[time-nuts] Interpreting and Understanding Allen Deviation Results

Attila Kinali attila at kinali.ch
Wed Nov 15 18:46:47 EST 2017


There are other, more qualified people who should answer your questions,
but until they get around to it, let me give you some pointers to read
up upon.

First of all, you probably want to read [1] and [2]. Especially the
latter does explain the effects of the different noise types and
how they look like in the *DEV plots quite nicely.

On Wed, 15 Nov 2017 09:12:22 -0700
"CubeCentral" <cubecentral at gmail.com> wrote:

> I then set the Time Lab V1.29 software to repeatedly acquire data for 12
> hours, starting the next test as soon as I could.  This means that,
> normally, a test was run during the day for 12 hours, and then overnight for
> 12 hours.

> The results are shown here:  [ https://i.imgur.com/0sMVMfk.png ]  The
> associated .TIM files are available upon request.

For this kind of test, I would rather use TDEV, as it shows more details
especially at longer taus, but if you are specifically looking for
frequency stability measures, ADEV (or MDEV) should be fine.

You should also switch on the error bars. Especially if you are looking
at the longer taus, close to your measurement length.
> 1)  Why are the plots a straight line from ~0.25s until ~100s?

Because they are dominated by white phase noise and flicker phase
noise which falls with 1/tau. The start point on the left side
is limited by your measurement precision, ie minimum resolution
of the instrument and its (white) noise.

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

Because other noise types (white frequency, flicker frequency,...) become
dominant. What you see there is basically the instability of the measurement
electronics, the change in delays within the instrument due to temperature,
humidity, aging and other effects, trigger point changes, etc

> 3)  What do the "peaks" mean, after the plot has fallen and begin to rise
> again?

They are probably statistically insignificant, but it's impossible
to tell without the error bars. What wavy *DEV usually mean is,
that you have some periodic disturbance (A/C unit cycling, diurnal temperature
change, people walking in at specific times, train passing by on track nearby).

It's also a good idea to look at the phase plot or frequency plot
to see whether there are any deterministic effects that you can see.

> 4)  Why is the period from ~1000s to ~10000s so chaotic?

Statistical instability. You are measuring for 12h, that's 43200 seconds.
So at a tau of 10k, you only have roughly 4 samples. You cannot do any
valid statistics with that.

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

Ideally, it should go down first (WPM, FPM), reach a minimum (WFM)
then go up again (FFM,...). But with such a short run it will not
be that way (statistical uncertainty). But then, very few plots
are really that way, because at the longer tau, the effects that
affect the measurement tend to be less and less gaus distributed
and you start to see patterns.

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

The repetition is a prime characteristic of a periodic disturbance.
But in this case it's more likely that it's just the bad statistics
tricking you into thinking you see a pattern where there is none
(at least none of statistical significance).

> 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?)

Yes. If you had only white and flicker phase noise. But this is
quite hard to achieve with frequency counters that have dead time
between measurements.

> 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)?

Lower is better... but where it should be lower depends on your
target application.

> 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 two documents I listed below should get you started.
The problem is, if you really want to understand what's going
on you will need to understand what the different noise types
are, how they behave mathematically and that's where things
get... weird. If you go that road, you will soon learn that
your college calculus will only be a very rough guide, like a
1:25'0000 map while trying to navigate a city. While white
phase noise is relatively easy to understand with Probability 101,
the higher order noises are not. 

I am currently trying to put a small document together of what
I've learned about noise, but it's increadibly hard as the math
is quite often beyond me. Not to mention the knowledge is very
fragmented over the fields of mathematics (statistics/probability,
fractals, stochastic calculus, fractional calculus, ...), physics
(solid state physics, fluid dynamics, ....) and engineering...
and each of these (sub-)fields using a different nomenclature
and different notation.

			Attila Kinali

[1] "Characterization of Clocks and Oscillators", NIST Technical Note 1337,
by Sulivan, Allan, Howe, Walls, 1990

[2] "Handbook of Frequency Stability Analysis", NIST Special Publication 1065,
by Riley 2008

PS: It's Allan Deviation, not Allen.
You know, the very powerful and the very stupid have one thing in common.
They don't alters their views to fit the facts, they alter the facts to
fit the views, which can be uncomfortable if you happen to be one of the
facts that needs altering.  -- The Doctor

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