[time-nuts] Re: Timestamping counter techniques : phase computation question

[Attila Kinali]

On Mon, 31 Jan 2022 17:42:38 +0100
Erik Kaashoek <erik at kaashoek.com> wrote:

> he clock is a 200MHz perfect clock.
> The events come from an unknown quality XCO at 10 MHz
> The measurement interval is 0.1 seconds
> The goal is to derive the phase (and also the frequency) of the XCO versus
> the clock from the counter data in the highest possible accuracy. Once this
> is done the rest of the post processing of multiple measurements can be
> done in tools like Timelab.

Ok, you seem to have fallen into the beginner's trap of frequency
measurement. You are trying to measure frequency using many samples
and then taking the average of this. Unfortunately, unless you are
using very stable oscillators and only short periods of total
measurement time, your average will get worse the more samples
you collect instead of getting better (i.e. your avarege will fluctuate
more and more the more samples you take instead of converging to a certain
value). This is the curse of 1/f^a noise (aka flicker noise) limited
measurements. It also goes as non-convergence of noise in clocks (or
generally metrological measurments). Assuming ideal oscillators does not
help either. Your oscillators aren't ideal. Not at the time scales you are
looking at. The only way to make them ideal in this sense and have
the measurement converge is to couple both oscillators through
some sort of PLL. But then, you wouldn't need to measure their
relative frequencies, you would already know it.

I suggest you to read at the very least IEEE 1139[1], NIST TN 1337[2] and NIST SP 1065[3]


				Attila Kinali


[1] IEEE Standard 1139 "Definition of physical quantities for fundamental
frequency and time metrology"

[2] "Characterization of Clocks and Oscillators" NIST Technical Note 1337,
by Sullivan, Allan, Howe and Walls, 1990
http://tf.nist.gov/general/pdf/868.pdf

[3] "Handbook of Frequency Stability Analysis", NIST Special Publication 1065,
by W.J. Riley, 2008
http://tf.nist.gov/timefreq/general/pdf/2220.pdf
-- 
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
        -- Richard W. Hamming, The Art of Doing Science and Engineering