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

[carl_lab]

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.

[zlymex]

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
http://physics.nist.gov/cuu/pdf/tn1297.pdf

[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.

Frank

[lars]

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.

Lars

[lars]

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.

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.

Lars

[lars]

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.

Interesting. Does the 34465A have a hermetic reference resistor? My measurements on older HP/Agilent 6 ½ DMM’s show humidity sensitivity and also quite a lot of drift the first year.

What uncertainty do you think it is possible to get after a new calibration (excluding the cal lab) for the 34465A? What I see is that the 24 hour spec for 10kohm is 25ppm at +-1C for the 34465A.

Another story: Maybe 15 years ago we had a lot of discussions with a calibration lab. We had a HP34970A (same DMM module as 34401 but with offset compensation availible) that we thought was very stable on the resistance ranges 100-100kohm but the calibration protocol showed that the values went up and down about 40ppm during the last years. They used the same calibrator with low uncertainty every year. We never found out if it was the 34970A or something else in their environment that made the calibrations differ so much between years. Of course the 34970A passed the calibrations as the one year spec is around 100ppm if I remember correct.

Lars

[carl_lab]

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.

Does that mean, measuring the value of "unknown" standard resistor by 3458A, taking this value as "applied value" for a second measurement by UUT (UUT = unit/DMM to test by selfmade standard, not the selfmade standard itself) ? Then applying the tolerance of UUT and narrow it by uncertainty of 3458A? (That sounds very similar to my very limited understanding of "guard banding"...)

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.

Can this known standard be a calibrated DMM (3458A)? Or did you mean a standard resistor?

[Dr. Frank]

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.

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.

Lars

Well, I call this the man-with-two/three clocks-problem.
In principle, you can determine any extensive drift of one member of a group of standards.
That's your only choice, if you've got "nothing better".
How else could the metrologists identify the kilogram prototype in Sèvre to be the 'stinker', which drift apart out of the whole group of its international copies?
How else could the Cesium-clocks be characterized, (w/o Masers and these new optical clocks), to have about 1E-15 stability, if not by comparing several units against each other?

Your objection is legitimate, that all these members might drift in the very same direction, due to the very same systematic drift mechanism.
Well, the probability is quite low, if all these members don't drift that much apart, over several years, i.e. if the spread of drift is very narrow also.
My five VHP202Z resistors have the same value, within about < 0.5ppm, over > 5 years. So I can assume, that the absolute drift is about on this order of magnitude.
I have never seen drifts of 10ppm/year, like you, obviously, and Vishay declares them to be stable to about <2ppm/6years, which I now believe, that this is true.

Another example is from Joe Geller, he monitored several dozens of LM199 over a year, or so. The spread was quite high, but he could clearly draw a baseline, where the zero-drift members would be situated.
You have to pay attention with zener references, the SZA 263 inside the 732B would probably drift +1ppm/year, and the LTFLU, líke the LTZ1000 mostly drift about -1ppm/year. (all at 45°C)
Again, you will always find units, which have drift in the opposite direction, which detects probable drift-correlations.
 
Well, I also tried to get reasonable fix-points from time to time (for free, of course) by comparison to calibrated material, but always found the deviation to be within the expected drift values.

Frank

[Dr. Frank]

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.

Interesting. Does the 34465A have a hermetic reference resistor? My measurements on older HP/Agilent 6 ½ DMM’s show humidity sensitivity and also quite a lot of drift the first year.

What uncertainty do you think it is possible to get after a new calibration (excluding the cal lab) for the 34465A? What I see is that the 24 hour spec for 10kohm is 25ppm at +-1C for the 34465A.

Another story: Maybe 15 years ago we had a lot of discussions with a calibration lab. We had a HP34970A (same DMM module as 34401 but with offset compensation availible) that we thought was very stable on the resistance ranges 100-100kohm but the calibration protocol showed that the values went up and down about 40ppm during the last years. They used the same calibrator with low uncertainty every year. We never found out if it was the 34970A or something else in their environment that made the calibrations differ so much between years. Of course the 34970A passed the calibrations as the one year spec is around 100ppm if I remember correct.

Lars

Well, the 3458A, and also the 34465A both have a VHP101, which should be stable enough, and both feature ACAL.
The specification of the 34465A is barn-door wide, as they maybe don't want to promote a bread and butter instrument as a metrology grade one.
 
I got some good confidence about the absolute values of my resistor and voltage references, by other calibrated instruments.
When I received two freshly instruments, which did not run hot during the transport, and could not drift (also not by humidity, as both internal references are hermetical types), I anyhow found agreement to less than 1ppm, for each instrument, and for both units, 10V and 10kOhm.
So, the other way round, what is the probability, that this circumstance is pure luck?

As Keysight uses frequently calibrated calibrators, nowadays very probably very close to the precise nominal values, and due to electronic calibration, the transfer to the end-user -lab in practice is much better, than estimated by these wide specs.

And again, I also found a very good agreement of the 10kOhm range for a 1year old 34470A, which further reduces the probability for a high drift rate, as given by the spec.
Its 10V range was about 5ppm off, in agreement to its 24/365 operation, and to the known drift rate of the LTZ1000A reference, when operated constantly at its 95°C.. which does not apply to the 10k reference.

As a summary, you have to collect as many trend information as possible, to get some confidence in such poor-mans calibration features.

Frank

[Dr. Frank]

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.

Does that mean, measuring the value of "unknown" standard resistor by 3458A, taking this value as "applied value" for a second measurement by UUT (UUT = unit/DMM to test by selfmade standard, not the selfmade standard itself) ? Then applying the tolerance of UUT and narrow it by uncertainty of 3458A? (That sounds very similar to my very limited understanding of "guard banding"...)

The 3458A has got three problems:
1) the test report in most cases is incomplete, mostly tested to the 1yr limits (~+/-10ppm) only
2) The temperature of the reference resistor can not be controlled or monitored precisely, as it's  not ovenized, and it's  just sitting in the un-controlled air draught.
Also, the inner temperature always is at least 13°C higher than the R.T., and can easily fluctuate by a dirty air filter, or by the external assembly of the instrument.
3) the resistor might be a 1.2ppm/K type, or a later VHP101, which should have 0.3ppm/K only

So the Ohm reference of the 3458A is quite unstable, in a tightly controlled environment, I see long-term fluctuations on the order of 1 ppm, compared to my external reference resistor ensemble, which fluctuate much, much less, on the order of < 0.2ppm.

So, to study any drifts of your D.U.T. you should always have a more stable reference than the 3458A available, although this instrument is capable of doing about 0.2ppm short term transfers.

In the end, you cannot bootstrap the absolute uncertainty by reversing 3458A and D.U.T. ( if I understand your comment correctly).
Some time, you really need an external, calibrated reference.

Frank

[zlymex]

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.

Can this known standard be a calibrated DMM (3458A)? Or did you mean a standard resistor?

I mean a standard resistor, which usually drifts very little per year(say less than 4ppm), and do not suffer from seasonal/humidity effect because most of the resistor elements within a standard resistor are hermetic sealed.

By means of 'known', it should be calibrated(externally) frequently(yearly say) and recently that not only the value and uncertainty is known, but the drift rate can also be derived from the past calibration so that you can predict the current value.
The calculation can be found in a spreadsheet of one of my previous thread:
https://www.eevblog.com/forum/metrology/spread-sheet-aided-calculation-for-standard-resistor-measurement/msg900297/#msg900297

Although there is a very good internal standard resistor inside 3458A, but the specification for direct resistance measurement is not very good(8.5ppm over 90days for 1k, 10k and 100k). However, if you use 3458A on those resistance range as a ratio device, you can achieve around 1ppm transfer/repeatability. If you use 3458A on 10V voltage range as a ratio device(as described by DiligentMinds.com on the 2nd post), you can achieve around 0.1ppm transfer/repeatability.

[Dr. Frank]

I mean a standard resistor, which usually drifts very little per year(say less than 4ppm), and do not suffer from seasonal/humidity effect because most of the resistor elements within a standard resistor are hermetic sealed.


Although there is a very good internal standard resistor inside 3458A, but the specification for direct resistance measurement is not very good(8.5ppm over 90days for 1k, 10k and 100k). However, if you use 3458A on those resistance range as a ratio device, you can achieve around 1ppm transfer/repeatability. If you use 3458A on 10V voltage range as a ratio device(as described by DiligentMinds.com on the 2nd post), you can achieve around 0.1ppm transfer/repeatability.

On the early units, up to about 1995, HP used a reference resistor, which was not so good, but they founded the Ohm specification on this component, obviously.

Later, a VHP101 was used, which should have a lower T.C. of about 0.3ppm/K, and much better long term stability.

Anyhow, the specification of the Ohm range has never been updated, nor has the Transfer Uncertainty been added.

In my unit from 2001, the drift over years is < 2ppm, and a Transfer Stability of about 0.2ppm can be achieved, by keeping the RT constant.
The T.C. itself is not detectable, i.e. there's no clear correlation between TEMP? and the gain factor relative to external resistance standards.
A trend line, containing much too high variation, indicates a T.C. <= 0.3ppm/K, though.

Frank

[zlymex]

Hi, Dr. Frank,
3458A measures 10k at 100uA/1V. Looking at the 1V transfer spec, it is 0.3pp+0.1ppm, worse than that of 10V(0.05ppm+0.05ppm), mainly because of the imperfection of the gain setting resistor pair(45k+5k) and the noise/error of the amplifier, and this has nothing to do with the improvement of the internal 40k standard. Also, the HFL version specify the transfer of 10k as 0.5ppm+0.1ppm. Therefore, I'd better stay on the safe side, although in reality, I can achieve 0.2ppm or better when transferring 10k with my 3458A.

[Dr. Frank]

Hi, Dr. Frank,
3458A measures 10k at 100uA/1V. Looking at the 1V transfer spec, it is 0.3pp+0.1ppm, worse than that of 10V(0.05ppm+0.05ppm), mainly because of the imperfection of the gain setting resistor pair(45k+5k) and the noise/error of the amplifier, and this has nothing to do with the improvement of the internal 40k standard. Also, the HFL version specify the transfer of 10k as 0.5ppm+0.1ppm. Therefore, I'd better stay on the safe side, although in reality, I can achieve 0.2ppm or better when transferring 10k with my 3458A.

hi Zlymex,

I did not want to determine the Transfer specification for the 3458A!

If Keysight metrology dept. would do that in the retrospect, well, they would have to specify something like >1ppm / 10min. / +-0.5°C only, as the Ohm circuit as whole, is quite mediocre.
The limitation to 1V test voltage is also   ridiculous.

I just wanted to state, what in a real experiment, with tighter temperature control, can be achieved, by monitoring the deviation between first and last measurement, after several hours w/o ACAL.
(Found that on measuring T.C. of resistors)

I think, this experimental approach is legitimate; the metrologically guaranteed parameters are another story.

Anyhow, next time, I'm doing such T.C. - experiments, I will do that in a bridge configuration, using 10V ratio measurements only.

[zlymex]

Hi Dr. Frank,
They do have transfer spec of ohm ranges for HFL version of 3458A.
The spec for 100k is better probably because the measuring voltage is 5V.

And expecting your measurement.

[Dr. Frank]

Hi Dr. Frank,
They do have transfer spec of ohm ranges for HFL version of 3458A.
The spec for 100k is better probably because the measuring voltage is 5V.

And expecting your measurement.

Hi Zlymex,

Good explanation, more logical.. I always thought about this item, that this 0.1ppm is due to the fact, that the 100kOhm range is closer related to the 40k internal resistance.

I already have shown such a T.C. measurement in the 'resistance' thread, maybe I still find that link..

Frank

[carl_lab]

Thanks for all your replies.

I don't need to calibrate 8,5 digit DMMs, only 6,5 digit instruments (34401, 34410, 34465, K2000...).

Could I use this approach for?

...measuring the value of "unknown" standard resistor by 3458A, taking this value as "applied value" for a second measurement by UUT (UUT = unit/DMM to test by selfmade standard)?
Then applying the tolerance of UUT and narrow it by uncertainty of 3458A?

I think, long therm stability and tempco doesn't matter (too much), if I measure the standard resistors every time I need to calibrate a 6,5 digit DMM. Room temperature is 23+/-0.5°C.

What do you think?