[time-nuts] Allan variance by sine-wave fitting

[Ralph Devoe]

Hi time nuts,
      I've been working on a simple, low-cost, direct-digital method for
measuring the Allan variance of frequency standards. It's based on a
Digilent oscilloscope (Analog Discovery, <$300) and uses a short Python
routine to get a resolution of 3 x 10(-13) in one second. This corresponds
to a noise level of 300 fs, one or two orders of magnitude better than a
typical counter. The details are in a paper submitted to the Review of
Scientific Instruments and posted at arXiv:1711.07917 .
      The method uses least-squares fitting of a sine wave to determine the
relative phase of the signal and reference. There is no zero-crossing
detector. It only works for sine waves and doesn't compute the phase noise
spectral density. I've enclosed a screen-shot of the Python output,
recording the frequency difference of two FTS-1050a standards at 1 second
intervals. The second column gives the difference in milliHertz and one can
see that all the measurements are within about +/- 20 microHertz, or 2 x
10(-12) of each other, with a sigma much less than this.
      It would interesting to compare this approach to other direct-digital
devices.

Ralph DeVoe
KM6IYN
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