[time-nuts] Phase microsteppers

Tom Van Baak tvb at leapsecond.com
Thu Mar 10 17:06:53 EST 2005

Before I answer the microstepper questions let me
first describe the alternatives.

Let's suppose you have the following:
- a working cesium (or rubidium) standard,
- a government reference (such as Loran or GPS),
- time interval counter, and perhaps
- some sort of PC logging (GPIB, RS-232, etc.)

Within hours, or certainly days, you notice your Cs
1 PPS is diverging from a UTC 1 PPS. So what to
do about this?

You can compute the average Cs frequency error
with just two data points since frequency is delta
phase over delta t. So you really don't even need
PC logging for this. Just look at your TI counter
display, wait a day and look at it again. 864 ns a
day is 1e-11, 86 ns a day is 1e-12, etc.

Or you can get fancy and plot phase and look at
the slope. If the slope is ragged, wait longer until you
see a clear trend. This could be hours or even days.

If you don't like amount of frequency error you can
try to adjust the C-field. It will take several tries but
you should be able to get your Cs accurate to within
1e-12; maybe better depending on your eBay luck.

If you want to get closer than this you may want to
first check the stability of the standard. After several
days or weeks of data you can compute the Allan
Deviation of your standard for, say tau 1 day. Even
just one data point per day for a week is enough to
give you a rough ADEV result.

If you find the ADEV doesn't get much below 1e-12
then there's no point in trying to set the accuracy
of your Cs below 1e-12. Stability is not affected by
accuracy but accuracy is limited by stability.

No clock is perfect. Clocks have noise floors. At the
1e-12 or 1e-13 level frequency will wander, phase
error will, over time, grow unbounded. The same is
true for wristwatches (just move the decimal point
over far enough).

The reason I stress computing the ADEV is so that
you can adjust your expectations. I'm pretty sure no
amount of C-field adjustment of a standard 5061A will
get you down to 1e-13 or the 14's.

All Cs standards, once set, will show accumulated
phase errors, no matter how carefully you set the
 rate or control the environment. So you should
expect over days, or weeks, or months, that your
Cs will be off by many nanoseconds, even many
microseconds, eventually.

It then becomes humbling that a $25 surplus GPS
receiver will easily beat your cesium as source of
a UTC tick ;-)

So the first point I wanted to make is don't expect
your Cs to ever be perfectly accurate.

The next question is, after you get the C-field set
to your liking, how to make further time or rate


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