On May 3, 2022, at 3:57 AM, Matthias Welwarsky <[email protected]> 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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