Moin,
I've been doing some resistance measurements lately and have
run accross a currious problem. I'm measuring a 10kΩ resistance
standard (L&N 4040-B) with my trusty HP3458 (vintage 1989 or 1990,
firmware rev 4.6 haven't gotten around to update yet).
I've noticed that already with 10kΩ the choice of DELAY and
NPLC vs APER makes a huge difference in measurement value.
To quantify that, I run some measurements yesterday.
Before each round, I did let the DMM rest for 5minutes,
then did an ACAL to ensure same starting conditions
and then, immediately after, run the following measurement
script:
----
$dmm->write(command => "ARANGE ONCE");
$dmm->write(command => "AZERO ONCE");
$dmm->write(command => "TARM HOLD");
$dmm->write(command => "TRIG AUTO");
$dmm->write(command => "NRDGS 1,LINE");
$dmm->write(command => "NDIG 9");
$dmm->write(command => "OCOMP ON");
$dmm->write(command => "NPLC $nplc") if $nplc != 0;
$dmm->write(command => "APER $aper") if $aper != 0;
$dmm->write(command => "DELAY $delay");
$dmm->write(command => "OHMF");
if($aper != 0)
{
$sleep = ($aper + $delay) * 4 + 2.25;
} else {
switch($delay)
{
case "5e-1" { $sleep = $nplc * 0.1295 + 0.775 }
case 1 { $sleep = $nplc * 0.23945 + 0.2825; }
case 2 { $sleep = $nplc * 0.422525 + 3.11125 }
case 3 { $sleep = $nplc * 0.614 + 5.5 }
}
}
$dmm->write(command => "TARM SGL,1");
usleep(2* $sleep * 1e6);
for($i = 0; $i < 210; $i++)
{
$ohmf = $dmm->get_value();
# throw away first 10 measurments as they have too much bias
$stat->add_data($ohmf) unless $i < 10;
$dmm->write(command => "TARM SGL,1");
usleep($sleep * 1e6);
}
----
Note that I throw away the first 10 measurements to avoid bias
due to initial settling. The first measurement was low by
0.2ppm to 3.9ppm versus the calculated average, APER almost
an order of magnitude worse then NPLC.
The attached graph is the result of this measurement.
(normalized to APER 1 DELAY 3)
Each box is the average of 200 measurement. The inner box shows
the uncertainty of the center point (3 sigma, width w/o meaning).
The outer box shows the "noise" of each individual measurement
(1 sigma) and the time span over which the whole measurement took
place. The whiskers show the maximum and minimum of the values
used.
The whole setup is in free air in an office, so the temperature
varies a bit. I whish it would have been more stable, but a
maximum deviation of less than 0.17°C over 9h is IMHO acceptable.
The temperature plots are the 5minutes and 30 minutes moving
averages, right next to the resistor (using a BME280).
The first and the last measurement use the same settings for
cross checking. First and last measurement are off by +0.97ppm.
You can find the measured and calulated values down below.
Now, what's curious is, that, although all measurements measured
for the same amount of time (50NPLC = 1s), the noise levels are
quite different. There is approximately a factor of sqrt(5) in
between, suggesting that the measurement is limited by the
sample noise of the ADC and not by some input related noise
(either from the signal or from the integration stage of the ADC).
The second thing to notice is that NPLC 50 DELAY 2 is still
off by -7ppm, compared to APER 1 DELAY 2 and APER 1 DELAY 3.
Which would suggest, that even a 2s delay is not enough for the
system to fully settle.
Now, the big question is, what to use for measurements?
APER has definitely less bias, but has much worse noise.
Yet, I am not sure how large the bias is (it's definitely
still non-zero).
I'm sure I am not the first one to attempt this kind of
measurement with an HP3458. And someone must have gotten
sub-ppm precision with it, otherwise the specs for accuracy
wouldn't be in the 2+0.2ppm range (24h after cal).
So, what are other people doing and how do they achieve
the spec'ed accuracy?
Attila Kinali
NPLC 0
APER 1
DELAY 1
Average: 10000.3894693035
STD-DEV: 0.00695488039639252
Min: 10000.37384
Max: 10000.4097
NPLC 0
APER 1
DELAY 2
Average: 10000.4733173134
STD-DEV: 0.0101684497040978
Min: 10000.39685
Max: 10000.49339
NPLC 0
APER 1
DELAY 3
Average: 10000.4681456219
STD-DEV: 0.0125243902670948
Min: 10000.37739
Max: 10000.54444
NPLC 0
APER 1
DELAY 5e-1
Average: 10000.3451104478
STD-DEV: 0.00706507704987731
Min: 10000.32884
Max: 10000.3677
NPLC 50
APER 0
DELAY 1
Average: 10000.2979074129
STD-DEV: 0.00363564657597388
Min: 10000.28872
Max: 10000.30701
NPLC 50
APER 0
DELAY 2
Average: 10000.3982425871
STD-DEV: 0.00482583949242416
Min: 10000.38485
Max: 10000.41723
NPLC 50
APER 0
DELAY 5e-1
Average: 10000.1577926866
STD-DEV: 0.00359873550247818
Min: 10000.14333
Max: 10000.17091
NPLC 0
APER 1
DELAY 1
Average: 10000.399188607
STD-DEV: 0.00790352248839778
Min: 10000.37715
Max: 10000.41973
--
The driving force behind research is the question: "Why?"
There are things we don't understand and things we always
wonder about. And that's why we do research.
-- Kobayashi Makoto
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