[time-nuts] Modified Allan Deviation and counter averaging

[Ole Petter Ronningen]

*Very* much looking forward to some insight on this method - I've done
pretty much the same experiment with an E1740A (48.8ps resolution); trigger
from a z3805A PPS, start TI measurement on the first rising edge of the
z3805A 10Mhz (on channel 1) following the trigger, stop the TI measurement
on (i.e.) the 30th rising edge on whatever signal is on channel 2.  Capture
100 samples gap-free every trigger, and average as described.  It is
severely bandwidth-limited by the GPIB interface as to the number of
samples that can be collected on a "per second basis", but the E1740A can
store up to ~500k samples, so it can all be batch processed after the
measurement is complete. It will be very interesting to see if the method
has any merit.

Ole

On Tue, Jul 28, 2015 at 11:51 PM, Poul-Henning Kamp <phk at phk.freebsd.dk>
wrote:

> 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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