Testing resistance standards

[rhb]

I bought a set of 8 decade step resistance standards 1-10M ohm. 1x Rubicon, Philadelphia, 2x  James G. Biddle, Plymouth Meeting, PA and the rest Leeds & Northrup, Philadelphia.

Now I want to figure out how to test and apply them.  I have 2x 33401A, and a 3457A w/ a 44492A 10 port multiplexer card.   So I am in the typical hobbyist situation.  I've got a bunch of stuff that is really cool if it works, but no simple way to test it.  I've got a DMMCheckPlus and the 34401As look OK with that, but this is a bit of a step up.  Both the 34401As were logged for voltage with the Cal Club Round 2 kit.  I'm very comfortable with them on volts. Not comfortable on resistance.

I'm not set up to do a proper bit of metrology with temperature control and such.  So for now I'm looking for suggestions on where to start.

The obvious thing is to wire up all the resistors for 4 wire measurements and log them over a  period of time along with a couple of voltage references.  At the moment I don't have a duplicate of the Cal Club temperature and humidity sensor.  I have the parts, but not yet assembled.

So suggestions?    On basic physics principles, it seems I should be able to solve for relative resistance standard errors if I keep them at close to the same temperature even though that is not constant without knowing the temperatures.

Reg

[bob91343]

What are you trying to accomplish?  It's unclear.  You have resistors that have pretty good specs and the same for your meters.  Comparing readings might give you an idea of the probable error, but of what?  The resistances, or the meters?

[rhb]

That, grasshopper, is the question.

How does one advance?

If the best measurement you can make is 1%, how do you get to 0.1%?

This is more art than science.  It takes a solid grasp of science and mathematics plus inspiration and cleverness. Modern metrology is amazing.  But we did not get handed fractional ppm standards  by God with which to build the instruments.

I shall repeat my question in slightly different form.  Given a set of standards, most  of which have not  been compared to external references, how does one verify them?  This is precisely the problem the national labs have grappled with for a *very* long time.  I am merely a hobbyist following in their footsteps in different circumstances.

Have Fun!
Reg

[SilverSolder]

I think our ancestors would have been thinking in terms of bridges and ratio transformers about now, if they wanted max accuracy.  Those things are good for sub-PPM measurements.

You can use a ratio transformer and a resistance standard as two legs in a bridge, and calibrate the resistance standards to the ratio transformer.  The RT never needs calibration (it is intrinsically accurate) and is really a quite amazing device.

[martinr33]

That these are decade resistors makes things ever trickier.

One idea you might try:

Put the two high value  resistors in series. So one is (say) 100%, and the other is 10%.
Apply  a voltage across them, current not to exceed 1mA

Measure the voltage across each.
Infer the current from the higher value resistor, and calculate the lower value resistor using that current and the voltage across the lowe value.

When you are doen, you will have estimates fro all the resistors, chained from the highest value.

Then work the process backwards, measuring the low value and calculating the high value.

You should have a closing error, which you can apply across all resistor. Repeat until all vales no longer converge.

You will then have to caclualte out the effect of the 100V range parallel resistance (thanks to Bill for that reminder).

You will be fighting the temperature coefficients of the resistors - if you have what I suspect, these devices are designed to be operated in a water bath.

The input resistance of the 100V range and meter temperature coefficients are another problem.

However, you are not subject to the variance of the resistance ranges. That said, you could meaure the resistance of each unit as you test each one.











 

[edpalmer42]

A variation on martin's idea would be to divide the pile into 4 groups.  Each group is 2 adjacent decade values.  Wire each group as a simple voltage divider with a 'low resistor' and a 'high resistor'.  If you connect all four groups across the same voltage source, the midpoint of each of the four groups should be at the same voltage.  The calibration of your voltage source or voltmeter doesn't affect the results.  The only assumption is that the meter can read zero volts correctly.  This would be a 'sanity check' to confirm that none of the resistors are far out of tolerance.

If you changed the voltage divider to skip a decade between high and low resistors you would get more data points.  I don't know if you could come up with enough patterns to be able to uniquely solve the set of equations to determine the value of all eight resistors.

[CatalinaWOW]

What are the specs on the resistors.  I suspect they have pretty low temp coefficients, and thus the accuracy of your temperature measurement should not be overly critical.  If your lab is temperature controlled to typical standards it will vary by only a few degrees with a cycle times of a a sizeable fraction of an hour.  By putting your resistors in an insulated box you can keep them with a fraction of a degree of the average temperature, which can be measured with any number of relatively simple and cheap instruments.

Some fiddling with tempco specs will tell you how well you have to do to get the results you want. 

Did you measure the standard resistors sent with the cal club kit?  Those measurements combined with the data taken by other cal club members (particularly the ones with calibrated 3458s) will tell you a lot about where you are with your instruments.

[bob91343]

This is why we have NIST, to nail down the basic units as closely as possible.  Even so, one never knows absolutely the value of any resistor or voltage.  Comparisons are the best we can do.  People in the ivory towers spend their lives refining standards but like everything else, you are never completely sure.

If we find that the 10k resistor is within 1 ppm of twice the 5k resistor, we still don't know the resistance.

If you choose to ignore the slight temperature variations, say 0.001 degree, you are ignoring a potentially important shift.  Dissipating 1 milliwatt in a resistor will increase its temperature somewhat, causing a shift in resistance even when using 'zero' temperature coefficient wire.

And we aren't mentioning thermal voltages which contaminate many supposedly precise measurements.

Like everything else in life, nothing is simple.

[alm]

What are the specs on the resistors.  I suspect they have pretty low temp coefficients, and thus the accuracy of your temperature measurement should not be overly critical.

At least for the common Rosa/NBS type manganin L&N resistors, the tempco isn't particularly low. I believe it's about 10 ppm/K, though I can't find a source for that right now. That's why they were designed to sit in a temperature-controlled oil bath (not water, as someone wrote in this thread earlier). They also have a hole in the middle to monitor temperature. That gives you yet another quantity to worry about

[CatalinaWOW]

The two prior answers illustrate the importance of the question, "How good do you want?".  The suggested temperature stability, combined with the suggested tempco would result in 0.01 ppm errors, which are implied to be important.  And may we'll be for some.  But at that level of precision, none of the instruments mentioned by the op is stabile enough to participate in the chase.

[MIS42N]

Many years ago I worked in a standards laboratory calibrating test instruments. To do resistance, we had resistors that were sent to the national laboratory for calibration every few months. These were the oil filled types with thermometers, and the laboratory was air conditioned to be within a degree and was enclosed in a Faraday cage. All resistance measurements were done using the Wheatstone bridge configuration. I don't remember the details but I believe that it only needs one resistor of known value to work out other resistances (I was a cadet at the time and this was done by others). I think we had many resistors of about the same resistance (I think 100 ohm), these were paralleled with decade boxes used in the Mohm region. Knowing one resistor accurately and shuffling the other three in the bridge all could be made the same by varying the decade boxes. Working backward from a not very accurate decade setting one could work out the actual resistances of the three unknown approx 100 ohm from the known one to about 100 times the accuracy of the decade boxes. The decade boxes were then calibrated using similar techniques and the process could be repeated to refine the measurements when they were used in parallel. It was very tedious but we quoted results to 1ppm (the calibrated standards were to 0.1ppm).

The Wheatstone bridge needs a very sensitive detector to determine that there is no voltage difference between the taps in the two legs. This was first determined using normal instruments but the final measurement used a "long throw galvanometer" (that is the description I recall, might not be right). It was effectively the movement from a meter with a mirror on it instead of a pointer. A picture of a circle with a split down the middle was projected onto the mirror, then to a second mirror on the opposite wall, and back to a screen near the galvanometer, maybe 30 feet. Any movement of the galvanometer mirror was easily seen. The null point was determined by swapping the detector leads, no movement meant no voltage. It was sensitive enough that we had a tram timetable so we didn't try measuring when a tram was nearby. The induced currents in the ground (despite the Faraday shield) would induce slight voltages in the measuring equipment.

Point of all this is that we could work out the relative resistances to a high degree of precision, but it needed one calibrated resistor (we had a few but I think one is enough) to make those relative measurements valid. If you have confidence in one of the resistors you may be able to calibrate the rest. IIRC it needed a lot of care and technique.

[SilverSolder]

Bridges are good at getting the ratio of two resistances laser accurate.  But you do need at least one accurately known value of resistance to dial in all the other ones! 

[alm]

Look at the ESI SR1010 documentation for some examples of transferring resistance between ranges. You don't strictly need an SR1010 for this, just sets of close to identical resistors that you can connect in series / parallel.

But indeed, you would normally start with 1 calibrated resistor to compare your other resistors to. I guess you could use bridge techniques to compare your resistors and get an idea of how good your comparisons are, and how close the resistors are compared to an estimated nominal value based on averaging. But deriving any accuracy based on this statistical technique is highly suspect, especially since the sources of drift are not all uncorrelated.

[Stray Electron]

At least for the common Rosa/NBS type manganin L&N resistors, the tempco isn't particularly low. I believe it's about 10 ppm/K, though I can't find a source for that right now.

   This should prove helpful Vishay, 'Temperature Coefficient of Resistance for Current Sensing', https://www.vishay.com/docs/30405/whitepapertcr.pdf

[Stray Electron]

I bought a set of 8 decade step resistance standards 1-10M ohm. 1x Rubicon, Philadelphia, 2x  James G. Biddle, Plymouth Meeting, PA and the rest Leeds & Northrup, Philadelphia.

   First, you need to be aware that step resistors are NOT Standard Resistors (E-bay sellers notwithstanding!)   They aren't made of the same material or use the same construction techniques.  Look up any of the old ads for Biddle or L&N and you'll see that they don't specify the same precision.  In fact, I don't think that the L&N ad that I looked at recently didn't even specified the precision or tolerance of their decade resisters. 

[Stray Electron]

Many years ago I worked in a standards laboratory calibrating test instruments. To do resistance, we had resistors that were sent to the national laboratory for calibration every few months. These were the oil filled types with thermometers, and the laboratory was air conditioned to be within a degree and was enclosed in a Faraday cage. All resistance measurements were done using the Wheatstone bridge configuration. I don't remember the details but I believe that it only needs one resistor of known value to work out other resistances (I was a cadet at the time and this was done by others). I think we had many resistors of about the same resistance (I think 100 ohm), these were paralleled with decade boxes used in the Mohm region. Knowing one resistor accurately and shuffling the other three in the bridge all could be made the same by varying the decade boxes. Working backward from a not very accurate decade setting one could work out the actual resistances of the three unknown approx 100 ohm from the known one to about 100 times the accuracy of the decade boxes. The decade boxes were then calibrated using similar techniques and the process could be repeated to refine the measurements when they were used in parallel. It was very tedious but we quoted results to 1ppm (the calibrated standards were to 0.1ppm).

The Wheatstone bridge needs a very sensitive detector to determine that there is no voltage difference between the taps in the two legs. This was first determined using normal instruments but the final measurement used a "long throw galvanometer" (that is the description I recall, might not be right). It was effectively the movement from a meter with a mirror on it instead of a pointer. A picture of a circle with a split down the middle was projected onto the mirror, then to a second mirror on the opposite wall, and back to a screen near the galvanometer, maybe 30 feet. Any movement of the galvanometer mirror was easily seen. The null point was determined by swapping the detector leads, no movement meant no voltage. It was sensitive enough that we had a tram timetable so we didn't try measuring when a tram was nearby. The induced currents in the ground (despite the Faraday shield) would induce slight voltages in the measuring equipment.

Point of all this is that we could work out the relative resistances to a high degree of precision, but it needed one calibrated resistor (we had a few but I think one is enough) to make those relative measurements valid. If you have confidence in one of the resistors you may be able to calibrate the rest. IIRC it needed a lot of care and technique.

  MIS42N,

 I've been playing around with a L&N 5 decade Resistance bridge, model number 4725, like the one that Conrad Hoffman has on his website and I have found some general instructions for it but I've wondered how sensitive the galvanometer needed to be.  The galvanometer is external to the bridge and nothing that I've found mentions it's requirements.  But I did learn that the cells used with this bridge are almost certainly 1 Volt or 1.1 volt cells!  The standard cells of that era (1915).   According to Conrad, this bridge is accurate to within 0.01% when used correctly. Can you shed any light on the requirements of the necessary galvanometer?

[rhb]

This is not what I bought, but it is the type.  All have the same connections and the hole in the middle.

https://www.ebay.com/itm/303551657397

I did measure the Cal Club resistors with both of my 34401As.  I did not have a 3457A at the time.

For the construction details for a sensitive galvnometer or electrometer:

Procedures in Experimental Physics
John Strong

sadly out of print again with Lindsay's retirement, but perhaps Dover will pick it up. 

Absolute Measurements in Electricity and Magnetism
Andrew Gray
Dover Press

has 94 pages devoted to the construction of galvanometers.  I would expect that using a modern low noise and offset precision instrumentation amplifier would yield a more sensitive null detector.  I'm sure that AoE discusses that in detail.

And yes, accurately measuring these will be a serious undertaking.  Not because of the mathematics, but the physical setup is non-trivial.

At the moment I'm looking for something I can set up without a lot of work just to play around.  For example  an oil bath in an insulated box inside another insulated box such that an assumption that all the resistors were at the same, unknown temperature was at least semi-plausible.  Then collect a very large number of measurements of each resistor over a period of several months.  That would not provide any absolute data, but would give me information about relative errors and temperature coefficients in a very general sense.

That would get the basic data collection and analysis infrastructure developed.

Reg

[MIS42N]

  MIS42N,

 I've been playing around with a L&N 5 decade Resistance bridge, model number 4725, like the one that Conrad Hoffman has on his website and I have found some general instructions for it but I've wondered how sensitive the galvanometer needed to be.  The galvanometer is external to the bridge and nothing that I've found mentions it's requirements.  But I did learn that the cells used with this bridge are almost certainly 1 Volt or 1.1 volt cells!  The standard cells of that era (1915).   According to Conrad, this bridge is accurate to within 0.01% when used correctly. Can you shed any light on the requirements of the necessary galvanometer?

Sorry, no idea. It wasn't switched into the circuit until the electronic voltmeter indicated no voltage, probably in the uV region. It had a screen about 2 feet wide and no volts on the other meter could be several inches on the screen.

I think the 1V cell you mention would be a Weston cell. The laboratory had them, I didn't get to use one, probably above my pay grade. I remember there was a recipe for making them. There was a container of liquid mercury, Not very big but heavy.

[Stray Electron]

This is not what I bought, but it is the type.  All have the same connections and the hole in the middle.

https://www.ebay.com/itm/303551657397

 Ahh! Nice!  I thought that you were talking about something more like this https://www.ebay.com/itm/General-Radio-1432-M-Decade-Resistor/254642278577?epid=1325132457&hash=item3b49dcd0b1:g:fCAAAOSwKKZdwvT2

[alm]

There are some NBS (NIST) publications and the Fluke book Calibration Philosophy in Practice (1st edition, I dug out my hardbound 2nd edition, but it only mentions these resistors in passing) give some details on working with those Rosa / NBS-type resistors. A temperature-stabilized oil bath (you might get away with thermal momentum if its just about equalizing the temperature, although temperature gradients could be an issue), and humidity are two factors. The humidity is often described as "seasonal effect". Also note that the oil might turn acidic, so consider replacing it with food-grade mineral oil.

From what I understand, you have eight different-value manganin resistors that are spaced a decade apart? Then any kind of permanent setup, short of just wiring each of them to the multiplexer and doing a direct resistance measurement with the 3457, will be tricky. You can build a bridge to compare say 1 Ohm with 10 Ohm, and then rewire the same bridge to compare 10 Ohm with 100 Ohm, but continuously monitoring all three values relative to each other would take a lot of switching, I'd think. And all this switching means hassle to build and design, and would likely introduce errors.

You could probably take a couple of values that are not too far apart, put them in series, run a constant current through them and measure the voltage across. But it will be a trade-off between having sufficient drop over the lowest value so thermoelectric voltages aren't too much of an issue and so your meter can measure it accurately (I'm pretty sure none of your meters can measure let's say 1 uV with any accuracy or precision), while on the other hand limiting the dissipation in the highest value resistor so their short term (or long term!) accuracy is not affected.

Based on the LN4xxx specs (the one from your eBay picture), the 100k resistor can take up to 1 mA while staying within 10 ppm, although I personally think 0.1W is pushing it, so I'd rather go for 0.3 mA (0.01W). With 0.3 mA, the drop across the 1 kOhm resistor would be 300 mV, and the 10 Ohm resistor would be 3 mV (probably the limit of what you could measure accurately). So let's say this could cover 3-4 orders of magnitude. And for the 100 kOhm resistor, the 10 MOhm in parallel for the DMM on the 30 V range would affect the accuracy. So this is certainly not the most accurate technique. But it is the simplest setup I can think of that could beat the built-in resistance feature if you can find / build a stable current source, and it would allow you to use the voltage measurement function that you trust.

[Stray Electron]

I think the 1V cell you mention would be a Weston cell. The laboratory had them, I didn't get to use one, probably above my pay grade. I remember there was a recipe for making them. There was a container of liquid mercury, Not very big but heavy.

  If it contained Mercury then it was probably a Weston Cell.  See https://en.wikipedia.org/wiki/Weston_cell. But that shouldn't be necessary if you were using a Bridge since the voltage should cancel out. OTOH if you were trying to measure resistance directly then you would need a Known and very precise and very stable battery such as Weston cell. The output of a Cadmium-Mercury Weston cell was about 1.018 volts but I think there were other alloys that gave different voltages.

  Conrad Hoffman has a nice article about the Weston cells http://conradhoffman.com/stdcell.htm]
[url]http://conradhoffman.com/stdcell.htm[/url]

   But since a bridge shouldn't require a precise voltage it appears that the cells used with my L&N Resistance Bridge c.a. 1915 were probably Daniell Cells  https://en.wikipedia.org/wiki/Daniell_cell.  I haven't found any specific reference to either the specification of the battery cells or to the galvanometer but those were the standard battery cell voltage at the time as far as I have been able to discover.

  I quote "The Daniell cell is also the historical basis for the contemporary definition of the volt, which is the unit of electromotive force in the International System of Units. The definitions of electrical units that were proposed at the 1881 International Conference of Electricians were designed so that the electromotive force of the Daniell cell would be about 1.0 volts.[1][2] With contemporary definitions, the standard potential of the Daniell cell at 25 °C is actually 1.10 V."

[rhb]

I love it!   You guys are totally bonkers :-)

Weston cells are very fragile, so drawing current from them is a major no no, as in destroyed Weston cell no no.  So a Weston cell in a bridge with a 1 ohm reference resistor strikes me as a very dicey proposition.  I've got NBS  Pub. 77 volume 1 which goes on for many pages about measuring resistance standards and has photos of the NBS precision bridge.  I don't plan to duplicate that, but I'll certainly study all the discussion closely.

I'm wanting to approach this in the manner that Chris of clickspringprojects.com is building a reproduction of the Antikythera mechanism.  He uses modern tools for much of the work to save time, but only after proving that he can do the same work with tools available 2200 years ago.  If you've not seen those you *really* should watch them.

Have Fun!
Reg

BTW  I have a 5 decade General Resistance Instruments Resist-O-Stat II I got from Sphere Research.   They also had a 4 decade GR, but I opted for the 5 decades.  But that's not a "resistance standard" by any reasonable definition.  But I had no resistance substitution box at all when I bought it.

It would be interesting to know the history of Rubicon, Leeds & Northrup and James G. Biddle.  I suspect there were several people shuffling among them.  I knew of L&N and bought these expecting them to all be L&N, but no complaints.  Rather fun to have examples from the other makers.

Next on the wish list are inductor and capacitor standards.  Unfortunately, those seem to be *very* pricey.

[tggzzz]

But since a bridge shouldn't require a precise voltage it appears that the cells used with my L&N Resistance Bridge c.a. 1915 were probably Daniell Cells  https://en.wikipedia.org/wiki/Daniell_cell.  I haven't found any specific reference to either the specification of the battery cells or to the galvanometer but those were the standard battery cell voltage at the time as far as I have been able to discover.

At school when we needed <1% voltage measurments in physics, we used NiFe cells, 1m of resistance wire, a Weston standard cell and a sensitive inaccurate analogue meter.

The NiFe cells powered the resistance wire, and the standard cell plus null meter used to find the point on the wire at 1.018V. That enabled the NiFe cells voltage to be calculated. Then the unknown voltage replaced the standard cell, and that null point was found. The unknown voltage was then calculated.

[thermistor-guy]

https://ieeexplore.ieee.org/document/1177931

Abstract:

The digit voltmeter (DVM) input and leakage resistances have been analyzed in the DVM-based resistance measurement system using one or two DVMs.
The results are given both theoretically and experimentally. Shunting errors due to DVM-input and leakage resistances were substantially reduced by using
a proper measurement method. The method is being further investigated for measuring high-ohm standard resistors.

If the OP can use two DVMs in the setup, then it is possible to reduce measurement errors due to DVM input resistance.
Lead author's papers are listed here, which you can use to find a free copy:
https://scholar.google.com/citations?user=zI9TlcQAAAAJ&hl=en

[martinr33]

Those resistors have a single element, so are quite thermally sesnitive - 10ppm/degree is quite likely, I think even for a low tempco one.

The metal foil vishays rely on the substrate changing dimensions with temperature, thereby mechanically changing the dimensions of the resistance element and hence compensating for temperature.

Judging by the comments about these Vishay resistors, they are still quite variable - at the PPM scale.

I like Ed's idea of the bridged pairs, as it provides more data for the ratio solution.