Jackson Labs PHASE STATION 53100A, User Manual

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PhaseStation 53100A User’s Manual V1.04 25-Apr-2022 44
You’re fairly certain you’ll get a different result if you calculate the Allan deviation for a set of readings
taken one week apart, and still another result for a series of readings taken annually. So you record at
least a few data points at these intervals as well.
Now you’d like to draw a graph that shows off your watch’s performance, perhaps for bragging rights at
the neighborhood pub. What sort of plot would be needed to portray everything you’ve learned about
the watch? The X axis obviously needs to be logarithmic, given that your timescales of interest range
from minutes to years. The deviation figures will need to be plotted on a log axis as well, because they
might be thousands of times worse at one-year intervals than they are at one-minute intervals. Finally,
even though you recorded several years’ worth of annual readings, your graph will need to end at the
one-year point. There’s simply not enough data to describe the watch’s behavior at longer timescales.
If you keep these guidelines in mind as you graph your data, you’ll end up with a legitimate ADEV plot.
It will have three data points, each containing the result (
sigma
) of an independent calculation based on
at least a few samples of the clock’s frequency that were taken at a specific interval (
tau
). Lines or
curves can be fitted to this collection of discrete points, and the result will be a plot like those drawn by
TimeLab and other ADEV applications.
TimeLab’s statistical capabilities aren’t limited to Allan deviation -- the Measurement menu allows you
to view any of five types of statistical plots, during or after acquisition. Formulas exist
5
to calculate Allan
deviation and other statistics on the basis of both phase and frequency samples. TimeLab always works
with phase data internally, using incremental calculations for fast processing and overlapped algorithms
for high statistical quality. As with other measurements made by TimeLab, the statistical plots are
updated simultaneously in real time.
Allan Deviation ( a )
Allan deviation, or ADEV, is the square root of the Allan variance, σ
2
y
(τ ). Like its related
statistics MDEV and HDEV, ADEV describes the fractional frequency deviation ( σ , or
sigma
) of a set of samples taken at an interval τ (
tau
).
ADEV has a few disadvantages that are addressed by other deviation types, such as
inability to distinguish white PM and flicker PM noise. It also exhibits relatively low
confidence in the presence of smaller sample sizes, compared to some newer statistics.
Still, ADEV is among the most commonly-used performance metrics for high-
performance clocks and frequency standards.
5
W. J. Riley, Handbook of Frequency Stability Analysis ( http://tf.nist.gov/general/pdf/2220.pdf )