> 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
