# [time-nuts] Time Interval Algebra?

Tom Van Baak tvb at leapsecond.com
Sun Dec 19 19:43:24 EST 2004

```Brooke,

If you're handy with C here's some code for Allan Deviation:
double adev (double phase[], long count)
{
long i;
double sum, y0, y, dy;

sum = 0.0;
if (count > 2) {
for (i = 1; i < count; i += 1) {
y = phase[i] - phase[i - 1];
if (i > 1) {
dy = y - y0;
sum += dy * dy;
}
y0 = y;
}
}
return sqrt(sum / (2.0 * (count - 1)));
}
/tvb

----- Original Message -----
From: "Brooke Clarke" <brooke at pacific.net>
To: <jra at febo.com>; <time-nuts at febo.com>
Sent: Sunday, December 19, 2004 16:07
Subject: Re: [time-nuts] Time Interval Algebra?

> 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
>
> --
> w/Java http://www.PRC68.com
> w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
> http://www.precisionclock.com
>
>
>
>
>
>
> 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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> > time-nuts at febo.com
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> >
> >
>
>
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```