Influence of switch resistance in Hamon Dividers

[Dr. Frank]

I only made a brief resistance measurement for the PTFE cables I've used, that may give some additional mOhm in total.
Leakage / resistance might be available in the ELMA spec, but that will be analysed and measured, later. For this aspect, as it was described as being the dominant error, I've chosen 25kOhm as the basic value, instead of 40k.
Frank 

[Kleinstein]

So Fluke "only" used a simple switchable series resistors, not sets of additional current compensation resistors like in a Kelvin bridge. Using such extra resistors can get quite messy and possibly causes more trouble than good due to additional errors from leakage. It may still be an option for lower resistance (e.g. for use as a 10 to 1 V step and not as a 100:10 V).

A lower base value would also give more self heating - one of the other limiting effects.

For the 1:100 divider mode the switch resistance is less critical, so they seem to get away without extra compensation.

[Lesolee]

If the switch resistance is really that critical, I wonder why it isn't verified periodically. Fluke wrote the Fluke 752A is a ratio standard and don't need any traceable calibration. It seems it is possible to Null the 752A and it might be off anyway, if the contact resistance has increased.

So basically the truth is finally out. The switch resistance is critical (and corrected for), but is not measured as part of their calibration procedure. If an ant crawls into the contacts and dies, taking the resistance up by a factor of 10, the absoluteness of the divider ratio is no longer correct, and you have no way to know, other than to have another better standard. One can say they have designed and manufactured the switches so that even after years of life they are still excellent on contact resistance. But if you live near the sea, and the corrosive salty air takes its toll, your reference standard is in an unknown state of mis-calibration.

I can just imagine the engineers saying "that needs to be in the manual", and some manager saying "the switches are good, and not suitable for the customer to measure, so just shut up about it."

[notfaded1]

If an ant crawls into the contacts and dies, taking the resistance up by a factor of 10, the absoluteness of the divider ratio is no longer correct, and you have no way to know, other than to have another better standard.

That's funny... we've seen some residue that looks worse than an ant dying before.  Sometimes looks like someone lived by the ocean and kept it in their shed outside or a soggy basement for 15 years.

[notfaded1]

Anyhow, I think that I now have fully understood this aspect. Sort of black magic inside the 752A, which is engineered very well, over all.
I also think, that it's possible to replicate its high accuracy using volt-nuts grade facilities.

Frank

I've been following this closely... can we take this to mean we may be able to replicate this black magic soon Dr. Frank?  Nice highlight on the 36.75 inches long AWG 22 solid Cu btw.  Also I like the replicated calculations and seems everyone is in agreement now.

B

[Kleinstein]

I check of the contact resistance would be a really good idea. However the requirements are not that dramatic - more like make sure they are not off by a lot (e.g. more than 100%).

Chances are the users at the primary labs will know that and do such a check. They will also not store there precious instrument in a damp basement or near the shore (which is quite a bit away from the NIST in Bolder).

[e61_phil]

Very nice analysis, Frank! 

For this kind of compensation it is obviously necessary to compensate one of the upper resistors.

I attached a graph which shows the error due to a changing switch resistance with the 49.4mR compensation.


@Kleinstein: I'm very sure, that there a primary labs, which don't do such checks.

@notfaded1: Noone, will stop you from replicating

[Kleinstein]

The tricky part to check is leakage: here it is nearly impossible to check at exactly the same positions. In addition contamination from deposits (e.g. nicotine, grease) and worst case a fungi growing or a small spider inside is a way to produce leakage. The best one could do is probably to keep the case well closed, clean and dry and do a leakage test for some dummy parts inside.

For a high precision divider there is a little the question if the Hamon divider is still the best choice: The alternative is a chain of some 10 equal resistors that are checked / measured before use. With modern instruments that allow for a reasonable fast and accurate measurement this may be a real alternative. Equal resistors may have some advantage as self heating could also compensate. Also checking for leakage is easier (i.e. no longer essentially impossible) with a simple string.
A good resistor measurement bridge with the associated switches is still not easy. Chances are it would be more switches, but less critical.

[Dr. Frank]

The resistance is specified as minimum 10¹² Ohm.
Indeed, I measured about 60pA @ 100V between adjacent pins, that gives 1.7 * 10¹² Ohm.
So good enough for my original design goal to get about 1ppm 10:1 and 100:1 transfer accuracy.
Frank

[Lesolee]

The tricky part to check is leakage: here it is nearly impossible to check at exactly the same positions. In addition contamination from deposits (e.g. nicotine, grease) and worst case a fungi growing or a small spider inside is a way to produce leakage. The best one could do is probably to keep the case well closed, clean and dry and do a leakage test for some dummy parts inside.

Interestingly, they do say that the switches are "sealed units" (section 4-15), and they stress the guard circuits in 3-23, 3-24, 3-25, and figure 3-9. But as you say, difficult to verify their claim of 0.057 ppm error due to leakage on the 10:1 range.

[quarks]

bookmark, because I missed it until now

[Lesolee]

magic did some analysis of the series parallel stuff

https://www.eevblog.com/forum/metrology/anyone-else-built-a-hamon-divider/msg2612673/#msg2612673

I found the maths a bit intimidating in his analysis, and I did a simpler version with just the three resistors.

[Dr. Frank]

Consistency Check with HP3458A

HighVoltage kindly lent me his 752A to check it and then to calibrate the HV ranges of my 5442A.
The 752A is from about 1993, 29 years old.



That vintage bears the risk that the resistance of the switch contacts increased considerably, busting its specification of 0.2ppm uncertainty @ 10:1 ratio.
The intrinsic problem with such Primary Ratio Standards is that they can not be calibrated by “something better” instrument. It’s written in the manuals, that they are working correctly “by design”, elaborate error analysis, and by auto-adjustment.
Therefore, I tried to check the 10:1 ratio by use of the 3458A. Its transfer uncertainty on its 10V DC range is specified to 0.55ppm, but its 10:1 transfer capability by linearity (INL + DNL) might be even accurate to about 0.3ppm of output, following hpj 4/1989, p.23.
The 752A was auto-adjusted following the setup from the manual addendum and using an 845AR w/o problems.
I tested the 10:1 transfer by measuring the 10V input directly at its INPUT jacks, as well as the 1V output, both with reversed polarity, which is critical concerning thermoelectric voltages. I repeated this procedure several times, but always found errors far beyond 0.2 or 0.3ppm ratio uncertainty.



So my conclusion was that the switches should have excessively higher resistance, after all these years.
HighVoltage allowed me to open the instrument with greatest care and white gloves, of course, to measure the resistances of the switch contacts. To my big surprise the switches were all ok, as described in the next chapter.
So I investigated further and finally discovered that the bias current in the 10V range of my 3458A caused these errors. It’s specified to have max. 20pA.
The bias current was determined between -10 .. +10V of input voltage, by measuring the voltage drop over an external 1MΩ resistor.



These bias current measurements changed over several sessions, probably over temperature, time, humidity and so forth, up to 20pA max. bias current.



My 845AR has an input impedance of  1MΩ. By closing and opening the input short, the difference in µV readings gave about 100.. 200fA of bias current. Reading carefully the manual, chapter 2-31 “Increasing Input Resistance”, I deduced that the bias current w/o that 1MΩ resistor would typically be 3µV / 1000MΩ ~ 3fA.

The 752A has quite a high impedance of 400 kΩ, so I calculated the ratio error of the divider loaded  by a bias current, see xls file below.
The error formula is: ε = -R₁* I_B / U_in



A 20pA bias current at 360kΩ and 10V input creates -0.72ppm of ratio error, so this obviously is the root cause.
The 3458A can be used, anyhow, for measuring 100V and 1kV at 10V output, as the ratio error is 10 times smaller in this case. Used as a Nullmeter, it still has e.g. +8pA bias, creating errors when using the 752A in its classical bridge configuration for calibrating 1kV, 100V, 1V and 100mV versus an external 10V standard.



Therefore, any Nullmeter to be used must have guaranteed bias currents well below 1pA.
Here’s another table for my Keithley 182A nV DVM. This shows, that even this class of nV-meters might not be the right choice.

[Dr. Frank]

Switch Resistance Check and circuit analysis

I disassembled top and front of the instrument.
There were indications, that this instrument had been serviced, replacing several broken jacks, see careless solder joints and flux residues.



Probably the divider resistors were re-adjusted by changing bridges on the adjustment board.



In the third picture, the black compensation wire, folded inside the cable tree, can be seen.



Then I measured most of the switch resistances and several crucial cable connections, using 4W Ohm method.

To my surprise, the switches all had very low resistance values between 0.6 mΩ and 3.8mΩ, far away from the 10mΩ as anticipated in the manual. Their initial values might have been 0.5mΩ only. After 29 years now, the resistances of the Hamon relevant switches were between 0.8 .. 1.2mΩ only. So they play a minor role only.



As shown in the schematic in green, only switches S2D/2 and S2C/8 contribute about 2mΩ, plus the connection to R35, those 4 brown wires, 10.5mΩ, that gives 12.5mΩ in total. This should be compensated by the red items, cable from Input High to and including S1A/5, this mysterious black 49mΩ cable, plus S2D/1, all giving 63mΩ in total. As the interconnection between R21-24 and R31-34 are linked directly at S2D/2, these cables are included in the divider resistors and contribute zero error.
Therefore, mostly this 10.5mΩ of ‘4 brown wires’ is compensated, and to a minor degree the switches, including their expected lifetime increase of resistance. Calculating the divider error of the initial state (all contacts having 0.5mOhm) gives about -0.046ppm.
If both switches increase to 5mΩ each, i.e. 10mΩ in total (what’s indicated in the manual), that would give an error of +0.049ppm. To check my explanations, please see also the calculation chart by Dr. Philipp  .

A compensation resistor like the black 49mOhm one is evidently missing for the calibration and use of the 100:1 divider ratio. A 630mΩ resistor would be required, instead of only 28mΩ, as measured between: IN HI – S1A/6 – GREEN Cable – S2C/1.
This way, the 100:1 ratio seems to have an additional, undisclosed +0.11ppm error, included in the 0.5ppm specification, if I did not overlook something.

I also briefly checked the leakage current, which was ok.
As a conclusion, this 752A seems to operate in near mint condition, at least I expect that it fully meets its specifications.

Edit:
The switches obviously are manufactured by MultiTech, 820 / 2000 family, which VgKid had found:
https://www.eevblog.com/forum/metrology/4-wire-switch-selectable-resistance-standard/msg1193999/#msg1193999
https://www.multi-tech-industries.com/test-switches.html
The wafers look identical, and the initial contact resistance is below 1mΩ.
FLUKE probably ordered a special version. 4 decks, 6 positions, 2 poles / deck, 5 stops.

[Dr. Frank]

For calibration and use of the 752A, I use an 845AR as a Null-Meter, which is line-powered.
It’s very important to use the grounding scheme of the addendum of the 752A manual, which I append, see fig. 1 and fig. 3.
There’s a difference between battery and line powered instruments. Only if these instructions are followed, the null readings will be comfortably stable and usable.

I also tried my 3458A as a Null Meter. I did not calculate the error for the calibration of the 752A, caused by its bias current.
So I speculate, that only the higher resistance of the 100:1 range might induce noteworthy errors.

But the 3458A is not as convenient and stable to use as an 845A, because the readings are very noisy, and sort of ambiguous – you have to test & feel this on your own. This is possibly caused by the 10V common mode voltage relative to earth, and also to the lacking proper grounding scheme as described above.
The errors by bias currents for the calibration of the DUT I have already described in the first part.

The 5442A has six ranges, i.e. 0.2V, 2V, 10V, 20V, 250V, 1kV, which were calibrated by a differential comparison against a known 10V reference, either by dividing the reference by 100 or 10, comparison on 1V, 100mV level, or by dividing the output of the DUT by 10 and 100, and comparison on 10V level.  Due to the bias induced errors of the 3458A, I followed the classical procedure in the manual, i.e. using the differential mode only.
The Fluke 7000 first had been trimmed to exactly 10.00000V, derived from the average of my reference group.

It turned out, that the 4 higher ranges (i.e. their ratio constants) had stayed very stable over at least 13 years (date of last full external calibration is unknown):
The 10V range, i.e. its internal 13V reference, SZA263 based, drifted about +1ppm.
The 20V range ratio drifted ~ -0.1ppm, 250V ratio -0.6ppm, 1000V ratio -1.6ppm.

The auto-calibration of the 5442A is able to measure and correct small drifts of the ratios at any given time, but a 10:1 cross-transfer between ranges is not possible, as in the 3458A, or the later 57xxA calibrators.
That means, that the calibration drift is mostly caused by its voltage reference drift (affecting all ranges in parallel), or by the linearity drift of its DAC, which might basically be on the order of its INL, as the ratio drifts are virtually zero by internal calibration.

Anyhow, Dr. Philipp might use this 752A to check the HV calibration of his 5730A.

[TiN]

Dr. Frank 
If you (or anyone else in community) have particular things would like to check with 752A for more data, please do let know.

We plan to have a CalFest 2022 in bit over a month from now with ppm members attending and will have more than four 752A's to test against. Idea was to perform self-calibration on multiple dividers and compare them between each other from fresh volt.   

[alm]

These bias current measurements changed over several sessions, probably over temperature, time, humidity and so forth, up to 20pA max. bias current.

Am I understanding you correctly that it's the variation in bias current, in particular with input voltage, that is causing the bias current correction as described by Fluke to not work in your setup? I wonder if the Datron / Fluke series of 8.5 digit DMMs have better bias current stability.

[magic]

magic did some analysis of the series parallel stuff

https://www.eevblog.com/forum/metrology/anyone-else-built-a-hamon-divider/msg2612673/#msg2612673

I found the maths a bit intimidating in his analysis, and I did a simpler version with just the three resistors.

I could try to comment my calculations if there is interest. But there is nothing really deep or clever in them (that I can see), I just hammered the formulas mindlessly with algebraic transformations until they resembled the form I wanted to see. I have reviewed that stuff (again) and it still looks good to me.

There is an error and a gotcha in your analysis. The final formula given for the series-to-parallel ratio of three resistors is:
Rs/Rp = 9 - 6·δ²
where δ is the matching tolerance.

The error is that the ratio is less than 9. My own calculations indicate it must be greater than 9. I tried a few examples and the ratio was always greater than 9. I haven't analyzed where the mistake came from.

The gotcha is that the proof relies on each resistor being a ratio of δ away from their average, rather than from the nominal value. For a skewed distribution like 9Ω, 9Ω, 11Ω the ratio is approx. 9.08, but naive application of the formula with δ=10% gives only 9.06 after correction for positive sign, or 8.94 as-is. That being said, it's not a huge difference and such distribution is likely the worst case that can possibly happen.

For the record, my own conclusion was:
9 ≤ Rs/Rp ≤ 9 + 12·δ²

[Kleinstein]

There are 2 types of error:
One is from a mismatch in the resistors. In the parallel configuration the smaller resistor get more weight and thus a smaller than wanted resistance for the parallel configuration.

The other is the added resistance of the switches. Without extra compensation this adds to the parallel confuguration and thus to small a ratio.
So there are 2 effects, one going up and one going down.

With some extra compensation in the wire length and choosing the right point to tap of the ratio the error can be reduced to some degree and the variations in the switch resistance can go in both directions. So the error can be both ways, depending on how stable the switch and cable resistance is. A point may be of there is a way to check the compensation. Testing the contract resistance is a good point and should be part of the self test.
The effect of the 3458 input impedance (800 Gohms range from the leakage data) shows that parasitic leakage and parallel resistance could also be an issue, not the the switch on resistance, but possibly also the switch off resistance. In that respect the cabeling does not look so great - though hard to tell how good the isolation actually is.

With the relatively large resistors the 752 seems to be made mainly for a 10 to 100 / 1000 V step and not really to go from 10 V down to 1 V and 0.1 V.
Is there a corresponding lower resistance Hamon divider, that is better suited for the lower votlages ?

[Dr. Frank]

These bias current measurements changed over several sessions, probably over temperature, time, humidity and so forth, up to 20pA max. bias current.

Am I understanding you correctly that it's the variation in bias current, in particular with input voltage, that is causing the bias current correction as described by Fluke to not work in your setup? I wonder if the Datron / Fluke series of 8.5 digit DMMs have better bias current stability.

Hello alm,
thanks for this hint.
Anyhow, this more qualitative article does not describe at all, what the decisive parameters for a given DMM are, which makes it usable as a 845A replacement, and how these parameters can be measured. Is it the bias current only, or are the impedance, isolation resistance, and so on also relevant?
Additionally, FLUKE only hopes, that the bias of their 8588 would be in most cases around 5pA. Fluke also does not measure the bias over different voltages, or do I miss something? I guess, that each DMM will show varying bias currents over their input voltage.
I think, I will add or cite a few documents, how other metrologists have characterized their long scale DMMs.

The problem I see is not especially the change of this bias (over temperature for example), but simply any absolute value above 1pA.

FLUKE themselves seem not to have calculated the errors like I did (see my xls table), which allows to estimate the induced error per range or mode, in a very clear and quantitative manner.
So it's true, that the 100mV and the 1V ranges are affected the most, and to my opinion a DMM can definitely NOT be used for that purpose.

I also feel confirmed by FLUKEs article, that the DMM solution suffers from those ground / isolation problems, e.g. this pump out effect and the noise problem they also mention, which the 845A probably does not have.

@ Kleinstein: The 752A is as it is, so there is no use to discuss that it has too high an impedance in these low DCV ranges.
I also don't know, how this new device from IET is engineered, nor do I know about any other commercial divider for that purpose.
The 752A simply does it job perfectly, provided you use an 845A or similar low bias, high isolation instrument.

Edit:
I got a lot of insight about the 3458A DCV input behavior from Rado Lapuh: "Sampling with 3458A", especially about the bias current measurement.
Two cited articles describe in detail, how to measure these input parameters.
They can be downloaded somewhere else (via Research Gate) for free, because I think I'm not allowed to upload the files here:

"Accurate determination of the input impedance of digital voltmeters", G. Rietveld
"Determination of High-Resolution Digital Voltmeter Input Parameters", Ivan Lenicek, Damir Ilic, and Roman Malaric

They find similar values for the bias current of their 3458A (they use a different sign convention), but also do not determine the bias at different input voltages.

[alm]

Anyhow, this more qualitative article does not describe at all, what the decisive parameters for a given DMM are, which makes it usable as a 845A replacement, and how these parameters can be measured. Is it the bias current only, or are the impedance, isolation resistance, and so on also relevant?
Additionally, FLUKE only hopes, that the bias of their 8588 would be in most cases around 5pA. Fluke also does not measure the bias over different voltages, or do I miss something? I guess, that each DMM will show varying bias currents over their input voltage.

The state that for the 8588A the bias current is "almost always less than 5 pA", so I imagine this is based on either inside knowledge of the 8588A design / production testing, or from characterizing a number of 8588As in their own labs. But it is very light on details indeed, like no procedure to validate this for your own meter. This is presumably an older version of the same article that contains slightly more details, like "The newest Fluke Calibration Reference Multimeters (the 8588A and 8558A) have significantly less bias current, at 20 pA maximum. This bias current is also adjusted to be effectively zero pA when they are originally tested. This virtually removes the bias current offset problem. Also, because the bias current changes very little over time, it remains near this level for an extended period into the future." and how to test for bias current.

Have you tested or calculated the effect of using the offset correction as described in the article?

Maybe this is worth a shot?

A detailed description of the entire self-calibration procedure with schematics can be obtained from the paper authors

The problem I see is not especially the change of this bias (over temperature for example), but simply any absolute value above 1pA.

Wouldn't you able to correct it if offset current is constant and impedance as seen from the DMM is constant, or you can measure the effect on multiple ranges (1:10, 1:100)?

I also feel confirmed by FLUKEs article, that the DMM solution suffers from those ground / isolation problems, e.g. this pump out effect and the noise problem they also mention, which the 845A probably does not have.

I agree that the article basically states that the 845A is superior in terms of uncertainty introduced by all the factors you name, but that the DMM is more convenient in terms of automation.

"Accurate determination of the input impedance of digital voltmeters", G. Rietveld
"Determination of High-Resolution Digital Voltmeter Input Parameters", Ivan Lenicek, Damir Ilic, and Roman Malaric

Thanks for the references! Both papers reported values well under 5 pA. This is consistent with the Fluke figure, although for the 3458A.

[Kleinstein]

The 3458 input uses switching directly at the input with relatively little fitlering capacitance. So it is not a steady bias current, but also includes spikes in the current and relatively little (e.g. some 100 maybe even 10 pF) of capacitance could make a difference in the settling and charge injection. So worst case the capacitance and source impedance can make a difference to the input bias. It may be a good idea to check the bias with 2 different resistors and maybe a little extra capacitance.
Besides the capacitane, a changing level of mains hum may also be a problem, effecting the input current.

I don't know the details on the Fluke meter, but only have information on the predecessor Datron 1281. If the input part is similar, one can expect the input bias to be relatively constant and not effected much by the voltage, as most of the input amplifier is bootstrapped. This could explain why they ( Fluke ?) claim essentiall constant bias.

The claim of the DA1281 to replace a null meter seems to be the DMM replacing the whole system of refrence, KV divider and nullmeter , not replacing just the null-meter and keeping the KV divider and extra reference.

A more or less constant bias should have about opposite effect on the tests with both polarities. So the correction should be relatively easy and may just be averaging over those 2 tests. The extra input impedance may be the larger problem. The real DMMs will have a combination of a constant bias and impedance parallel to the input. The input impedance does not even have to be constant. The change in input current can be nonlinear in the votlage.

[alm]

Attached to this post (the second attachment) is a Fluke presentation that appears to was made before they made their own long-scale DMM, is more critical about the use of DMMs instead of null meters and goes into more detail about the DMM selection and measuring the stability of the observed offset.

[Kleinstein]

It is a bit odd, that they assume a 40 K source impedance:
AFAIK the 752 has a 120 K:120 K auxiliary bridge arm for the 1:1 self cal step. The main arm is 40 K and 40 K in this step. So the source impedance in the self cal setp is 20 K + 60 K = 80 K.
Reversing the external 20 V supply (not just the bridge arm turn over for the adjustment) for the adjustment step should to a large part cancel out the offset / bias problem.

The 40 K are approximate (though more like 36 K as 1:10) for the later use as a 1:100 divider. That would also be the case with significant votlage at the DMM input.

[e61_phil]

The 3458 input uses switching directly at the input with relatively little fitlering capacitance. So it is not a steady bias current, but also includes spikes in the current and relatively little (e.g. some 100 maybe even 10 pF) of capacitance could make a difference in the settling and charge injection. So worst case the capacitance and source impedance can make a difference to the input bias. It may be a good idea to check the bias with 2 different resistors and maybe a little extra capacitance.
Besides the capacitane, a changing level of mains hum may also be a problem, effecting the input current.

I don't know the details on the Fluke meter, but only have information on the predecessor Datron 1281. If the input part is similar, one can expect the input bias to be relatively constant and not effected much by the voltage, as most of the input amplifier is bootstrapped. This could explain why they ( Fluke ?) claim essentiall constant bias.

The claim of the DA1281 to replace a null meter seems to be the DMM replacing the whole system of refrence, KV divider and nullmeter , not replacing just the null-meter and keeping the KV divider and extra reference.

A more or less constant bias should have about opposite effect on the tests with both polarities. So the correction should be relatively easy and may just be averaging over those 2 tests. The extra input impedance may be the larger problem. The real DMMs will have a combination of a constant bias and impedance parallel to the input. The input impedance does not even have to be constant. The change in input current can be nonlinear in the votlage.

Some time ago I had a Datron 1071. That also had a bootstrapped input stage, but I never looked deeper into it. The calibration included to connect a 1Meg in parallel with a small capacitor and that was used by the meter to cancel out/reduce the input current. Unfortunately, I never measured the input current of that meter.