Hi James,
On 07/30/2015 06:34 PM, James Peroulas wrote:
My understanding is that MVAR(m*tau0) is equivalent to filtering the phase
samples x(n) by averaging m samples to produce x'(n)
[x'(n)=1/m*(x(n)+x(n+1)..x(n+m-1))] and then calculating AVAR for
tau=m*tau0 on the filtered sequence. Thus, MVAR already performs an
averaging/ lowpass filtering operation. Adding another averaging filter
prior to calculating MVAR would seem to be defining a new type of stability
measurement.
Yes, fhat's how MVAR works.
Not familiar with the 5370... Is it possible to configure it to average
measurements over the complete tau0 interval with no dead time between
measurements? Assuming the 5370 can average 100 evenly spaced measurements
within the measurement interval (1s?), calculating MVAR on the captured
sequence would produce MVAR(m*.01)) for m being a multiple of 100. i.e.,
tau0 here is actually .01, not 1, but values for MVAR(tau) for tau's less
than 1s are not available.
The stock 5370 isn't a great tool for this. The accelerator board that
replaces the CPU and allows for us to add algorithms, makes the counter
hardware much more adapted for this setup.
Shouldn't the quantization/ measurement noise power be easy to measure?
Can't it just be subtracted from the MVAR plot? I've done this with AVAR in
the past to produce 'seemingly' meaningful results (i.e. I'm not an expert).
You can curve-fit an estimation of that noise and "remove" it from the
plot. For lower taus the confidence intervals will suffer in practice.
I calculated the PSD of x(n) and it was clear where the measurements were
being limited by noise (flat section at higher frequencies). From this I
was able to estimate the measurement noise power.
It is. Notice that some of it is noise and some is noise-like
systematics from the quantization.
AVAR_MEASURED(tau)=AVAR_CUT(tau)+AVAR_REF(tau)+AVAR_MEAS(tau)
i.e. The measured AVAR is equal to the sum of the AVAR of the clock under
test (CUT), the AVAR of the reference clock, and the AVAR of the
measurement noise. If the reference clock is much better than the CUT
AVAR_REF(tau) can be ignored. AVAR_MEAS(tau) is known from the PSD of x(n)
and can be subtracted from AVAR_MEASURED(tau) to produce a better estimate
of AVAR_CUT(tau).
Depending on the confidence intervals of AVAR_MEASURED(tau) and the noise
power estimate, you can get varying degrees of cancellation. 10dB of
improvement seemed quite easy to obtain.
Using the Lambda counter approach, filtering with the average blocks of
Modified Allan Variance, makes the white phase noise slope go 1/tau^3
rather than 1/tau^2 as it is for normal Allan Variance. This means that
the limiting slope of the white noise will cut over to the actual noise
for lower tau. so that is an important tool already there. Also, it
achieves it with known properties in confidence intervals. Using the
Omega counter approach, you can get further improvements by about 1.25
dB, which is then deemed optimal as the Omega counter method is a linear
regression / least square method for estimating the frequency samples
and then those is used for AVAR processing.
The next trick to pull is to do cross correlation of two independent
channels, so that their noise does not correlate. This can help for some
of it, but systematics can become a limiting factor.
Cheers,
Magnus
James
Message: 7
Date: Tue, 28 Jul 2015 21:51:07 +0000
From: Poul-Henning Kamp <[email protected]>
To: [email protected]
Subject: [time-nuts] Modified Allan Deviation and counter averaging
Message-ID: <[email protected]>
Content-Type: text/plain; charset="us-ascii"
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
[email protected] | 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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