[time-nuts] What is the best counter for a Time Nuts?

Bruce Griffiths bruce.griffiths at xtra.co.nz
Thu Oct 9 12:08:58 UTC 2008


Magnus Danielson wrote:
> I think you mixed up the HP 53132A A-approximation with the Pendulum 
> linear regression. They are two distinct methods of improvements for the 
> intended application. Both have properties which does not make their 
> readings appropriate for Allan deviation calculations, as indicated in 
> the paper.
>
> Ulrich particular concern was the HP 53132A and then the triangular 
> approximation is the relevant one.
>
> One should recall that the properties of a system cannot be concluded in 
> a single parameter. Single-shot resolution is not everything, trigger 
> jitter, low frequency modulations, cross-talk, etc. etc. all come into 
> play to skew results before we can treat them by beutiful math.
>
> Single-shot resultion is an indication at best.
>
> Look at the HP 53132A where the single-shot resolution is 150 ps but the 
> trigger jitter is only 3 ps. Those numbers behave differently to gate 
> time and averaging. Increasing the gate time between a start and stop 
> trigger will increase the number virtual cycles you have, but the 
> trigger jitter for each start and stop will remain at 3 ps and thus 
> forming the floor which pure gate time cannot reduce. For this averaging 
> is needed.
>
> This is really what those ugly formulas in the back of the manual says. 
> Staffans papper above give some insight.
>
> Cheers,
> Magnus
>   
Magnus

When measuring the frequency of a signal using a conventional counter, 
increasing the gate time decreases the noise contribution of trigger 
jitter to frequency measurement noise although jitter is invariant with 
gate time. The jitter simply becomes a smaller fraction of the total 
gate time. Similarly the frequency measurement resolution increases with 
increasing gate time although the resolution (measured in picoseconds) 
is invariant with gate time it simply becomes a smaller fraction of the 
total gate time.

However if one timestamps a few more signal zero crossings within the 
gate time interval than just those and the start and end of the gate 
time lower noise estimators of the frequency are available.

The HP53132 averages the frequency estimates for a series of identical 
duration overlapped gate times.
Enrico's paper analyses this case.
The Australian paper corrects some of the errors in Enrico's analysis 
and hints how the analysis may be extended to cover the case of counters 
that use other resolution enhancement techniques.

Counters like the Pendulum CNT91 in effect time stamp every Nth zero 
crossing of the signal and fit a linear regression line to the sequence 
of time stamps. The frequency is then estimated from the slope of the 
regression line. However the CNT91 has limited memory and processing 
power so that full advantage isnt taken of the resolution offered by 
this technique.
AFAIK no one has yet done a similar analysis to that done for the 
"triangular" averaging counter (by Enrico and the Australians) for a 
counter that does a regression line fit.

Bruce



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