A Low Cost OSHW Voltage Calibration Reference Project

[rhb]

No I don't have IEEE access.  I'd be grateful for any papers you can send me.   I'll send a PM.

The Vishay paper was quite interesting, but the analysis depends entirely on the behavior being linear on a log plot.  As noted, that may not be the case.  This is where the sparse L1 pursuit comes into play.  One can reasonably compute 100,000 or more possible curves based on physical models which do not follow the  Arrhenius’  equation and then select the best solution.  The Vishay paper employs the analysis I was taught in grad school 30 years ago.  There's nothing wrong with it.  But Donoho and Candes discovered something better.  Having spent the better part of 3 years studying the mathematics, I'd like to try it out on some practical problems that either have not been tried or have not reached COTS status.

The point of this is to substitute  non-recurring engineering cost for BoM costs.  This is an outgrowth of @svenskelectronik's desire to promote OSHW.  I don't have anything to contribute to classical designs using precision components.  I do have something to contribute to device modeling if that would allow using lower cost parts.

This is just a side venture for me.  My primary effort is a compressive sensing DSO based on COTS Zynq based instruments. I have almost all the infrastructure for that in place.  The big obstacle at the moment is having several days free to devote entirely to  MicroZed tutorials.  Mathematically I know what I need to do, but I have no FPGA experience so I need to learn that first.

I don't mind discussing compressive sensing with someone who is willing to actually read the papers and has a solid grasp of traditional analysis, but I discovered to my dismay with the DSO project that most will just spout dogmatic opinion and no amount of time spent explaining the matter is of any use.

[ArthurDent]

Although I'm fully aware of the 'knack' of learning to fly reference mentioned above, I don't think it applies here.

What I believe is that if you try to build a relatively great car by just using cheap parts you're more likely to end up with a Yugo than with a Rolls.

[mycroft]

Please, post the links. Some members may have access to IEEExplore.

rhb, do you have access to IEEExplore? I ask because not everyone does. I did a quick search and there look to be some good papers there I could send you a link to.

[zhtoor]

Although I'm fully aware of the 'knack' of learning to fly reference mentioned above, I don't think it applies here.

What I believe is that if you try to build a relatively great car by just using cheap parts you're more likely to end up with a Yugo than with a Rolls.

i also agree, the "knack of flying" metaphor probably does not apply here,
more likely would be building a car with electronic ignition vs. mechanical ignition,
and not a Yugo vs. Rolls.

-zia

[ArthurDent]

My reference to the "knack of flying" metaphor has a lot to do with my log-in name and very little to do with its applicability. 

[BNElecEng]

Here are a few links to papers I found interesting about factors that affect resistor stability:
http://ieeexplore.ieee.org/document/6898501/
http://ieeexplore.ieee.org/document/5544765/
http://ieeexplore.ieee.org/document/676956/
http://ieeexplore.ieee.org/document/850998/
http://ieeexplore.ieee.org/document/546537/
http://ieeexplore.ieee.org/document/278563/
http://ieeexplore.ieee.org/document/6250962/
http://ieeexplore.ieee.org/document/6513303/

This rabbit hole runs very deep. If you already have access to IEEExplore, search for the term "standard resistor" and you'll get a few hundred hits.

[ch_scr]

So on one hand you propose to make a reference and calibrator with cheap components, based on the other hand on (nice looking) data you get from references that are built with high stability components?
I believe you need data from references with low stability components and base your assumptions on that.
This just crossed my mind, i do not want to discourage the general idea.

[dl1640]

If a few ppm can be achieved under $50 for a calibrator why would one need Fluke?

I'm not saying it is impossible to do it, but how is reliability?

You'll need even more expensive equipments to test the "cheap" components and designs...

[Kleinstein]

The idea of using mathematical ways to correct errors instead of using expensive parts is a good idea. However with predicting drift this is difficult as it takes a very long time to verify the models or only determine the parameters, especially if many processes (and thus more parameters) are involved. So the math can fix quite some errors (e.g. Temperature effect, maybe more than just linear), but with to many factors to compensate it just gets impractical to find a suitable model, as the time needed goes up faster than linear.

It might be a surprise to someone not used to it, but a simple resistive divider can become quite a delicate part when it comes to high precision. Something like a TC could be compensated, but resistor quality is more than just the TC. However the TC is just the easy part and thus used in data-sheets. The difficult parts are those you can't easily put into simple numbers.

There are alternative ways to divide down / scale a reference voltage:
1) a PWM divider
2) feedback through an ADC  (the gain stability of something like an LTC2400 is not that bad compared to similar priced resistors)
3) a transformer
4) capacitive divider / charge pump

[hwj-d]

So, gradually, the whole thing visibly becomes what it actually is, a joke 

[ArthurDent]

 The idea of modeling different variables affecting overall accuracy to predict future performance isn’t new or confined to volts. HP used this idea in their Z3801 GPS frequency standard using their ‘SmartClock’ technology back around 2000. The idea was to continually monitor the variables used to discipline a 10 Mhz crystal oscillator used in the unit compared against the GPS 10 Mhz reference and use that information to predict how to compensate the local oscillator in the future if the GPS signal was lost.  It took a long time for the unit to learn the ways the different variables affected performance but the longer the unit was on the better the prediction was and if the signal was lost the algorithm did a pretty good job of keeping the 10 Mhz oscillator on frequency for up to 24 hours. When the signal was lost the unit was no longer making continual corrections and had to use its ‘best guess’ of how time, temperature, aging, etc., were affecting the performance at the moment the GPS reference signal was lost and the oscillator went freewheeling. HP realized that as soon as the signal was lost the accuracy was going to get worse and worse and the spec on holdover was for 24 hours and this was with one of the best commercially available oscillators at the time.
 
 If you try to design a voltage standard with elaborate microprocessor control using less accurate parts it will kind of work, and I don’t doubt that, but unless it is continually referenced to a standard except during a short period of time when you are using it as a transfer standard, the uncertainty seems to be a big problem.  The butterfly effect so elegantly demonstrated in Homer Simpson’s toaster time machine episode shows the difficulty in predicting future results.

[zhtoor]

So, gradually, the whole thing visibly becomes what it actually is, a joke 

"What can you do, thought Winston, against the lunatic who is more intelligent than yourself,
  who gives your arguments a fair hearing and then simply persists in his lunacy?"

-George Orwell 1984 part 3 chapter 3

[rhb]

I read a number of papers yesterday and looked at some of TiN's data.   I've had a long think about the system this morning.

Error terms I have identified so far:

temperature
pressure
humidity
age
thermal gradient
current level
surface leakage
resonant modes in the enclosure

The errors introduced by changes in temperature,pressure and humidity have demonstrated hysteresis, particularly affecting the resistors.  As a consequence, to mathematically correct for errors they introduce would require a complete record of the environmental changes.  It would also require developing models which would require an extraordinary amount of data.  The effects are near linear with small hysteresis for small excursions, but quickly become problematic. The most appropriate means of addressing these is to control the environment as tightly as possible.

While not appropriate for the requirements posited, in general a thick wall enclosure machined from a block of 1008 low carbon steel, filled with dry nitrogen and sealed is the most economical and easiest option to fabricate.  The thick walls have the additional benefit of providing good magnetic and electric shielding.  Such an enclosure should be annealed after fabrication which requires a very specific temperature cycle over 1-6 hours.  Unless one happens to have the requisite machine tools and furnace, such effort is only relevant to an ultra precision reference because of the cost

If one is willing to forgo very tight pressure control, a lightweight steel enclosure can serve for controlling temperature and humidity at an economical cost while still providing some damping of pressure changes.  An American pattern .50 BMG ammo  should provide a satisfactory  enclosure, allowing plenty of room for insulation and a large battery for hot shipped travel standard use.

Thermal gradient and current levels are probably first order effects.  Irrespective of the enclosure temperature, device heating leads inevitably to thermal gradients.   Thus it is useful to minimize currents as much as is consistent with electrical noise. In the case of a buried zener reference such as the LM399, minimizing the heater current will serve as a better proxy than using a temperature sensor.  However, such an approach may necessitate logging temperature so as to correct for hysteresis and aging effects upon the resistors.

Current levels are a significant factor both in resistor aging and hysteresis.  The latter can be avoided by avoiding changes in current level.  The effect on aging must be dealt with mathematically.

Surface leakage is not something I have any real sense of and undoubtedly varies widely depending upon board cleaning, materials etc.  That will require some investigation.  It may well be a 3rd order error term that can be neglected.  For a high precision device I should expect that a ceramic substrate would be desirable.

Zener diodes are intrinsically broadband noise sources.  Placed in a metal enclosure will it will develop resonances controlled by the enclosure dimensions. Without adequate filtering this can interact with the sampling to produce errors.  While estimates are readily made of the frequencies, power levels and radiation efficiency have a dominant effect.  This argues for a PCB layout which minimizes radiation.

The level of noise which I have observed in the data from TiN suggests to me that it might be better to forgo the PLC sampling and collect measurements at the maximum rate the DMM can make and then use a Fourier transform to determine the DC value.  If one discards all but a random subset of the data, then the requirements for compressive sensing are met and aliasing does not take place.  The use of the Fourier transform has a rather significant advantage in that it  should permit making readings to 8.5 digits with a 5.5 digit DMM by taking a sufficiently long sample.   There are a number of mathematical constraints which must be satisfied, but this is often the case. 

I think I should note that one can acquire data with arbitrary amplitude resolution using a single bit ADC.  Sam Allen published a good bit of work on the subject in the '70s.  In his case he was acquiring very high fold vibroseis data (1024 channels when others were only collecting 48).  The rapid evolution of seismic recording systems overtook him and the technique is largely forgotten.  It's actually a trivial application of the work of Norbert Wiener.

As regards the choice of resistors I have nothing more to say at this time other than they need to be "good enough".  There is wide variation among manufacturers and processes in the behavior of resistors and their sensitivity to environmental factors.  I shall eventually have three LM399s running in a controlled chamber which use low spec resistors.  One is running the best matched pair which had an initial resistance before soldering within 0.02%.  Temperature coefficients were not measured.

As regards the mathematics.   In pore pressure prediction a common approach is to use a reference function which is the sum of a constant and an exponential with a constant exponent.    As I had a vast amount of data I could see that such a form was not a particularly good fit.  It looks pretty good with a small data sample from a few wells, but not when you have thousands.  Ultimately I found that I could get a much better fit by using a function of the same form, but with a polynomial exponent.  Were I to do the same project today, I should construct a vast array of curves calculated from the physics of fluid flow in porous media and then use a sparse L1 pursuit to find the best solution.  None of the papers I've read to date suggest that any of the authors knew how to do the sort of approximation I was doing over 10 years ago.  There may well be a group which has.  If so I look forward to reading their work.

[hwj-d]

The butterfly effect so elegantly demonstrated in Homer Simpson’s toaster time machine episode shows the difficulty in predicting future results.

So, we present a new nickname to rhb 

[eurofox]

While not appropriate for the requirements posited, in general a thick wall enclosure machined from a block of 1008 low carbon steel, filled with dry nitrogen and sealed is the most economical and easiest option to fabricate.  The thick walls have the additional benefit of providing good magnetic and electric shielding.  Such an enclosure should be annealed after fabrication which requires a very specific temperature cycle over 1-6 hours.  Unless one happens to have the requisite machine tools and furnace, such effort is only relevant to an ultra precision reference because of the cost

I have the intention is to apply a thermal treatment (annealing) to remove the mechanical stress after the machining work, I have a oven and equipment for this as well the knowledge to do it.

With respect to filling with inert gas, it cross my mind but somehow at least in my case I have a buffer to output 10V and need to be tuned in the metal container after aging, this mean there need to be an small hole just above the trimmer and need to be closed hermetical, not easy to do with gaz ....
I will mill under the PCB an area to place 2 packets of silicate gell, they will suck the humidity that could enter te container during the trimming job.

eurofox

[rhb]

I have the intention is to apply a thermal treatment (annealing) to remove the mechanical stress after the machining work, I have a oven and equipment for this as well the knowledge to do it.

With respect to filling with inert gas, it cross my mind but somehow at least in my case I have a buffer to output 10V and need to be tuned in the metal container after aging, this mean there need to be an small hole just above the trimmer and need to be closed hermetical, not easy to do with gaz ....
I will mill under the PCB an area to place 2 packets of silicate gell, they will suck the humidity that could enter te container during the trimming job.

Braze an inner tube or tubeless tire stem to the hole for access to the trimmer.  Then use a metal cap and gasket to seal it after adjustment.  It does require having a tank of dry gas around, but I suspect you've got a bottle of argon or argon/CO2.   Nitrogen is just cheaper.  Assuming everything is dry, the gas just displaces any moist air.  It doesn't need to be under pressure, though it will if the atmospheric pressure drops.  I'm suggesting a tube you can poke into the unit to inject the gas near the bottom.

[eurofox]

I have the intention is to apply a thermal treatment (annealing) to remove the mechanical stress after the machining work, I have a oven and equipment for this as well the knowledge to do it.

With respect to filling with inert gas, it cross my mind but somehow at least in my case I have a buffer to output 10V and need to be tuned in the metal container after aging, this mean there need to be an small hole just above the trimmer and need to be closed hermetical, not easy to do with gaz ....
I will mill under the PCB an area to place 2 packets of silicate gell, they will suck the humidity that could enter te container during the trimming job.

Braze an inner tube or tubeless tire stem to the hole for access to the trimmer.  Then use a metal cap and gasket to seal it after adjustment.  It does require having a tank of dry gas around, but I suspect you've got a bottle of argon or argon/CO2.   Nitrogen is just cheaper.  Assuming everything is dry, the gas just displaces any moist air.  It doesn't need to be under pressure, though it will if the atmospheric pressure drops.  I'm suggesting a tube you can poke into the unit to inject the gas near the bottom.

I do have a TIG welding equipment and of course pure argon is available and needed for the TIG welding, is maybe an option. 

eurofox

[rhb]

hello,

if i may suggest a simpler approach first, that would be:-

1. take a standard LM399AH (or LM329AH) the hermetically sealed versions, as a reference element.
2. do not use the heater in case LM399
3. no resistive dividers, use another reference (auxilliary, maybe another LM399) to provide the zener current or bootstrap, direct 6.95V ref would do
4. use a water (gallium) double point cell to locate the electronics in (possibly coated with conformal coating and submerged in compatible oil)
5. now start measuring the reference after the initial couple of 100 hours of operation
6. fit the initial model and proceed where the data leads you

I have 3 basic-lm399 references I was given by @cellularmitosis, so my intent is to use them.  I have a *lot* of work to do on EMI mitigation.  And even more work to do to log data automatically.  I'm looking for the inflection point on the price performance curve, so I want to work my way along.

I have to have some form of buffer amp,so the OP07s that were provided seem a good starting point. Comparing 3  references with a $12 BoM seems to me a useful data point to collect.  Also he is running a slew of LM399s himself.  I don't know if they are all the same design, but I'm sure at least some are.

The LM399s he gave me are used, so I don't think I can determine the  shape of the aging function from them.  For my purposes the first few hundred hours are probably quite important.  Once the rate of change starts to flatten out it becomes difficult to identify the correct function and coefficients.  Correctly finding parameters from measurements near the asymptote is nearly impossible if there is any noise.  The result is that  the error becomes larger over time than it would be if one had the earlier data.

@eurofox  LoL  I was pretty sure I had it right.

[Jay_Diddy_B]

Hi,

What are you going to measure the LM399 reference with during the characterisation phase? you need an LTZ1000 class instrument. You also need low thermal leads etc.

The Solartron 7081 uses this technique in the reference. There are two reference diodes in series in the DMM. A pile of reference diodes were characterised, for several months, separately then pairs were selected, so that the combination has some desirable traits. The meter then compensated for ambient temperature using software. I have one of these meters and it is horrible. It may be o.k. in a 23C calibration lab. It takes a long to stabilize in a normal environment, compared to a heated reference which is stable in a minute or two.

Regards,

Jay_Diddy_B

[MisterDiodes]

RHB:

Not trying to discourage - but more areas you might want to have a think about:

What are your plans and equipment list for a robust measuring system for checking Vref/ resistor drift with low uncertainty??  Groups of LM399's still drift, and if you've ever tried this in the real world any group over 9 begins to offer very minimal returns on noise reduction - and don't forget every resistor in the averager contributes noise as well.

Preferred method of measuring a resistance most accurately is via a resistance bridge, manual or automatic, using a calibrated standard resistor as its reference.

More typically for measuring down to low PPM you'll need something like an 8.5 digit meter, and because those are not long term transfer standards you'll need that backed up by typically 3ea 732a/b Vrefs (at least one in current calibration) and/or SR-104 for uncertainties down to around 2ppm...IF you're interested in calibrated & traceable absolute value measures.  For sure you'll need a system of that caliber to verify long term drift of a Vref accurately if you're claiming 4ppm /yr drift rate.

Always keep an eye on the daily drift & uncertainty of your measuring equipment while you're measuring your Vrefs & resistors as well - if you're trying for  Vref of 4ppm / year on your calibrator box, you'll need sub-ppm drift per 24hrs, and that's something to consider even on a 3458a (check 24hr uncertainties):

http://literature.cdn.keysight.com/litweb/pdf/5965-4971E.pdf

Plus you'll want a low thermal EMF scanner system to test LOTS of resistors of different values, power levels, environmental effects and across several manufacturing batches...And so on.  This could take years.

It still sounds a lot easier to me to buy a few good resistors to put in your Cal box and achieve a more robust, lower noise and more stable end Vref result - but to each his own.

[zhtoor]

hello,

could you please elaborate on this?

The use of the Fourier transform has a rather significant advantage in that it  should permit making readings to 8.5 digits with a 5.5 digit DMM by taking a sufficiently long sample.   There are a number of mathematical constraints which must be satisfied, but this is often the case.

best regards.

-zia

[rhb]

There are a couple of considerations;

If we take the data into the frequency domain then we can characterize the 1/f noise at moderate frequencies to estimate the noise at lower frequencies. That permits setting bounds on error which are tighter for any given measurement period.  There are other methods such as plotting Allan deviation that serve a similar function.

The main reason is it  avoids the truncation and aliasing of signals which are not related to the power line frequency by integrating the measurements.  Instead one takes a long sample, applies a Gaussian taper at the edges and Fourier transforms the series.  The DC value of the transform is the least squares (L2) estimate of the true value.

I would attribute that not being done in the 3458A simply to historical practice in precision voltage measurements.  It's quite easy to build an analog gate and counter  that triggers on the mains zero crossing.  Almost limitless processing power came along, but seems to  not have  permeated precision voltage measurements yet.  Customers are expecting PLC gating, so Keysight provides it.

Going beyond classical Fourier analysis an interesting application of sparse L1 pursuits would be to discard about 80% of the samples collected at regular intervals.  That completely eliminates the need for an anti-alias filter ahead of the ADC thus eliminating the errors associated with those components.

At present it appears that I can characterize a voltage reference and buffer amp with a first order  linear approximation:

expected_value = vref_initial_value + ref_aging + vref_1/f_noise + vref_temp + amp_initial_offset + amp_aging + amp_temp + r1_initial + r1_aging + r1_temp + r2_initial + r2_aging + r2_temp + r3_initial + r3_aging +r3_temp

All of the terms in the linear approximation are non-linear.  However, a sparse L1 pursuit will allow selecting the best choice for each from a very large number of possible non-linear approximations for each term.  That's the reason that I have a rather more optimistic expectation than others.  Aside from being a good bit of work to setup the equations the first time, I see no obstacle to having 10,000 or more approximations of each term above from which to choose.  The actual computation associated with a calibration would take at most a few minutes using a sparse L1 solver on a PC.  Prior to the work of Candes and Donoho, the only known solution was an L0 exhaustive search which is NP-hard.  The universe would end before you found a solution. For the case stated above there are 10,000**16 total choices for the solution.  That is a *very* large number.

Hopefully this will make the project motivation a bit more clear. My primary goal is to improve precision voltage reference performance.  The low cost, OSHW design constraints are to make a better standard available to hobbyists.  The mathematical solution and software applies equally to both a national lab class instrument and the hobby instrument.  I don't need a fancy set of references.  If I can calculate the expected value of the differences among 3 references which is constant with the bounds set by the 1/f noise and tighter than current estimation techniques my work is done.  I *may* build a higher precision reference, but I don't need it to develop the mathematics.

[TiN]

So what you need to get started?

[hwj-d]

So what you need to get started?

A big kick, to come away from mirror fighting   

[rhb]

Mostly free time.  Long term data such as Andreas has presented, but in ASCII.  I can  do quite a lot with the data you have collected already. I've only spent a few hours with the data.  It will need weeks to fully exploit.  This is looking for shadows within shadows.  Or peeling layers from an onion to use Bob Pease's metaphor.  Identify and correct the biggest factor, then the next biggest and so forth.  Bob wrote about it in the context of measurement probing noise, but it applies here as well.

For each of the terms which are a function of another variable I need to get a curve shape which is a close approximation to the device behavior.  The high precision resistors are carefully engineered to have nearly linear tempcos.  While very useful in practice, it's very hard to accurately find the underlying curve form.  Some of the better low end Vishay metal films  with low sensitivity to humidity and mid-range tempcos are probably a good choice for establishing the functional form.  Looser tempco precision metal foil also.  Some precision foils under varying pressure.  In particular, run some metal foils from high atmospheric pressure down to 40,000 ft pressure.  That would be very useful for applying this to a high precision traveling reference.  There is a known and documented hysteresis effect.  But I think it's just documented for increases in pressure, not decreases.  It would be very useful to know if this is a one time  change or if the change is cumulative with the number of pressure cycles.

I can't see any reason we can't have sub-ppm traveling standards.  I can think of *lots* of reasons we don't.  To date the efforts have been focused on making better parts.  I think we are pretty close to the limit of what can be accomplished doing that.  So we need to better describe how and why references change as a consequence of traveling.  If we can accurately describe the cumulative effects of temperature and pressure cycles and age we should be able to correct for it.

Success is reducing the residual error after correction to quantum level noise.

The flat aging curves of the used LM399s I have will make finding the functional form from those difficult if not impossible. Once I'm set up and able to collect good data, I'll replace all the LM399s with new devices so I can measure the first 2000-3000 hours.  A sample of 3 will have a large variance, but it's better than what we have now.  A modest amount of cooperation from Keysight, Keithley et al in collecting early aging data on a large number of voltage references would nail down the mathematical form of the aging curve quite tightly.  However, that involves having tens of thousands of aging curves.

Sparse L1 pursuits are not widely known among the professionals I know.  I can only think of a handful of seismologists.  So I see an opportunity to make a significant contribution to metrology.  I think it would be pretty neat for a bunch of amateurs to pull something like that off.

In 1948 Scientific American published a long series of articles about the construction of a new ruling engine under the leadership of John Strong.  In the article it was mentioned that a number of amateurs had destroyed their health and wealth attempting to build a ruling engine.  In 1958 an Amateur Scientist column described a ruling engine built as a hobby project by a gentleman in England.  He was a professional laboratory instrument technician and builder, so "amateur" may have been a bit of a stretch.  Strong's team followed traditional practice,  A screw made to an accuracy of the order of a millionth of an inch, a vast room size vat of oil held at constant temperature. A human in the room for too long would ruin a grating by perturbing the oil bath temperature.

The amateur project used a cast iron box in which he placed a cadmium lamp interferometer, the best screw he could readily obtain and the ruling carriage, etc.  He counted fringes to position the carriage.  Stick slip made the errors random, so the periodic errors that produce Rowland's ghosts were absent.  Despite being in a sealed cast iron box, he was limited to certain times of year when he could make gratings and the machine had to be in a room on the north side of the house.  But he made gratings reported to be as good as any and better than most.