[time-nuts] ADEV noise floor vs counter gate time
jpbridge at aol.com
jpbridge at aol.com
Sun Mar 22 08:10:15 EDT 2015
Hi Bill,
Thanks for the pointers.
I should say that my results reported so far have been with my older TTi TF930 reciprocal counter, not with my FCA3100 which I have only just got (it arrived a few days ago) and I'm in the process of writing software to talk to it via the USB.
I did discover the website, in fact I'd downloaded the manual before buying the counter, and it is fortunate I did because the website for me didn't work - I'm currently talking to Tek support about it.
The problem is that to download software you must have your details registered. Every time I register my details and press the "save" button the site wipes all my details and returns to a blank form. When I try to down load the software it then stops me and tells me to update my details. I update my details and it blanks the form and so on... slightly frustrating. I've tried both Firefox and IE.
The other thing is that the manuals don't show on the European site (I'm in the UK), you click on them but the download screen just shows a blank line. I got round this by going to the international site and just closing the screen asking me for my area rather than responding to it - I had to do this several times.
I have now downloaded NI-VISA and have managed to do a bit of talking to the instrument over USB though I've not yet had time to do this properly.
So in summary - I'm pleased with my counter but the Tek website for Europe at least has some serious bugs which hopefully will be fixed soon. The Tek support person I spoke to on the phone was helpful but she wasn't in a position to fix the web site issues directly so has forwarded my case to Tek IT.
I intend repeating my TTi TF930 experiment with my FCA3100 when I've got everything working ok and am looking forward to seeing the results.
James
-----Original Message-----
From: Bill Byrom <time at radio.sent.com>
To: time-nuts <time-nuts at febo.com>
Sent: Sun, 22 Mar 2015 2:27
Subject: Re: [time-nuts] ADEV noise floor vs counter gate time
Hi, James. I'm a Tektronix RF Application Engineer in Dallas and thought
I
would throw in a few points about your FCA3100 (if you haven't read up
on these
already):
All Tektronix manuals and technical reference documents can
be
downloaded for no charge on our website (http://www.tek.com), but
some
items may require you to register and sign in. The detailed
specification
and performance verification document (document number
077-0495-01) has many
details about the specifications, and is
at:
http://www.tek.com/frequency-counter-supplies/mca3027-manual/fca3000-and-fca3100-series-mca3000-series
All
downloadable files for this product can be found in the list
at:
http://www.tek.com/search/apachesolr_search/fca3000 If you have a
used
counter, be sure you check the firmware version and update it if
needed.
If your exact model is "FCA3000", you have a 300 MHz counter with 100
ps
single-shot resolution. This counter has reciprocal counter features
(based
on a 10 ns main counter time resolution), but also uses 100 ps
RMS jitter
interpolation to determine edge location with an additional
X100 resolution.
When the initial edge of the signal you are measuring
is detected, the
interpolater resolves this edge with 100 ps resolution
relative to the internal
10 ns clock. After the desired measurement
interval, the final edge is also
resolved with 100 ps resolution, and
the number of signal edges and
interpolated intitial-to-final time are
used to determine the frequency (for
example). The analog interpolation
circuit uses a constant current charging a
capacitor with a sampler and
A/D converter. Counting a 100 MHz signal, this
provides 12 digits of
resolution per second of measurement
interval.
--
Bill Byrom N5BB
On Wed, Mar 18, 2015, at 05:49 PM, James
via time-nuts wrote:
> Hi Dave,
>
> Thanks for another detailed
response.
>
> I've now programmed a version of my code that attempts to
recover the
> raw data by trying different counts up and down from the nominal
and
> finding the one with the smallest rounding error.
>
> One problem is I
need to restrain the amount it goes up or down
> otherwise it finds erroneously
small or large numbers of cycles (+/- 2
> is believable, more than that
isn't).
>
> As an experiment I then changed the data to match the "raw data".
This
> doesn't change the shape of the curve but it lowers it so it starts
>
below 10^-15! This is suspiciously good so I think I'm smoothing out
> changes
that are really there.
>
> Now that my new fca3100 has arrived I'm hoping to
find time to get
> measurements with it which should be proper time-stamped
ones and much
> more accurate - then I can compare the two.
>
> To answer
your question on ADEV aggregating values, and speaking as a
> total newbee
myself, the approach to different tau sizes is to
> aggregate all measurements
within a bin of size tau and average the
> frequencies (or average the time
differences and invert - for small
> variations it makes very little difference
as (1+delta)^-1 is 1-delta
> ignoring delta*delta terms). Then each term in the
Alan Variaton
> summation is the square of the difference between the
average
> frequency in adjacent bins.
>
> So with 1 second values at a tau of
100 secs, 100 values in each cell
> are averaged whilst the 100 sec gate value
results just have a single
> value for each bin. But given that the counter
itself should be
> averaging there should be good agreement between the two -
hence my
> puzzlement.
>
> The fca3100 calculates ADEV directly so I'll have
a check on my code.
>
> James
>
>
>
>
>
>
>
> -----Original
Message----- From: Dave Martindale
> <dave.martindale at gmail.com> To: jpbridge
<jpbridge at aol.com>
> CC: Discussion of precise time and frequency
measurement
> <time-nuts at febo.com> Sent: Wed, 18 Mar 2015 15:22 Subject:
Re:
> [time-nuts] ADEV noise floor vs counter gate time
>
>
>
> The
counter always has a 1 count uncertainty in the timebase
> measurement, which
is a 2e-8 error with a 1 second gate time. If the
> value being displayed
starts with the digit 9, and 8 digits are
> displayed, then that translates to
+- 2 counts in the last place. But
> the measurements are synchronized to the
input signal, so it always
> measures an integer number of input cycles, and
there should be no
> comparable uncertainty in the input (other than some noise
in deciding
> exactly when the edge crosses the input threshold, which should
be
> tiny compared to the 20 ns timebase period).
>
>
>
> But that's
comparing the counter reading to the real world. My table
> was comparing the
displayed output to the likely raw measurements, and
> it seems to show that
the counter's internal math is being performed
> to the full 10 digits of
precision in the USB data, even when the gate
> time supports only 8 bits of
accuracy. That's good news because it
> allows you to know when you have
correctly guessed the input counts.
>
>
>
>
> When trying to calculate the
raw data from the reading, you do need to
> try an input count of 91 in
addition to 90 and 92. 91 did show up in
> the small sample of period-mode
measurements, even if it did not
> appear in any of the frequency-mode
measurements.
>
>
>
>
> I don't think the counter is doing "averaging", in
the sense of making
> multiple independent short-period measurements and then
averaging them
> for higher precision. Instead, it is just making one long
continuous
> measurement, sampling the signal periodically, and then
actually
> calculating frequency or period from two measurements separated by
an
> appropriate time. For a simplified example:
>
>
>
>
> Suppose the
counter generates a time stamp approximately every 1
> second (always aligned
with the input signal active edge) and then
> stores the two pieces of raw data
(the current input cycle counter and
> the current timebase counter) in a small
memory buffer. The counters
> are never reset; they just need to be large
enough to never overflow
> twice within the longest input period allowed (1000
s for the TF930).
> To display a frequency or period based on a 1 s gate time,
the counter
> simply subtracts two successive data records to get delta-input
and
> delta-timebase counts, then does its calculations based on those
>
deltas. To display a 10 second gate time measurement, the counter
> looks back
through its memory to find a time stamp about 10 seconds
> earlier than the
most recent measurement (with high input frequency,
> that will generally be 10
measurements ago, but when measuring a
> signal with a 0.2 Hz frequency it's
only 2 measurements ago). For a
> 100 second gate time measurement, the count
er needs to find a saved
> time stamp that is about 100 seconds ago. Once it
has found the
> correct data record, it calculates the difference in input
and
> timebase counts between that one previous data record and the most
>
recent, and then calculates the displayed value from it.
>
>
>
>
> One
second later, the counter can calculate a new 100 s measurement,
> using the
new data point just captured and a different stored data
> point 100 seconds
ago. But 99 of the 100 seconds in the new gate
> period are shared with the old
gate period, so the displayed value is
> not likely to change very much simply
because 99% of the observation
> period is shared.
>
>
>
>
> Thus, every
displayed value is calculated from only 2 time-stamped
> measurements. The
longer gate time places those measurements further
> apart, reducing the
uncertainty due to the +- 1 clock of the timebase.
> Because the counters run
continuously without resetting, no clock
> edges are lost and a 100 s gate time
measurement has only 20 ns
> uncertainty in the whole 100 s period. Also, any
wander in the input
> frequency between those two measurements is invisible if
it cancels
> out over the gate time. So there is "averaging" in the sense that
the
> counter display always reflects what is happening on the scale of the
>
gate time, but it's not computing and then averaging multiple
numbers.
>
>
>
>
> I have not tried doing my own ADEV calculations, so I
can't say what
> it is about the shorter gate periods that make the oscillator
appear
> noisier than it really is. How does the ADEV calculation aggregate
a
> stream of short-time calculations into measurements for large tau
>
values? My intuition is this: If you just take readings from the
> counter with
a 1 s gate time, each reading has a 2e-8 uncertainty. If
> you average a bunch
of these readings, and the errors are independent,
> the accuracy should
improve by a factor of sqrt(N). But if you unwrap
> each reading into an
integer number of input and timebase cycles, you
> essentially have a series of
phase samples that can be added or
> subtracted without increasing the absolute
uncertainty. So when you
> combine 100 1 second measurements, you get a
relative accuracy that is
> 100 times better, not the sqrt(100) you'd get from
averaging.
>
>
>
>
> - Dave
>
>
>
>
>
>
> On Wed, Mar 18, 2015 at
6:33 AM, <jpbridge at aol.com> wrote:
>
> Hi Dave,
>
> Interesting analysis.
The accuracy stated in the manual is ...+ 2
> counts and though this relates to
the 50MHz clock, perhaps they use a
> similar algorithm for the input
frequency.
>
> I completed the 0.3 second measurements and the curve is
similar to 1
> second but higher up (i.e. as you'd expect by extrapolation from
the
> behaviour of the other curves).
>
> My ADEV calculation is based on the
average frequency in each bin, the
> varying size of the bin should be
insignificant as long as it is not
> affecting the average value within the
bin. If the average frequency
> shifts by delta_F in one bin time step and the
first bin is delta_T
> short (as a fraction of one bin time step) then the
first frequency
> will be delta_T*delta_F low and the second bin perhaps that
much high
> but the key point is that it is the product of the two deltas so
it
> won't materially affect the accuracy of the calculation. At least I
>
think that is correct.
>
> Taking the worst possible case where the delta in
bin size always went
> the wrong way so every term in the Alan Variance sum was
multiplied by
> (1+2delta)^2 then the final Alan deviation might be (1 + 2
delta) too
> big but as delta is of the order of 10E-8 or less this wouldn't
even
> register on the graphs.
>
> What I might try doing is programming your
approach into the code to
> try and get at the raw data - I only need to try
88,90 and 92 as
> possible counts - though to be sure I'll try mean frequency
+- 5 say
> and then try and get the 50MHz clock values out as integers. What
I
> might also do is then do a least squares fit (linear regression) to
> get
the frequency over each bin and use the slope (this perhaps is
> what the
counter does internally - I don't know).
>
> I'd like to get to the bottom of
this if only to understand my
> counter better.
>
>
James
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> -----Original Message-----
From: Dave Martindale
> <dave.martindale at gmail.com>
>
>
> To: jpbridge <
jpbridge at aol.com>; time-nuts < time-nuts at febo.com>
> Sent: Wed, 18 Mar 2015
1:26 Subject: Re: [time-nuts] ADEV noise floor
> vs counter gate
time
>
>
>
> I believe I see the pattern. As you figured out, you wouldn't
expect a
> single period to be a multiple of 20 ns; you expect the length of
>
(about) 90 periods to be an integer multiple of 50 ns, since that's
> what the
counter actually measures. Further, the measuring time isn't
> exactly 1
second, it is an integer number of periods of the input
> frequency that makes
up at least 1 second. If the counting logic was
> all hardware, you would
expect to capture either 90 or 91 cycles of
> the input, depending on whether
the input frequency was slightly below
> or above 90 Hz respectively.
>
> I
built this table of your frequency data in Excel. Math is 64-bit
> floating
point, equivalent to about 16 decimal digits, so plenty
> accurate enough to
simulate this counter:
>
> Reading Input Count TB Count Rounded Frequency
Interval 90.00006359 92
> 51111074.998 51111075 90.00006359 1.022221500
90.00007591 92
> 51111068.002 51111068 90.00007591 1.022221360 89.99999640
90
> 50000002.000 50000002 89.99999640 1.000000040 89.99998740 90
>
50000007.000 50000007 89.99998740 1.000000140 90.00006007 92
> 51111076.997
51111077 90.00006007 1.022221540 89.99996040 90
> 50000022.000 50000022
89.99996040 1.000000440 90.00008648 92
> 51111061.999 51111062 90.00008648
1.022221240 90.00008472 92
> 51111062.999 51111063 90.00008472 1.022221260
90.00011465 92
> 51111046.001 51111046 90.00011465 1.022220920 90.00014459
92
> 51111028.998 51111029 90.00014459 1.022220580
>
> The first column is
your data. The second column is a guess about how
> many input cycles were
captured. The third column is the number of
> timebase cycles that have elapsed
since the previous reading, based on
> the first two columns. I hand-tweaked
the numbers in the second column
> until the number in the third column was
within 0.003 of an integer.
> The fact that I was always able to do this tells
me that my guess is
> probably correct, and the small residual (which is a few
parts in
> 1e-10) is due to the counter rounding the results to 10 digits.
The
> 4th column is the result of rounding the previous column to the
>
nearest integer. This is what I believe is the actual number of counts
> the
counter saw. The 5th column is a fresh calculation of frequency,
> based on the
integer number of input cycles in column 2 and the
> integer number of timebase
cycles in column 4. When the result is
> rounded to 10 digits, you can see it
matches the 10 digits that the
> counter provided back in column 1.
>
>
>
Oddly, the counter never captured 91 input cycles. If the input
> frequency was
a little higher than 90 Hz, it always measured at 92
> cycles, even though 91
cycles was well more than 1 s since the
> previous reading. I guess the
microprocessor running the counter only
> checks periodically (e.g. every 20
ms) to see if the gate time has
> elapsed, and then latches the counts on the
next active edge of the
> input signal.
>
> So, I claim that with this small
sample, at least, we recovered the
> exact number of 20 ns periods between
samples, and the number of
> integer input cycles as well. Also notice the 6th
column. This is the
> actual sample interval, based on the number of elapsed
timebase
> counts. Note that the sample period is **not** exactly 1 second,
nor
> is it even close to a constant value, since some measurements are of
>
90 cycles while others are of 92 cycles. Does your ADEV calculation
> algorithm
take into account the variable spacing of the input samples
> in time? If it
assumes they are regularly spaced (i.e. every 90
> cycles) it may get confused
by this variable-spacing data.
>
> Now here is almost the same process applied
to your period data:
>
> Reading Input Count TB Count Rounded Period Interval
0.01111107736 91
> 50555401.988 50555402 0.01111107736 1.011108040
0.01111110130 92
> 51111065.980 51111066 0.01111110130 1.022221320
0.01111110769 91
> 50555539.990 50555540 0.01111110769 1.011110800
0.01111110435 92
> 51111080.010 51111080 0.01111110435 1.022221600
0.01111110593 91
> 50555531.982 50555532 0.01111110593 1.011110640
0.01111110022 90
> 49999950.990 49999951 0.01111110022 0.999999020
0.01111114000 90
> 50000130.000 50000130 0.01111114000 1.000002600
0.01111110000 90
> 49999950.000 49999950 0.01111110000 0.999999000
0.01111110370 92
> 51111077.020 51111077 0.01111110370 1.022221540
>
> Again,
column 2 was hand-adjusted for each row to keep the third
> column close to an
integer. The residual errors here are larger, since
> the maximum rounding
error of 0.5 in the last place is a larger change
> relative to a 10-digit
value of 11111111 than it is to a value of
> 90000000, but all are still within
0.02 of being an integer. This
> time, the counter grabbed measurements after
90, 91, or 92 cycles.
> Again, after rounding the timebase count to an integer
and calculating
> a 10-digit period for display, the result always matched what
the
> counter output. Again, I think we know with high probability just how
>
many input and timebase cycles were counted for each measurement.
>
> I
adjusted column 2 by eye, while looking at the results of column 3,
> but that
process could be automated pretty easily (just not in Excel).
> As I tried 90,
91, and 92 in sequence, there was always just one of
> those which gave a small
residual error.
>
> So I think your TF930 is making measurements and
accurately converting
> them to frequency or period, with a +- 20 ns
uncertainty for each
> measurement. Since it is a time-stamping counter, the
uncertainty in a
> 10 s or 100 s or 1000 s measurement time (assembled by
external
> software) is still only 20 ns. That's great, but to actually get
that
> accuracy over a long measurement time, you will need to determine and
>
add up the actual number of input counts and timebase counts. And you
> will
have to understand that the counter does not make measurements at
> constant or
near-constant intervals (e.g. every 90 cycles of input,
> without exception).
It gives you measurements whenever it gets around
> to measuring them.
>
>
Too bad there doesn't seem to be a way to get it to return the raw
> observed
data (input cycle count, timebase cycle count) instead of
> the frequency or
period derived from them. That would make it trivial
> to string together a
bunch of 1s measurements into arbitrarily long
> gate times.
>
> -
Dave
>
>
> On 17/03/2015 05:57, jpbridge at aol.com wrote:
>
>
> Hi
Dave,
>
> Thank you for your detailed response.
>
> I use the E? command
because it returns results at the gate time
> intervals rather than at the LCD
update rate (as you point out). I
> think that this is working correctly
because I get very different
> file sizes.
>
> The numbers are returned as
strings of 10 digits - here are some for 1
> second gate:
>
>
>
>
>
90.00006359e+0Hz
> 90.00007591e+0Hz
> 89.99999640e+0Hz
> 89.99998740e+0Hz
>
90.00006007e+0Hz
> 89.99996040e+0Hz
> 90.00008648e+0Hz
> 90.00008472e+0Hz
>
90.00011465e+0Hz
> 90.00014459e+0Hz
>
> I generally use the frequency mode
but I also tried time period and
> found I got the same curve in essence, which
was comforting in a way
> but showed it wasn't rounding in converting to
frequency.
>
> The numbers above, on my calculator at least don't exactly
match
> counts of 20 nanosecs.
>
> Here are some time period results:
>
>
11.11107736e-3s
> 11.11110130e-3s
> 11.11110769e-3s
> 11.11110435e-3s
>
11.11110593e-3s
> 11.11110022e-3s
> 11.11114000e-3s
> 11.11110000e-3s
>
11.11110370e-3s
>
> Again they don't seem to be integer values of 20 nanosec
exactly,
> though quite close. For example
> 11.11107736E-3/20E-9 =
555,553.868 555,554 x 20E-9 = 11.11108E-3
>
> But I guess what it returns is
the ratio of counts within the gate. So
> 11.11107736E-3 period will occur 90
times in a second (as it is
> slightly short) and so I should take the
ratio:
>
> 90 x 11.11107736E-3/20e-9 = 49,999,848.12
>
> so still not quite
an integer but if I assume the count (of 50MHz
> periods) was 49,999,848 and
calculate one 90 th of it I get:
>
> 49,999,848 x 20E-9/90 =
1.1111077333333
>
> Still not exact agreement. I note that .12 is very close
to .125 or
> 1/8 but I don't know if that is significant. It is probable that
it
> rounds the ratio in binary and then converts to decimal to print
out.
>
> I've tried assuming 89 periods and 91 periods but still don't get
>
exact integer ratios.
>
> Anyway, as I get good agreement between period and
frequency
> measurements at 1 sec, I don't think that it is a rounding
issue.
>
> I do think it is a quantization issue down to the +/- 20
nanosecs/gate
> time but I can't quite work it out.
>
> I'm currently doing a
run at 0.3 secs gate time and I'll see what sort
> of curve that
produces.
>
> Tomorrow I should receive my new Tek counter (I went for the
fca3100
> in the end as I got a very good discount on an ex demo unit) and
>
that should give something to compare (once I've worked out how to
> program
it).
>
> James
>
>
>
>
>
>
> -----Original Message----- From: Dave
Martindale
> <dave.martindale at gmail.com> To: jpbridge <jpbridge at aol.com>;
>
Discussion of precise time and frequency measurement
> <time-nuts at febo.com>
Sent: Tue, 17 Mar 2015 0:27 Subject: Re:
> [time-nuts] ADEV noise floor vs
counter gate time
>
>
>
>
> 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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>
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