[time-nuts] Re: Simple simulation model for an OCXO?

[Attila Kinali]

On Wed, 04 May 2022 19:31:08 +0200
Matthias Welwarsky <time-nuts at welwarsky.de> wrote:

> However. I'm looking for something reasonably simple just for the purpose of 
> GPSDO simulation. Here, most of the finer details of noise are not very 
> relevant. 

If you want it very simple, then I would only add white noise (i.e. uncorrelated
Gaussian noise) and 1/f^4 noise (integrate twice) at the approriate level.
This should give you the simplest yet, kind of faithful approximation.

But be aware that you will miss a lot of the corner cases, of the dynamic
things that happen, which make the control loop design of a GPSDO challenging.

> I don't really care for PSD, for example. What I'm looking for is a 
> tool that can produce a phase vector that just resembles what a real 
> oscillator is doing, looking from afar, with a little squinting. 

This is what we are getting at: a pure noise simulation might not get
you close enough for a faithful simulation to design a GPSDO control loop.


> This gives me a vector that, as far as Allan deviation is concerned, looks 
> remarkably like an LPRO-101. With some other parameters I can produce a 
> credible resemblance to a PRS10.

Oh.. a big fat warning here: ADEV and friends are very bad tools to check
whether two oscillator data sets are similar in behavior or not. *ADEV
do a lot of data compression. And it's logarithmic too! You enter a million
data points and get ~50 data points out. You enter 10 million data points and
get ~60 data points out. There is a lot lost in this compression. Unless
you make some quite limiting assumptions on what kind of behaviour the
oscillators are allowed to have, *DEV cannot be used for validation.

Attatched is the ADEV plot of an LPRO against an GPSDO. I guess yours looks
similar? You can see the shoulder due to the GPSDO's internal oscillator,
then going down with 1/tau down to a few parts in 1e-13 and going up again.
Looks pretty normal and you can identify white/flicker phase noise and
a frequency random walk region. A white frequency noise region
seems to be absent. So we expect to see mostly white noise and frequency
random walk.

Let us now look at the phase plot.... Does it look like what we expect?
Not quite. We see two/three distinct regions where the frequency seems
to be pretty stable, but inbetween there is a change in frequency which occurs
over the stretch of a few hours/days. Not quite what we expected. It definitely
does not look like frequency random walk. At best we can approximate it with
3 regions of almost constant frequency.

Now, let us zoom in into the first 114 days, which sem to be pretty stable.
This doesn't look like frequency random walk either. Again, we have regions
of almost constant frequency, that are seperated with hours/days of close to
constant frequency drift. But not only that, there seems to be an overreaching
arc of decreasing frequency, but it does not go linearly, but seems to be in
discrete steps that take time.

With this in mind, a faithful model of a LPRO would look quite different
than what one would have guessed from the ADEV.

(Before anyone asks: no, the frequency changes are not correlated with temperature
or ambient air pressure. My best guess is that they are light shift related, or
changes in the vapor cell but I cannot prove it)


				Attila Kinali

-- 
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
        -- Richard W. Hamming, The Art of Doing Science and Engineering
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