[time-nuts] Time Interval Algebra?

[Tom Van Baak]

John,

You've got the correct setup. The TI counter need
not be clocked by anything special. My guess is
in your case each TI reading is only a couple of
digits, for example 12.345 us, so you don't need
an atomic timebase; you don't need an OXCO
timebase, just a relatively stable timebase - which
most ns counters will already have.

It is a very common misconception that you need
a precise (say 9, 10, or even 12 digits) and/or an
accurate (OCXO or atomic timebase) TI counter to
make phase measurements against GPS. As long
as your phase measurements are under 10 us, or
even 100 us, any dirt cheap ns TI counter will do.

You don't need a GPSDO with near zero offset
either. Just don't let the interval get up into the
millisecond level or the accuracy and stability of
the counter timebase will start to have an effect.

What you're looking for is not a particular phase
value, but a *trend* in phase. Now it may take
hours or even days before a clear phase trend is
apparent but when it shows up above the noise
the slope of the line is your frequency offset.

For example, if your phase grows by 100 ns a day
then your frequency offset is around 1e-12. To be
exact 1e-12 is 1 ps per second which is 86 400 ps
per day which is 86.4 ns per day. You get the idea.

This is a frequency *difference* between your Rb
and GPS. At this level you can assume GPS is
correct and so all the frequency offset is due to
your Rb. No need to divide or adjust anything.

You can compute ADEV directly from the phase
measurements you have recorded. As before the
results you get are the stability of Rb *relative* to
GPS. Here you have to be careful since you are
not quite sure how much is due to GPS and how
much is due to Rb, and it varies depending on tau.

It depends a lot on where your GPS 1 PPS is
coming from (VP, M12+, Z3801A, etc.) and what
tau you're looking at. You can be fairly sure that
for tau less than 100 s Rb beats GPS and for tau
more than a day GPS beats Rb. In this case also
there is no need to adjust the raw ADEV values.

But between those two extremes there's a gray
area where you need to measure rather than
assume. For a particular tau, only in the event
that GPS stability equals Rb stability can you
divide by sqrt(2) to guess the true stability.

/tvb

----- Original Message ----- 
From: "John Ackermann N8UR" <jra at febo.com>
To: <time-nuts at febo.com>
Sent: Sunday, December 19, 2004 14:36
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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