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

Arnold Tibus Arnold.Tibus at gmx.de
Thu Nov 30 13:58:18 EST 2006

```Hello Tom,
many thanks as well from my side, in lieu of a lot of interested people,
for your short but splendid teaching excursion!
I had realized this crossing of values, a minor point, but now it is fully
clarified.
It will be hard to beat the explanation.

greetings,

Arnold

On Thu, 30 Nov 2006 10:26:20 -0800, Tom Van Baak wrote:

>> 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

```