[sdiy] VCO reset time

[Don Tillman]

   > 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