[time-nuts] Interpreting and Understanding Allen Deviation Results

[Magnus Danielson]

Hi Randal,

On 11/15/2017 05:12 PM, CubeCentral wrote:
> The results are shown here:  [ https://i.imgur.com/0sMVMfk.png ]  The
> associated .TIM files are available upon request.

As mentioned before, the preferred way of doing this is to do a time 
interval measurement between a start and a stop signal.

Typically you trigger on the GPSDO PPS output as a start signal and then 
stop with another signal. That way the time-base for re-trigger does not 
care as long as it is shorter than a PPS period.

> So, now we get to the heart of the matter and the questions this test and
> results have raised.
> I am trying to understand what the data is telling me about the test, and
> therefore the character of the counter.
> 
> 1)  Why are the plots a straight line from ~0.25s until ~100s?

The straight line slope, we call it 1/tau slope, is typically due to 
white phase noise and the counter time-quantization. Without going into 
details about how they mix, you often find that slew-rate limiting and 
non-ideal trigger-point can push this limit upwards. One reason for 
slew-rate limiting is low amplitude while the trigger point should be 
somewhere with a high slew-rate, that is quick change of voltage per 
time unit.

The starting-point of ~0.25 s is due to time-base setting in your setup, 
and it would not surprise me if the different levels is due to slight 
different time-base settings. Avoid using the time-base like that using 
the trick above.

Also, one should make sure that one get all the samples, they can play 
havoc with you.

The slope ends when other noise-formms become strong enough to reach 
over the slope. We try to use better counters to push this slope 
downwards, such that we can see the other noises for shorter 
time-intervals. If you don't really care about ADEV until 100 s or so, 
you are fine.

> 2)  Why, after falling at the start, do the plots all seem to go back up
> from ~100s to ~1000s?

That's where thermmal of A/Cs, house heating etc. starts to come in.
Also, the top part of the plot should not be too much trusted, it needs 
to run for a time to average out other noiseforms that obstruct the 
reading of a particular tau. Another way of saying this is that the 
confidence interval is very high for the top taus, and decreases.

> 3)  What do the "peaks" mean, after the plot has fallen and begin to rise
> again?
> 4)  Why is the period from ~1000s to ~10000s so chaotic?

These probably is a combination of thermal and lack of convergence 
effects. I would try to redo the measurement as described above, you 
should get more consistent results.

> 5)  The pattern "Fall to a minimum point, then rise to a peak, then fall
> again" seems to be prevalent.  What does that indicate?

Cyclic disturbances such as a house heater or A/C can create such patterns.

> 6)  Why does that pattern in question (5) seem to repeat sometimes?  What is
> that showing me?

You should be looking at the phase-plot, I expect you to see a few 
cycles of some pattern there. As you look at different distances they 
self-correlate or not at different multiples of time, as cyclic or 
semi-cyclic patterns tend to do. ADEV was never made to handle such 
systematic noises, so you need to cancel them out as they form an 
disturbance to your measurement.

> And finally, some general questions about looking at these plots.
> a)  Would a "perfect" plot be a straight line falling from left to right?
> (Meaning a hypothetical "ideal" source with perfect timing?)
> b)  Is there some example showing plots from two different sources that then
> describes why one source is better than the other (based upon the ADEV
> plot)?

You can expect a 1/tau slpoe from the source, to can expect it to 
flatten out and you can expect an sqrt tau slope up before hitting the 
tau slope, which often is obstructed by the tau slope from linear drift 
of oscillator. The later usually settles down.

The amplitude of these slopes represents the noise level of different 
noise types, but can only be seen once systematics have been reduced to 
negligable.

> c)  I believe that if I understood the math better, these types of plots
> would be more telling.  Without having to dive back into my college Calculus
> or Statistics books, is there a good resource for me to be able to
> understand this better?

The math behind these is kind of difficult if you are somewhat out of 
tune, but look at the Allan deviation wikipedia article, I tried to give 
some clues there.

> Lastly, thank you for your patience and for keeping this brain-trust alive.
> I am quite grateful for all the time and energy members pour into this list.
> The archives have been a good source of learning material.

As it should be. Be patient, try to learn from mistakes and you will 
pick up and learn tricks of trade. What you have in toys suffice to 
learn a lot useful stuff and get hands on practice.

Cheers,
Magnus