[sdiy] Unstability of oscillators and psychoacoustic qualities

[Magnus Danielson]

From: "jhaible" <jhaible at debitel.net>
Subject: Re: [sdiy] Unstability of oscillators and psychoacoustic qualities
Date: Mon, 23 Sep 2002 02:54:13 +0200

> Hi Magnus,

Hi Jürgen,

> >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.

I know! I am highly aware of it! ;O)

Also, it was on 1st degree PLLs which is what I expect to find here too, so I
was really sure it was in your courtyard for sure.

> 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.

Right. Where as I have spent hours in front an oscilloscope to measure the
hold-in/pull-in limits of my digital-implementer PLL (with as much analog feal
as you could expect from me on a 6-7k gate budget), so I know how
beating/pullin works by now. Trust me. What you gave was an spot-on description
of what I know as the beat/pull-in behavior. It would have been shame on me not
to see it!

> Thanks for making this connection. A real "missing link"!

Well, then there is a discovery right there!

We have already learned something important and I haven't even started
measuring anything!!!

> >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.

Yes, that is what we call the loop gain. I would not be supprised to find that
it depends on the input waveform amplitude for some (but not all) oscillators.

> 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!

Oh, thanks for the faith in me! ;^)

Naturally, I have been pondering on this problem, and I now have a stable model
for how it works. It is indeed the comparator in action. You can model the
comparator as being a summation (of the sync signal and the output waveform,
with the later having a negative sign, thus forming a subtraction) followed
by a limiter (i.e. the high raw gain of the comparator). The limiter output is
then being added with the control current (being pulled from the
expo-transistor pair) and sent into the current-integrator (capacitor over an
op-amp). The output of the current integrator is the output waveform.

The initial summation and limiter then in practice acts like the phase
comparator.

> >> > 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 have to some degree avoided the use of the term "fat" in these discussions.
I am not ruling out that "fat" is hotter than "warm" but right now I want to
keep things simple at first.

> >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.

I am not sure it turns out to be an EXOR function. I view it as a form of
analog sampling or limiter system in both the sawtooth and triangle comparator
cases. The phase error translates to a phase adjusment.

> 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.

Indeed!

> 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.

As I have already said, I think we have a sampling phase detector. The sampling
of a sawtooth waveform is a very good phase detector infact. I've used it
myself to great success!

> >> 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.

My point is that I think the issue has not been as clear to designers other
than "I guess it is a good thing to keep it down" and not "I need to keep
thermal noise to this leverl to make a warm (or cold) oscillator". I think
there is a high risc of afterconstruction, thus assuming that certain thoughts
where in place even when they where not. It is not sure it was known, it just
got "right" anyway. Or rather, because it got "right" we know of the succesfull
cases.

If there was designer(s) that had it in their minds, good for them!

Cheers,
Magnus