultaneous AM of multiple harmonically related 
carriers.  Yet another way to look at PWM is by thinking of it as on-off 
keying (AM with 100% modulation depth) of multiple phase-shifted carriers of 
the same frequency using minimum width pulses.  That would maybe be useful if 
you later want to explain how delta-sigma modulation shifts the noise to 
mostly high frequencies where they are easier to filter or if you want to 
slowly introduce distribution theory and the concept of the delta pulse.

> Amplitude modulation of pulse trains has some other name I'm sure (oh, look!
> It does: http://en.wikipedia.org/wiki/Pulse-amplitude_modulation )
> 
> The width of the pulses is what's being modulated here, not the amplitude.
> If they're going to convince me that those two are equivalent, I want a bit
> of explanation of how that works.

You can convert each form of modulation into all the others, but sometimes 
that's getting quite contrived (like needing an infinite number of carriers 
plus a lot of conditions to keep the resulting system physically realizable by 
constraining it to consume or produce finite energy).



Regards,
Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+

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