# [time-nuts] Time Interval Algebra?

Tom Van Baak tvb at leapsecond.com
Sun Dec 19 21:31:49 EST 2004

```Brooke,

> 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.

Note in John's case there are actually three sources
of error: GPS, Rb, and counter. For tau on the order
of 1 second the counter is probably more limiting than
the Rb.

Just like there is a long-term crossover point in the
stability of Rb vs. GPS there also is a short-term
crossover point in the stability (or resolving power)
of the counter vs. Rb.

> 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.

True, most TI counters have dead time. But as long as
the interval being measured is less than hundreds or
tens of milliseconds and the source being measured
is 1 PPS there is plenty of time for a modern counter
to make the TI measurement, upload the result over
RS-232 or GPIB, and re-arm for the next pulse. In this
case the counter will never miss a measurement.

The only time you can get into trouble is if your initial
UUT 1 PPS sync is off or the UUT 1 PPS drifts so far
from GPS 1 PPS that you approach one full second
of time interval.

> I'd like to see how the math works when using my SR620 counter so that I
> could write my own Allan Variance software.

The SR620 is one of the few TI counters with built-in
AVAR calculations. In the config menu select Out,
then Jitter, then choose "Allan" instead of "Std Dev".
Or roll your own with the algorithm I sent previously.

/tvb

```