Most predictable resistors and capacitors

[rhb]

What are the most predictable parts?  I intend to model temperature coefficient and aging, so I don't care about those (within reason).  What matters is that the part conform to the model.  I have in mind enclosing R&C with a thermistor and possibly a heater with silicone thermal grease to help equalize temperatures.

My intent is to use the RC charge-discharge curve to measure ADC, DAC and other errors using a sparse L1 pursuit.  This has some rather astonishing mathematical properties.  However, I'll leave that for another time.

The cumulative effects of humidity changes seem to me the most obvious source of unpredictable behavior.  There may be others. Any literature references are extremely welcome.  I'd especially appreciate references to the literature not encumbered by the exorbitant IEEE paper charges.  But I should be able to access those by traveling to the nearest university which is about 75 miles.

The ultimate purpose is developing  a low cost OSHW (<$100) voltage calibrator good to 10 ppm or better over a 3 decade full scale range from 10 V to 10 mV.  I don't know if this is possible, but it seems it might be and I'm sure the exercise will be educational even if it can't be done.

A general outline of the design  is 3-4 LM399s sharing a single quad op amp with a Cortex M4 MCU with 12 bit ADC and a display that shows the output voltage for a series of steps in an R-2R ladder DAC.  The RC circuit is intended to measure ADC and DAC errors so that the MCU can correct them.  Periodic calibration data would be written to the device via a USB interface.  The purpose of the RC circuit is to make the calibration interval as large as possible.  The system would simply require being connected to a calibrator for a few minutes for updating the correction factors after a suitable warm up and be light enough to be inexpensively sent out for periodic calibration.  Something that can be economically calibrated for $10 plus postage.

This project was instigated  by the generosity  of @cellularmitosis  sending me 3 of his basic-LM399 board kits and the interest of @svenskelectronik in promoting open source hardware.  Almost everything that can be done by one person has been done.  What's left takes more than one.  Even if you have the ability, you'll forget half of it by the time you finish the other half.

Thanks for your attention.

Have Fun!
Reg

[Magnificent Bastard]

What are the most predictable parts?  I intend to model temperature coefficient and aging, so I don't care about those (within reason).  What matters is that the part conform to the model.  I have in mind enclosing R&C with a thermistor and possibly a heater with silicone thermal grease to help equalize temperatures.

My intent is to use the RC charge-discharge curve to measure ADC, DAC and other errors using a sparse L1 pursuit.  This has some rather astonishing mathematical properties.  However, I'll leave that for another time.

The cumulative effects of humidity changes seem to me the most obvious source of unpredictable behavior.  There may be others. Any literature references are extremely welcome.  I'd especially appreciate references to the literature not encumbered by the exorbitant IEEE paper charges.  But I should be able to access those by traveling to the nearest university which is about 75 miles.

The ultimate purpose is developing  a low cost OSHW (<$100) voltage calibrator good to 10 ppm or better over a 3 decade full scale range from 10 V to 10 mV.  I don't know if this is possible, but it seems it might be and I'm sure the exercise will be educational even if it can't be done.

A general outline of the design  is 3-4 LM399s sharing a single quad op amp with a Cortex M4 MCU with 12 bit ADC and a display that shows the output voltage for a series of steps in an R-2R ladder DAC.  The RC circuit is intended to measure ADC and DAC errors so that the MCU can correct them.  Periodic calibration data would be written to the device via a USB interface.  The purpose of the RC circuit is to make the calibration interval as large as possible.  The system would simply require being connected to a calibrator for a few minutes for updating the correction factors after a suitable warm up and be light enough to be inexpensively sent out for periodic calibration.  Something that can be economically calibrated for $10 plus postage.

This project was instigated  by the generosity  of @cellularmitosis  sending me 3 of his basic-LM399 board kits and the interest of @svenskelectronik in promoting open source hardware.  Almost everything that can be done by one person has been done.  What's left takes more than one.  Even if you have the ability, you'll forget half of it by the time you finish the other half.

Thanks for your attention.

Have Fun!
Reg

I think that you will find that the most stable resistors and capacitors are of the hermetically sealed type.  There are some Russian military surplus hermetically sealed silvered-mica capacitors and hermetically sealed PWW resistors on junkBay.  Put these inside of an oven (controlled to 0.01^oC or better) and then get them calibrated, and there you go-- some very nice standards.

Just so you know, there is a member of this forum, Ian Johnston, that already makes a calibrator such as you describe.  I looked at the design, and it looks solid to me.

[rhb]

I sat down with AoE 3rd ed this morning, so I'm rather better informed than I was.   

I've looked at Ian's device.  It's quite nice and a very fair price, but not cheap.  TANSTAFL.  For cheap (i.e. <$100), one must make some compromises.

I was just looking at part prices.  I've been led astray by @cellularmitosis on the cost of a basic  LM399 reference board.  He was *very* generous sending me 3 complete closely matched kits and declining my offer to pay for them.  He offered me a bare PCB and then threw some "extra goodies" in the package.

I spent some time this morning refining use case.

Unit
----------------
LM399
MCU
LCD display
pushbutton
USB or RS232 connection for calibration & remote control
output terminals

Operation
---------------
Pushing the button selects a tap on a divider and displays the corrected value of the output.  Output is whatever you get, not user selectable.  This is strictly for calibration with 5-10 steps per decade.

Compensation for temperature, aging, initial value based on calibration data stored in flash for LM399,  resistors and op amp based on linear programming solution

Automated calibration procedure.  Device is attached to a PC  and a precision DMM.  Prior calibration data is read from flash, measurements taken, new correction coefficients computed and results stored back to flash.

Initial calibration performed during LM399 burn in period.

[cellularmitosis]

Cool project idea!

For the R/C calibration idea, is the idea that the discharge curve can be made so smooth and predictable, that all you need to do is know the time of your measurement to a very high level of precision, and then you also know what the voltage value should be?

rhb is kind, but I should note a disclaimer: I didn't use parts from digikey for the "getting started" kit which I sent him.  LM399's are from taobao, OP07's are from tayda, boards from dirtypcb's.  About $5 cost per circuit.  Will they perform as well as digikey parts?  Who knows!  But attempting to measure the difference will lead to a deeper understanding of precision circuits (and a hole in the wallet .

[Conrad Hoffman]

For caps, you can get larger values of NP0/C0G types than in the past. They can be very stable and close to zero TC. As an example, look at the Kemet 399-5385-1-ND on Digikey. 0.47 uF, 50 V. I haven't tested that one, but it looks like a good candidate, depending on the value needed. I have some 0.01 uF Corning Glass Works (CGW) NP0 parts (long obsolete) that I've used as standards that hold withing a few ppm over long periods of time.

I'm sure the Vishay metal foils are very good, but I've used plain old Yaego 1/4 W metal films in my old Mini Metrology article standard, and the calibration is usually still within a few ppm even many years later. I selected pairs for matched TC by dipping them in hot oil. Just a few dollars for a couple hundred.

[rhb]

The idea is exactly that. There is an analytic solution for the voltage as a function of time.  So if you can measure time to a high degree of precision you have a  very accurate voltage divider.  The key is being able to write a set of linear equations for the voltage taking all the error terms into account. If you can do that, then an arbitrary precision simplex solver should provide very accurate values.  I suspect that ADC jitter would be a significant problem. Initial resistor and capacitor value and TC should not be a problem as long as they are stable. 

Sparse L1 pursuits are rather bizarre.  They solve problems I was taught you couldn't solve when I was pursuing a PhD at Austin.  The mathematical justification is *very* painful to read, but actually using the method is quite easy.  It's just Ax=y with the constraint that any combination of the columns of A are uncorrelated. You can't check for that property because it's NP-hard,  so you just try to solve the problem.  If you get an answer it's the correct answer. If not, the particular instance is NP-hard and can't be solved.  It blew my mind when I stumbled across it 5 years ago.  I *knew* it worked, but I didn't know why.  As it happened, "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut came out at that time.  So I got a copy and started reading.  I'm still amazed.

I had rather leaned in the direction of metal films and ceramics.  Since I intend to calculate the displayed value I should not need to match TCs.  The voltage will change with temperature, but as long as I can accurately calculate the value it doesn't matter.

[Kleinstein]

Capacitors are not that perfect as one might think. One effect that is often overlooked is dielectric absorption (DA) - this adds memory for the past to the capacitor and will increase the number of parameters to accurately describe the cap by quite a bit. Dielectric absorption gets visible in higher resolution dual slope ADCs and would likely also effect the simple decay once you aim for better than 0.1 % accuracy. Mica caps are usually relatively good when it comes to aging, they have quite a bit of DA.

The aging of many parts is not that predictable. The often used square root of time functions are just general approximations and may not be accurate. Besides the parts itself also way of mounting them can have an influence. Especially SMT parts can react quite a lot to mechanical stress. e.g. due to board bending. Especially those rather stable parts can show individual aging, depending on the sample used.
 
The compensation of secondary effects also has limits, as with a larger number of parameters it gets increasingly difficult to get the right numbers for some combinations. There is essentially no (at least no fast) way to get good numbers for those parameters to describe aging - especially not for the future. With luck 5 years are enough to get enough data to reasonably predict the next year of aging.

[Conrad Hoffman]

I think it was Bob Pease that talked about DA in relation to analog computer accuracy. There was a bunch of research, if you can find it. Given its good loss performance, the DA of silver mica caps is surprising, but well known. The NP0 caps are good in that regard. I have a suspicion that DA may not be linear with voltage, but you'd have to check. It may be less, proportionally, at lower voltages. Test, test, test! I've also noticed that Mylar film caps have some unexpected non-linearities compared to other films.

[Kleinstein]

Usually DA is modeled to be linear. Also the typical microscopic models with slow turning dipoles are linear to a large extent.  It is only in applications like track and hold or dual slope converters that linear DA can lead to nonlinearity. Still much of the effect of DA can be linear.  The DA effect is however not instant and can appear at different time scales. Much of the DA in Mica, MKS and similar caps is rather slow and thas leading to loss in the low frequency (e.g. 1 Hz) range.  The low loss for mica caps applies to the MHz range. So DA is not fully characterized by just one number. Just like with the related loss it is frequency / time dependent. The time constants are expected to be highly temperature dependent. So just a single contribution to DA should be modeled with 3 parameters (e.g. strength, time scale (or attempt frequency) and temperature coefficient (or activation energy)). Depending on the capacitor there may be several contributions.

There can be nonlinear effects in capacitors too, especially in electrolytic ones and high K dielectrics.

[Conrad Hoffman]

Which leads me a bit OT- capacitor models in simulators are completely worthless for the things we care about.