Absolute Divider Concept

[Lesolee]

I have been recently disappointed by the technical merits of the Fluke 752A reference Divider, as highlighted by the excellent analysis work done by e61_phil (https://www.eevblog.com/forum/metrology/influence-of-switch-resistance-in-hamon-dividers/).

Then there is Conrad Hoffman’s budget Kelvin-Varley divider (http://conradhoffman.com/mini_metro_lab.html) at the other end of the financial scale (from 1996)

It got me thinking, could I do good Absolute Divider at a pretty low cost? I have no use for such a beast, and don’t have any kit to use it with, but just as a design exercise, and secondarily as a tutorial for others. There are lots of skilled specialists on this site, many of whom are not reticent about pointing out errors, so anything said here is automatically checked --- which is good for the purposes of a peer-reviewed tutorial!

Conrad selected his resistors from 1% metal film resistors. I suspect that the relative cost of tighter tolerance components has come down considerably in the last 24 years. And a 0.1% resistor that you buy is not the same as a 0.1% resistor selected from a whole bunch of 1% resistors. The load life stabilities of the two beasts are not the same thing.



My first choice is the prime divider resistors, picked from a local distributer’s range. https://uk.farnell.com/vishay-foil-resistors/y145310k0000t9l/res-10k-0-01-600mw-radial/dp/2820505

They are not “cheap” at £12.74 (10 off price) but we have to make a box, and put on binding posts, and so forth, so it is a reasonable expense for the most critical part of the whole design.

And the specs are just AWESOME. Voltage coefficient < 0.1 ppm/volt. Power coefficient of resistance less than 5 ppm at full rated power. Those numbers just scream “make an attenuator out of me”. The 0.2 ppm/°C spec quoted by the distributer is pretty dodgy. The data sheet says 0.2 ppm/°C typical, but 1.8 ppm/°C max. But when you dig into the curves, the TC is second order so the equivalent linear TC drops according to the ambient range. 0.2 ppm/°C apparently drops to 0.05 ppm/°C over the restricted range 25°C ±25°C. It makes me think that over the ±5°C required lab range, 0.2 ppm/°C is a pretty realistic expectation.

The power coefficient of resistance is a number you don’t usually see. What it means is power heats up the resistive element, and the resistance changes due to its own TC. Normally you have to work this out for yourself. They have done the work for you. At 25°C the rated power is 250mW, which for a 10K resistor is 50V. I want to run the attenuator at up to 100V, so that is 10V per stage.

(10/50)² = 0.04. It means the self-heating error is expected to be 0.04 x 5 ppm = 0.2 ppm. The voltage coefficient is a different effect and at 10V per resistor we get 1ppm. But this effect should match between near identical resistors run at the same voltage, so it should not be much of a worry.

I have 0.01% resistors and I need to adjust them all up to a common value. There is no point in putting in a series resistor at 0.01% of 10K (10 ohms) because we don’t need the 10K to be an absolute value. 0.02% is a bit tight on adjustment range, but should be ok. It means we can use a shunt 1M resistor. Again a 0.1% has been chosen for better long term stability, but also a 5ppm/°C spec was needed. The shunt resistor is 100x larger so it contributes TC to the overall resistance by a factor of 1/100. It means a 15ppm/°C part would contribute 0.15ppm/°C, which is pretty high compared to our 0.2ppm/°C expected value. I would therefore prefer a 5ppm/°C part. https://uk.farnell.com/vishay/ptf651m0000bzek/res-1m-0-10-250mw-axial-metal/dp/1703752.

Next we have a trimmer. The sensitivity to the trimmer is a factor of 5000 down, so the 100ppm/°C becomes 0.02 pm/°C and can be neglected. The stability and setability are another matter. The 0.02% adjustment range is 200 ppm. We would like to set the attenuator to better than 1ppm, and preferably better than 0.1 ppm. This is too tight for a single turn pot. To get better stability, instead of using a track that is the same size as a single turn pot, the huge linear track has been chosen. https://uk.farnell.com/bourns/3006p-1-203lf/trimmer-15-turn-20k/dp/9352341

The binding posts are a key feature of the design, but I don’t have any practical experience of choosing them for such an application. Farnell has 167 to choose from! Some of the voltage ratings are really low, but we want lots of insulation on these posts, so I would pick a voltage rating above 1kV to get good insulation. That’s down to 46 types. Now we pick gold plated contacts for 18 results.

For this distributor the choice would seem to be a POMONA 3750, since it is available in several colours. At £7.35 (with no price breaks) that is quite expensive, but the last thing you need is a broken terminal on a standard you want to use for 20 years. https://uk.farnell.com/pomona/3750-2/binding-post-15a-turret-red/dp/2406404. Probably worth shopping around though. (EDIT: Use gold plated copper for lower thermal EMF. See post by splin below.)

The panel on which the binding posts are mounted is potentially the most expensive part of the whole design. It should not be metal because then it cannot be guarded for leakage (Although the metal is good as a shield of course). The problem here is that you can clean the panel, and measure the insulation resistance when nothing is fitted. As soon as you fit the parts you can no longer measure the leakage current. As dust and grime build-up over the years, you have no idea how badly they are affecting the performance. Hence guarding the posts reduces the error by a factor of 500, hopefully reducing the worry.

One idea is to use a plain plastic panel and paint on guard tracks on both sides with conductive silver paint. It’s just a bit – nasty. Another idea is to use a double sided copper clad laminate board and use a Dremel to mill out gaps so you can guard large copper lands. But now we have exposed laminate which will allow moisture ingress, and it looks a bit nasty again. Finally we have a custom double sided pcb with guard tracks built in. Clean and nice, with solder resist all over, except on the guard tracks. But the cost is pretty high. Any other ideas?

EDIT: It took a couple of goes for the comments from Conrad and Kleinstein to sink in. The adjustment of one resistor set affects the voltage across all other resistor sets horribly. For example a 0.01% resistance change in one, changes the current in the chain by 0.001%, and therefore all other voltage stages by the same amount. Given that each null-to-1V step takes some significant time, this "design" is pretty nasty. I really ought to delete it to "save face". On the other hand one does need to admit errors occasionally. 

EDIT: Up-issued PDF to highlight the nasty errors and delete the author.

[Conrad Hoffman]

Interesting, but not cheap! I have to wonder if all the attention to low leakage is warranted. Not because it isn't needed, but because of the small size of the resistor bodies. I'd think they're the weak link in the chain, not the generous amount of insulation material on the binding posts. A metal panel could be used, though I've seen contamination over the years that has to be avoided. I like a metal chassis with a floating metal guard chassis inside. I don't fully understand the calibration method and how the interaction gets removed, though you've obviously got it figured out. 

[Lesolee]

I have to wonder if all the attention to low leakage is warranted. Not because it isn't needed, but because of the small size of the resistor bodies. I'd think they're the weak link in the chain, not the generous amount of insulation material on the binding posts.

So a small resistor body can leak across itself, changing the resistance of the resistor. But leakage to ground is quite different. The resistors are inside the box and therefore not as subject to the debris floating around in the air. In principle we can calibrate out the leakage across the resistor body. The leakage to ground is more problematic as it affects the attenuator accuracy after we think it is all set up correctly.

I don't fully understand the calibration method and how the interaction gets removed, though you've obviously got it figured out. 

Not necessarily. 
I may have missed something obvious which you have spotted.

My simplistic notion is that you measure and calibrate each output pair individually to 1V (for example). The floating null-to-reference box is entirely isolated from ground so theoretically calibrating one pair has no effect on the others. Unlike you, I am an "armchair metrologist" these days, and I have never built such a device. My Datron 1051 (which I made from manufacturing reject parts when I worked there) died many years ago 

It is therefore entirely possible that I have made some rookie mistake in my thinking! I await correction. 

BTW: I enjoyed reading your Mini Metrology Series the other day  , although I admit to downloading them as JPGs, then converting the whole lot to a PDF before reading, as that makes it easier scroll on the screen.

[Conrad Hoffman]

If there's a calibration issue, it probably goes away when you do multiple passes. How many for perfection? No idea. Those resistors are about $17 each, depending on the exchange rate. No idea from local vendors but probably not much different.

It's been a long time since I got permission to post the Mini-Metrology article but I think there was some requirement that I keep it in the form of jpgs for each page. Every time I count the years back to that article I go into shock. It was originally proofed by Jim Williams. It seems whatever I do in electronics, I find his footsteps ahead of mine. He's one of the people in this business I miss the most.

[splin]

It got me thinking, could I do good Absolute Divider at a pretty low cost? I have no use for such a beast, and don’t have any kit to use it with, but just as a design exercise, and secondarily as a tutorial for others.

A pretty expensive piece of kit you have no use for - are you intending to actually build it or is this just a thought exercise? As a design exercise it would be seriously compromised if you don't have any means to test its performance, otherwise it could just as well be an exercise in how not to go about designing a high precision piece of test kit. Without reliable test results, I'm afraid neither you, or us, would learn a great deal.

Conrad selected his resistors from 1% metal film resistors. I suspect that the relative cost of tighter tolerance components has come down considerably in the last 24 years. And a 0.1% resistor that you buy is not the same as a 0.1% resistor selected from a whole bunch of 1% resistors. The load life stabilities of the two beasts are not the same thing.

Why not? If they have the same part number I'd suggest that it is extremely likely that 1% and .1% parts are made on the same production line using the same processes and equipment. After 100% testing the 1% parts may be those that fail to meet the .1% tolerance.

Of course it is possible that, when producing higher grade parts, the same production process may be operated slightly differently with more rigorous control - eg. operating more slowly, controlling temperature more closely etc. I'd think that unlikely however. Testing time is an expensive commodity so I'd expect a 1% manufacturing run (if such exists) would simply test for 1% limits. The tester would be capable of rather better accuracy but to do so would likely have to operate more slowly to allow more settling time.

If they are made the same way their load life stability should not be any different.

My first choice is the prime divider resistors, picked from a local distributer’s range. https://uk.farnell.com/vishay-foil-resistors/y145310k0000t9l/res-10k-0-01-600mw-radial/dp/2820505

The starting place for selecting the resistors is surely to specify the requirments? Eg. What short stability (time and temperature) is required of each resistor, to enable the overall specification (not stated) to be met? From that you can search for suitable resistors that would enable you to meet your goal - assuming they actually exist that is.

Choosing decent components, at prices that you believe to be acceptable is really the wrong way of going about it. Having said that, as you haven't stated a target spec you can of course attempt to calculate the performance of the kit using the selected parts and decide then if it is acceptable.

It has been stated many times here that you have to treat Vishay foil resistor specs with a certain amount of skepticism, especially with respect to the temperature coefficient specs. They are good resistors, but I suggest you search these forums thoroughly before spending a lot of money on foil resistors. Andreas has done a lot of resistor testing so do look for and read his thread.

For this distributor the choice would seem to be a POMONA 3750

That is a gold plated brass part which will have rather high thermal EMFs which could contribute significant errors. Much better would be the 3770 gold plated copper parts; they aren't much more expensive.

[Lesolee]

A pretty expensive piece of kit you have no use for - are you intending to actually build it or is this just a thought exercise? As a design exercise it would be seriously compromised if you don't have any means to test its performance, otherwise it could just as well be an exercise in how not to go about designing a high precision piece of test kit.

It's a thought exercise. The "interesting" thing about an absolute divider is that it is "too good" to calibrate. You will note in Hamon's original 1954 article it was better than the available standards. So you have to then compare against what is avaialble to build up confidence. Obviously you could just send it out for calibration, but that would cost quite a lot. Only practical for a commercial design.

If they have the same part number I'd suggest that it is extremely likely that 1% and .1% parts are made on the same production line using the same processes and equipment. After 100% testing the 1% parts may be those that fail to meet the .1% tolerance.

Of course it is possible that, when producing higher grade parts, the same production process may be operated slightly differently with more rigorous control - eg. operating more slowly, controlling temperature more closely etc. I'd think that unlikely however. Testing time is an expensive commodity so I'd expect a 1% manufacturing run (if such exists) would simply test for 1% limits. The tester would be capable of rather better accuracy but to do so would likely have to operate more slowly to allow more settling time.

If they are made the same way their load life stability should not be any different.

Right, but if you look at the load life stability of a typical 1% resistor it will probably be 1%. The load life stability of (good) 0.1% resistors should be better than 0.2% or there is little point. They should not be of the same design. That's the whole reason to buy precision resistors. Otherwise you could just calibrate out the error.

The starting place for selecting the resistors is surely to specify the requirments? Eg. What short stability (time and temperature) is required of each resistor, to enable the overall specification (not stated) to be met? From that you can search for suitable resistors that would enable you to meet your goal - assuming they actually exist that is.

Choosing decent components, at prices that you believe to be acceptable is really the wrong way of going about it. Having said that, as you haven't stated a target spec you can of course attempt to calculate the performance of the kit using the selected parts and decide then if it is acceptable.

I agree for a commerical design. For a hobby project the starting point can be "what can I afford". Clearly I have in mind the order of magnitude of acceptable error. It can be adjusted to the range around 1ppm. Would it reach such a spec when thermals are taken into account? That's more difficult to assert for a paper exercise.

[Lesolee]

For this distributor the choice would seem to be a POMONA 3750

That is a gold plated brass part which will have rather high thermal EMFs which could contribute significant errors. Much better would be the 3770 gold plated copper parts; they aren't much more expensive.

That's a good catch. Thanks. 

From National Instruments:

[Conrad Hoffman]

And that's the reason you want clean copper!

[Kleinstein]

It takes a lot of effort to adjust the individual stages. One point is that for the initial run there is some interaction and it may need 2 or 3 adjustments each. But this is still the easy part. Even with good resistors the stability will not be much better than 1 ppm over a longer time. So it would need an adjustment before each use. This needs a stable 10 V and 1 V source. As the 1 V source is floating this would need a separate low noise, low drift reference (e.g. Fluke 734 class). Even than there is the noise of the 2 references that may limit the accuracy and speed of the adjustment.

In comparison the Hamon type divider is far less critical. The 752 may not be best implementation, but the idea behind it is superior. It does not need 2 high grade reference sources for the adjustment, but just the null meter. In addition the adjustment before use is much faster (only 2 or 3 points instead of 10).

With some extra current sharing resistors one could reduce the effect of the switch resistance quite a bit. I don't know for sure the 752 includes this, but between the lines it looks like it does. So the 752 may be better than the simplified picture. This may need some additional adjustment, but this is not as critical and could be a once at production point. One could argue this may need a check / calibration from time to time (e.g. every 10 years or so).

There is no need for clean copper - a thin gold layer would not have much temperature difference across and thus not much thermal EMF.  However something like brass (for the whole terminal) can be a bad idea.

[splin]

If they are made the same way their load life stability should not be any different.

Right, but if you look at the load life stability of a typical 1% resistor it will probably be 1%. The load life stability of (good) 0.1% resistors should be better than 0.2% or there is little point. They should not be of the same design. That's the whole reason to buy precision resistors. Otherwise you could just calibrate out the error.

I think you are misunderstanding the resistor specs. For example, look at these NIC components NTR series precision Nicr thin film resistor specs:



Yes each specification is tighter for Tol <= .05% than for higher tolerance, but note that the typical values, for tol > .05% parts all comfortably meet the <.05% specs. That's not surprising as the lower tolerance parts, being the same parts made using exactly the same processes will have much the same characteristics as the high tolerance parts.

All it means (I believe) is that higher QC levels will be applied to the high spec parts to ensure they will meet the better specs. Obviously most of those specs are not for individual resistors but will be batch tested - eg. load stability.

Of course the lower tol parts won't be guaranteed to meet all the specs of the high tolerance parts but I'd expect the vast majority will do so - unless someone has good experince to the contrary. It is of course quite possible that batches that don't meet one or more of the <=.05% tol specs may be sold as > .05% tol parts (even if they are actually <= .05%) but I doubt that happens often.

The production process will, IMO, be set up to ensure they can produce parts such that the vast majority will meet the highest specifications, selecting only for the most variable characteristics which are the resistor tolerance and temperature coefficient.

[EDIT] Note the most interesting aspect of the attached specs are how the typical specs vary for the different resistor sizes. This isn't something I've seen in a resistor datasheet datasheet before and some of the numbers are surprising (to me at least) - especially that the 0805 numbers are rarely the best and often worse than for 0402 and 0603.

[Lesolee]

It takes a lot of effort to adjust the individual stages. One point is that for the initial run there is some interaction and it may need 2 or 3 adjustments each. But this is still the easy part.

Conrad mentioned interaction, but without specifics. I was too thick to catch-on 

I was thinking 0.01% resistance change would have almost no effect on the current. But each stage I increase by 0.01% increases the current by 0.001%, and that increased current directly affects all other stages without any desensitisation. It ideally needs to be calibrated from a constant current source! 

I think that constitutes a gotcha. 
Well spotted guys.

[Conrad Hoffman]

I didn't work it out exactly, just gut feel. I still think that some finite number of calibration passes would take care of it.

I once had a boss who didn't have a clue about technical details. In spite of that, he'd walk into the lab where we were having a problem and point to something and say, "what about that?" More than half the time he was pointing right at the problem.

[Kleinstein]

The interaction between the resistors in the dividers should not be that bad. A 1 % change in one resistor would require to change the others by some 0.1% . So after one run of adjustments expect the settings to be better by maybe a factor of 5 or 10. So it is a finite number of adjustments needed. So maybe change every pot 2 or 3 times if the initial error is not so large.
With some extra math (e.g. only change the voltage by 90% of what is needed to be spot on, things could get even better).

The real weak point is that one needs 2 very stable references. So the divider alone is only a small part: one also needs those 2 references (possibly better than an LTZ1000), including one with a divider down to 1 V. One would also need to adjust that ratio to work with a conventional null meter. So the shown divider would be only a small part of the solution.

The more practical way would be to adjust the resistors to be the same as the neighbor, with a resistor bridge, that one would move around. One would still need to include those extra resistors to compensate for contact resistance.

[e61_phil]

Interesting thread. I missed it until now.

The question ist, what do you want to achieve? I'm not a fan of adjusting something, if measurement is enough. Therefore, I often used my SR1010-1k to verify my 1V against 10V. The resistors in the SR1010-1k are very equal. Equal enough to not suffer from INL issues of the DMM. To verify the 1V range of my DMM (34401A or 3458A for example) I applied 10V to 10 resistors in series and measured the voltages on each resistor. The sum of all voltages must be equal to the sourced 10V (sourced from the calibrator (Fluke 5440B) with 4 wire connection). As long as the DNL of the meter, the input current and the leakage to ground is ok, it is an easy method to make a 10:1 transfer. With 10x 10k resistors it should also work for a 100V to 10V transfer.

It is still a lot of work and one have to be careful to not heat the connectors too much by touching it with the fingers, but nothing to adjust.

[Lesolee]

I'm not a fan of adjusting something, if measurement is enough.

As compared to the rest of us, who (apparently) just like to fiddle with pots. 

Therefore, I often used my SR1010-1k to verify my 1V against 10V. The resistors in the SR1010-1k are very equal.

I have attached the datasheet so people don't have to hunt around for it. A very nice piece of kit.

I see they have not (leakage) guarded anything because they claim >1E12 leakage. But in this case it is nice because you can just apply 100V to the whole chain, and provided you measure less than 1mV into a 10M ohm input DVM that 1E12 is then proven at any point in the future. It's something you can't do with a complete instrument like the 752A, with all its switches and leakage paths.

"Each transfer standard contains twelve equal value precision resistors connected in series by specially designed true 4-terminal junctions. These special junctions assure that a 4-terminal measurement of a series of resistors agrees with the sums of the individual resistors in the series."

The Guildline 9350 also mentions tetrahedral junctions, with a paper by Chester Page, but there are no detailed descriptions or pictures. I need the hobbyist's guide to making your own tetrahedral junction. Sounds like a job for Conrad.

I like the SR1010-1K, but how much are they (rough estimate)? I am guessing £3k.

[e61_phil]

I think you don't need a tetrajunction between the resistors. Just make sure you have a proper connection to the series connection of the resistors. I think it should be enough to build your box without all the trimmers. Better TC than the SR1010 would also be nice.

There are also some papers about a step-method. In that method you use a (known) 10V source which is switchable (0V and 10V), a calibrator and a DMM with good DNL. In the end you add up your 10V source n times. The nice thing here is, you can run it fully automated.

https://ieeexplore.ieee.org/document/6399596

[Lesolee]

I think you don't need a tetrajunction between the resistors. Just make sure you have a proper connection to the series connection of the resistors. I think it should be enough to build your box without all the trimmers.

The basic resistors are 0.01% (100ppm). I notionally wanted 1ppm. Adjustment is essential, especially as the main resistors will drift by more than a few ppm over time.

In theory, with a good enough bit of kit, each stage could be measured, and the values typed into a suitable (clever) piece of software so each stage only needed to be adjusted once. But that somewhat defeats the idea of having a simple easily-calibrated absolute divider.

>I think you don't need a tetrajunction between the resistors.
Agreed. That was for other applications. Such a divider as this, automatically has 4-wire sensing, since there is no current in the sense leads.

[Kleinstein]

A tra junction is not that complicated and can be be done DIY. There are several possible solutions, two simple ones use a equal sided triangle or a small disc of plate copper with contacts at the 3 corners or equally spaced at the edge. The 4 th contact would be in the center of the disc or triangle.  If needed on can check the 4 wire resistance and do some trimming of required.

Exactly equal resistors would be nice and easy to use, but in times of pocket-calculators it would not be so bad if if one would get an accurate divider that is slightly off integer ratio. An accurate 1:10 ration is nice, but a stable 1:9.9 is nearly as good.

[e61_phil]

I think you don't need a tetrajunction between the resistors. Just make sure you have a proper connection to the series connection of the resistors. I think it should be enough to build your box without all the trimmers.

The basic resistors are 0.01% (100ppm). I notionally wanted 1ppm. Adjustment is essential, especially as the main resistors will drift by more than a few ppm over time.

The idea is to not adjust the resistors at all. They should be closely matched to give very close readings on the DVM to not suffer from INL issues (100ppm should be fine).

Just do it like this:

Apply your known 10V. Switch your meter into the 1V range. At this stage the calibration of the meter doesn't matter and the absolute values of the resistors also doesn't matter.

Now, you start measuring the voltages above all resistor. All the readings are close to each other (~1V). In the end you sum up all the readings. The error of the sum regarding to your known 10V is the error of the meter. At this point you have derived everything what is interesting. You know the exact gain of the 1V range of the meter and you also know the ratio of your divider. That works without adjustement and a 6.5 digit meter is sufficient for roughly 1ppm of output. You don't need a special meter. Just DNL and isolation should be good.

[MegaVolt]

I need the hobbyist's guide to making your own tetrahedral junction. Sounds like a job for Conrad.

I like the SR1010-1K, but how much are they (rough estimate)? I am guessing £3k.

ebay 300$

[Conrad Hoffman]

Been there, done that. Just some copper plate and a hacksaw. There should be another thread here from way back with some simulations using FEMM for current flow. Ahhh, here... https://www.eevblog.com/forum/metrology/zero-ohm-diy-4-wire-standard/msg1079328/#msg1079328

[splin]

You might like to take a look at this thread:

https://www.eevblog.com/forum/testgear/dmm-linearity/msg698554/#msg698554

Do read (or at least speed read) the paper linked in reply #3

Then read this thread which links to the above, especially zlymex's responses starting at reply #18:

https://www.eevblog.com/forum/metrology/which-is-the-next-best-ratio-measurement-device-after-the-3458a/?nowap

[Lesolee]

Phew! There is so much to read. I have been clicking on the links, that lead to links, ... It's hard to know where I've been.

There's a wealth of expertise on this site, and lots of generous contributions of photos and measurements.

Much appreciated 

[dietert1]

The document of Jonas Wissting (Wiss) explains very well the mathematics that you need to arrive at better accuracy than each single resistor in the divider has. I think Andreas used a similar method with his ADCs.
One thing that i would recommend, though: Add some extra resistors to have roughly the same source impedance on each node of the divider. Otherwise there may be minor errors due by the small current the DMM input takes. The middle of the divider chain determines the minimum source impedance.

Regards, Dieter

[Lesolee]

Add some extra resistors to have roughly the same source impedance on each node of the divider.

My divider already had impedance balancing resistors. The difficulty is that the SR1010 allows 4-wire measurements of each individual resistor, which makes setting it up as a divider much easier.

I also note that there is an adjustable SR1010 with 100ppm adjustment, almost exactly like my effort.



Source balancing resistors and 4-wire setup of the individual resistors are mutually exclusive, since the balance resistors are so large compared to the divider resistors. The required I+ compliance of a 4-wire ohms measurement would be prohibitive (and also another error source).

I downloaded the Wiss paper, but I have (unusually) some pressing domestic issues to resolve.