Wednesday, March 16, 2011

Still hangin' with Allan...

* Mike had problems this morning & couldn't make it to meet the Symmetricom rep. He said he'd leave a catalog outside the door but I didn't find it when I got here.

* Re: The Allan deviation computations. I realized after leaving last night that I forgot to divide the sum of squares by the number of samples to get the mean. I also didn't normalize to dimensionless units (dividing by the nominal oscillator frequency) as is normally done. That is fixed now. Also, on Ray's advice, I vectorized the Allan deviation calculation, so now it is much faster. I dumped the data to a CSV file and graphed it in OpenOffice calc. Chekkit out! (Click on image to enlarge.) The red line, for comparison purposes, indicates the 1/2 power-law slope that would be expected if all of the deviation was due entirely to the (fixed) quantization error of oscillator phase measurement (which is at most +/- 100 ns), where the magnitude of these errors gets divided by the window size τ twice - the 1st time because there are τ independent phase samples that contribute to the overall phase offset for each data point, so the errors get averaged away by a factor of τ, and the 2nd time because the magnitude of the frequency delta gets divided by the window size to get a rate of frequency drift. (The starting point is sqrt(1/2)*1e-7, which is the expected deviation based on 1/sqrt(12) - the variance of the uniform distribution over [0,1], and the quadrature rules for combining x1+2x2+x3; though I'm still unsure if this is the right calculation.)


* Interestingly, the Allan deviation attains a minimum at a window size of almost exactly 1 day (86,400 seconds). Perhaps this means that, despite the OCXO's corrections, environmental temperature deviations over the course of the day are responsible for some of the frequency variation that we're seeing on smaller (multi-hour) timescales. Then, when you look at adjacent pairs of window longer than 1 day, you lose alignment with the day boundaries, so some of the error re-occurs. This suggests that we should also see minima at 2-day, 3-day, etc. window sizes. This is not the case, so perhaps this theory is wrong. It might just be a coincidence.

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