Metrology Meeting in Stuttgart/Germany

[Kleinstein]

The ADEV is a more detailed desctiption of the noise. It is a bit comparable to a noise spectrum. The normal standard deviation is just the first point of the ADEV curve.  In how fast the curve flattens out or even goes up to longer times is an indication of the extra low frequency noise. This part can be impartant if averaging over longer time is used to reduce the noise.

For the measurements with the 10 V references the noise is usually only a small part of the uncertainty and other errors (e.g. cable thermal EMF, temperature drift, long term drift, linearity) dominate the uncertainty.

[e61_phil]

I calculated an uncertainty of 3.4 ppm for my 10 VDC measurements with branadic's 3458A based on GUM (k=2). The procedure was calculate standard error of the mean for my samples, convert the uncertainty of the calibration to standard error (95% confidence interval, so divide by 1.96), convert 90 day voltage specifications for 3458A option 2 to standard error by assuming it's a rectangular distribution, and add them all up as sum of squares, and multiply this by k. I'll publish the results when I'm done analyzing them all.

If I understood it correctly the calibration of the 3458A already had an uncertainty of 5.5ppm?

[alm]

The calibration uncertainty was 1.5 ppm (95% confidence interval). See attachment.  The 90 day accuracy of the 3458a option 2 at 10 VDC is 2.65 ppm relative to the calibration (see datasheet), which I treated as a rectangular distribution.

[e61_phil]

Ahh, thanks. I misinterpreted that post:

..
André provided a 3458 witch was calibrated (+- 5.5ppm ) a few days before the event.

[alm]

There's an offset of I believe 5.4 ppm in the 10 VDC calibration, but that's not uncertainty, that's a known value you can calculate from the calibration certificate: the expected value is (min limit + max limit) / 2, and the 3458a reading is also in the certificate, so you can calculate the offset from that (keeping the 1.5 ppm uncertainty), and correct the readings from that. Just pay attention to the sign.

I don't have the numbers in front of me, so I can't tell you the offset that I used.

[e61_phil]

I would calculate a correction gain not an offset. But for comparison of just 10V it doesn't matter. For measuring of 7V it is important.

[alm]

That's fair, but the only data I have was for references that measured 10 V +/- 10 ppm, so there offset or ratio does not matter. If you're analyzing data from ~7V references, then ratios is absolutely is the way to go.

[alm]

I finally got done with analyzing all data I collected, so here are the results. For all data from banadic's 3458A my procedure was that I calculated the expected value from the calibration certificate by the formula the certificate gives: (lower limit + upper limit) / 2, and divide this by the reading to get the correction factor to convert the observed reading to what at the time of calibration would have matched the value of the cal lab. I did not have access to a calibration certificate for the Keithley 2182A, so I have not corrected these values. For all 3458A measurements the unit was set to defaults, NDIG 9, NPLC 100.

For the uncertainty, in the case of the 3458A, per GUM, I calculated it from these three terms:
1. The standard error of the mean from the observed measurements
2. The uncertainty from the calibration certificate (a 95% confidence interval) divided by 1.96 (the coverage factor of a 95% confidence interval as recommended per GUM)
3. The 90 day uncertainty (for absolute measurements) or 10 minute transfer stability (for voltage comparisons) as a rectangular interval converted to a standard uncertainty by \$\frac{a^2}{3}\$ where a is the specified uncertainty.
I calculated the sum of squares of these terms, and multiplied by the coverage factor k = 2.

For the Keithley 2182A I did not have a calibration uncertainty, and the uncertainty fo the 2182A was small compared to the observed standard error of the mean, so I took the most conservative 2 year specifications with analog filter on, converted this to standard uncertainty the same way, calculated the sum of squares of this and the observed, standard error of the mean, and multiplied this by the coverage factor.

DC voltage references
First the results of comparing the various Fluke/Wavetek 7000 DC voltage standards. I did both absolute measurements with branandic's 3458A that had been calibrated about two weeks before the event, and also did relative measurements between my F7001, which was running on battery all the time and not running inside the mainframe, by connecting the negative terminals using a low-EMF spade lug lead, and then connecting the Keithley 2182A as measuring between the positive terminals.

With both methods I measured a roughly equal number of samples using both polarities of the meter, took the average of either sign, and then inverted the sign of the negative polarity readings, and report the average of the two groups with the standard error of the mean propagated all the way through. There was some confusing with the guard switch on the 3458A, which appears to become a tradition at the Metrology Meet events: Both branadic and I had verified the guard switch was set to open in the morning. But somehow at the end of the day the switch had changed to connect guard to lo. And even without any other meters connected in parallel, connecting the guard to the same W7000 terminal as the lo lead resulted in a -2 ppm shift in reading compared to without guard connected (or with guard connected and the switch set to open). I don't understand this, and want to try to reproduce this on my own 3458As. So I ended up ignoring all data with guard connected and the guard set to lo.

I measured the ambient temperature using a Uni-T UT330C environmental logger and combined this with the other data based on time stamps.

Absolute measurements using 3458A

device under test	guard	count	ambient temperature (°C)	mean value (V)	expanded uncertainty (V, k=2)
Fluke 7001 on battery (alm)	with guard to open	50	22.60	9.999935	0.000034
Fluke 7000 on battery (#4)	with guard to open	3	22.50	9.999986	0.000034
Fluke 7000 on battery (#1)	no guard, to lo	5	22.50	9.999959	0.000034
Fluke 7000 on mains power (#2)	no guard, to lo	10	22.45	9.999987	0.000034
Fluke 7000 on mains power (#4)	no guard, to lo	10	22.50	9.999987	0.000034
Fluke 7001 on battery (alm)	no guard, to lo	10	22.40	9.999937	0.000034
Fluke 7001 on battery (alm)	with guard to open	5	22.40	9.999936	0.000034

The first set of readings of my F7001 was done right after ACAL DC with a larger number of readings and proper guard connection, so is probably the best absolute DCV measurement of the bunch. The rest roughly an hour later, some on battery and some on mains power due to a low battery condition.

Relative comparisons using Keithley 2182A
As a secondary check we measured the difference between my F7001 and the other F7000 units using a Keithley 2182A nanovoltmeter. We used my F7001 as reference because it was fully independent, running from battery and not connected to the mainframe. This reduced the risk of ground loops, although in theory the F7000's isolated power supply should prevent those ground loops even when all are plugged into the same mainframe and running from mains power. I converted the mV values to ppm of the F7001 (alm) reference, and the expanded uncertainty to ppm of F7001 (alm).

device under test	count	ambient temperature (°C)	mean difference to F7001 (alm) (ppm)	expanded uncertainty (ppm)
Fluke 7000 on battery (#1)	27	22.500000	2.127129	0.008974
Fluke 7000 on battery (#2)	26	22.500000	4.986389	0.012099
Fluke 7000 on battery (#4)	25	22.540909	5.107528	0.011392

Comparing 3458A measurements and Keithley 2182A measurements
To compare the 3458A values to this, we can also consider the 3458A readings taken within 14 minutes as a series of relative comparisons between the references. This reduces the uncertainty to the 10 minute transfer stability. For this, I converted the values to the difference to my F7001 (in ppm), since the 2182A measurements were also relative to my F7001. I also converted the expanded uncertainty to ppms of the F7001 (alm) value based on the transfer stability. For this I only considered readings with the guard disconnected (and set to lo).

device under test	count	ambient temperature (°C)	mean difference to F7001 (alm) (ppm)	expanded uncertainty (ppm)
Fluke 7000 on battery (#1)	5	22.50	2.263002	0.11695064
Fluke 7000 on mains power (#2)	10	22.45	5.096005	0.11834481
Fluke 7000 on mains power (#4)	10	22.50	5.098005	0.12231724
Fluke 7001 on battery (alm)	10	22.40	0.000000	0.11564350

These sets of measurements can be compared, with the K2182A clearly having the better resolution and noise under these conditions (error bars are expanded uncertainty at k=2):


The data as table:

label	mean difference (ppm)	expanded uncertainty (ppm)
1 - 3458A	2.263002	0.11695064
1 - K2182A	2.127129	0.008974
2 - 3458A	5.096005	0.11834481
2 - K2182A	4.986389	0.012099
4 - 3458A	5.098005	0.12231724
4 - K2182A	5.107528	0.011392
alm - 3458A	0.000000	0.11564350

To me the agreement confirms the validity of both setups, and that there were no ground loops or other things going on here.

AC voltage reference

I brought a Fluke 510A 2400 Hz AC voltage standard that I had no history on. I'll report the value here in case someone else measured this unit. I measured it using the 3458A and calculated expanded uncertainty the same was as DCV (obviously using different values for calibration data and specifications).

device under test	count	ambient temperature (°C)	corrected mean (Vrms)	expanded uncertainty (V, k=2)
Fluke 510A	16	22.5	10.000704	0.001895

Resistance
I brought an almost full decade set of standard resistors from 10 Ohm to 10 MOhm. I measured them using branadic's 3458A, relying on its absolute accuracy, with the following settings. For <= 1 kOhm range, I used 4-wire Ohms, NPLC 100, OCOMP ON, DELAY 0, NDIG 9 and otherwise defaults. For the 10 kOhm range, I used the same settings, but DELAY 1. For the 100 kOhm range, I used the same settings, but DELAY 5. For ranges >= 1 MOhm, I used 2-wire Ohms, OCOMP OFF, DELAY 0.

I had three temperature sources for this: The UT-330C measuring ambient temperature, an industrial PT100 sensor measured by a Fluke 189 that I put in the temperature well for the resistors that had one (including the SR104), and in the case of the SR104 the internal thermistor measured by branadic's HPAK 34401A.

device under test	count	ambient temperature (°C)	temperature PT100 (°C)	SR104 thermistor (°C)	mean resistance (Ohm)	expanded uncertainty (Ohm, k=2)	difference from calibration value in ppm (year)
SR104-alm	20	22.650000	24.679978	22.43565	9999.930300	0.099929	-5.57 (1993)
SR104-S	1	22.400000	25.000000	22.96400	10000.071999	0.099854	+2.90 (2002)
SR104-alm	5	22.500000	25.000000	22.68200	9999.981600	0.099856	-0.44 (1993)
Guildline 9330-100k	5	22.660000	24.993153		100004.459999	1.034870
HP 11103A	12	22.550000	24.605662		1000.012408	0.010093
Fluke 742A-10	9	22.533333	25.944744		10.000391	0.000237
Fluke 742A-1M	10	22.600000	25.274134		1.000020e+06	18.132762
Guildline 95206	51	22.492157	25.279643		9.999867e+06	728.569857

I'm slightly confused by the SR104 measurements: The initial series of measurements, shortly after ACAL DC+OHMS on the 3458A, had a lot of drift during the measurement, producing a standard deviation of 0.9 ppm over 20 measurements, while it was much more stable during the later series of 5 measurements, about 3 hours after ACAL. There is a 5 ppm difference between the two readings, which is more than I would expect either the SR104 or 3458A to change over the span of 3 hours. So I'm unsure which value to trust. The second value is closer to its 1993 calibration value, for whatever that's worth.

I attached all raw data as  a zip file. Note that the UT330C clock was set to UTC+1. All other times are in UTC. I corrected for this in my results.

2023-11-20 Edit: I made a mistake calculating uncertainty for the 3458A DCV transfer measurements. I mistakenly included the calibration uncertainty, which is not relevant for ratio measurements like this, in the uncertainty calculation. I updated the two tables showing relative measurements based on 3458A data, and the figure comparing HPAK 3458A measurements to Keithley 2182A measurements.

[Dr. Frank]

Thanks alm for for your very interesting analysis!! 

Concerning manual resistance measurements, I strictly recommend these settings:
'OHMF 1000;APER 1;OCOMP ON;TRIG HOLD;DELAY 0.1;';  // up to and for 1kOhm
'OHMF 10000;APER 1;OCOMP ON;TRIG HOLD;DELAY 1;';  // OCOMP requires settling time, 1s for 10k due to polarization
'OHMF 100000;APER 1;OCOMP ON;TRIG HOLD;DELAY 5;';  // OCOMP requires settling time, 5s for 100k

and then NRDGS 16; STAT ON; TRIG; reading statistical data afterwards.

You have to check, though, if 1sec delay time is sufficient for the SR104. Think of the mass of oil and these many stacked resistors inside. The polarization relaxation effect might take longer than with a 5450A or a VHP resistor. The StD should always be around 0.2ppm, using PTFE cables with its shield connected to Guard and to case of the reference resistor.

APER 1 (equiv. to NPLC 50) makes only a 1sec long uninterrupted A/D conversion and 1 sec OCOMP phase, 4sec in total for 10k, therefore DELAY time applies 2 times only, whereas with NPLC100, which are 10 times NPLC10 measurement cycles, 20 times DELAY time apply, i.e. for 100k that takes forever, 100sec plus x.
I have no clue, why the 3458A behaved that different a few hours later.

By chance, didn't you compare Andrés travelling LM399, which many of the absent volt-nuts measured in the ring-comparison, with evidently or hopefully < 1ppm uncertainty?

Frank 

[alm]

Thanks for your response and insights, Frank! Those settings are close to what I used. I'll use DELAY 0.1 instead of DELAY 0 for 1k and under in the future. I was using ~1m PTFE cables with shield attached to guard (with guard set to open) on the 3458A and to the resistor guard / shield when available. I'll run some tests with the SR104 using different values of DELAY. TiN also suggested that measuring the 10 kOhm on the 100kOhm range of the 3458A is more stable because the 100kOhm range uses the most stable VHP 40 kOhm resistor. I've always used NPLC 100 and lived with samples taking forever at 100 kOhm, but APER 1 makes more sense with large delay values indeed.

I'm used to recording values via GPIB, so I recorded the individual values on paper. This has the advantage that it allows a more in depth analysis. For example I found for some of the measurements I did in the past that using certain procedures the first or last sample in a series might be off, and by recording individual values it's easy to check if leaving them out substantially improves the standard deviation. For example, re the unstable SR104 readings, I can easily plot the values and learn that it's not a monotonic drift, and that the range of the values is a little under 3 ppm. Something not easily learned from descriptive statistics.



What's your opinion of using 2-wire vs 4-wire for resistances up to 10 MOhm? I've always used 2-wire for 1 MOhm and up, since the Fluke 742A-1M only has two terminals, and I figured they know what they're doing in balancing contact resistance and leakage. But on the 3458A cal certificate they test the 1 MOhm resistance only in 4-wire mode, and 10 MOhm in both, so maybe I should use 4-wire resistance for 1 MOhm?

I wasn't aware of the traveling LM399 until late in the day, otherwise I'd have certainly liked to measure it. I hope my data on the F7000s at least helps anyone who measured relative to one of the references to relate the values to the other references and to the 3458A's calibration. That's one of the motivations for publishing this data: if someone measured for example one of my resistors using their multimeter, then this gives my best estimate of their absolute value with uncertainty.

[Kleinstein]

The APER1 uses a 1 second integration at a time (=50 PLC), but noise wise this is not equivalent to 5 x 10 PLC conversions because of 1/f noise. Chances are this would be more comparable to 2-3 x 10 PLC. There is little return in extending the integration time very much.  Using the 10 or 100 PLC setting has the advanatge that most of the calibrations and CAL also use this mode. So there is no additional step between different integration times (though likely not a big difference).

For the delay needed the relevant factor is not the physical size of the resistor, but the parasitic capacitance and the quality (especially dielectric absorbtion) of the dielectric there.  If in doubt one should do a measurements with 2 different delay settings (e.g. dealy 5 and delay 10 for the 100 K resistor) to see if there is a difference.
The needed delay should depend on the resistor to test and not the range. So for testing the 10 K resistor in the 100 K range the shorter 1 second delay should be sufficient.

The 100 K resistor range does not directly use the the VHP40K resistor, but the 50 µA current source is directly measured to this resistor in the ACAL procedure.
The source for the 10 K range uses the 100 µA current source and this could also be (and likely is) directly measured relative to the 40 K resistor.
A difference is that the 10 K range would use amplification of the voltage, while the 100 K range uses directly the 10 V range.

[Dr. Frank]

TiN also suggested that measuring the 10 kOhm on the 100kOhm range of the 3458A is more stable because the 100kOhm range uses the most stable VHP 40 kOhm resistor.

That's all not correct. The 40k VHP101 resistor is used only during ACAL, but not used during measurement. See CLIP.

10k measured in 100k range is at least 10 times less "stable", because you have 10 times less resolution, and because the reference current is 10 times smaller only half as big as in 10k range, leading to increased noise. You should see that in the StD.
TiN might have confused this with the HFL specification, where Fluke obviously specified a better uncertainty Transfer Accuracy for the 100k range compared to 10k. This I can not confirm, as I regularily achieve transfer accuracies of about 0.2ppm for the 10k range.
10k resistors measured on the 10k range, and 100k on 100k range both yield a StD of around 0.2ppm as well.
That's also valid for a 1k resistor in 1k range, of course. Concerning absolute uncertainty, that might be different, depending on how or where the 40k VHP101 resistor is implemented in the ACAL chain, i.e. which of the Ohm ranges is transferred first. Each consecutive 10:1 range transfer then always increases the uncertainty by about 0.33ppm, or so. But the uncertainty specifications are quite wide, anyhow.
One should study the description in the hp Journal 4/89, once more.

I've always used NPLC 100 and lived with samples taking forever at 100 kOhm, but APER 1 makes more sense with large delay values indeed.

That's mainly a question of measurement time. In the end, using APER 1 is about 6 times faster compared to NPLC100. The lesser averaging is also sufficient, if you simply judge that from the achievable StD value of 0.2ppm, i.e. NPLC100 won't give you an advantage here. 

I'm used to recording values via GPIB, so I recorded the individual values on paper. This has the advantage that it allows a more in depth analysis. For example I found for some of the measurements I did in the past that using certain procedures the first or last sample in a series might be off, and by recording individual values it's easy to check if leaving them out substantially improves the standard deviation. For example, re the unstable SR104 readings, I can easily plot the values and learn that it's not a monotonic drift, and that the range of the values is a little under 3 ppm. Something not easily learned from descriptive statistics.

Yes, I also make these measurements via GPIB and calculate the statistical data inside my program, using the Welford algorithm. As well for DCV measurements.
Mostly, there is no need to skip any extreme values (outliers), but the first sample of an armed and triggered data set might be off, sometimes.
There's even a small footnote in the specification, I think for each DC mode of the 3458A, that the first reading might be off by several ppm.
I append an example from my old TP program.
I always measure the resistors temperature and correct for its T.C. to R(25°C), 4th column.
The measured resistance values directly from the 3458A are in the 3rd column, and you see how stable these are, giving 0.12ppm StD in the end.
I read the data with 8 or 9 digits, using DREAL format, as normally the resolution of Ohm would be limited to 7 digits only.
But this was an exceptionally good measurement.

What's your opinion of using 2-wire vs 4-wire for resistances up to 10 MOhm? I've always used 2-wire for 1 MOhm and up, since the Fluke 742A-1M only has two terminals, and I figured they know what they're doing in balancing contact resistance and leakage. But on the 3458A cal certificate they test the 1 MOhm resistance only in 4-wire mode, and 10 MOhm in both, so maybe I should use 4-wire resistance for 1 MOhm?

Well, calibrating and measuring are two different stories, concerning 2W or 4W.
For regular measurements, I also use 2W for 10M and above, because it's really less noisy, due to less cables involved.
If you want to measure 1M with < 1ppm "accuracy", you must use 4W, that should be evident due to around 0.2 Ohm cable resistances.

I wasn't aware of the traveling LM399 until late in the day, otherwise I'd have certainly liked to measure it. I hope my data on the F7000s at least helps anyone who measured relative to one of the references to relate the values to the other references and to the 3458A's calibration. That's one of the motivations for publishing this data: if someone measured for example one of my resistors using their multimeter, then this gives my best estimate of their absolute value with uncertainty.

Yes, much appreciated!

Maybe you have a look to Andrés publication of our ring comparison
https://www.eevblog.com/forum/metrology/eu-calclub/msg4385281/#msg4385281

which indicates that his calibrated 3458A (#18) reads a bit higher compared to the two calibrated references with low uncertainty (#2, #13), which we had in our group.
In the end, the readings of his 3458A seem to be within 1ppm, If I estimated that correctly.

Frank

[branadic]

Hello,

at the "Metrologietage" 2020 in Kassel I heard a talk "Neue Messmöglichkeiten im Hochohmbereich" given by B. Schumacher and C. Rohrig, both from PTB. They presented the results of a K2 comparison:

- participation in CCEM K2 1999 and 2012
- in 1999 unknown systematic error detected
- apparently, a solution had been found
- Re measurement in 2012 showed:
the error is back again

where PTB was off measuring a 10meg and a 1G resistor.
They came to the conclusion:

- Looking at the result, the possible discrepancy in the CCEM K2 can be attributed to excess dielectric absorption in the wiring used.
- A change of the wiring reduces the necessary waiting time for the measurement.

Beforehand they were using PTFE insulated cables (known for piezo electric effects) as most of us do, but changed to some low noise cable with additional carbon film? to avoid effects coming from the cables.

Just in case someone is interested in this info.

-branadic-

EDIT:
https://www.koax24.de/produktinfos/triaxialkabel/uebersicht/001101.html
https://www.koax24.de/produktinfos/triaxialkabel/uebersicht/g-02330-ht.html

[alm]

For the delay needed the relevant factor is not the physical size of the resistor, but the parasitic capacitance and the quality (especially dielectric absorbtion) of the dielectric there.  If in doubt one should do a measurements with 2 different delay settings (e.g. dealy 5 and delay 10 for the 100 K resistor) to see if there is a difference.
The needed delay should depend on the resistor to test and not the range. So for testing the 10 K resistor in the 100 K range the shorter 1 second delay should be sufficient.

I'm going to run some tests here with different resistors and cables, but collecting the data will take a while given I'm testing up to delay 10.

The 100 K resistor range does not directly use the the VHP40K resistor, but the 50 µA current source is directly measured to this resistor in the ACAL procedure.
The source for the 10 K range uses the 100 µA current source and this could also be (and likely is) directly measured relative to the 40 K resistor.
A difference is that the 10 K range would use amplification of the voltage, while the 100 K range uses directly the 10 V range.

10k measured in 100k range is at least 10 times less "stable", because you have 10 times less resolution, and because the reference current is 10 times smaller only half as big as in 10k range, leading to increased noise. You should see that in the StD.

You're both right, the standard deviation when measuring 10 kOhm is substantially higher on the 100 kOhm range. I picked some equal length sequences of samples, so there will be some difference in environmental conditions etc, explaining the variance of the variance :

dut	dut_setting	range	mean	std	count	sem
SR104	10 kOhm	10000	10000.058187	0.001831	44	0.000276
Fluke 5450A	10 kOhm	10000	10000.447271	0.001022	44	0.000154
Fluke 5450A	10 kOhm	10000	10000.468134	0.001130	44	0.000170
SR104	10 kOhm	10000	10000.069491	0.001294	44	0.000195
SR104	10 kOhm	100000	10000.070929	0.002691	44	0.000406
Fluke 5450A	10 kOhm	100000	10000.475453	0.003017	44	0.000455

Yes, I also make these measurements via GPIB and calculate the statistical data inside my program, using the Welford algorithm. As well for DCV measurements.
Mostly, there is no need to skip any extreme values (outliers), but the first sample of an armed and triggered data set might be off, sometimes.

The program I commonly use to collect data will sample continuously and automatically change a change in DUT by a change in value over an absolute and relative threshold. But sometimes when changing connections late during a sample the change is too small to be detected, but just enough to affect the standard deviation. For those measurements I'll discard the last sample in each series.

I append an example from my old TP program.
I always measure the resistors temperature and correct for its T.C. to R(25°C), 4th column.
The measured resistance values directly from the 3458A are in the 3rd column, and you see how stable these are, giving 0.12ppm StD in the end.
I read the data with 8 or 9 digits, using DREAL format, as normally the resolution of Ohm would be limited to 7 digits only.
But this was an exceptionally good measurement.

The normal ASCII result gives me 10 digits for the 10 kOhm range using NDIG 9. Looks like a nice program. I separate acquisition and analysis, so my acquisition programs just write raw data to CSV files, and the main thing is to record all important parameters, for example last ACAL time or TEMP? value. I just added a column "delay" for resistance measurements with the 3458A, since I'm going to be changing that. I do the analysis separately in Jupyter notebooks, where I then write functions to analyze a set of voltage reference comparisons, for example. There I will combine data from multiple sources like environmental sensors in addition to the meter readings. In the case of the MM2022 data I manually entered it in CSV files but otherwise used pretty much the same analysis I use for the data I generate in my own lab.

Well, calibrating and measuring are two different stories, concerning 2W or 4W.
For regular measurements, I also use 2W for 10M and above, because it's really less noisy, due to less cables involved.
If you want to measure 1M with < 1ppm "accuracy", you must use 4W, that should be evident due to around 0.2 Ohm cable resistances.

Well, I don't expect <1 ppm accuracy (or "accuracy") from a 3458A measuring a 1 MOhm resistor, but I guess I should start using 4w measurements for 1 MOhm in the future either way.

Well, calibrating and measuring are two different stories, concerning 2W or 4W.
which indicates that his calibrated 3458A (#18) reads a bit higher compared to the two calibrated references with low uncertainty (#2, #13), which we had in our group.
In the end, the readings of his 3458A seem to be within 1ppm, If I estimated that correctly.

Based on my analysis of the last calibration certificate (nominal and as found), the 3458A read 5.4 ppm high measuring 10 V, on the 10 V range at the time of calibration, with a calibration uncertainty of 1.5 ppm (95 confidence interval), and 2.6 ppm of value + 0.05 ppm of range 90 day accuracy (I assumed this to be a uniform distribution). The points where reported as passing but within one expanded uncertainty of the limit (P‡). I corrected the results and uncertainties I gave for this. Based on this, I'd think it would have been more than 1 ppm high, although this is of course a measurement at a single point of time on August, 17. If you'd compare it to previous calibration certificates, which I don't have a copy of but I'm sure branadic could share, you might be able to establish a better estimate of what the value was X months ago.

- Looking at the result, the possible discrepancy in the CCEM K2 can be attributed to excess dielectric absorption in the wiring used.
- A change of the wiring reduces the necessary waiting time for the measurement.

Beforehand they were using PTFE insulated cables (known for piezo electric effects) as most of us do, but changed to some low noise cable with additional carbon film? to avoid effects coming from the cables.

Interesting! Was it really dielectric absorption? Or tribo / piezoelectric effects? I'd expect measuring MOhm resistors to be a DC only process that would not use offset compensation or AC excitation. Would dieletric absorption really be so slow that it added substantial waiting times? According to Keithley's low level measurements handbook, PTFE is quite good for dieletric absorption, but not so great for piezo/triboelectric effects. Something like polyethlyne, which is I believe what the low noise Keithley cables use, with additional lubrication between layers to to reduce the effects even further, might perform better, then. I do have such cables that I use with electrometers, but adapting them to binding posts might be a pain.

[Kleinstein]

Dielectric absorbtion does extend to very low time scales, it just gets a bit more tricky to measure when very long. The US MIL standard uses some 15 minutes waiting time.
With longer time the effect on the resistance measurement gets naturally smaller: due to the DA a small fraction of the capacitance effects the reading longer than normal. The required waiting time is not so much dectated by the time constant of the DA but more by the size / amplitude and the capacitance. The dielectric absorbtion kind of extends the RC time constant by a factor of the materials DA (some 1E-5 for PTFE to 1E-2 for PVC) divided by the required accuracy (e.g. 0.1 ppm).

There is not just dielectric absorbtion of the isolation material (that part should be relatively small with good isulators), but there are also more macroscopic partially isolated islands that can act like dielectric absorbtion. An especially bad example to avoid would be a floating shield / guard. Part of the absorbtion can also be inside the meter (e.g. from the PCB, terminals,protection circuit).

The lower ohms ranges may have some thermal effect in the ohms current source. Here it can help to use the same 10 or 100 PLC and delay as during ACAL.  So for the 10 and 100 Ohm ranges extra delay may be more of a problem than good.

For the stability of the 3458 resistance ranges one contribution is the OP-amp to regulate the current source. This is a low bias JFET OP-amp that does have 1/f noise. More waiting time can lead to additional noise as the overall time gets longer.  Ideally the offset compensation part would also correct drift and some 1/f noise of the OP-amp, but with the current hardware it does not look like this is done.
A good warm up and the time from ACAL may be important to get the best accurcy for the resistance measurements.

For the metrological measurements the noise would however usually only be a small factor to the uncertainty. The more tricky part is drift and similar errors.

[alm]

Dielectric absorbtion does extend to very low time scales, it just gets a bit more tricky to measure when very long. The US MIL standard uses some 15 minutes waiting time.
With longer time the effect on the resistance measurement gets naturally smaller: due to the DA a small fraction of the capacitance effects the reading longer than normal. The required waiting time is not so much dectated by the time constant of the DA but more by the size / amplitude and the capacitance. The dielectric absorbtion kind of extends the RC time constant by a factor of the materials DA (some 1E-5 for PTFE to 1E-2 for PVC) divided by the required accuracy (e.g. 0.1 ppm).

But apparently the presentation claimed that switching away from the standard PTFE cables improved the situation. I'm not sure if you can do much better than PTFE for DA, so maybe some very low capacitance cable? Or reducing the capacitance with a driven guard?

[alm]

We again had the issue of a 3458A guard switch mysteriously getting set to LO while the guard was connected to the low lead at the voltage reference side and this affecting our voltage reference measurements. On branadic's 3458A, the effect was about -2ppm for both positive and negative values relative to the guard switch set to OPEN. Disconnecting guard has no measurable effect compared to connecting it while it's set to "OPEN". I find it truly odd that setting the switch to LO while the guard is connected to the LO lead has any different effect than not connected the guard, so I tried to replicate it on my 3458As at home. I am using a different shielded 2-wire PTFE cable with low EMF spade lugs than at MM2022, and was measuring the Fluke 7001 while powered from battery and not connected to anything else to prevent ground loops.

On both my 3458As, #1 and #2, there was a clear effect. See these two plots. I plotted the absolute values of both positive and negative measurements, and marked measurements with and without guard. The first conclusion was that the guard switches on my 3458As are very intermittent. A clear sign of how often I do unguarded measurements. I actually had to hold down the guard button for a reliable connection when setting it to LO.


For #1, the effect of connecting guard to low appears to be about -6 ppm to -8 ppm for both positive and negative (note that the negative values are shown as absolute values). Error bars indicate standard deviation, but are barely visible because the standard deviation is < 0.1 ppm. I measured the resistance between the guard and lo terminal, and with the switch set to LO it measured ~1 Ohm, and with the switch set to open it measured roughly 390 Ohm. On my #2 unit I measured > 40 MOhm when the switch was set to open.


For #2, the effect is about -2 ppm. I don't know if this is related to the higher open resistance.

Here is the same data as table:
3458A #1

	dut	dut_setting	guard_setting	ag3458a_1_dcv
	last	last	last	mean	std	count
group
13	F7001bat	10 V	open	9.999944	3.452683e-07	19
14	F7001bat	10 V	lo	9.999881	2.727258e-07	19
15	F7001bat	10 V	open	9.999945	4.649933e-07	18
16	F7001bat	10 V	lo	9.999882	3.685633e-07	16
17	F7001bat	10 V	open	9.999944	4.956515e-07	33
18	F7001bat	-10 V	open	-9.999945	2.952243e-07	24
19	F7001bat	-10 V	lo	-10.000015	4.131728e-07	17
20	F7001bat	-10 V	open	-9.999945	3.375280e-07	18
21	F7001bat	-10 V	lo	-10.000015	3.458366e-07	18
22	F7001bat	-10 V	open	-9.999945	3.184028e-07	40

3458A #2

	dut	dut_setting	guard_setting	ag3458a_2_dcv
	last	last	last	mean	std	count
group
1	F7001bat	-10 V	open	-9.999981	1.874827e-07	21
2	F7001bat	-10 V	lo	-10.000002	1.782087e-07	16
3	F7001bat	-10 V	open	-9.999981	1.541816e-07	19
4	F7001bat	-10 V	lo	-10.000004	1.949000e-07	17
5	F7001bat	-10 V	open	-9.999981	1.374771e-07	20
6	F7001bat	10 V	open	9.999969	3.444780e-07	32
7	F7001bat	10 V	lo	9.999949	2.418221e-07	18
8	F7001bat	10 V	open	9.999970	1.736869e-07	17
9	F7001bat	10 V	lo	9.999949	1.559997e-07	16
10	F7001bat	10 V	open	9.999970	2.599496e-07	57

So clearly this effect is not isolated to branadic's 3458A or the setup at the MM. I don't understand it, but it's not generally a problem for me since I always have the guard switch set to open and guard connected on the DUT side.

[dietert1]

I would check whether both guard binding posts of reference and meter are of low thermal EMF quality.

[alm]

One side is the 3458A (with original binding posts) the other a Fluke 7001 voltage reference with also original binding posts. The connections stay the same during the measurement, except when switching polarity. The shield is on the 3458A side connected to the guard terminal, and on the F7001 side the same terminal that the low input lead is connected to. The only thing that changes is the guard switch on the 3458A.

We saw the same effect (with different equipment) at MM2022 and I believe at the mini MM2020.

I guess it would be interesting to connect another meter in parallel and see if that reading is also affect, and try with different voltage references.

[MiDi]

Did you take the measurements with GPIB connected?
@MM21 there was a difference between readings w/ and w/o GPIB connected.

I would check whether both guard binding posts of reference and meter are of low thermal EMF quality.

Why would that make any difference if there is some t-emf for guard?

[dietert1]

Thermal EMF is a possible explanation for the observed deviations by some uV, when guard terminals/connections were mixed into the measurements.
Guard terminals are not made for that, and it isn't guaranteed they are of similar quality as the measurement terminals although they may look similar.

Regards, Dieter

[alm]

Did you take the measurements with GPIB connected?
@MM21 there was a difference between readings w/ and w/o GPIB connected.

I remember. These results I posted were with GPIB connected, but the voltage reference was fully floating. At MM2022 where we observed the same effect with branadic's 3458A, a different PTFE 2w cable, and several F7000 references, both running from battery and mains, nothing was connected to the GPIB connector.

Thermal EMF is a possible explanation for the observed deviations by some uV, when guard terminals/connections were mixed into the measurements.

The low input remains directly connected throughout the measurement, so in my mind guard is merely a higher impedance parallel path. I guess it's worth investigating, though.

[Dr. Frank]

One side is the 3458A (with original binding posts) the other a Fluke 7001 voltage reference with also original binding posts. The connections stay the same during the measurement, except when switching polarity. The shield is on the 3458A side connected to the guard terminal, and on the F7001 side the same terminal that the low input lead is connected to. The only thing that changes is the guard switch on the 3458A.

We saw the same effect (with different equipment) at MM2022 and I believe at the mini MM2020.

I guess it would be interesting to connect another meter in parallel and see if that reading is also affect, and try with different voltage references.

I  also use the GUARD connection at the 3458A side, always OPEN, but never connect GUARD at the DUT side to its negative jack.
So I let it flapping in the breeze for the F7000, but connect it to GUARD jack on the FLUKE 5442A, and on my DIY LTZ1000 references.
Latter GUARD and GND connections are illustrated here: https://www.eevblog.com/forum/metrology/ultra-precision-reference-ltz1000/msg3886166/#msg3886166

I think that the 3458A GUARD is connected to its internal shielding box, and will create a parasitic ground loop if the GUARD switch is set to LO, and may influence the 3458A itself, and maybe the DUT as well.

I struggled in a similar manner when I used the 752A with either the 3458A, or the FLUKE 845AR as Null meters.
https://www.eevblog.com/forum/metrology/influence-of-switch-resistance-in-hamon-dividers/msg4207093/#msg4207093

I used my F7000 as a 10V reference to calibrate my 5442A. In the addendum to the 752A manual, there are corrected GND and GUARD connections shown, which are different for battery and mains operated 845A. You need to precisely follow this scheme, otherwise you get shifts of zero and unstable null readings.

I assume, that's a related problem, though I have to admit, that I still have not understood this issue.

Frank

[alm]

I  also use the GUARD connection at the 3458A side, always OPEN, but never connect GUARD at the DUT side to its negative jack.
So I let it flapping in the breeze for the F7000, but connect it to GUARD jack on the FLUKE 5442A, and on my DIY LTZ1000 references.
Latter GUARD and GND connections are illustrated here: https://www.eevblog.com/forum/metrology/ultra-precision-reference-ltz1000/msg3886166/#msg3886166

I think that the 3458A GUARD is connected to its internal shielding box, and will create a parasitic ground loop if the GUARD switch is set to LO, and may influence the 3458A itself, and maybe the DUT as well.

I struggled in a similar manner when I used the 752A with either the 3458A, or the FLUKE 845AR as Null meters.
https://www.eevblog.com/forum/metrology/influence-of-switch-resistance-in-hamon-dividers/msg4207093/#msg4207093

Let me be clear is that I don't think the guard switch to lo and guard connected at the DUT side is a valid configuration. But I don't yet understand why it's causing such a big difference either. I believe in 2020 you reported also seeing a 2 ppm offset in other meters connected in parallel. I have not yet checked if I measure the same effect. If that's the case, then I'd think it's some sort of offset voltage, current or capacitance affecting the F7000 output.

My approach to guarding is based on HP AN 123: Floating Measurements and Guarding, which is the most complete and clearest treatment of guarding I've found. However, I'm the student who read the textbook and mostly understands it, but certainly not an expert.

Two rules of thumb (from page 7 are):

1. Connect guard so that it and the low terminal are at the same voltage, or as close to the same voltage as possible.
2. Connect guard so that no common mode current or guard current, flow through any of the low resistance, or more generally, so that no common mode current flows through any resistance that determines the input voltage.

At the bottom of page 8 it says:

Don't Leave the Guard Open
Just about any connection is better than leaving the guard open. Any connection that diverts any of the common mode current from Rb [the resistance between the DUT low terminal and DMM], or brings low and guard closer to the same voltage will improve your CMR.

When connecting to a voltage reference like F7000 without a guard terminal, I follow figure 7A from the app note and connect it to low at the DUT side, aka the F7000 lo terminal for the 10V output:


For references with a guard terminal, like Fluke 732A or Datron 4910, I connect the guard to that guard terminal and assume the Fluke / Datron engineers knew what they're doing, but I didn't do any thorough analysis from that. It could be that connecting the guard also to lo at the reference would improve CMR even further.

The Fluke 752A example is a lot more complicated, and it looks like they're worried about ground loops when the null detector is line operated. With the Fluke 7000 battery powered an on its rubber feet, I think the risk of ground loops is low, though of course there will be plenty of capacitance to ground.

My empirical evidence at MM2022 where I did a quick comparison of 5 measurements with various guard configurations (it was well past 17.00 by the time we noticed this):

guard	mean	std	count	sem
no guard connection, switch to lo	9.9999896e+00	8.3666003e-08	5	3.7416574e-08
with guard connection, switch to lo	9.9999707e+00	1.5811388e-07	5	7.0710678e-08
with guard connection, switch to open	9.9999900e+00	1.1401754e-07	5	5.0990195e-08

Obviously no reliable estimate of standard deviation can be derived from this, but the fact that the means of guard switch to lo and guard unconnected at reference, and guard switch open and guard connected to F7000, are within 400 nV (0.04 ppm) suggests to me that both methods are pretty valid, although I'd expect the guarded method to have a lower noise. Based on this I concluded there was no need to redo the measurements without guard connected and the switch set to lo.

I did not test guard switch open and guard unconnected at the F7000, since in my mind based on reading AN 123 this is not a valid configuration either. If you don't want to connect the guard at the DUT, then at least connect it at the meter.

[alm]

I'm going to run some tests here with different resistors and cables, but collecting the data will take a while given I'm testing up to delay 10.

I did this test and posted the results in a new topic.