# [time-nuts] Characterising frequency standards

Magnus Danielson magnus at rubidium.dyndns.org
Fri Apr 10 20:09:33 UTC 2009

```Tom Van Baak skrev:
>> Nevertheless leaving every second sample out is NOT exactly the same as
>> continous data with Tau0 = 2 s. Instead it is data with Tau0 = 1 s and a
>> DEAD TIME of 1s. There are dead time correction schemes available in the
>> literature.
>
> Ulrich, and Steve,
>
> Wait, are we talking phase measurements here or frequency
> measurements? My assumption with this thread is that Steve
> is simply taking phase (time error) measurements, as in my
> GPS raw data page, in which case there is no such thing as

I agree. I was also considering this earlier but put my mind to rest by
assuming phase/time samples.

Dead time is when the counter looses track of time in between two
consecutive measurements. A zero dead-time counter uses the stop of one
measure as the start of the next measure.

If you have a series of time-error values taken each second and then
drop every other sample and just recall that the time between the
samples is now 2 seconds, then the tau0 has become 2s without causing
dead-time. However, if the original data would have been kept, better
statistical properties would be given, unless there is a strong
repetitive disturbance at 2 s period, in which case it would be filtered
out.

An example when one does get dead-time, consider a frequency counter
which measures frequency with a gate-time of say 2 s. However, before it
re-arms and start the next measures is takes 300 ms. The two samples
will have 2,3 s between its start and actually spans 4,3 seconds rather
than 4 seconds. When doing Allan Deviation calculations on such a
measurement series, it will be biased and the bias may be compensated,
but these days counters with zero dead-time is readily available or the
problem can be avoided by careful consideration.

I believe Grenhall made some extensive analysis of the biasing of
dead-time, so it should be available from NIST F&T online library.

Before zero dead-time counters was available, a setup of two counters
was used so that they where interleaved so the dead-time was the measure
time of the other.

I can collect some references to dead-time articles if anyone need them.
I'd happy to.

Cheers,
Magnus

```