[time-nuts] Modified Allan Deviation and counter averaging

[Bob Camp]

Hi

The “simple” way to see what this does is to plug your sampling approach
into the DSP world and see what sort of filter it creates. Put another way - would you 
use this to make a lowpass filter? If so how good a filter would it be?

At least with a hand wave, I would not deliberately use this process as a lowpass. Since
it averages, it does have lowpass properties. Until you get to the point that you are averaging
a cycle, it’s not got *much* of a lowpass. It’s a discontinuous boxcar, you likely will get 
a few zeros in the passband around the width of your sample window. 

Now the question: Does this lowpass (crummy though it is) impact your noise? Well sure, to some 
degree it does. The big way it would is if those zeros (which probably aren’t as deep as you might think) line
up with a messy spike in your noise. 

So where are the zeros? If you take 100 samples of a 100 ns period waveform, your boxcar is
10 us wide. Expect zeros (or at least dips) at 100KHz XN. Move the samples up to 1,000 and your
dips are at 10 KHz X N. I’d suggest that most “normal noise” spectra are going to look pretty much
the same with and without what’s been taken away.  

Now, take it up to 10% of the total 1 second window and you are at 10Hz. Those zeros *are* going
to mess with your spectra and likely will impact your 1 second MVAR or AVAR or whatever. 

All that *assumes* you are taking a reading every cycle with the uber-5370. If you are doing it old school,
your sampling process will wrap the noise spectrum a bit. That’s going to make the analysis a bit more
messy. 

Bob


> On Jul 28, 2015, at 5:51 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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