[time-nuts] Time Interval Algebra?

John Ackermann N8UR jra at febo.com
Sun Dec 19 20:20:44 EST 2004

Tom Van Baak wrote:

>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.

There's where the light went on for me.  I hadn't considered that the 
importance of any offset was related to the length of the measurement 
interval.  In my current measurement, I'm looking at about a 30ms 
interval, so it perhaps is an issue.  The problem is that I'm using a 
very stupid 1pps divider that doesn't have a sync capability -- so the 
only way to adjust the interval is to momentarily disconnect the 5MHz 
drive and re-plug it until the offset gets down to some reasonable 
level.  I had figured less than 100ms was good enough, but now I know 
that's not so.  And, soon I'll have a better divider system...

(This, by the way, is the same measurement run we corresponded about not 
long ago, where the Rb had an unexplained temporary rate change about 17 
days into the record.  I now about 25 days of data (with one gap of 
about 6 hours) and in the last day or so the rate seems to have returned 
to normal.  I hope to keep it going for another couple of weeks to see 
what happens next.)

And, thanks for the refresher on the phase measurement details below.  
That part I think I have a reasonble grip on; it was the impact of 
having the unknown signal represented in two out of three measurement 
terms -- start and counter reference -- that had me confused.  The key 
learning from your message is that with a short interval the counter 
reference isn't critical.  That clears things up nicely.



>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.

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