# [time-nuts] Predicting clock stability from thevariouscharacterization methods

Tom Van Baak tvb at leapsecond.com
Thu Nov 30 13:26:20 EST 2006

```> Tom -
>
> Excellent description of the process. Glad you took the time to explain
this
> so clearly. While I do understand the process, I do not believe I could
have
> stated it so well. Not to nit pick, but you did make a small typo in that
> you interchanged the predicted and measured value of P2 in your example.
For
> most of us that will be obvious, and non relevant, but, to some it may be
> confusing. Regards - Mike

Ah, right. In the example, the prediction, P2', should
be 32 and the actual, P2, is 35; a prediction error of
3 us. Thanks.

----

By the way, here's extra credit for some of you:

(1) With one point you get phase, or time error.

(2) With two points you get change in phase over time,
or frequency.

(3) With three points you get change in frequency over
time, or drift. The standard deviation of the frequency
prediction errors is called the Allan Deviation.

This is a measure of frequency stability; the better the
predicted frequency matches the actual frequency the
lower the errors. A little bit of noise or any drift causes
the errors to increase; the ADEV to increase. In the
summation you'll see terms like P2 - 2*P1 + P0. You
can see why constant phase offset or frequency offset
doesn't affect the sum.

(4) With four points you get change in drift over time.
The standard deviation of the drift prediction errors is

This is a measure of stability where even drift, as long
as it's constant, is not a bad thing. In the summation
you'll see P3 - 3*P2 + 3*P1 - P0. You can see why
constant phase, frequency, or even drift doesn't affect
the sum.

----

So imagine a situation where you're making a GPSDO
and very long-term holdover performance is a key design
feature. What OCXO spec is important?

In this application phase error is easy to fix - you just
reset the epoch.

Frequency error is easy to fix. After some minutes or
perhaps hours you get a good idea of the frequency
offset. You then just set the EFC DAC to a calculated
value and maintain it during hold-over. In this case the
OCXO with the lowest drift rate (best Allan Deviation)
is the one to choose.

But with a little programming even drift is also easy to
fix. After some days or perhaps weeks you get a pretty
good idea of frequency drift over time and so you ramp
the EFC DAC over time to compensate.

The only limitation to extended hold-over performance
in such a GPDO is irregularity in drift rate.

In this example, the Hadamard Deviation would be a
good statistic to use to qualify the OCXO you need.
Drift, as long as it's constant (e.g., fixed, linear, even
log, or other prediction model) is not the limitation.

/tvb

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