Electronics > Metrology

Yet Another Hammon Divider (YAHD)

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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!   :D

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.)

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