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 >called the Hadamard Deviation. >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 _______________________________________________ time-nuts mailing list [email protected] https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
