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

Magnus Danielson magnus at rubidium.dyndns.org
Wed Oct 8 15:20:29 UTC 2008


Ulrich,

> 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.

To a reciprocal counter base measurement. For an insight in what
calculations is performed to shape results, see the HP 5372A programmers
manual which discloses a lot of details.

> 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.

Actually you need to multiply by two since both the start and stop channel
has independent errors. If you look in the 53131A/132A manual you see

RMS resolution = sqrt(t_RES^2 + Start Trigger Error^2 + Stop Trigger Error^2)

                 53131A  53132A
Trigger Error    500 ps  150 ps
t_RES            750 ps  300 ps

There is further details in the operational manual (chapter 3: Measurement
Specification).

> 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.

Certainly, and it matches the graphs in their manual very well.

> 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 ???

No. I think you are seeing the result of the 53132A gliding window
averager. There are articles that details this estimator and basically
cuts it into small pieces for use in Allan deviation measures.

You are right in not believing your eyes.

I have a 53132A at work and a SR-620 at home. I could compare them to
verify your measurements. 10 MHz sources are plentiful.

What you really should do is to take a number of raw TI difference
measures and calculate the Allan deviation plots for both counters. I
think you will find that they will match the 500 ps and 150 ps curves will
match better.

Notice that the timing jitter changes from 50 ps to 3 ps between the models.

I can dig up more details as I get home if you don't get enought here and
from fellow time-nuts.

The short story is: Do NOT estimate expected Allan deviation noisefloors
from the (display) readings of your counter. There exist several
"resolution improvement" algorithms. These are to our benefit when using
the counter as a frequency or period estimator as we can get result
quicker, but these improvements does not ripple over to the Allan
deviation plots.

Cheers,
Magnus



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