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

[Matthias Welwarsky]

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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