Yet Another Hammon Divider (YAHD)

[rockstedy40]

Hi everyone,

   I’d like to get some feedback on this proposed design for a 10:1 and 100:1 Hammon divider.   Nothing to special here, just using multiple resistors in parallel to keep the power dissipation to 1mW or less. 

  The resistors are Tyco YR1B’s which claim to be 0.1% with a TCR of 15 ppm.  Not exactly Metrology quality, but good specs for $0.60 each.  I’m hoping to use this for checking my Fluke 45, HP 3456A and various hand held meters.  I realize that this is not up to the accuracy/stability required to really calibrate the HP, but I’m hoping it will give me a warm feeling that it’s good to 4 or 5 digits.

  I’m also including a 1:1 divider to use as one half of a bridge to calibrate the Hammon Dividers.

  I’m in the rotation for the Cal Kit and am hoping to use that to drive the divider to yield 1V and 0.1V outputs.  I have the 10k and 100k resistors on order and plan on hand picking ones that allow for tweaking the last resistor to set the dividers.

Thanks all for your contribution to this great forum.  This is a wealth of knowledge.

Bob Hammon Divider 10-1 and 100-1 2023-04-10 Rev -.pdf (125.8 kB - downloaded 429 times.)

[GigaJoe]

for fun you may try this :

for 1:10 , 2 major factors:
equal value of resistors
equal value of thermal coefficient, regardless of absolute value

so you may have a fun to buy a volume nonexpensive metal film (nonsmd) 1/4 W 50-100 ppm of desired value.
and about the same kind with value x10 approx.

pick 6 with the same TCR for both value ; as much as same , regardless of value.
next need to adjust all 6 to be the same resistance #  ;  that can be done by altering metal film,  so resistance can be only increased

so we do in parallel -  resistor one and another that x10 more, measure and pick one with highest resulting value,   then altering by filer both original (if need)  and x10 - to reach exact all 6 would the same. the better adjustment - the more precise divider would be

then construction depend on your  desire of state of power dissipation , additional copper fins and oil bath or  in brick of epoxy \ urethane , or oil filled sealed container.  just remember that resistor coat need to be restored back ...

and before all measure you may do thermal stress by keep resistors for a few days at 110 - 130 Celsius

personally i use melf , and result some good one around less 0.1ppm TCR and 20 ppm dividing
an additional adjustment do even better when all finally assembled

[rockstedy40]

GigaJoes, thanks for sharing your ideas.  Not sure if I'm up to all this but let me at least try to understand.

1) Age/thermal stress all resistors for several days between 110 and 130 deg. C.

2) Measure TCR of each resistor and select 6 with the closest TCR's.

3) Using a file, adjust each resistor to match the one with the highest resistance. Now we have 6 resistors with close to the same TCR and resistance.

4) Not sure what you meant by the following:
 "so we do in parallel -  resistor one and another that x10 more, measure and pick one with highest resulting value,   then altering by filer both original (if need)  and x10 - to reach exact all 6 would the same. the better adjustment"

[Conrad Hoffman]

Non-expensive metal films generally have a spiral pattern. No idea how you'd adjust them with a file or anything else. Just buy a bunch and select. Also, be sure to use hemostats or some kind of heatsink when you solder them, lest they change value by more than you might think!

[rockstedy40]

"be sure to use hemostats or some kind of heatsink when you solder them,"  Good point!  Thank you!!!!!!  What a disaster to have soldered everything up only to find that all the resistors had drifted.

[Kleinstein]

The 3 S - 3 P divider does not really need the resistors to be that close.  If one does an adjustment for the groups of 3 to give the same sum just before use, one also does not need that good an TC matching. For the TC it is more about getting a low absolute TC or a low power coefficient. In the divider mode the resistors see different power levels and thus different amouts of self heating.
A somewhat larger form factor or a combination of a few can also help.

The configuration I know uses the extra resistors for the 1:100 on the high voltage side. With an adjustment for the high value resitor.
The auxiliary half-bridge can be connected to the main divider at the low end and should have a switch for swapping the resistors. In addition to 1:1 would would also need an auxiliary divider for 9:1.

The adjust mement should be possible for both directions, not just towards a higher resistance. For the trim circuit I would avoid using low value trimmers, as the wiper resistance is not that stable there.

An alternative to the extra trim for the 100:1 divider, one could have a divider in a similar configuration. E.g. as 9S - 9P for a resistor ratio of 81:1. The may be good enough to test the higher ranges.

[GigaJoe]

"have a spiral pattern. No idea how ... "
naaa that much easy as we assume,  basically make a surface thinner to increase resistance, sharp knife, some blade, filer to remove epoxy.
the major point of operation to remove residue after let say a few blade passes .... contamination spoil the result.

"does not need that good an TC matching."
that the easiest way to get lowest tempco if desired;  from set of 20-30 usually, 6 are easy to find  ;   otherwise who bother ..

melf assembly, and adjusted resistor as an example

[rockstedy40]

The 3 S - 3 P divider does not really need the resistors to be that close.  If one does an adjustment for the groups of 3 to give the same sum just before use, one also does not need that good an TC matching. For the TC it is more about getting a low absolute TC or a low power coefficient. In the divider mode the resistors see different power levels and thus different amounts of self heating.
A somewhat larger form factor or a combination of a few can also help.

The configuration I know uses the extra resistors for the 1:100 on the high voltage side. With an adjustment for the high value resistor.
The auxiliary half-bridge can be connected to the main divider at the low end and should have a switch for swapping the resistors. In addition to 1:1 would would also need an auxiliary divider for 9:1.

The adjustment should be possible for both directions, not just towards a higher resistance. For the trim circuit I would avoid using low value trimmers, as the wiper resistance is not that stable there.

An alternative to the extra trim for the 100:1 divider, one could have a divider in a similar configuration. E.g. as 9S - 9P for a resistor ratio of 81:1. The may be good enough to test the higher ranges.

Kleinstein, thank you for your comments.  The resistors I've chosen have a relatively low TCR and I'm limiting the power dissipation to 1mW or less. So, if my calculations are correct, I should only have a few uV of variations due to self heating.  This is also true for the 100:1 divider where my plan is to use three groups of 9 100k resistors to keep the individual power dissipation to 1mW or less.  I have changed the trim pot configuration to use a higher value pot (5k) to minimize any wiper contact resistance variance issue.  The adjustments are centered around the desired values.  I wanted to keep a trim on the 100:1 divider as I'm planning on using it to provide a 0.1V output when connected to a 10V source.  This way I can check 10V, 1V and 0.1V ranges.  100V range would also be possible but finding a stable and accurate 100V source may not be easy.

As for using a switch in the aux divider, I was thinking of just manually swapping the polarity of the banana plug.  This is also why the low side of the reference is connected to the low side of the divider.  If anyone can recommend a good switch with low contact resistance I will certainly look into that.

Thank for all the constructive comments and ideas.
Bob

Circuit Rev A

[Dave Wise]

In the divider mode the resistors see different power levels [than in Calibrate mode] and thus different amounts of self heating.

Also different voltage, so we have to consider Voltage Coefficient of Resistance.  I will test several randomly-selected adjacent pairs in my divider (actually two stacked 10:1's), to see how well they match.

If my resistors turn out to be poor in the Hamon 3S-3P configuration, I'll be tempted to build a new divider using the HP 740/741 1-2-2-4 scheme.  Ten identical resistors are grouped as 1-1-2-2-4.  Each of the four upper groups has its own trim.  Trim 1 to 1, then 2 to 1+1, then 2 to 2, then 4 to 2+2.  If you scale voltage to resistance, this scheme puts the same stress on every resistor whether you're dividing or calibrating.  What are your thoughts on this?

What's a good cheap reversing switch?  Since I wanted to  trim my Hamon upper divider at up to 1000V, I used a 3-position plastic rotary switch with the center position dead.  But I get annoyed with it because the null detector is pinned as one crosses through the dead position, and it takes time to recover.  Is there a two position switch with enough creep and break-before-make to survive at 1kV?

[Dave Wise]

UPDATE.

I tested my homemade Hamon divider (10K resistors) in three configurations, R0 vs 3P R1-9, R0 vs R1, and R0-4 vs R5-9.  I tested at 1V per resistor* and 10V per resistor, using my Fluke 895A Differential Voltmeter in ratiometer mode.  I did not test the 100x range, which one calibrates as R0-9 vs 3P R10-99.

* In the Hamon config, the 3P cluster sees 1/3V or 10/3V per resistor.

I powered the divider's fan so the 10V results wouldn't be confounded by self-heated TCR.

If we assume the Fluke's KVD is perfectly voltage-invariant, then my divider resistor groups vary by 2-3ppm.  I will not change to the HP 1-2-2-4 scheme.

[rockstedy40]

Dave,

   Thank you for sharing your test results.  I'm still a little new to the Hammon Divider nomenclature, so I'm not following the configurations you tested.  Would you please explain in more detail, or possibly a sketch/schematic?  (I used to love Bob Pease's sketches.  Zero time creating, and 100% info)

  I like the idea of a fan to minimize self heating.  That had crossed my mind but was thinking that it might introduce more problems than it solves, but maybe not.

Thanks
Bob
p.s.  I'm still working through some final trim configurations for my divider, after "aging" the resistors for several days at 115 deg C.

[bastl_r]

What is the key advantage of a Hammon divider?
When switching 10 to 1, due to the changing input impedance, there is a changing load on the input voltage.
And I have already noticed in my Solartron 7065 when measuring at its reference that the standard impedance of 10M of a 34401 is much too low and causes a change.

regards

[Kleinstein]

For precision measurements it is standard to have more then 10 M input impedance at the meter. The 34401 also supports this for the lower ranges (up to 10 V).

The point is a relatively simple circuit to get a divider quite close to 1:10. The loading on the input side would not be an issue for a proper voltage source with driven and sense lines. Just a simpel 2 wire connection may not be good enough.

[bastl_r]

In the meantime I know that too and had also found out how to activate the 10G mode on the 34401.

From the knowledge of these measurements, I am somewhat surprised that the Hammon divider is given so much importance in the dimensioning of the resistors.
After all, the input resistance is reduced by a factor of 100 in the example of the start article. Therefore, I wonder why such "small" resistors are used at all.
In the end, it might be cheaper and more practical to use a small Kelvin-Varley divider. These are available again and again with four decades for small money on ebay.  I had toyed with the idea of building a Hammon divider with 0.01% resistors. But since I have a small decade from Muirhead I will spare myself that....

[Gyro]

The thing about a Hamon divider is that you can make it 'self-calibrating'. Having an accurate 10:1 ratio divider is very useful for calibration purposes. With ebay purchased KVDs etc, you are relying on their last-calibrated accuracy, they can drift over time, might have been overloaded etc. without your knowledge, unless you get them re-calibrated.


P.S. I built my own Hamon divider too, and also have a Muirhead potentiometric (non-KVD) constant resistance 4 decade voltage divider. I use both. The Muirhead is pretty close, but only trust the calibration of the Hamon.

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

https://www.eevblog.com/forum/testgear/kelvin-varley-reistor-porn/msg773770/#msg773770

It's also worth reading the manual for the Fluke 752A (self calibrating Hamon)

[donlisms]

The origins of the 1:100 Hamon Buildup Resistor were based on the known (and easily provable) fact that if you put a set of N resistors with a tolerance of C in series for an effective (R + C) * N, and then in parallel for an effective (R + C) / N, the ratio between the two is N^2 with an error term of C^2.  That means with ten 0.1% resistors, the ratio between the two configurations is 100:1 with an error term of 1ppm.  With resistors of better tolerance than that, the error in the ratio gets remarkably small, quite easily.

So the value of a Hamon divider is that it is pretty easy, and relatively inexpensive, to get extremely accurate resistance ratios from moderately-accurate resistors.

There were two commercial original implementations I know of, one by Hamon working with Leeds & Northrup to create the (rather beautiful) 4321 and family.  The other was by ESI, called the SR1010 and variations on the theme.  The SR1010 manual explains how to get accurate 1:10 ratios, and also a 1R resistor made of 3x3 that has a much lower error than the individual resistors.  It also has a fairly complete explanation of how to use the buildup resistor in other configurations; there's really quite a lot you can do with it.  For example, it is not difficult to compare each resistor with a buildup of the others, accomplishing the self-calibration that's been referred to.  Those relative accuracy numbers are useful in other configurations.  With ten resistors (actually eleven), you can create ratios of 1, 4, 9, 16, 25, 36, 49, 64, 91, and 100 (and 121), but the general use is 1:10 or 1:100, from some given base R.  Thus... calibrate a resistor that's 100 times your standard reference.

Conrad used N = 3, and then transferred one of the S or P configurations to a second resistor (or set of them), thereby making both the R * 3 and R / 3 values available at the same time, creating a 9:1 ratio, or 0.1x divider.  Quite convenient, but a little different than the original configuration, which only talked about one value at a time.

So in my view, there is some confusion about the purpose and value of the thing, and what the name actually means, especially for those who were introduced through Conrad's articles, which don't really go too deep into the background of the thing.  I think it might be good to call one "the Hamon buildup" and respectfully call the other "the Hoffman divider," but that's just a personal view.  I usually read the posts here for a little while before I figure out which one the author is talking about!   

[alm]

Re loading due to the DMM's input impedance, the classic way to use a Hammon divider is to compare it to either another adjustable voltage divider (eg KVD) or an adjustable voltage source (eg DCV calibrator). You can then use a null meter with a very high resistance to ground and a very low input bias current to measure the differences between the two voltages and adjust the one side until the difference is zero. You could hook your DMM to the other, much lower impedance, voltage source. This way you're not relying on the absolute accuracy of the second voltage source, just its short term stability.

[bastl_r]

Thanks for the understandable explanation.

[Conrad Hoffman]

Original paper here- https://sci-hub.hkvisa.net/10.1088/0950-7671/31/12/307

"Hoffman Divider" Ha! I think that would be taking far too much credit. No reason you can't stack and rearrange any way you like. IMO, my page must have been useful, as there seem to be far more references  on line than back when I wrote it.

[donlisms]

Extremely useful and successful, for lots of folks!  It definitely played a big role in sending me down this resistance journey.  Another major element has been papers from the early days; Wenner, Thomas, Northrup, and others.

It must have been fun to study resistance in those days...  wire, batteries, a magnet, and some effort.  No bits or amplifiers in sight!  (Well, unless you count the optical path of a galvanometer resolving nanoamps.)

[rockstedy40]

After looking at my previous schematic I realized that I needed to go back to the drawing board and simplify things.  So below is my Rec C design that I’ll be going with.

You’ll note that the 100: section is much simpler now.  That’s because I decided to not go for a 100V design due to issues with the resistors I chose.  It turns out that the manufacture had a problem and ~10% of the resistors were out of tolerance and the entire lot was skewed above nominal.  So the Rev C design will provide a 0.1V output with 10V in.  So, with the 10V Cal-Kit standard, I’ll be able to get 10V, 1V and 0.1V to calibrate those ranges of my 3456A.

Now to start assembly.

[rockstedy40]

Attached are long overdue pictures of the completed divider.

[thermistor-guy]

.... Also, be sure to use hemostats or some kind of heatsink when you solder them, lest they change value by more than you might think!

Good idea in principle. Another point: after soldering, give the resistor network a day or two to settle (unpowered).

I've had a situation where some cheap metal film resistor networks I made were way out of tolerance soon after soldering,
but measured almost exactly right the next day. I thought I'd ruined the networks, by soldering them without a heatsink,
but no - they turned out fine.