# [time-nuts] Time Interval Algebra?

Brooke Clarke brooke at pacific.net
Sun Dec 19 19:07:05 EST 2004

```Hi John:

I would think you would want to use your most stable (lowest Allan
variance at 1 second) 10 Mhz source as the clock for your time interval
counter.

It's all relative as to what's being measured.  Just think that you are
measuring the GPS 1 PPS (which in my view is the more correct point of
view since the short term (1 second) variation on the GPS is way larger
that that on the Rb if you want to see the GPS 1 second variation.).

If you assume the Rb is perfect then whatever the variation you see can
all be attributed to the GPS system.  This is probably correct for a 1
second Allan variation.  From the other point of view if you are looking
at very long term drift then it's certain to all be in the Rb source.
This would be the case for a 10,000 second Allan variation.

Some TI counters can make a new measurement once per second, but most
can not.  As an example of the latter case suppose that at time 0
there's a start signal, then at time 0.999 seconds that there's a stop
signal. The counter displays 0.999 but has not yet armed in time to
respond to the next start trigger at 1.000 seconds and so waits until
the next start signal at 2.000 seconds and then stops at 2.999 seconds
for another display of 0.999.

I'd like to see how the math works when using my SR620 counter so that I
could write my own Allan Variance software.

Have Fun,

Brooke Clarke, N6GCE

--
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John Ackermann N8UR wrote:

> I have what may be a dumb question but I can't get my head around it
> (having lousy high school algebra grades is not a good omen for a
> future time-nut).
>
> I'm doing a time-interval measurement of Rb vs. GPS, using 1pps
> signals.  For convenience, I'm using the Rb as the reference for the
> counter.  The Rb 1pps is going to the counter "start" input, and the
> GPS 1pps from a UT+/TAC is going to the "stop" input.
>
> Over many days, the phase record indicates about a -1x10e-12 frequency
> offset.
>
> My confusion stems from the fact that the counter is clocked by the
> device under test (the Rb), not the real reference (GPS).  Does that
> mean that the measured phase is actually twice the actual drift, so my
> -1x10e-12 is actually -5x10e-13?  I think so, but I don't have a lot
> of confidence in that conclusion.
>
> Once that question is resolved, next is what impact, if any, this has
> on the AVAR calculation.  Is it the equivalent of measuring two
> identical units, so you'd divide AVAR by sqrt(2)?  (This I'm not so
> sure about, since true "identical units" would have independent noise,
> while here the "two" devices would be walking together.)
>
> I suppose the real answer is to use a GPSDO as the counter reference
> to effectively have zero offset against GPS, but I didn't think of
> that in time :-).
>
> Thanks for any enlightenment...
>
> John
>
>
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```