Electronics > Metrology

Method to determine uncertainty of a selfmade or unknown resistance standard?

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How can I determine uncertainty of a selfmade resistance standard or a standard with unknown spec?
I can measure resistance by Keysight 34465A and use its statistic functions (average, s-dev) or a HP3458A and log by PC.

Normally the value of a home made standard can be determined by a comparison to a known standard.

Roughly and simply speaking, the uncertainty can be calculated by RSS(root-sum-square) of all the participate uncertainties which mainly consist of
- type A uncertainty, the repeatability of your comparison.
- type B uncertainty, the uncertainty of the known standard.

Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Dr. Frank:
You have to take two different steps, I assume.

First step, you may characterize your resistor, i.e. measuring its specification parameters.
2nd step would be to get an estimate for its absolute value, which includes the instruments used and the whole uncertainty chain, relative to PTB.

For the characterization, the most important are its value at a certain temperature relative to the test equipment, its T.C., and its annual drift parameter.
Further (minor) parameters would be dependency on pressure and humidity, and maybe the e.m.f. 

Both the 34465A, and the 3458A are suitable to make a first determination of the DUTs value, but only if you also measure its temperature.
You should put it in a proper metal case, with 4 jacks for 4W / Kelvin measurement to cancel lead resistances, and using OCOMP to cancel the e.m.f.

The case should be coupled to a precise thermometer, like a PT100 or a precision NTC.

At that point, you already can apply the GUM, i.e. type A uncertainty would be the statistical ones, given by usage of the statistics of the instruments.
That is the standard deviation, and the uncertainty, for 95%  would be twice that StD value, divided by SQRT(N), if I guess that correctly.
Type B uncertainty are the systematic errors, that is mainly the calibration /uncertainty of the instruments, relative to PTB or NIST.
You can already estimate that from the specifications of the instruments, and also from the calibration certificate. 
It is also necessary, to account for the instruments internal temperature, which should be identical to their calibration temperature.

Then, you should change the temperature of this assembly and measure the temperature dependency.
The 3458A is suitable for that, also stable enough, if you are able to keep its temperature constant over the run of this measurement.
This is a relative measurement, so the absolute uncertainty of the 3458A plays no role.
After that procedure, you can always determine the value of your DUT by measuring its temperature.

The ageing can also be determined,  if you would have a set of equivalent resistors, which you might compare against each other over one year, or so.

The 2nd step would be to get access to a calibrated standard resistor with known uncertainty relative to PTB or NIST.
Or you might send in your assembly for calibration.
Poor mans / volt-nuts solution is, to simply use the calibration certificate of either the 3458A, or the 34465A, and estimate the type B (systematic) uncertainty limits.
In the certificate, tighter limits are given, than in the specification.
That's of course no proper calibration chain, but in practice, you will get a very good uncertainty estimate.

My own five VHP202Z, 10k resistors agreed within 1ppm to two freshly calibrated 34465A, and two calibrated instruments of two other volt-nuts.

Maybe, we also might exchange our resistors, some day.

In the precision resistor thread, you may find more useful hints about these subjects.


I am not so sure the humidity is a minor parameter for a lot of resistors. Last year I intended to build a couple of references with precision wire-wounds that was supposed to be humidity insensitive. I ordered 100-1Mohm in decades. I probably shouldn´t have done humidity tests as they drifted a lot. Just by putting them unsoldered in a box with about 70-80%RH the 100kohm drifted 200ppm upwards. The time constant was a couple of months. The 100ohm drifted ”only” 20ppm. After a while the manufacturer admitted it was a production problem. I haven´t yet got any humidity insensitive wire-wounds.

I also have old resistor standards from 1k to 1M that was earlier used in a Swedish calibration lab. I have no specification (uncertainty) so I have characterized them myself. Temperature scans is easy but humidity and aging takes time. Aging of all four is below 1ppm/year but for humidity the 10kohm is 0.5ppm/%RH (20ppm for a seasonal variation of 40%RH) but the 100kohm and 1Mohm is less than 0.1ppm/%RH. As my best resistance uncertainty (with good confidence) is 10ppm it has taken some years to get this data. Sorry to scare someone but aging and humidity is not so easy to characterize in short time (but I really encourage you to do these tests as you learn a lot). Even if you have references with much better uncertainty than I have you can be cheated by aging mechanisms that cancel each other in the beginning but due to different time constant starts to deviate. The VHP tests from Vishay are interesting in this case… .
Of course if the uncertainty is just for yourself you can learn a lot in much shorter time.



--- Quote from: Dr. Frank on August 23, 2016, 10:09:58 am ---
The ageing can also be determined,  if you would have a set of equivalent resistors, which you might compare against each other over one year, or so.

--- End quote ---

Can you really do it this way or isn't it likely that the two equivalent resistors also have equivalent drifts?
Long ago I also tried it this way with voltage references but was cheated. Now I believe that you at least need to have some traceable calibration points with some time difference in between and specified uncertainty for all points. Of course if you have say VHP202 resistors and want to characterize some less good resistors you probably can do some assumptions from data from others (a kind of uncertainty spec?). From my (few) VHP long-term tests I have never seen more than 10ppm drift the first year.



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