[sdiy] Analogue Drift (was Re: HF VCOs and tracking problems)

[Magnus Danielson]

On 11/14/2012 12:33 PM, Ian Fritz wrote:
> Thanks for that nice report, Richie.
>
> A little while back a person popped up asking why his analog VCO was
> drifting all over the place. Upon further questioning he indicated he
> was hearing fluctuations of a cent or less (0.06%). This is about the
> noise level I see when tracking a VCO (f-meter fluctuations). My
> tracking measurements are always done with an isolated VCO carefully
> shielded from drafts. It's also the reproducibility I get repeating a
> tracking curve measurement. So I'm guessing that's a typical drift
> number. (There has to be some drift, of course, from intrinsic
> semiconductor noise. The question about the Moogy Jitter is whether
> there is a large noticable effect.)
>
> Someone also posted some wav files of a Moog system a couple of years
> ago. He gave examples of the final output and the output of the
> oscillator itself. The VCO sounds pretty clean, with most of the grunge
> coming from the downstream circuitry.
>
> As for the kind of noise, my first inclination would be to look for a
> strong 1/f component. That comes up a lot in real physical systems and
> can easily be dominant at low frequencies.
>
> I recently built my first digital oscillator (whoa!) and can definitely
> hear a small difference between it and a side-by-side analog VCO. Doubt
> youl'd hear it in a mix, though. :-)

A typical oscillator should indeed have 1/f noise in it. Actually, the 
types of oscillators we have should all fit the Leeson model [1]. In 
short, the Leeson model assumes that the oscillator consists of a linear 
amplifier with a feedback loop as well as a resonance mechanism, where 
the Q-value will determine the bandwidth. The interested should get and 
read [2]. The oscillator models we have in analogue synthesizers is a 
bit different from the oscillators Leeson was modelling, but the 
concepts remains more or less the same. The amplifier noise of white and 
flicker noise is there for both gain-stage as well as comparator stage. 
The integrating capacitor with the charging current forms the forward 
step, with the comparator forming the feedback loop. Noise will modulate 
the exact voltage that trigger the comparator, and the slope will 
convert that to time, and it will offset the next cycle, so the 
integrating part also it forms matches the Leeson model. We can thus 
expect the phase noise to contain white noise (flat), flicker noise 
(1/f) or random walk (1/f^2) and flicker frequency noise (1/f^3). These 
noise forms then comes of top of all the systematic effects such as 
temperature dependencies. When trying to analyse the noise forms, 
traditional statistical methods comes short, so Dr. Dave Allan 
introduced [3] a unified measure stick which he called 2-sample 
variance, but we now know as Allan Variance (AVAR) but in real life we 
plot the Allan Deviation (ADEV). For more information on Allan 
Deviation, please see [4].

For full characterization of an oscillator, both the noise and 
systematic effects needs to be measured, and for a widely tune-able 
oscillator these properties will change over the range. The noise 
properties will be different at 150 Hz, 440 Hz and 3 kHz.

Cheers,
Magnus

[1] Leeson, D. B (February 1966), "A simple Model of Feedback Oscillator 
Noise Spectrum", Proceedings of IEEE 54 (2): 329–330, 
http://ccnet.stanford.edu/cgi-bin/course.cgi?cc=ee246&action=handout_download&handout_id=ID113350669026291

[2] Rubiola, Enrico (2008), Phase Noise and Frequency Stability in 
Oscillators, Cambridge university press, ISBN 0-521-88677-5

[3] Allan, D Statistics of Atomic Frequency Standards, pages 221–230. 
Proceedings of IEEE, Vol. 54, No 2, February 1966., 
http://tf.boulder.nist.gov/general/pdf/7.pdf

[4] Wikipedia, Allan variance, http://en.wikipedia.org/wiki/Allan_variance