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

Wed May 4 17:31:08 UTC 2022

Magnus, Attila, Bob,

thanks again for the inspirational posts, truly appreciated.

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. 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. For example:

synth_osc(N, -1e-8, 2.5e-11, 2e-11, 0, 0);

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. Add a bit of temperature wiggle and it's 
enough to run it through the simulator and tune parameters. The finer details 
are anyway completely lost on a GPSDO. Reaction to transients, especially from 
GPS, are much more interesting, which is why the logical next step is to 
produce a GPS (or GNSS) phase vector that can be parametrized and spiked with 
some oddities to see how different control loop parameters influence the 
output. But for that I don't have an immediate need, the GPS data files on 
Leapsecond.com are enough for now.

Regards,
Matthias

On Dienstag, 3. Mai 2022 22:08:49 CEST Magnus Danielson via time-nuts wrote:
> Dear Matthias,
> 
> On 2022-05-03 10:57, Matthias Welwarsky wrote:
> > Dear all,
> > 
> > thanks for your kind comments, corrections and suggestions. Please forgive
> > if I don't reply to all of your comments individually. Summary response
> > follows:
> > 
> > Attila - yes, I realize temperature dependence is one key parameter. I
> > model this meanwhile as a frequency shift over time.
> > 
> > Bob - I agree in principle, real world data is a good reality check for
> > any
> > model, but there are only so few datasets available and most of the time
> > they don't contain associated environmental data. You get a mix of
> > effects without any chance to isolate them.
> 
> Environmental effects tends to be recognizeable by their periodic
> behavior, i.e. period of the day and the period of the heating/AC. Real
> oscillator data tends to be quite relevant as you can simulate what it
> would mean to lock that oscillator up. TvB made a simulator on those
> grounds. Good exercise.
> 
> > Magnus, Jim - thanks a lot. Your post encouraged me to look especially
> > into
> > flicker noise an how to generate it in the time domain. I now use randn()
> > and a low-pass filter. Also, I think I understood now how to create phase
> > vs frequency noise.
> 
> Happy to get you up to speed on that.
> 
> One particular name to check out articles for is Charles "Chuck"
> Greenhall, JPL.
> 
> For early work, also look att James "Jim" Barnes, NBS (later named NIST).
> 
> Both these fine gentlement is recommended reading almost anything they
> write on the topic actually.
> 
> > I've some Timelab screenshots attached, ADEV and frequency plot of a data
> > set I generated with the following matlab function, plus some temperature
> > response modeled outside of this function.
> > 
> > function [phase] = synth_osc(samples,da,wpn,wfn,fpn,ffn)
> > 
> > 	# low-pass butterworth filter for 1/f noise generator
> > 	[b,a] = butter(1, 0.1);
> 
> Notice that 1/f is power-spectrum density, straight filter will give you
> 1/f^2 in power-spectrum, just as an integration slope.
> 
> One approach to flicker filter is an IIR filter with the weighing of
> 1/sqrt(n+1) where n is tap index, and feed it normal noise. You need to
> "flush out" state before you use it so you have a long history to help
> shaping. For a 1024 sample series, I do 2048 samples and only use the
> last 1024. Efficient? No. Quick-and-dirty? Yes.
> 
> The pole/zero type of filters of Barnes let you synthesize an 1/f slope
> by balancing the properties. How dense and thus how small ripples you
> get, you decide. Greenhall made the point of recording the state, and
> provides BASIC code that calculate the state rather than run an infinite
> sequence to let the initial state converge to the 1/f state.
> 
> Greenhall published an article illustrating a whole range of methods to
> do it. He wrote the simulation code to be used in JPL for their clock
> development.
> 
> Flicker noise is indeed picky.
> 
> Cheers,
> Magnus
> 
> > 	# aging
> > 	phase = (((1:samples)/86400).^2)*da;
> > 	# white phase noise
> > 	phase += (randn(1, samples))*wpn;
> > 	# white frequency noise
> > 	phase += cumsum(randn(1, samples))*wfn;
> > 	# 1/f phase noise
> > 	phase += filter(b,a,randn(1,samples))*fpn;
> > 	# 1/f frequency noise
> > 	phase += cumsum(filter(b,a,randn(1,samples))*ffn);
> > 
> > end
> > 
> > osc = synth_osc(400000, -50e-6, 5e-11, 1e-11, 5e-11, 5e-11);
> > 
> > Thanks.
> > 
> > On Montag, 2. Mai 2022 17:12:47 CEST Matthias Welwarsky wrote:
> >> Dear all,
> >> 
> >> I'm trying to come up with a reasonably simple model for an OCXO that I
> >> can
> >> parametrize to experiment with a GPSDO simulator. For now I have the
> >> following matlab function that "somewhat" does what I think is
> >> reasonable,
> >> but I would like a reality check.
> >> 
> >> This is the matlab code:
> >> 
> >> function [phase] = synth_osc(samples,da,wn,fn)
> >> # aging
> >> phase = (((1:samples)/86400).^2)*da;
> >> # white noise
> >> phase += (rand(1,samples)-0.5)*wn;
> >> # flicker noise
> >> phase += cumsum(rand(1,samples)-0.5)*fn;
> >> end
> >> 
> >> There are three components in the model, aging, white noise and flicker
> >> noise, with everything expressed in fractions of seconds.
> >> 
> >> The first term basically creates a base vector that has a quadratic aging
> >> function. It can be parametrized e.g. from an OCXO datasheet, daily aging
> >> given in s/s per day.
> >> 
> >> The second term models white noise. It's just a random number scaled to
> >> the
> >> desired 1-second uncertainty.
> >> 
> >> The third term is supposed to model flicker noise. It's basically a
> >> random
> >> walk scaled to the desired magnitude.
> >> 
> >> As an example, the following function call would create a phase vector
> >> for a 10MHz oscillator with one day worth of samples, with an aging of
> >> about 5 Millihertz per day, 10ps/s white noise and 10ns/s of flicker
> >> noise:
> >> 
> >> phase = osc_synth(86400, -44e-6, 10e-12, 10e-9);
> >> 
> >> 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?
> >> 
> >> Best regards,
> >> Matthias
> >> 
> >> 
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