[time-nuts] Time Interval Algebra?

John Ackermann N8UR jra at febo.com
Tue Dec 21 19:53:42 EST 2004

Hi Bill --

You're right that to get a drift value you only need two measurements 
spaced at the appropriate time interval for what you want to measure.  
It gets more interesting when you want to look at stability more 
closely.  Attached is the phase plot I've been running for the last few 
weeks.   If you look at the first 17 days, you have a nice clean 
accumulating offset of about -1x10e-12.  But at day 18 something happens 
(who knows what -- I was in India at the time, and there's no sign of a 
temperature change or any other factor to cause a change) and the offset 
flattens out.  Then five days later it starts trending down again.  If I 
only measured from days 19 through 21, I'd think the oscillator had 
virtually zero offset.

So, to see what the long term stability looks like, I'm taking readings 
at regular intervals over, well, a long term.  In this case, I'm using 1 
second intervals because that's what the output is from the GPS, but 
each line in the data file is an average of 300 readings (5 minutes) 
because with anything shorter the GPS noise overrides any useful 
information.  Averaging more readings also increases the effective 
resolution of the counter.

With a set of these equally spaced phase readings, I can do an Allan 
Variance calculation that will quantify the stability of the oscillator 
over various averaging times.  I've also attached an AVAR plot of the 
run so far.  (By the way, the tool I use for this analysis is a 
commercial package called Stable32, but as Tom noted you can generate 
the AVAR values from a fairly simple piece of code.)

Noise in the divider chain can be a problem, but for these long-term 
measurements it doesn't add too much uncertainty.  The divider I'm 
currently using is a simple set of 74LS390 chips, but I'm about to 
replace that with a PIC-based single chip divider based on a design that 
Tom did a few years ago.  I've worked with a friend who has more PIC 
skills than I to modify Tom's code to work with a 5MHz, rather than a 
10MHz, clock.

Bill Hawkins wrote:

>Why is it important to get every measurement? If I turn the counter on
>Monday afternoon, get a reading of 0.500000 seconds, turn it off and 
>next Monday afternoon get a reading of 0.500027, then I have an offset
>or error of 27 +/- 1 microseconds in 7 days. Each reading has been accurate
>to 1 microsecond, which requires that the counter clock drift less than
>0.1 microsecond per second.
>I suppose that the problem is that this doesn't allow an Allan Variance
>calculation based on one calculation per second. Why must it be one per
>second, not one in 10 or 100 seconds? Or why not 100 per second?
>A larger problem may be the variance in the counter that is dividing the
>Rb output into 1 pulse per second. Are the counters all clocked by the
>Rb clock or is it a simple cascade of decade counters?
>Bill Hawkins
>time-nuts mailing list
>time-nuts at febo.com

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