[sdiy] Ridiculously PC (Phase Correct)

[Magnus Danielson]

From: Don Tillman <don at till.com>
Subject: Re: [sdiy] Ridiculously PC (Phase Correct)
Date: Sat, 3 Nov 2001 22:52:56 -0800 (PST)

>    Date: Sun, 04 Nov 2001 01:20:46 +0100 (CET)
>    From: Magnus Danielson <cfmd at swipnet.se>
> 
>    > For audio signals, the fundamental components of all waveforms are in
>    > phase, so that panning, switching, or mixing the individual waveforms does
>    > not result in any FM artifacts or unexpected changes in the amplitude
>    > of the fundamental.
> 
>    You mean Phase Modulation, not Frequency Modulation. If two of the
>    output waveforms have different phases for the same base or overtone
>    will the change in mix between them cause a shift in the phase of the
>    output waveform. 
> 
> I meant FM generically (like Chowning does!); PM is certainly more
> accurate.

OK. I understand but do not agree. I know that Chowning where carrying
the mixup of the expressions being used at the institution back then
and I know he did work on both FM and PM, but naturally all called
"FM". Outside of this little world I prefer if we stick to the
engineering terms. Technically is a perfect frequencymodulation
equalent to the derivate of a perfect phasemodulation since a perfect
oscillator fundamentally behaves like a perfect integrator with a
phase output.

> [equations omitted]
> 
>    According to this little investigation only the sawtooth is of phase
>    wise, if you derive the PWM and sine from the triangle waveform.
> 
> Yes, the sawtooth is the problem.
> 
> Historically many VCOs have derrived the PWM square from the sawtooth
> (MiniMoog, Moog901, Moog921, ARP2600, etc.) creating a waveform whose
> fundamental component shifts with the pulse width.  It's just as easy
> to derrive it from the triangle assuring constant phase.

Indeed. This is also why I chose the triangle as a source in this
case, since I *knew* that it also gets phasemodulated with the CV and
not only pulsewidth modulated. For someone not familiar with this
phenomena, consider a PWM wave, the center of the "high" and "low"
allways have the same phaseposition for all the overtones contained in
it. If you derive the PWM from a triangle these center positions are
stable in relation to the phase of the triangle, and thus is stable in
phase throughout the overtone spectra. If you derive the PWM from a
sawtooth, the high and low centerpositions move in relation to the
sawtooth waveform, and thus will the phase of all the contained
waveforms change.

An interesting note on the change of phases. If you have two PWMs
derived from the same sawtooth oscillator (just for simplicity) the difference
in PW between these will set the overtones in different phases in such
a way that modulating the PW will create a nulling pattern in the sum
of these. This nulling pattern will behave just like a phaser,
providing the comb pattern.

> The weirdest variation I know of is the ARP2600 VCO with the sine wave
> polarity opposite the triangle (!!!).  Presumably this make it easier
> to create an anti-triangle, but it's *so* unintuitive.

I can't see how it would make it easier to make an anti-triangle, but
never the less a curious detail.

> I've never heard of a commerical VCO with the correct saw/triangle
> phase relationship.

Indeed. Things are built according to tradition. I usually dive in to
Buchla schematics to get new ideas on how things can be done.

>    Phase-shifting the sawtooth waveform can be done using something
>    similar to my sawtooth phaseshifter at:
>    http://home.swipnet.se/cfmd/synths/schematics/
> 
> Yes, though it doesn't seem optimal to have a sawtooth core, and it's
> attendant reset time issues, when the core sawtooth wave gets chopped
> up in the phase shifting process.

Indeed. I find the triangle cores quite interesting in this
respect. Buchla used triangle cores, which gives triangle and
squarewave by default. From that he cooked the sawtooth in the
postprocessing. The trouble to cook a sawtooth out of only a triangle
is avoided by the squarewave, so it is all very simple indeed. The
sine is cooked out of the triangle wave. In this scenario the
sawtooth is just generated and not really used for much else instead
of being the core waveform. If you want to do PWM you can take either
the saw or triangle, all according to your needs.

A few km away from me a certain gentleman is cooking up a clone of a
Buchla VCO in a sligthly modernized way. I will be tracking that
project with interest, maybe even build a few.

Cheers,
Magnus