Anyone else built a Hamon Voltage Divider?

[Gyro]

Hi all,

I just wanted to share my Hamon Divider build (aka Poor man's Fluke 752A Reference Divider) and was wondering if anyone else had constructed one?

In case you haven't heard of it, the Hamon divider (invented by B.V. Hamon in 1954) is a way of creating a precision Divide by 10, 100 etc that is effectively self-calibrating. Fluke used this principle in their 752A Reference Divider and they still use in some form with Josephson Junctions.

My build was inspired by Conrad Hoffman's article, which I found whilst browsing Joe Geller's excellent site....

http://conradhoffman.com/HamonResistor.html

http://www.gellerlabs.com/752AJunior.htm

I happened to have a matched set 10, 1970's vintage, 1k precision wirewound resistors which fitted the bill perfectly for a 10:1 divide. Basically for calibration the upper 9 resistors are arranged in 3 parallel groups of 3 resistors to create a compound 1k resistor which can then be compared with the bottom 1k resistor as a 2:1 divide - as long as the voltage across the two 1k resistors is exactly equal the when the resistors are all placed in series the divide ratio will be exactly 10.

The main photo shows the finished divider (together with 100:1 extender) and my dodgy adjustable 2:1 divider which I used, Wheatsone Bridge style to measure the 2:1 ratio with my 1uV resolution Datron 1045 DVM.



The 10:1 divider mode selection is done with a barrier strip and links - at these resistance levels switch contact resistance would be an unacceptably high error source (Fluke managed it by using higher resistance  chains but this gives other challenges with leakage and guarding).

The internal view shows the internal resistor mounting and wiring, the resistors are mounted on an internal insulated sub plate, connected to Input Lo in an attempt to provide some screening and hopefully reduce thermal gradients. The resistors are mounted on PTFE barb standoffs - but that's because I have a big bag of them,  , not needed at this resistance level.



Things have evolved since I built the 10:1 divide, I found a batch of 10k Vishay MPR24 5ppm 0.01% resistors going really cheap on ebay so decided to add a 100k 100:1 divide. This uses the same arrangement (as Conrad Hoffman's article), but this time I was able to use a sealed toggle switch without worrying about contact resistance (leakage on a large barrier strip would probably be more of a concern). Having a 100:1 divide is useful for 'leapfrogging' ranges when meter calibrating.



I still need to box the adjustable 2:1 checking / calibration divider and add a reversing switch (it's fiddly having to keep reversing leads). Basically it consists of a pair of matched 50k Vishay foil resistors in series with a 5 ohm 10 turn pot (all 1970s vintage again), I added a couple of low value (10 and 13 ohm) resistors to balance the center of the pot's span.With 1V input this gives a span of 50uV (5uV per turn).

For testing, the Hamon divider (in 2:1 mode and adjustable divider are put in parallel across a 1V (approx. non critical but low enough to avoid resistor heating as one of the 1k resistors is made up of 9 resistors in series parallel in this mode) and with the DVM on 10mV range (1uV resolution) connected between the taps. The pot is then adjusted to null as close as possible. Reversing the adjustable arm then gives an offset which you adjust the pot to halve. After a few iterations reversing the adjustable arm causes no change in offset (ie it is exactly 2:1) - any remaining offset is then due to error in the Hoffman divider. This is the way it's done in the 752A too.

I calibrated the divider using fixed resistors rather than pots, high value shunt resistors on the 10k 10:1 and low value series on the 100:1 (the resistor in the 100k 100:1 is 1.3 ohms  ). I've had the whole thing built for about a year now and it really hasn't drifted significantly - in 2:1 test mode at 1V input it's about 2uV off on the 10:1 (2ppm?) and 5uV on the 100:1 (5ppm?). That seems a pretty good result to me, it's about a tenth of the stated accuracy of the 752A.  Probably just luck and aged resistors though.

If I was doing it again I might be tempted to put it all in one box (the 100:1 add-on is a bit messy), but it does make the it smaller this way and the adjustable divider (when I eventually box it) will be useful for resistor matching.

Sorry it's a bit long folks. 

Edit: added 'Voltage' to the subject line, added photos

[TimFox]

Are you going to use a guard string to reduce leakage current from the high-impedance nodes?

[Gyro]

I don't think I need to in this case (open to opinions). The Fluke 752A has very high value resistors in it's divider chain, their 100:1 divider is 4 Meg. In addition it is a lot more spread out internally and has a 1000V maximum input.

Because of the high resistance values the 752A is very sensitive to loading, I thought for home use going for 1mA in the chain (Edit: at 10V 10:1, 100V at 100:1) would give a more practical 900 ohm output resistance.

Using 10k resistors in the 100:1 chain, and mounted on PTFE standoffs I don't think there should be any significant leakage error. The voltage ratings I chose are somewhat arbitrary - I though it was probably a good idea to aim for 1mW each in the main 10:1 divider. I later stretched this to 10mW in the 10k resistors for the 100:1 (10V each), not much choice given the available parts and wanting to get to 100V. It has been run at 100V for a while a few times and there doesn't appear to have been any significant ratio change. It's a shame I cant get to 1kV, maybe time to add a 1000:1 stage, but voltage coefficient and Tc matching would probably be lousy.

The 752A manual (referenced from Joe Geller's page) gives some useful examples of usage - the obvious one of feeding from a reference (I use a boxed SVR-T), but also calibrating higher voltages using an external voltage source and a null detector to compare the reference with the divider output.

[Gyro]

Think I may have partially answered my own question, Dr. Frank appears to have built his own impressive Hamon type reference dividers, including a 1kV one. I can't see whether he uses guarding on the PCB or not, there are certainly plenty of resistors...

https://www.eevblog.com/forum/testgear/hp34401-measurement-of-linearity/msg357971/#msg357971

Pictures in Reply #7

I would be grateful for more details. Dr Frank, particularly resistor type / values, and more pictures, I assume your dual one is !0:1 / 100:1?

Anyone else built one ? What do the rest of you guys use for reference dividing / meter range checking / calibration... or don't you?

[Dr. Frank]

Think I may have partially answered my own question, Dr. Frank appears to have built his own Hamon type reference dividers, including a 1kV one. I can't see whether he uses guarding on the PCB or not, there are certainly plenty of resistors...

https://www.eevblog.com/forum/testgear/hp34401-measurement-of-linearity/msg357971/#msg357971

Pictures in Reply #7

I would be grateful for more details. Dr Frank, particularly resistor type / values, and more pictures, I assume your dual one is !0:1 / 100:1?

Anyone else built one ? What do the rest of you guys use for reference dividing / meter range checking / calibration... or don't you?

Hi Gyro,
you are correct, it's a 10:1 / 100:1 Hamon divider like the 752A, but it contains 100 identical metal foil precision resistors, like the Datron 4902S, but 25kOhm each.
4 additional of them are used in the Wheatstone Bridge configuration.

They are from AE electronics, a Japanese manufacturer, now acquired by Vishay.
I bought them from UK distributor Rhopoint components.
I use a precision switch from ELMA, which also withstands the 1kV.
I do not use guarding, and no nylon standoffs.

I were able to confirm the precise divider alignment, ratio uncertainty to ~ 0.1ppm, by my 3458A.

Recently, I checked dynamically the power dependency of the 100:1 ratio @ 1kV, and estimate that to be stable to about 1ppm.
Instead of T.C. matching the divider resistors, I instead reduced the burden on each resistor to equally 4mW, which gives a rise of about 0.5°C at 10V.
In conjunction with the typ. 1ppm/°C, and the statistical matching of that component batch, you might also calculate theoretically an upper limit of around 1ppm at 1kV.

So I checked the performance of the AutoCal function of the 3458A and the 5442A in the 100V.. 100mV ranges, and was able to measure the drift of about 3.6ppm in the 1kV reading of the 3458A, due to self heating, and as given in the specification (12ppm *(U/1000V)²).

Frank

[Gyro]

Hi Frank,

I wasn't expecting such a fast and comprehensive answer. Thanks very much!

you are correct, it's a 10:1 / 100:1 Hamon divider like the 752A, but it contains 100 identical metal foil precision resistors, like the Datron 4902S, but 25kOhm each.
4 additional of them are used in the Wheatstone Bridge configuration.

Ah, 100 foil resistors, not something I have in my collection of vintage resistors!  I'll have to investigate pricing on that one. Your substantial investment in your quest for performance clearly paid off in terms of ratio accuracy.

I may need to downgrade to decent low TC metal films, hopefully the higher voltage coefficient wouldn't be too significant when distributed over such a large chain and, as you said, keeping temperature rise low. It sounds as if the dissipation limits I am allowing in my divider are in the right area, probably rather conservative in my 10:1 wire-wound divider, I can probably safely extend it to 30V continuous (10mW) but optimistic on the 100:1.  It's helpful to know that you managed without guarding - my PTFE standoffs were clearly severe overkill! (as I said, I only used them because I have a bag full).

Thank you again for the valuable information.

Chris

P.S. Damn, I should have bought more of those Vishay MPR24-05, I only paid $10 for 30pcs, free shipping on ebay. No longer listed.

[Vgkid]

Thanks for posting yours. I have been meaning to build one for fun, i have some low resistance switches for putting the resistors in parallel for balancing the circuit. 5m ohm. Though that is a multi pole switch, so I could parallel them up.

[Marcus_S]

Yes, now I built one. Some days ago I made a simple little box, taking some aluminium...

The divider is made using the standard concept. But I added some additional connectors and a 100R multiturn potentiometer for fine adjustment of the voltage (so the divider can be used as a simplified 750A) and filled the box with selected Dale RH25 10k-resistors.

I combined the resistors so that the differences of the resistances of the 3*R-branches were within 5 ppm (calculated from the measured values of the single resistors).

As switches I took two old 4-pole switches with two contacts in parallel. The contact resistance was approx. 2 mOhm each. For adjustment of the divider I took 2 multiturn potentiometers (100R). But with 100R the balancing was nearly impossible. So I narrowed the adjustable range of the potentiometer to 2 ohms by paralleling some resistors. Wiring was done in my ugly-wiring-technique as usual.

It's nice to play around with this box but it's a bit boring, too. Feeding it with 10 V from the Keithley 230 shows no interesting effects during monitoring the internal 1:1-divider vs. the hamon-divider with my TEK4050. And adjusted to 10,00000 V at the hi-output gives 1,00000 V at the divided output when measured with my 3456A. Perhaps I should test my other multimeters...

Best regards

Marcus

[001]

Great job 

Since links from http://www.gellerlabs.com/752AJunior.htm are dead now. can You share schematics of 752A clone project?

[Gyro]

Unfortunately I don't have copies of the JPGs from that page, grab anything of interest now as the site is no longer supported. What Joe is actually referring to is the board on wooden supports in the middle of the main photo. It is just a Hamon divider network wired between the sockets as described in the text. The other photos did not include any other trimming / divide by two comparison circuit  - as he describes in the text, he didn't manage to get this stable enough (most of the sockets were unconnected). The link to Contrad Hoffman's article (also in my original post) is the most useful one at this stage.

The schematics of the actual Fluke 752A are available on the xdevs site though...  https://xdevs.com/doc/Fluke/752A/Fluke_752A_Schematic.pdf   You should hopefully be able to find the user manual too with a bit of googling.

P.S. A useful reminder that I still need to box my accurate 2:1 divider too.

[001]

Thanx a lot 

[beanflying]

Before project Swiss Cheese begins with its 45 binding post holes 

I am going to knock up a 1% 1206 smd version to these values to try it out. 

[branadic]

I was thinking about building a Hamon Voltage Divider with the design presented by Frank and started getting the bill and cost of the material.

Elma Rotary switch Type 04 Eyelets 3 Wafers 6 x 6 Non-Shorting °30, 04-3264 109,20 € excl. vat

Alpha Electronic Resistors  FLCY 25k for 3,99€ each + shipping

+ case + binding posts + pcb
So in total costs of about 600 - 650€ are to be expected. This is about what you can pay for a Fluke 752A of evilbay.

-branadic-

[Dr. Frank]

I ordered several of these switches directly @ ELMA, >10 years ago, it was 60 € only.. maybe you should not look at Audiophools.

[Gyro]

I've had very good results with this style of NSF rotary wafer switch in the past (and yes, I've used them for signal level audio too  ):



Yes, I know they're rated at 250VAC 6A but the contacts are heavily silver plated copper with high contact pressure and excellent wiping action, making them workable for dry switching. They're specified at 5mR contact resistance.

Not quite clear from the photo but unlike standard wafer switches, the inner plastic 'barrel' contains big coil sprung wiper(s) that bridge between the contacts on the two wafers. They're about as close to the traditional large decade box stud switches as you'll find these days. You can also pull them apart and swap wafers to make funny configurations, eg. 12 completely isolated single pole positions. Note that they are break-before-make.

I have a few of the Elma stud switches, and apart from being gold plated, I don't see anything in their construction to justify the price. Contact pressure and contact stability simply don't compare. They do have the advantage of being physically smaller though.

The NSF switches are available from RS or local equivalent. eg. https://uk.rs-online.com/web/p/rotary-switches/0327585/

EDIT: and Farnell: https://uk.farnell.com/nsf-controls/msd1206n-mu454493msd1/switch-2pole-6-pos/dp/1165279?st=nsf

[magic]

Some year ago I have built one in 50:1 ratio to calibrate millivolt ranges on DMMs from 5V reference without using precision resistors and needing to trust them.

For that end I have produced some math which estimates how much error is expected when n resistors matched to ±ε are switched from series to parallel, maybe somebody will find it useful.

Everything up to the definition of E is strict equality, E is the exact difference between n² and the actual ratio. E^ is an honest upper bound, with E~ I cheated a bit to simplify things.

The error is roughly equal to relative matching tolerance squared times division ratio. For 10:1 division, 100ppm matching yields 0.1ppm error indeed. 5ppm matching is surely huge overkill, swamped by other errors. Time is probably better spent repeating selection at different temperatures for better thermal tracking.

A perhaps useful observation is that the error is always positive, the actual ratio greater than intended. This cuts uncertainty in half, for what it's worth.

[Conrad Hoffman]

Glad to see some interest again. I've got a 752, but one of the nice things about building your own divider is you can fix it. The 752 is known for resistors going too far out of tolerance to correct with its internal jumpers, and a repair from Fluke is beyond the resources of most hobbyists. Mine needed to be "re-jumpered" when I got it, but was still OK last time I checked. BTW, the 752 is quite large (long) and doesn't fit easily on the bench. Those builds above look really nice!

[beanflying]

Just waiting on a set of Resistors from Edwin along with some LTZ sets. I gave up in disgust with the Vishay option via Texas C's.

[magic]

Some year ago I have built one in 50:1 ratio to calibrate millivolt ranges on DMMs from 5V reference

I dug up my 100mV calibratior. It's built from ordinary 1% 50ppm/°C 0.6W metal film resistors (Vishay MBB0207) with a bit of selection. I hoped for seven resistors matched to ±0.1%, got much better than that. They were matched to ±0.02% of mean at temperatures of 26°C and 18°C when I soldered them in and they still are at 23°C three years later. Individual ratios may or may not have drifted some 0.01% - hard to tell with 4.5 digit resolution. Error of paralell-to-series ratio due to mismatch should be <2ppm.

The resistors are 1.5kΩ for reasonable input and output impedance without buffers. But this forced me to get creative with switches - these are female BLS plugs soldered to thick copper wires, single digit milliohms. IIRC they dominated the 50ppm figure written at the top - it was a gotcha I didn't expect until I did the math. Self heating is <0.3mW per resistor worst case so no big deal.

The upper branch is seven resistors in series, the lower branch is seven switchable. Remaining six resistors from a lot of twenty make a second divider for adjustment (which is also a 10:1 Hamon divider). Pots are 10Ω simply in series with the upper branch. Surprisingly, division ratios in 1:1 mode also held up well, both dividers are <50µV off and I adjusted them to 0.1mV resolution at the time

Not bad for what it is. I wanted not to compromise the accuracy of my 5V±1mV reference too badly and I think I got that much.

[magic]

By the way, proper Kelvin sensing across the lower resistor network and switches is absolutely essential in a low resistance divider like this one. Otherwise even a modest stray resistance easily swallows full 5 digit error budget. In the example below, output voltage is 49ppm off but the differential voltage across R2 is still fairly correct. With Kelvin sensing, all strays outside the switching network appear effectively in series with the input impedance of the divider (~10.7kΩ here) where their effect is less severe and easily predictable.



The simple topology (7 in series + 7 switched) was motivated by two factors: only 14 resistors instead of 50, and both sections benefit equally from cancellation of random drifts. If I were to pick a single resistor whose drift matches the average of the remaining 49 it would be a very different game.

[GigaJoe]

just a note , that in overall TC resistors not so important as it TC to be equal.
Better TC matching 6 resistors ,  better result,  25 or 50 PPM resistors can achieve, 0.01 ppm\C
altering metal surface to get precise same resistance, or in something in parallels

melf 50ppm resistors, with identical tempco an altered to the same resistance, in urethane coat
approx 0.12 ppm\C resulting and 2ppm error on dividing, resistors was aged for 3 days at +140C
( wasn't so patient to select tempco, and final dividing was adjusted when everything was assembled, scratching just 1 resistor)
after 4 years , I dont see any significant shift, as it dividing 10V to 1 and 10V drifting more then divider..


UPD:  actually TC identical in average between shoulders, a much easy to pick a set with same average #

[Gyro]

Seeing this thread resurface reminded me that I had acquired 10 of these 100k wirewound resistors on ebay for the next, 1Meg, decade of my (OP) Hamon divider.

I know little about them apart from the obvious. They are ERG TSPR23 wirewound 0.1% resistors in stud mounting Aluminium cases, with ceramic hermetic seals. They were sold as ex MOD NOS and came in their original waxed paper packaging. Dimensions are 25mm dia x 45mm length, excluding stud.

The hermetic sealing bodes well for long term stability, absolute TC wouldn't be an issue for a standalone divider, but it remains to be seen how well they match the existing decades (already a mixture of wirewound 10k divider and metal film on the 100k decade). I think I want to limit the input voltage to 1kV this time, this would limit the largish resistors to just 100mW each, but I don't think I would want to exceed 1mA loading at that sort of voltage anyway.

At this resistance level, it is probably time to introduce guard shielding on the resistors, using a separate, probably 10M, maybe 100M, guard divider chain. The metal cases and stud mounting makes them ideal for this anyway.

I'm just wondering if anyone has come across these resistors before?


P.S. No, I didn't pay £24 each for them, I negotiated 10 of them for not much more than that (different seller).

[magic]

What's the resistance of those cables that connect the 3×1kΩ resistor strings to the barrier strip?
Per my calculations, you gain ~0.81ppm (output referred) per each 1mΩ of resistance added to both connections. That may be more than the error due to bridge imbalance.

You can't escape resistance of the external links, but cables could be eliminated from the equation by creating Kelvin points on the barrier strip and running a dedicated cable to each resistor string. Then they all effectively become merely part of the resistors.

[Gyro]

Good point. They're fairly heavy, 16/0.2 or higher irrc, Silver plated in ptfe (from a drum of mil screened that I found years ago), so the insulation is thinner than it would look in PVC. Yes, creating Kelvin connections at the barrier strip tabs would be an excellent idea though. It hadn't occurred to me. I'll go back and implement that one.


P.S. I still need to put the nullable 2:1 divider (the one with the 5R pot) in a box with a proper reversing switch - I've since found a few of the heavy NSF switches, in 3 pole 2 way, that I linked previously. Maybe it's time I chucked the whole lot in a single box to make a real poor man's 752A.

[magic]

BTW, the effect of those Hamon parasitics is very easily calculated with SPICE.

Back in the day I used some trickery to solve this problem, like multiplying each stray resistor by the number of resistors sending their current through it and cloning it separately in series with each of said resistors, which I believe gives a fairly good approximation at moderate effort but still requires some manual labor. A simulator may not be perfect either due to numerical resolution, but at least much faster

Resistance of things like cables and connectors can be measured with a 0.1A current source (TL431 is your friend) and a DMM - that's what I did in absence of a good milliohmmeter.

just a note , that in overall TC resistors not so important as it TC to be equal.

absolute TC wouldn't be an issue for a standalone divider

That's true until self-heating occurs, which is different in 1:1 and 10:1 configurations. Definitely something that needs to be accounted for.

[Gyro]

BTW, the effect of those Hamon parasitics is very easily calculated with SPICE.

Back in the day I used some trickery to solve this problem, like multiplying each stray resistor by the number of resistors sending their current through it and cloning it separately in series with each of said resistors, which I believe gives a fairly good approximation at moderate effort but still requires some manual labor. A simulator may not be perfect either due to numerical resolution, but at least much faster

Resistance of things like cables and connectors can be measured with a 0.1A current source (TL431 is your friend) and a DMM - that's what I did in absence of a good milliohmmeter.

...

That's true until self-heating occurs, which is different in 1:1 and 10:1 configurations. Definitely something that needs to be accounted for.

I have a battery powered current source with Kelvin clips that is pretty accurate in decade steps from 1mA to 1A, based on Maxim AN106. Together with 1uV - 100nV resolution on my old Datrons, I can go pretty low (after subtracting thermocouple effects!).

Yes, agreed. Differential heating between the single resistor and the 3x3 resistors is an issue, I keep the test voltage below 1V (1mW on the single 1k) for the 10k stage. Matching between the 100k stage and the 10k stage turned out pretty well considering. I've no idea how those ERG TSPR23 100k resistors will match them. At least above the 10k stage, it's possible to use switch contacts with negligible impact, rather than messing about with the barrier strip.

Once I get the Null 2:1 divider cased, at least it will be a quick job to take a measurement at whatever ambient temperature. Even the 752A needs to be self calibrated before use.

Spice is great, I'm just too old for it to be fun these days!    It, sadly, doesn't take much frustration for me me shelve a project (I've had those 100k resistors for a year or more).

[knightzdw]

Hi Gyro:

Many thanks for your sharing, I am interested to build one myself. 500:1 ratio. so it would be 50:1 (7 resistors) and 10:1. During planning I wonder how accurate it would be. So...

have you ever try to figure out the final accurate with this approach?

The error source I can think of:
2:1 bridge reference accuracy
error during 2:1 triming
Hamon method error (itself plus error due to contact resistance)
TC and drifing

any other I missed? comments welcome.

The error can add-up very quick. (the first two, I am thinking with 6.5 DMM, it can be controlled within PPM level, the meter accuracy is not critial, but stability. The third and fourth could be much worst)

Have you ever try to calculate the worst case or measure it directly?

also is the item on the right, is your 2:1 reference?
I am thinking just trim 2:1 reference with a 6.5 dig meter. So I can acheive PPM level 2:1 bridge reference accuracy level.

[Kleinstein]

A point missing is the self heating and voltage coefficient of the resistors. Especially with higher voltage the resistors tend to get a bit warm and this changes their value. In the divider the 3 in series get warmer than the 3 in parallel. So TC matching is not that effective for the extra heating. This kind of nonlinearity of the resistors may be overall limiting effect.

The 1:1 auxiliary arm for the trim step can be checked by a reversal step, but also this step may not be perfect.

Besides the contact / switch resistance there can also be some thermal EMF from the contracts.

With 6.5 digit meter (usually mains powered) instead of a nullmeter leakage currents to ground may be an issue.

[Gyro]

Hi,

Yes, as Kleinstein says, potentially the main source of 10:1 vs 2:1 deviation is the relative dissipations of the upper and lower resistors in the two configurations. This is why I keep the voltage as low as possible in the 2:1 configuration. I don't have the TC specs of the resistors in the main decade, other than knowing that they are a numbered (not my white numbers) matched set.

No, I was never able to calculate the worst case accuracy, only an empirical measurement of drift on the 2:1 reference ratio after about a year, which came out at low ppm levels on each decade after a year, as mentioned in my OP.

The errors in the 2:1 configuration comparison are relatively easy to minimize, basically keeping everything as isothermal as possible to minimize thermocouple effects and repeated measurements until you're happy that you have minimal drifting. The separate adjustable 2:1 divider that I cobbled together (and still need to box and add the NSF reversing switch that I have) easily has sub-ppm resolution (5ppm/turn) short term (long enough to cope with a few reversals) rather than long term stability. My highest resolution meter is an old Datron 5 1/2 digit but usefully has 100nV resolution, so null detection is no problem.

Your other error source is loading - the meter's input resistance and bias current, and, again as Kleinstein says, ground leakage currents. Keeping the divider resistance as low as possible, consistent with the conflicting requirement of minimal dissipation helps greatly compared to dividers like the 752A.

[Kleinstein]

The heating is not so much an issue for the 2:1 adjustment step. For this step the resistors see the same amout of heat and symmetry thus helps. The problematic phase is the 1:10 setting where the parallel resistors see only 1/3 the current and thus 1/9 the heat.

For a DIY solution one could also allow to use the 3 in parallel configuration on both ends. This would make the trim step with the 1:1 divider less critical as the error from a asymmetric start would about cancel out for the average.  I have not done the math, but chances are one may even get away without a trim just before usage, maybe even just a trim every few years or so.
Having the switches for a parallel configuration on both sides would also allow to do the trim with both side in the parallel configuration that is lower impedance and thus maybe easier to test.

[Gyro]

The heating is not so much an issue for the 2:1 adjustment step. For this step the resistors see the same amout of heat and symmetry thus helps. The problematic phase is the 1:10 setting where the parallel resistors see only 1/3 the current and thus 1/9 the heat.

Do we have a confusion between 2:1 and 1:1 here? For a 2:1 divide (ie. voltage between input high and output = voltage between output and common gnd) you have 9 resistors in 3 parallel chains of 3 resistors (1/9 heat each) against a single resistor, and in 10:1 you have all 10 resistors in series.

[Dave Wise]

I agree, Gyro, and I'm confused.  Kleinstein, can you sketch it please?

In my own divider, made with 100:10 or 10:1 10K resistors, I saw noticeable drift going between Hamon 2:1 (333 vs 1 or 303030 vs 10) and 10:1 (100:10 or 10:1).  My resistors are strung in a zigzag line in a box.  I ended up adding a fan that I spin any time I operate above 30V or 300V; that pushes the error down into the "noise".

[knightzdw]

@Gyro @Kleinstein many thanks for all the comments and thoughts.

To stop the confusion, I relist those, so we can refer to the items more accurately 

A   1:1 auxiliary arm accuracy (for 2:1 hamon trimming)
A.1   trimming with 6.5 DMM loading, bias current, leakage current to ground

B   Hamon method error
B.1   Method itself,
B.2   10:1 vs 2:1 deviation due to voltage or power
B.3   Contact/switch resistance
B.4   EMF from the contracts
B.5   Trimming error due to again DMM loading, bias current, leakage current to the ground

C   Hamon divider resistors
C.1   resistors TC and drifting
C.2   10:1 vs 2:1 deviation due to voltage or power
C.3   more voltage or power on resistors, deviation due to voltage or power

for A.1 B.5 trimming, I am planning 9V battery + 6.5 DMM,
so bias current impact (max 50pA, for 10k load, the worst case would be 500nV maximum) can be observed with 9V off, it can be checked and compensated,
regarding loading, DMM can be set at high impedance mode (10Gohm), so for the impedance 10k resistor range, this error is considered to be sub ppm
leakage current, the whole system would be floating, so it can be ignored?

for B.2 10:1 vs 2:1 deviation due to voltage or power
the resistance would in 100k to 10k range, so the power on the resistor would be 10mW or 1mW, so hopefully those can be designed out with proper hamon resistor sizing. they are all low PPM resistor + select input voltage carefully + fan maybe

for C.3 power or voltage deviation
I googled and my understanding, VC more obvious for resistor more than 100M, so sub PPM again if the select hamon resistor less than 10M?

the devils are all in the details. Surely, I will find out more when I start building them.

With all the assumptions about possible errors, I am not that confident without checking the end result (maybe some bridge method)

thanks again for sharing your thoughts and happy new year.

[Kleinstein]

The confusion with 1:1 vs 2:1 comes from looking at the resistor ratio or the voltage ratio.

The trim steps are usually done with a fixed voltage, and thus no error expected from the power effect one the auxiliary arms. If there is a linear voltage coefficient this can hower effect the polarity reversal.

Powering the bridge part during the trim steps from a battery is a good idea. It offers extra isolation and this way can avoid much of the DMMs leakage currents to ground.  This way the DMM can do the job of a null-meter. This still does not help with the bias current, that adds a small offset. For the bias current it alread help to reverse the polarity at the drive side. If an extra 0 V step is used one should not just remove the power, but also shorten the power pins

For the final use, if the DMM is actually reading a voltage 10 Gohm impedance is good, but still not perfect. Luckily the specs are usually >10 Gohm and the actual impedance can be significanly higher.

If relatively large resistors are used, there is also leakage current at the switches and cables that can be an issue.

[Conrad Hoffman]

IMO, if you haven't read it, the 752A manual has a good theory section. Some of the service notes are also useful regarding cleaning and such.
https://us.flukecal.com/literature/product-manuals/752a-instruction-manual

[knightzdw]

@conrad

No I haven't, and the manual covers everything. Thanks

I also did some quick dirty simulations with excel. It seems 752A using 3mohm as contact resistance with 40k Rbase to predict 0.044PPM error.

I will keep refine the excel file and hopefully to predict the possible worst case