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

[Bob kb8tq]

Hi

The gotcha is that there are a number of very normal OCXO “behaviors” that are not
covered by any of the standard statistical models. Coping with these issue is at least
as important at working with the stuff that is coved by any of the standard statistical 
models ….

Bob

> On May 3, 2022, at 3:57 AM, Matthias Welwarsky <time-nuts at welwarsky.de> 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.
> 
> 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.
> 
> 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);
> 
> 	# 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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> 
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