[sdiy] Unstability of oscillators and psychoacoustic qualities

[jhaible]

Hi Magnus,

>Hmm... are we discussing a form of PLLing here?

>I view a synched VCO as an oscillator being repeatedly and abruptly phase
>modulated.

>What you seems to describe looks to me like that of a PLL, which beats
until
>the frequency is close enought for the loop to be strong enought to
>"pull it in" and actually move the center frequency of the oscillator and
thus
>reduce the modulations from the synching. You can form a PLL from basically
>nothing once you have an oscillator as such. You, Jürgen, of all people
here
>should known that!

You are right! (blush)
This was in fact the topic of my diploma work. Only that I have used it
to build a demodulator for FM radio, where the VCO never left the lock
condition. Strange that I never thought about the Korg Lambda's VCOs
under this aspect. Thanks for making this connection. A real "missing link"!

>The question is how one best analyses this behavior in a real oscillator?

That was more than 10 years ago - let me try to recall it - I think the
lock range depends directly on the "weights" of the integrator signal
and the external VCO's signal, respectively, to the comparator input.
In that straigt forward FM demodulator application, it was just a resistor
ratio. I'm pretty sure that with saome analysis of a given VCO structure,
and measurement of the lock range at a given frequency, one can precisely
determine the strength of the unvoluntarily coupled signal from the other
oscillator. Looks interesting, and looks like a typical Magnus project
to calculate it!


>> > I also think that near equal frequency tones feel "warmer" than any
>> > of those notes on their own.
>>
>> Certainly.
>
>It should be noted that this is also similar to having a single tone
amplitude
>modulated by half of the difference signal.


Here is where the waveform aspect comes in, too.
With sine or square waves you get "100% beating" between total cancellation
and signal doubling. With saw waves (of equal polarity) its much less, and
you also get a periodical change of "colour". Especialy when you run the
beating saw waves into a nonlinear function that clips the extremes, like
a filter at overdrive. A filter that sounds pleasant when it's heavily
overdriven
can make beating saw waves much fatter (or warmer ?) than a linear filter,
because it allows for more delta_f between the VCOs without an unpleasant
out-of-tune impression. I think this is another aspect of filters
contributing
to "warmth", in addition to Dave Krooshof's excellent point on VCFs he just
posted.

>I wonder if it is not the reset comparator that acts the phase detector
when
>the oscillator PLLs in.

Yes, sort of. For a triangle VCO with resistive coupling to the integrator,
you can model (in theory) the phase reversal function of the VCO
with an EXOR gate, where one input is controlled by the comparator, and the
other input sees the CV for the VCO in form of a (fictious) PWM rather than
a continuous signal. Then you'se using a second EXOR gate as Phase Detector
(PD), with no loop filter between its output and the fictious VCO-EXOR.
(No loop filter means 1st order PLL.)
The PD EXOR has the external (master VCO) signal at one input, and the
internal (local) VCO signal at the other input.
If you draw this on a piece of paper, you see that both EXOR gates have
the local VCO signal at one of it's inputs, so the effect of the two EXORs
*cancels* under any condition, i.e. you can replace the two EXORs with
a straight connection.
This is the proof that a triangle VCO with resistive coupling to its
integrator
acts like a PLL under certain circumstances) with an EXOR function for
its PD.

I guess these would be a very similar description for a saw VCO. I don't
know if it also comes down to an EXOR PD - maybe it's a different function
then.


>> Some VCOs use noisy components and have that modulation built-in,
>> some VCOs avoid noisy components and give the choice between
>> stable and warm, by choosing external modulation.
>
>Yes, but do people really *think* actively about phase noise when designing
>oscillators for musical applications? Please present me a designer that
does
>this! ;O)

I guess the first VCO designs used the opamps / zeners / whatever was
available and had to live with the noise that was introduced. In some
cases noise even saved the VCOs from unwanted locking and contributed
to the sound of a classic.
Later VCO designs tried to keep the noise out of the VCO core, giving
the user more freedom to choose whatever form of modulation they
wanted to use or to avoid. And of course they didn't have that instant
built-in modulation known from Moog or EMS. (I would put Emu,
probably ARP, and MOTM in that category.)
Whether the designers expicitely thought about "phase noise" or just
"noise" I don't know. I know for certain that Emu pointed out the importance
of a clean CV path for filters for a clean filter function quite early
in the data sheet of their SSM chips.

JH.