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

[Attila Kinali]

On Mon, 02 May 2022 17:12:47 +0200
Matthias Welwarsky <time-nuts at welwarsky.de> wrote:

> There are three components in the model, aging, white noise and flicker noise, 
> with everything expressed in fractions of seconds.

So far so good, but you are missing one major component that is
important for a GPSDO: temperature dependence. All OCXO have
a slight temperature dependence that can be anything from a
few 1e-12/K to tens of 1e-9/K. It's often also not linear
and, generally, not well specified in OCXO data sheets.
There were plenty of discussions about this on time-nuts
and especially Bob Camp has shared a lot of good information.

 

> The third term is supposed to model flicker noise. It's basically a random 
> walk scaled to the desired magnitude.

Random walk is not flicker noise. Random walk has a PSD
that is proportional to 1/f^2 while flicker noise has a PSD
that is proportional to 1/f.

Though, at the time scales that are interesting for a GPSDO
(i.e. (mili-)seconds to minutes) the dominant noise would be flicker
frequency with a (phase) PSD of 1/f^3 or even random walk
frequency with a (phase) PSD of 1/f^4.

 

> What I'd like to know - is that a "reasonable" model or is it just too far off 
> of reality to be useful? What could be changed or improved?

The model is ok, though I would definitely add the model for
temperature dependence. Also, for a GPSDO you will need to model
more than just a day. A lot of effects, not just temperature,
have periodes of 12-24h. If you simulate only a single day, you'll
not properly simulate all those long term effects. Not to mention
that temperature looks weird when looking at it on a larger scale.

Attached are two representative plots of what the temperature in
a normal (small) office looks like, when nobody is allowed to enter.
One graph is for Jan-Sept of 2021 and one for May (units in °C).
You will see that there is quite some structure and "weirdness"
to it. Especially note that here is a not-quite daily spike in
temperature when the heating comes on somewhen between 18:00
and 22:00 and shuts off again between 21:00 and 00:00.

The noise in the temperature is mostly due to convection in
the room and not due to the noise of the temperature sensor.

I would also recommend that you create your noise vector with
something like sigma-theta by François Vernotte[1,2].
The bruiteur tool can generate all types of noise directly and
give you a single vector to read and process. This should be
faster than building your own power law noise simulator.


			Attila Kinali

[1] https://theta.obs-besancon.fr/spip.php?article103&lang=fr
[2] https://sourcesup.renater.fr/www/sigmatheta/

-- 
The driving force behind research is the question: "Why?"
There are things we don't understand and things we always 
wonder about. And that's why we do research.
		-- Kobayashi Makoto
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