[sdiy] VCO reset time

[JH.]

The two of you have convinced me.
So there is no angle modulation involved.
What I remembered was that there are sidebands on the harmonics
(not the fundamental) created - much less than in the saw pwm case,
but still there. Of course the sidebands are completely explained
by AM - no FM/PM needed.

The "moving notches" (comb filter effect) can certainly be traced back to
AM as well.

The sidebands which are created from modulation (as opposed to
simple waveform / sound changes of a very slow, quasi static 
PW change) are responsible for the remaining chorusing / detuned
effect. It's more prominent at low notes (for a fixed PWM rate
and depth), as the relative frequency deviation from sidebands
of harmonics to original harmonics is bigger there.


JH.



----- Original Message ----- 
From: "Don Tillman" <don at till.com>
To: "JH." <jhaible at debitel.net>
Cc: <cfmd at bredband.net>; <synth-diy at dropmix.xs4all.nl>
Sent: Sunday, June 06, 2004 6:25 PM
Subject: Re: [sdiy] VCO reset time


>    > From: "JH." <jhaible at debitel.net>
>    > Date: Sun, 6 Jun 2004 14:14:12 +0200
>    > 
>    > I only was partially surprised, because tri based PWM still
>    > _sounds_ like having some angle modulation components; it's just
>    > surprising when you look at the modulated waveform and see that
>    > its symmetry is is never changed.  I would have to dig this up,
>    > but I'm sure Magnus you are faster developing the formula
>    > yourself than me finding the old calculations. If memory serves,
>    > the fundamental of a tri based pwm has no angle modulation
>    > component, but the higher harmonics still do.
> 
> Email posts are not the best medium for this, so we'll just have to
> pretend we're all sitting around a table with a large pad of paper, a
> few pens, and a pitcher of "Fat Tire Amber Ale".
> 
> The topic is PWM from a triangle vs. PWM from a sawtooth.
> 
> Magnus just reached over and pulled out the equations for triangle-
> based PWM, and, strangely enough, the fundamental and all the
> harmonics are all in phase.
> 
> Triangle-based PWM sounds great.  It's like the harmonics are all
> phasing around.  Yet remarkably, the phases of the harmonics are not
> actually changing.
> 
> What's happening is a comb filter effect.  At this point I take the
> pad of paper and draw out the harmonic spectrum of a pulse stream, and
> it shows that the strength of the harmonics take the overall shape of
> a decaying full-wave-rectified sine wave.  [scribble-scribble...]
> 
> As the pulse width narrows, the FWR sine shape spreads out.  And for
> the theoretical case of an infinitely narrow pulse, the spectrum is
> flat and the harmonics all have the same level.  [scribble...]
> 
> As the width of the pulses increase, going toward a square wave, the
> FWR sine shape compresses.  And for the case of a symmetrical square
> wave there's a null for each of the even harmonics and we get the
> classic all odd harmonics sound.  [scribble...]
> 
> It's the moving shape of the spectrum that we hear as the
> triangle-based PMW sound.
> 
> Now...
> 
> Triangle-based PWM and sawtooth-based PWM are essentially the same
> thing.  The difference is that with sawtooth-based PWM, everything is
> moving back and forth in time with the modulating signal compared to
> the triangle version.  So the phase of the fundamental is changing,
> and the phase of each harmonic is changing by multiples of that.
> 
> For an audio VCO, triangle-based PWM is more "correct".  The duty
> cycle of the waveform is changing and nothing else.  An audio VCO with
> sawtooth-based PWM has all these other phases and timings changing;
> that may sound better for some applications, and it makes a great
> optional feature, but it's not what was asked for.
> 
> For an LFO, folks care less about phase, it's more about where the
> waveform starts.  So for an LFO it may be more reasonable to have
> falling-sawtooth-based PWM because the effective start of the
> waveform, the rising point, stays in place as the modulating
> voltage changes.
> 
>   -- Don
> 
> -- 
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
> 
>