[time-nuts] ADEV measurement question

Magnus Danielson magnus at rubidium.dyndns.org
Wed Aug 19 15:52:56 EDT 2015

Dear Mathias,

On 08/19/2015 06:40 PM, Matthias Jelen wrote:
> Hello,
> I´ve got a question concerning ADEV-measurements.
> I´m measuring the 15 MHz output of a KS-24361 with my SR-620 with it´s
> internal (Wenzel) OCXO using Timelab. For the first shot I used the
> counters frequency mode with 1s gatetime. ADEV at tau=1s turned out to
> be arounf 2E-11, which fits the 20 ps single shot resolution of the
> SR-620 nicely.
> To overcome this limitation without setting up a DMTD system, I used the
> counter as TIC, feeding 1 kHz (derived from the counter´s reference) to
> the start channel, the 15 MHz to the stop channel and put the counter
> into average mode / 1k samples. This gives me one averaged result per
> second.
> The idea was that this shouldn´t change the measurement itself, because
> like in frequency mode with 1s gate time I get the averaged value over
> one second, but I expected trigger noise etc. to be averaged out to a
> certain amount. I have to watch out for phase wraps, but as the two
> frequencys are quite equal, this is not a big issue here.
> As expected, ADEV at tau=1s got much better, it is now in the 4E-12
> area, which sound reasonable.
> What makes me wonder is the fact that result are significantly better
> now at longer taus (10..100s) also, despite of the fact that also in
> frequency mode these result were well aboce the noise floor (2E-12 @ 10s
> and so on...).
> So, is it a good idea to use this kind of averaging, or am I overlooking
> something which turns the numbers better than they really are? I´m
> pretty sure I am not the first one to try this...
> I´m looking forward to your comments.

OK, averaging or filtering of data before ADEV processing is tricky, as 
it filters the data. Whenever you do that, you actually convert your 
measurement from an ADEV measure to something else. If you do proper 
post-processing, this something else can have known properties and thus 
we can relate the amplitude of the curve to amplitude of various noise 
sources, as it will cause biasing from the ADEV properties.

The reason you get better results is because the ADEV response on white 
noise depends on the measurement system bandwidth (see Allan deviation 
wikipedia page), and by averaging you do reduce the bandwidth.

Sometimes when you do this, you loose the gain as you increase the tau, 
since the dominant frequency will lower and become more and more into 
the pass-band of the fixed bandwidth filter you created. What you see is 
that it flattens out to the length of the average before lowering down, 
as if there was no filtering, so you have only achieved a gain in skewed 
value for very short taus, but then no gain at all for longer taus, so 
no real gain.

This was realized in 1980-1981 and in 1981 an article was published in 
which they realized that they can change the bandwidth along-side the 
change of tau, so that the gain remains. This became the modified Allan 
deviation (MDEV), and was inspired by the methods for improving 
frequency measures for lasers as presented by J.J. Snyder in 1980 and 
1981. J.J. Snyder was doing what you proposes, averaging of blocks, and 
then extended this in software, and this became a direct inspiration for 
the MDEV development, which does a pre-averaging over tau before 
processing through ADEV, and this combined is the MDEV.

Doing TIC averaging and then continue the processing with MDEV 
processing should produce a proper MDEV curve, unless my tired brain 
does not miss out on details. If you then analyze it as a MDEV (rather 
than ADEV) then you use the values properly. MDEV have the benefit that 
white phase noise drops by tau^-1.5 rather than the ADEV tau^-1, and 
starting with the SR-620 means you for fairly low taus hit actual 
measurement noise. The averaging makes this trip from tau0 of 1 ms in 
your setup.

So, you can go down this route, but you need to be careful to ensure 
that you have done the processing correctly enough that you get the 
results that can be interpreted properly.

Oh, as you average, phase-unwrapping becomes "interesting". :)


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