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

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Oct 8 20:34:28 UTC 2008

```Ulrich Bangert wrote:
> Gentlemen,
>
> up to now I have been thinking that I am pretty well informed about
> current counter technology but some experiences of the last days make me
> doubt. The following applies to frequency measurements of a 10 MHz
> signal.
>
> I have received some data measured with an Agilent 53131 counter from
> Time Nuts member James Miller. That data shows a resolution of 3 digits
> after the decimal point for a frequency measurement of 1 s "Gate time"
> and 4 digits for a 10 s "Gate time".
>
> This is perfectly in line with what I thought to know about modern
> counters: Internally EVERY type of measurement is reduced to a time
> interval measurement. Since a frequency measurement with 1 s "Gate time"
> equals a time interval measurement of an 1 s interval and the counter
> has an single shot resolution of 500 ps the relative statistical error
> due to this resolution is 500 ps / 1 s = 5*E-10. As the frequency is
> computed from the time interval measurement is has the same relative
> error and for that reason displaying 3 digits after the decimal point is
> a good choice because 0.001 Hz (1E-10) is the least digit of
> significance. Using a digit more would suggest a resolution that is not
> available, using one digit less would decrease the numerical resolution
> below the measurement resolution.
>
> Up to this point my statement of beliefs is in harmony with Agilent.
>
> Now comes the strange part: In the course of a discussion between Time
> Nuts member Bernd Neubig of AXTAL Germany and me I received data
> measured with an Agilent 53132 which is the 53131's big brother with a
> better single shot resolution of 150 ps.
>
> I have been prepared to see this better resolution in the data but what
> I really have seen SHOCKED me a lot. Not only does the 53132 generate 5
> (!) digits after the decimal point for a 1 s "Gate time" (with 0.00001
> equal to 1E-12) a sigma tau diagram of the data revealed that the last
> digit was not only "noise" but seemed to be of real significance. I had
> been presuming that perhaps the counter's statistics had been enabled
> for that but as it turned out this was not the case. From that data one
> must make the conclusion that the overall jitter of the 53132 including
> the resolution quantification, trigger errors and everything else is
> <=5E-12 !!!!!!
>
> Big question: If the single shot resolution is only 3-4 times better
> that that of the 53131 and much inferior to the 20 ps of my SR620, how
> does the 53132 manage to be THAT GOOD A PERFORMER? Magic? Black art?
>
> I immediatly made the same measurement with my SR620 to receive a
> counter noise floor of 6E-11 for 1 s frequency data, pretty much a
> decade worse of the 53132. Must we throw our 5370s and SR620s out of the
> window and settle for second hand  53132 from eBay to make precise
> stability measurements ???
>
>
> Ulrich Bangert
> www.ulrich-bangert.de
> Ortholzer Weg 1
> 27243 Gross Ippener
>
>
>
Ulrich

These effectively counters time stamp every Nth signal zero crossing and
then fit a linear regression line to the results.
This reduces the effective noise contribution from the interpolator.
Since the noise transfer function is thereby altered over that of a
conventional counter or reciprocal counter one cannot use the results to
compute the Allen deviation directly.

Read the papers on the Pendulum site for further details.

Enrico Rubiola published a paper on the effect of using the output from
such counters in that Allen deviation calculations.

http://arxiv.org/abs/physics?papernum=0411227

A recent Australian paper purports to correct some of the errors in
Enrico's paper, but the basic conclusion is the same one cannot
calculate the Allen deviation directly from measurements obtained with
such a counter.

Bruce

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