# [time-nuts] Time Interval Algebra?

Bill Hawkins bill at iaxs.net
Sun Dec 19 18:56:50 EST 2004

```John,

I think that it depends on the resolution of the counter. I'll bet
that you don't have a 12 digit counter. So, every time the counter
starts it counts some number of cycles of the Rb before it is stopped
by the GPS tick. The display resolution is considerably less than
10E-12 (in the sense of 10E-8 or -9) and so a drift of 10E-12 in the
Rb has no effect on the counter display.

The thing is, you start counting again every second. There is no
accumulation of error in the counter.

Eventually, enough phase shift shows up in the delta time recorded
from the counter. It is the true phase shift, not doubled because
the Rb was also used as the counter reference. The time difference
method is a fine way to get high resolution results from a low
resolution instrument. The Racal 1995 can be bumped out to 10E-12
resolution for frequency measurement. Then you would want less than
10E-12 (in the sense of 10E-13) stability in the reference.

My high school algebra class was disrupted by a guy who later dropped
out and made a fortune hauling trash. Made it tough to get through
MIT without that foundation.

Bill Hawkins

-----Original Message-----
From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com]On
Behalf Of John Ackermann N8UR
Sent: Sunday, December 19, 2004 4:37 PM
To: time-nuts at febo.com
Subject: [time-nuts] Time Interval Algebra?

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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