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

Brooke Clarke brooke at pacific.net
Thu Nov 30 16:31:53 EST 2006

```Hi Tom:

Is there a way to use the Allan plot to predict the variation in a reading?
For example if you use the plot comparing the 1 PPS from a GPS receiver
to a good Cesium frequency standard, then:
(1) what size of variation would you expect if the Cesium standard was
divided down to 1 kHz and that was compared to the GPS 1 PPS, or
(2) what size of variation would you expect if the Cesium standard was
divided down to 1 Pulse/1,000 seconds?

Have Fun,

Brooke Clarke

w/Java http://www.PRC68.com
w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
http://www.precisionclock.com

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
>
>
>
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>
```