[time-nuts] Modified Allan Deviation and counter averaging

Poul-Henning Kamp phk at phk.freebsd.dk
Tue Jul 28 17:51:07 EDT 2015


Sorry this is a bit long-ish, but I figure I'm saving time putting
in all the details up front.

The canonical time-nut way to set up a MVAR measurement is to feed
two sources to a HP5370 and measure the time interval between their
zero crossings often enough to resolve any phase ambiguities caused
by frequency differences.

The computer unfolds the phase wrap-arounds, and calculates the
MVAR using the measurement rate, typically 100, 10 or 1 Hz, as the
minimum Tau.

However, the HP5370 has noise-floor in the low picoseconds, which
creates the well known diagonal left bound on what we can measure
this way.

So it is tempting to do this instead:

Every measurement period, we let the HP5370 do a burst of 100
measurements[*] and feed the average to MVAR, and push the diagonal
line an order of magnitude (sqrt(100)) further down.

At its specified rate, the HP5370 will take 1/30th of a second to
do a 100 sample average measurement.

If we are measuring once each second, that's only 3% of the Tau.

No measurement is ever instantaneous, simply because the two zero
crossings are not happening right at the mesurement epoch.

If I measure two 10MHz signals the canonical way, the first zero
crossing could come as late as 100(+epsilon) nanoseconds after the
epoch, and the second as much as 100(+epsilon) nanoseconds later.

An actual point of the measurement doesn't even exist, but picking
with the midpoint we get an average delay of 75ns, worst case 150ns.

That works out to one part in 13 million which is a lot less than 3%,
but certainly not zero as the MVAR formula pressume.

Eyeballing it, 3% is well below the reproducibility I see on MVAR
measurements, and I have therefore waved the method and result
through, without a formal proof.

However, I have very carefully made sure to never show anybody
any of these plots because of the lack of proof.

Thanks to Johns Turbo-5370 we can do burst measurements at much
higher rates than 3000/s, and thus potentially push the diagonal
limit more than a decade to the left, while still doing minimum
violence to the mathematical assumptions under MVAR.

[*] The footnote is this: The HP5370 firwmare does not make triggered
bust averages an easy measurement, but we can change that, in
particular with Johns Turbo-5370.

But before I attempt to do that, I would appreciate if a couple of
the more math-savy time-nuts could ponder the soundness of the
concept.

Apart from the delayed measurement point, I have not been able
to identify any issues.

The frequency spectrum filtered out by the averaging is waaaay to
the left of our minimum Tau. 

Phase wrap-around inside bursts can be detected and unfolded
in the processing.

Am I overlooking anything ?


-- 
Poul-Henning Kamp       | UNIX since Zilog Zeus 3.20
phk at FreeBSD.ORG         | TCP/IP since RFC 956
FreeBSD committer       | BSD since 4.3-tahoe
Never attribute to malice what can adequately be explained by incompetence.


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