MM2022: DELAY and OCOMP on the 3458A with different resistors and cables

[alm]

Introduction
In the discussion of my Metrology Meet 2022 results there were some insightful comments about how some standard resistors might need more than the standard 1s for 10kOhm and 5s for 100 kOhm recommendation that's a common rule-of-thumb for resistance measurements with the HPAK 3458A. To not interfere with the other discussion in that topic I created a separate topic.

This topic has discussed multiple times before, in particular by Dr. Frank's great investigation work:
Precise Offset Compensation Ohm Measurements and Validation of DMMs
optimal configuration of HP 3458A to measure 10k

In short, offset compensation in the 3458A switches on and off the current source during the measurement cycle to measure both the voltage without any current (the offset voltage it's trying to compensate) and the voltage with current applied (the IR drop of the resistor under test). But due to dielectric absorption in the cables and rest of the system, this voltage step might have an effect on the measured voltage even after the default 30 ms delay. This voltage has been noticed as depending on the resistance, with 1 kΩ and below barely needing any delay, 100 kΩ needing the most delay, and above 100 kΩ offset compensation is disabled by the 3458A either way.

The question here was if the SR104 due to its large size and oil tank suffers more strongly from this effect than say a Fluke 5450A or VHP bulk metal foil resistors.

Setup
In these tests I have taken a series of measurements with different delay values, cables and resistors. All measurements were taken by a HP 3458A with ACAL ran at least every 12h, but not while performing a measurement for a specific combination of settings / DUT / cable. All measurements were in 4W Ohms mode, with offset compensation on, 100 NPLC.

I picked my best standard resistors with nominal values of 1 kΩ, 10 kΩ and 100 kΩ:

• HP 11103A 1 kΩ
• ESI SR104 10 kΩ
• Guildline 9330 100 kΩ
• The Fluke 5450A resistance calibrator set to 1 / 10 / 100 kΩ (using the rear binding posts)

I used cables assembled from parts sold by Forum user ap (Adrian). They are four wire PTFE cables with a woven outer shield terminated in gold-plated copper (low-EMF) binding posts crimped with the proper Knipex crimper and die. I used two cable lengths: 1m (which I used at MM2022) and 2m (which I normally use at home because my 3458A is high above my bench). In all cases the shield was connected to the guard terminal on the 3458A and if available (SR104, 5450A) to the guard terminal on the resistor and the four wires to the force / sense terminals on both sides.

I then had the 3458A take a series of samples starting from DELAY 0 up to the highest value, one measurement per delay value, and then repeat this process at least 10 times. This way I could see the relative change between samples with different delay values and then average the effect over the multiple rounds.

Error bars are standard error of the mean. N >= 9. See for more details the attached CSV file with the results as table. I fit an exponential decay (charging capacitor) model using the Levenberg-Marquardt model weighted by standard error of the mean which I felt made sense and wouldn't overfit. To make sure even the delay=0 point had a finite standard deviation, I used 0.01 (an order of magnitude below the smallest) there.

Results
Here are the mean relative differences compared to the measurement with DELAY=0 over all rounds I did with the same resistor / value / cable:


It appears that the wire wound resistance standards have much less effect due to dieletric absorption than the 5450A with all its extra wiring and relays. The effect is stronger in the 100 kΩ wire wound Guildline 9330 than in the 10 kΩ SR104, but it's especially strong in the Fluke 5450A when set to 100 kΩ. Based on this 1s for 10 kΩ seems plenty for the SR104, but for the 5450A at least 2s seems necessary, and for 100 kΩ, at least with the 5450A, 5 seconds seems a sensible value.


The results with the 2m cable look quite similar to me. The 5450A-100k measurement has a lower number of rounds compared to most others (only 9), so that explains the larger error bars. The fit is clearly failing for the Fluke 5450A 100 kΩ result.


The 1 kΩ results are on a vertical scale that is a factor 20 magnified, so we're getting down in the noise here.


The results with 2m cable don't look very different from the 1m cable results.

Discussion & conclusion
The fit results are summarized in this table:

			V0	tau (s)	time (s)
cable	dut_setting	dut
4w PTFE 1m	1 kOhm	Fluke 5450A	0.21	5.16e-02	0.07
		HP 11103A	-0.13	2.14e-01	0.20
	10 kOhm	Fluke 5450A	4.34	5.87e-03	NA
		SR104	0.50	3.82e-01	0.88
	100 kOhm	Fluke 5450A	11.91	4.45e-01	2.43
		Guildline 9330	5.43	4.21e-01	1.97
4w PTFE 2m	1 kOhm	Fluke 5450A	0.24	5.25e-02	0.08
		HP 11103A	-0.12	2.95e-01	0.27
	10 kOhm	Fluke 5450A	4.20	4.40e-01	1.95
		SR104	0.77	2.37e-01	0.65
	100 kOhm	Fluke 5450A	13.66	4.12e-01	2.31
		Guildline 9330	7.61	4.10e-01	2.06

I calculated time with the condition that the contribution of the dielectric absorption to the uncertainty should be at most 0.05 ppm, which I admit is a somewhat arbitrary number. I used the inverse of the exponential delay function to calculate this time based on the fitting parameters. Obviously the fit for the 5450A 10k 1m measurement did not yield a valid tau. The cable length seems to have a pretty minor effect. The wire wound resistor standards, including the SR104, need less delay than the Fluke 5450A resistance calibrator. I suggest using longer delays when measuring a calibrator like the 5450A than for a bare resistor. I'd summarize the advice as:

• For 1 kΩ and below, use 0.1 s (I don't trust the 11103A results much due to the huge uncertainty, maybe I'll redo those)
• For 10 kΩ with bare resistors, use 1 s
• For 10 kΩ with a calibrator, use 2 s
• For 100 kΩ with bare resistors, use 3 s
• For 100 kΩ with a calibrator, use 5 s (I'm not so convinced by the knee of the fit for the 5450A-100k results)

Note that this is purely based on my cables, resistors, etc, so it may not be applicable to other setups. I'd love to hear feedback on both the data and my analysis of it.

Data as table
My results are also available as a table as the attachment measurement-tests-delay-test-results.csv.txt. if you want to look more in depth. I also attached my raw data as a CSV file.

[alm]

Reserved for future results.

[dietert1]

Can you ask the 3458A about the zero current offset it actually determined and subtracted? Or use some programmed sequence to get that (resistance measurements with no offset correction interleaved with offset voltage measurements)? This may be missing to prove the basic assumptions.

Regards, Dieter

[alm]

It's an automated sequence that measures the voltage without the current source on, then with it on and subtracts the difference. All we can do is add a delay in this cycle to wait for the residual voltage due to DA to go away. Frank illustrated it with some scope shots here: https://www.eevblog.com/forum/testgear/precise-offset-compensation-ohm-measurements-and-validation-of-dmms/msg833855/#msg833855

[Kleinstein]

For the effect of DA the time dependence would not be exponential, as there are usually multiple time constants involved. the expexted time dependence would be more like 1/ (t+a).
An exponential part would be there for the normal capacitance, but this part should be well fast enough to not be a problem after a few ms.

Besides the capacitive (inluding DA) part, there could also be a thermal effect - though with the high quality resistors this should not be a big issue and more a point for the smaller resistors like 1 K.
There is also a possible effect inside the meter, with the current taking time to settle, but this part should obviously be independent of the DUT.

For the guard it can make a difference if it is connected to the low side. I think it could be bad idea to have the guard unconnected both at the 3458 (switch to open) and the DUT. With a floating guard one can an addition slow time constant from charging the guard vie leakage resistance at both ends.
Where the guard is connected (at the 3458 or the DUT) and if the drive low or sense low is used should not make a difference, as the connection is low resistance.

[dietert1]

I don't know whether calibration is affected in a similar way. If so, it isn't completely obvious which are the correct results.

I was asking, as the observed time constant of 0.4 seconds or so would mean a capacitance of about 4 uF in conjunction with 100 KOhm. If you are looking for 0.1 ppm, you can roughly divide by 14, as you wait 2 time constants for each decade. Then still it is equivalent to 200 nF. Of course there is no such capacitor. The cable may have 200 pF, so a factor 1000 is missing. The effect you observe may be something else, e.g. a thermal effect.

Regards, Dieter

[Kleinstein]

The delay dependence would obviously also effect the resistance measurement (10 K) in the calibration.

The pure capacitance effect is obviously not the problem, as the capacitance is quite a bit smaller.
Thermal effects are possible. At first one would expect the effect to be smaller with the 100 K resistor. However the test current for the 10K/100 K ranges are 100 µA and 50 µA. So the 100 K resistor would actually get more power. The internal heating in the current source would be not that much different.
The other possible slow effect is dielectric absorbtion. This can be quite a bit slower than the pure capacitive effect. However to get a significant effect it still needs quite some capacitance with poor dielectric, or some floating parts ( not connected shield) to produce an analog to DA on the macro scale.

For comparison it may be interesting to also check the 10 K resistor in the 100 K range.
A thermal effect in the DUT should be half the size from half the current. The DA effect should be the same for the DUT contribution.

[alm]

Thanks for your feedback, both! I totally agree with you, Kleinstein, about not leaving guard floating. I didn't intend to do that, but in retrospect:

For the 5450A measurements, guard was open on the 3458A but connected to lo through a 100 Ohm resistor on the 5450A (ext guard not pressed). I figure the Fluke engineers probably had a good reason for this 100 Ohm resistor and I shouldn't short it. So these measurements were guarded.

For the SR104, I also connected guard to the guard terminal, but that terminal in the SR104 is isolated from the other terminals, so what I created a big floating shield. I think the better solution is to connect guard to force lo on the SR104 side.

The other resistors don't have a guard terminal, so I pressed the 3458A guard button to connect it to lo. But I forgot that that switch is bad and only makes contact when you keep it pressed all the way. So here the guard was also floating. I'll redo them by connecting guard to lo at the resistor.

I'll redo a couple of tests with different guarding, and also measure the SR104 on 100 k range, and report back later. It might take a bit of time since running each test takes hours.

I'll also have a look at fitting a different model instead of the exponential model.

[Kleinstein]

The interresting part seems to be the times up to 1 second. Later going to even more is more for a good piece of mind for the last sub ppm part.