[time-nuts] ADEV noise floor vs counter gate time

[Dave Martindale]

How is the counter configured?  Are you reading period or frequency?  Are
you in "E?" (Every Result) mode, or "C?" (Continuous Result) mode?  The
former should give you continuous but independent measurements, while the
latter gives heavily overlapped measurements.  (For example, with a 100
second gate time, you get one E output every 100 seconds, which covers a
different 100-second period than the previous measurement.  In C mode, you
get one output every 2 seconds, each of which is an estimate from 100
seconds of measurement, but 98 seconds of that data was also part of the
previous output and only 2 seconds of new data is included).

What does the data returned by the counter actually look like?  The manual
implies that you always get 10 digits worth of result (not including the
exponent) regardless of gate time, but are the values rounded for display
in 7, 8, or 9 digits at the shorter gate times, or are they a full 10
digits always?  Given any particular value of frequency or period you get,
you should be able to reverse-calculate the number of whole cycles of the
input signal that the counter used as a gate time, and the number of cycles
of 50 MHz timebase that were counted in that period.  Since the counter
doesn't have interpolators, both of these values should be integers, and so
the possible output values are a small subset of all possible 10-digit
values for the shorter gate times.

For example, if the difference frequency is exactly 90 Hz, the period
between two "1 second" measurements will be exactly 1 second, and the
counter will record 90 cycles of input and 5e7 cycles of timebase,
exactly.  In frequency mode, the output should be 90.0 Hz exactly, and in
period mode the output should be 11.11111111 ms.  Now suppose that the
difference frequency is just a hair slow, enough that 90 cycles of input
spans 50,000,001 counts of the timebase.  The reported frequency should be
89.99999820 Hz and the reported period should be 11.11111133 ms.  With a 1
s gate time, no values between those are possible unless the values are
being rounded (or there is an error in the calculation, which is always
possible).  Looked at another way, the smallest possible change in the
reported period is one timebase clock (20 ns) divided by the number of
input cycles in one gate time (90 for 1 s).

If the counter is rounding, you may be able to unambiguously figure out
what the actual inputs (cycles of input and cycles of timebase) to the
calculation were, and use that instead of the rounded value in your
calculations.  Rounding may round up or down, but if the two oscillators
are stable enough the direction can be predominantly "up" or "down" for
long periods of time, adding a bias to the actual frequency or period
you're measuring.  (I don't know what effect this bias would have on ADEV).

- Dave

On Mon, Mar 16, 2015 at 10:15 AM, James via time-nuts <time-nuts at febo.com>
wrote:

> Hi All,
>
> I'm in the process of getting a better counter, but at present I'm using
> my TTi TF930 counter.
>
> For those who don't know it, it is a reciprocal counter which should be
> continuous, it counts periods in terms of its internal 50MHz clock which
> I've locked to an external 10MHz reference.
>
> There are 4 gate times available, 0.3 secs, 1 sec, 10 secs and 100 secs.
>
> These correspond to 7, 8, 9 and 10 digits.
>
> I've been experimenting with using a single mixer (mini circuits ZAD+)
> along with a 1MHz low pass filter and appropriate attenuators to measure
> Alan Deviation (using my own software).
>
> My set up is a 10MHz reference source (MV89A which I've approximately set
> using a 10kHz GPS signal).
>
> The reference is used as the external reference for an Agilent 33522A
> arbitrary waveform generator.
>
> The 33522A generates an 9.999910 MHz (10MHz - 90Hz) sine wave at 300mVpp
> to the mixer and the mixer is also fed by the 10MHz reference output of the
> 33522A via an attenuator to get it to roughly the same level.
>
> The second output of the 33522A generates a 10MHz square wave as a
> reference for the counter (the counter requires quite a high reference
> signal and the reference out of the 33522A is too low a voltage to be used
> directly).
>
> I initially ran this with a gate of 1 second and the LOG10(ADEV) curve
> drops linearly vs LOG10(tau) but then curves back up again. (I tried many
> variants such as using period rather than frequency and so on.)
>
> But when I set the gate time to 10 seconds or 100 seconds then I get both
> lower curves and ones that no longer curve upwards.
>
> The attached pdf shows the three curves on the same graph.
>
> What puzzles me is that the counter at longer gates is only averaging to
> get more digits so the difference must come down to quantization in terms
> of the number of digits that are passed to the computer over the USB/RS232
> link.
>
> I find it rather puzzling.
>
> James
>
>
>
>
>
>
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