Anyone else built a Hamon Voltage Divider?

[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