[sdiy] jitter in oscillators for music purposes

[Czech Martin]

I keep on thinking about this. And reading.

http://arxiv.org/pdf/physics/0204033

This nice article shows a study where a guy 
captured the noise of a bunch of op amps
for three months (!) (page 7).
The idea was to look after the 1/f component, if
it will finally saturate. No! Even in such a long timeframe
the 1/f (or 1/f**a with 1<a<2) law will be visible,
no saturation of noise level in the low end.

The author also makes some proposal why the appearent catastropy for
f=0 is not really such a big problem for a power density function
like 1/f**a.


More practically I scetched up a sawtooth vco core.
We have two major sources of hissing noise.
1.) the current source (with certainly a nice amount of noise
    for the very low currents)
2.) the comparator (assuming that buffer and comparator is
    a single block)

I assume , that no other interference is present, because
residuals of the 50/60 Hz stuff should add problems instead
of beauty, if they are too visible (locking).
Perhaps this exclusion is not justified.

Now, as Magnus said, the voltage noise on the comparator input
certainly leads to frequency modulation. Even if it is white,
the laws of small frequency modulation will shape the spectrum
accordingly. So we only need to compute the total noise
voltage at this point, following traditional methods.

The input voltage noise source of the comparators
translates directly, the current noise source will translate 
into input voltage noise via the oscillator
capacitor. I.e. the later noise voltage should scale with 1/f, and the
power accordingly with 1/f**2. 

So, additionally to the frequency modulation shaping, we
have a strong low frequency domination for the noise current.

At the same time we notice, that the partials (or should I say
partials + sideband) are very closely correlated.
You can not phase modulate them seperately, they are dependend
on each other.
So the example of noise driven bandpass filters is interesting,
but IMHO not really a good model for this single oscillator
business.

The noise current from the oscillator current source will have 
components of this transitor as well as of uncorrelated 
previous stages (op amps, summing circuit). Further more
the noise level will depend on the current. Anyway, the
spectral shaping due to integration through the timing cap
will take place.

All three components will add up (in the average) in a 
geometric sum expression, given that the have no correlation.
>From this I'd assume that the noise voltage that we sum up
at the comparator input is certainly NOT WHITE but contains
a very dominating 1/f*2 and maybe a 1/f region until flattening out 
in the frequencies of interest (0.001 Hz - 100kHz ?).

Unfortunately the main interest on investigation of this kind is
towards on chip plls (well, this is one of the biggest problems
for SoC). 

btw. when tuning the oscillator to very low frequencies we can
actually listen to the noise on the buffer or view
it on scope , from time to time disturbed by a large transient.

So, a DSP model of an analog vco should not modulate the frequency
with white noise allone, but with 1/f**2 noise as well.

m.c.