# [time-nuts] Time Interval Algebra?

John Ackermann N8UR jra at febo.com
Sun Dec 19 17:36:57 EST 2004

```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

```