T.C. measurements on precision resistors

[Dr. Frank]

..

Another question is: why do I see always a non-linear (convex) T.C. curve?
I think I have to check NTC linearity influence. (and possibly correct the curves).

With best regards

Andreas

Andreas,

for the NTC, you probably have a calibration table in your measurement program, so that should not be the root cause at all.

This convex shape - it is probably real - is where your measurements are really interesting under physical aspects.

Well, all pure metals as platinum (in the Pt100), or alloys as Manganin, NiCr, etc. have a strictly linear R(T) behavior. Also the precision wire wound types should show that.

But for the metal foil technologies (C-, K-, Z- foil) it is claimed, that this linear R(T) is eliminated by the thermal expansion of the ceramic where the metal foil is bonded to.

So in the ideal case, there should only be left effects of higher order, like R(T²), that is the superimposed curvature you probably see.
Therefore, only in the case of nearly perfect match between metal foil and ceramic, those ultra low average T.C. of "typical 0.05ppm/K" will result.

See the appended scientific paper of Vishay.

The incomplete compensation of the linear behavior increases the T.C. greatly, and is covered in the datasheets by the additional "+2ppm/K max. spread".

If they cannot guarantee better, compared to those incredible low 0.05ppm/K, then this means, that Vishay still is not able to control this technology (the matching) good enough in series production.

I also have one VHP202Z resistor, where you can separate the huge linear and a much smaller quadratic term. I'll show that later, perhaps.

Frank

[Andreas]

Hello Frank,

I also see that curve on the UPW50 wire wound resistor. With -0.022 * dT² part.
See updated UPW50 section on page 1.
https://www.eevblog.com/forum/projects/t-c-measurements-on-precision-resistors/msg462300/#msg462300

As all here are on the opinion that WW resistors should behave linear I have to examine that.

P.S. someone dropped that paperweight yesterday afternoon in my front garden.
I will see how I can use it.
Thanks @ branadic.

With best regards

Andreas

[branadic]

Hi Andreas,

do you have another ADC board available? I could sent you 2x leaded PT1000 tomorrow for your measurements, if you like to.
I would also suggest to check the NTC calibration, as they have nonlinear behavior and the calibration is a linear approximation.

branadic

[Andreas]

Hello branadic,

To ADC: I still have 2 with VRE3050A reference (but i dont like them because they are rather noisy).
I only run out of multiplexers (and probably good pull up resistors) so I can do no 4 wire measurement.
With a Z201 resistor as pull up to reference I will get a sensitivity of around 2.8 mV / K.
(against 55mV/K average on a 10-40 degree span with the NTCs).
That should probably work.

Which diameter shall I plan in for the hole?
The NTCs use around 3.3-3.8 mm. I have a 3.2 and a 4mm drill in that range.
Also for the UPW50 the question is if its better to buy 6.5-6.7 mm drills or use the 6.8 mm that I have.

With best regards

Andreas

[branadic]

Which diameter shall I plan in for the hole?

Okay, I will send them tomorrow, so they should arrive on tuesday. Please refer to the following link for the required dimensions:

http://de.farnell.com/ist-innovative-sensor-technology/p1k0-232-6w-b-010/sensor-pt1000-600-c-klasse-b/dp/1266940?Ntt=1266940

[Edwin G. Pettis]

To Galaxyrise,  (reply #48)

Thank you very much for the welcome and thank you for the compliment.

You are in the right neighborhood, Dr. Frank's setup is quite interesting but a bit complex and all those Vishays are going to cost.  It does indeed involve the LTZ1000/A's zener diode and its TC.  A very good guess for a start, my compliments, keep thinking you are close.  The 12.5K / 1K divider could also benefit as well.

[Dr. Frank]

It was so darn sticky outside, that I moved back to our cool and comfortable basement.

See what I've tinkered there, quick 'n dirty:

A thermal block for those epcos precision NTC S862, for a precision Lake Shore PT103, and for a G.R. 10k PWW.

Drill holes being 0.2mm broader in diameter than the DUT is just fine; for the 10k resistor with 6.3mm I used a 6.5mm drill.

The comparison / calibration measurement of the NTC vs. the PT100 sensor is currently running.
Note the cool football box (from 2010)!

The 10k resistor will be done later in the evening, I think.

Frank

[Andreas]

Fine,

so we will also have a 8E16 resistor in comparison :-)

Today (before I change the setup) I did a measurement with a 3 hrs rest at 25 degrees and the UPW50.
The UPW50 on a SK09 heat sink with thermal grease for the NTCs.
It seems that the hysteresis is still there ...
I will update the UPW50 post on page 1 the next days ..

With best regards

Andreas

[Edwin G. Pettis]

To Andreas (reply #53)

Thank you for pointing me to those resistor specs, I remember the VHP100 series, as I recall they came out in the late 1980s or 1990.  I was rather amused that in the app note, the address given for Vishay/Ultronix was still Grand Junction, even the phone number.  Vishay had already moved Ultronix out of Grand Junction around 1984 and that address/phone number still appeared on documents for several more years after 1991 when the Linear Tech AN86 was first published.

Careful examination of the VHP100 series data sheet shows that Vishay has been busy updating it, nothing wrong in that, but they have also did their best to pull the older data sheets off line.  At any rate, in 1990 when the Linear Tech boys were working on this app note, the claims by Vishay about these resistors being the best available technology was partially true.  None of the 'regular' PWW houses specs could come very close and unfortunately,  the Ultrohm Plus resistors were not available through regular channels.  We had operated as what is termed a 'captive operation', we could only make resistors for one customer and no one else.   Although some word-of-mouth got around, we were pretty much unknown.  It didn't matter at the time as we could not sell to anyone else anyway.

I see Dr. Frank answered your question about the convex curve, he is mostly right in his answer.  Vishays precision foil resistors have two types of curves, sine wave and hyperbolic.  The C, K, and Z all have hyperbolic curves, if Vishay actually published readable curves instead of purposely obfuscated curves, you would see the hyperbolic curve.  These are the sum of all of the various stress sources working on the foil and Vishay has done a very good job getting them down to a very low level.  The design of the internal resistor is more complex than the earlier drawing I showed in another reply.  Vishay has basically done what was done to the Manganin resistors over the decades, the alloy was 'tweaked' so that temperatures around the cardinal point resulted in the lowest TCRs but, like Manganin, the foils are still susceptible to permanent change from stresses inside and outside.  It has been minimized but not eliminated.

[Dr. Frank]

To Andreas (reply #53)

Thank you for pointing me to those resistor specs, I remember the VHP100 series, as I recall they came out in the late 1980s or 1990.  I

...

I see Dr. Frank answered your question about the convex curve, he is mostly right in his answer.  Vishays precision foil resistors have two types of curves, sine wave and hyperbolic.  The C, K, and Z all have hyperbolic curves, if Vishay actually published readable curves instead of purposely obfuscated curves, you would see the hyperbolic curve.  These are the sum of all of the various stress sources working on the foil and Vishay has done a very good job getting them down to a very low level.  The design of the internal resistor is more complex than the earlier drawing I showed in another reply. 

Dear Edwin,

I have uploaded that Vishay scientific paper here, and within that, all those "real" curves for C, K, Z foil are shown, and explained. They all feature a quadratic shape of T.C., either negative or positive orientation, which should be a typical characteristic of the foil technology used.

There is also a hint about a combination of C and K resistors in one housing, which is complicated to match, but gives the best T.C. performance by additional compensation by the contrary running T.Cs.
This type also has that strange convoluted T.C. shape.

As I were told from Vishay, the actual VHP100 series are exactly those, i.e they contain two resistor chips (of C,K foil) inside.
Vishay told me, that this type currently is the best they could offer.

But I really wonder, why Z foil technology is still not outperforming this hybrid type.

Frank

[mzzj]

The 10K metal foils of Dr. Frank are between -0.3 ... -1 ppm. My first measured 1K is around 0.9 ppm at 25 degrees.
So what is in between? Of cause not all metal foil alloys will have the same TC so the values might vary from batch to batch.

My luck with  VHP202z's
5pcs of 100 ohm resistors: TC <0,3ppm/K 
5pcs of 25 ohm resistors TC 1,5....2.2ppm/K 

I Have also full set of VHA516-4z resistors but I haven't had time or interest to measure those yet. 

[Dr. Frank]

@ Andreas,

yesterday I made  two quick 'n dirt experiments on this new thermal block.
Mainly, I wanted to check the thermal coupling of the different components, and also if I could create hysteresis loops by fast temperature changes.

The results are  a mixed bag, and interesting for your set up, also, I think.

Starting at room temperature, I used a hair dryer to heat the alu block to about 45°C within a few minutes.
I let it slowly cool down back to RT, and then inserted a cooling pad, which cooled down the block to about 13..14°C in about 1/2 an hour. Then, again, I removed the pad so that the block slowly warmed up to RT again.

The curve for the NTC vs PT100 shows a small kind of hysteresis loop, the temperature deviation is 1°C maximum.

This loop is not a real hysteresis / difference between both sensors.
They indeed follow each other very exactly and with no real delay.
The maximum real deviation is about 0.2°C, that means, that the NTC is really very precise.

The visible loop is caused by the measurement program only:

The NTC is measured by the HP34401A, with about 200ms sampling time.
The HP3458A measures the PT100, but only after the 34401A has been read, and it needs a much longer sampling time of 2sec or so, because of the Offset compensation, and because I have chosen a too long NPLC for that purpose.
Therefore, the 3458A measures the PT100 at a considerably higher temperature, than the foregoing NTC measurement.

If I would trigger both instruments simultaneously, with the same sampling time, I would for sure see absolutely no loop at all.
That also means, that both sensors are sensitive to heat changes by their bodies, not by their leads.
 

The 2nd experiment was done the same way, but on the 10k PWW vs the NTC.
I also had to use a long sampling time for the 3458A, about 4sec, due to the necessary ppm resolution.

But this was obviously not the problem which caused those gruesome hysteresis loops you see in the 2nd diagram, as I would have expected a maximum temperature difference of < 1°C between PWW and NTC, instead of over 10°C.

I think, that the PWW mainly transfers external heat via its leads, (which I did not want to cut short), and not over its body.

In such cases, another trick is to thermally "catch"/absorb the wires also.
That means, to solder the ends of the wires to a pad on the alu block, which is electrically isolated, but thermally coupled to the block.

Ok, to mitigate that problem otherwise, I would surround the whole assembly by another aluminium box, so that also the wires would be protected from air draught.

If you just use the linear parts of the curve, i.e. when the sample cools slowly down from 40°C to RT, and warms up from 14°C to RT, the T.C. is calculated to about 2.2ppm/K.

Specification was 3ppm/K typ.

 Frank


Edit:
From the inner construction of the 8E16 PWW, it's clear that mainly the leads transfer the heat:
The outside of the bobbin is thermally isolated by a rubber protection, following epoxy, following a plastic tube.

The copper wires go deeply inside the bobbin core, and an additional resistance tape is assembled.
See drawing, taken from the specification.

[babysitter]

My setup at work is a brass cylinder with a center drill that takes the DUT or my reference thermometer. A small Heraeus Pt100 is glued on the block too, on the same height as the center drill. A layer of teflon tape from your friendly GaWaSch is wound around it with the heating coil (enamelled cooper wire) on top of it. A HP6632B feeds thet heater, reading back the heater resistance used to limit heat and a 34401A reads the Pt 100 to control a simple Regulator programmed in EZGPIB - usually fixed at 38°C, but sometimes heated to 46°C and slowly cooling down. (Heat flow is always something I want to prevent, but..)

All the heated part is embedded in a big blox of polystyrol foam - the hard yellow kind, recovered from a trash bin, with only very little clearance to the heater block and just a small diameter tunnel to insert the DUT or Thermometer.

[Edwin G. Pettis]

To Andreas (reply #55) and Dr. Frank

I've compared the data sheets of RhoPoint Econistors and the Neohm UPW series, from the descriptions, they both use essentially the exact same bobbin designs, absolutely nothing proprietary there, materials and encapsulation.  Also, they both specify 0 +/- 5 PPM/°C TCRs, then say 0 +/-3 PPM/°C is typical.  Depending on where you look, the 5 PPM/°C spec may be left out, naughty.  The power ratings are a bit different between the two considering they both are the same, I think the UPW50 is a bit over rated in power for its size and is going to run rather hot above 0.33W.  The derating curves are also different, the RhoPoint curves are more realistic.

Dr. Frank, you are mostly right about the thermal conductivity, because the epoxy bobbins have very low thermal conductivity, as does the silicone rubber coating and shell, some of heat is 'pulled' out of the resistor by the leads and whatever they are soldered into.  If they are using an unfilled epoxy the thermal conductivity is ~0.00047 cal/sec/cm/°C, for a filled epoxy, ~.00123 cal/sec/cm/°C, quite low indeed.  Depending on just what kind of epoxy these guys are using, the resistor's characteristics will be different, mostly evident in the linearity of the TCR line.

Given enough time, the thermal 'lag' of the resistor will catch up to the change in temperature and will stabilize at that point, until that point is reached, any readings will be in error and could show up as a 'hysteresis' error.  Once stabilized, the resistance readings should be consistent, if they are not, some other form of 'error' is evident, possibly within the resistor itself if all else remains the same.  Unfortunately, you cannot directly read the internal temperature of the resistor without a temperature probe (such as a NTC) in close contact with the resistor's windings, quite impractical.  At best, you can only come in close contact with the resistor's shell and try to compensate for the thermal lag by waiting a sufficient time.  Indeed, TCR measurements have many ways of cobbing things up.

However, compared to the other type of PWW resistors which are molded in DAP or alkyd, the thermal conductivity is much higher but the molding process imparts a severe strain on the resistor's windings which cannot be completely relieved by any stability bake, the resistor will continue to drift at an unknown rate over its lifetime.

Obviously, oil filled resistors are probably going to have a shorter heat lag as mineral oil has a higher thermal conductivity than epoxy but the same situation still applies here, sufficient time must be given for temperature stabilization or the readings are inaccurate.

While I'm thinking of it, in the postings on stability curves, I still have not seen any references to reading uncertainties, while I've seen some very well done stability measurements, the readings are consistently inferred as accurate, such as 0.2 PPM/°C, while that number may be consistent, the actual value could be anything within +0.5 PPM/°C to -0.1 PPM/°C (the uncertainty I chose is a ballpark figure, it could be a bit less or even a bit more).  No calibration lab would ever give an measurement number without an uncertainty figure of the measurement.  The measurements I have seen here do indicate a good stability figure but do not represent an accurate one and there are uncertainties in regression calculations as they are only as accurate as the data being used at best.  Another source of error (and this one is fairly big) is that, at a minimum, the instruments and references must be calibrated/accurate to a known figure that is at least 5 times better, preferably 10 times better than the measurements being attempted.  None of the equipment nor references used here have specifications good enough to even come close to accurate readings; linearities, resolution (big one), ect., are no where near good enough, the uncertainties are very significant.

My own instruments, the ESI 242D, in a direct comparison to my calibrated SR-104 would be on the ragged edge of sub-PPM measurements and the uncertainties makes the absolute measurement of those quantities rather suspect.  If I can make repeatable measurements within a given time period, that only means that the uncertainties are also stable with time but that does not improve the accuracy of the measurement.  This is quite acceptable if one is attempting to match resistor TCRs, the uncertainty is still there but the matchup of the resistors remains very accurate, only the absolute accuracy is suspect.

If you are working with a resistor that has linear TCR qualities, the best way to improve the accuracy of the TCR measurement is to measure it at several temperatures over as wide a temperature range as possible, a 100°C range is typical if the resistor can stand those temperatures.  If the TCR curve is nonlinear, then it becomes much more difficult without very high grade laboratory equipment and if accuracy is important, a 4-wire Kelvin bridge is really not up to the job.  A much more complex setup is required, primary calibration labs usually employs such a bridge for very precise measurements or a DCC bridge if the resistance in question is below 10K ohms.

Dr. Frank's setup has shown very good stability over a given time period, he has done an impressive job in that respect but I still caution readers here to not accept any readings as anything more than a figure of stability which may, after all, be the only characteristic intended.

[Conrad Hoffman]

Some time back there was an Audio Precision Powerpoint presentation, http://www.ap.com/download/file/747  where they talked about the common resistor technologies. One thing they said was that the low frequency modulation distortion was surprisingly worse than expected for metal foil resistors, and that metal film were better. I toss this out because not everybody is working with DC, and it might be a useful bit of trivia.

[Edwin G. Pettis]

To Dr. Frank (reply #63)

Interesting item about the VHP100 series, Vishay rarely revealed any details about the inner workings of their resistors but I am not surprised that they used two opposing resistor TCRs for compensation.  The practice of selection to get an end result is still common today.  I know that Vishay claims that some of the Z foil resistors are 'designed' to produce sub-PPM performance, but I am still a bit skeptical about that.  I've never seen a alloy process that could consistently produce such results without any selection.  That could be little more than Vishay buttering the specs again.  After all, who could challenge such a claim?  The only ones privy to the actual processes are under a no disclosure contract.  While I have some knowledge of the general processes used in the various C, K, and Z foils, I do not have really specific details that I could say they are telling the truth or lying.

With the Z foils, I think that Vishay is pretty close to as good as it is going to get without some new advances in materials.  The resistors I produce are pretty close to as good as they can get until improvements in materials come along.  In some respects, the Evanohm alloy is nearing its limits as well in wire form.  It is very difficult to control minute mixtures and heat treating processes either in wire or foils.

I am looking into new improvements in my resistors if it is possible, which could make significant changes to some characteristics but that is still a ways off.  I don't have the fat R&D budget of Vishay to work with.

I suppose if I use the marketing method that Vishay and others use, I could validly claim that my typical TCR is 0 +/-1 PPM/°C since the majority of my resistors fall into that spec and I wouldn't be lying.

[branadic]

I suppose if I use the marketing method that Vishay and others use, I could validly claim that my typical TCR is 0 +/-1 PPM/°C since the majority of my resistors fall into that spec and I wouldn't be lying.

My suggestion is, that if you come along with a real datasheet this would be a good point to start at and to compete with other resistors. How do your resistors behave under same condition to PWW by competitor?
It's hard for me just to "Bolieve" in the specs you ensure without showing any graph or measurement. No doubt that you have long experience in PWW and that the resistors you manufacture are damn good, but it's one thing to complain about specs given in datasheets by competitor but to not have an own datasheet of resistors that are fabricated by you for long time. That is somewhat strange, won't you agree?
However, the details and historical facts you have given are for sure very interesting, but for me there is something left.

[Andreas]

In such cases, another trick is to thermally "catch"/absorb the wires also.
That means, to solder the ends of the wires to a pad on the alu block, which is electrically isolated, but thermally coupled to the block.

Hello Frank,
good Idea.
I will try to make an experiment with some "chip" heat sinks + thermal tape connected to the wires.
And also I will have to look for some "software" effects. But since I measure similar values with
a 0.3K/minute and a 0.12K/minute ramp I do not believe that there is such a effect.

Edwin: thanks for giving the numbers on the thermal conductivity. That confirms the theory of Dr. Frank.
And yes you are right: my measurements are intended only as comparison between different types of resistors and intended to pair a set of resistors for a stable voltage divider. (Thats what I wrote in the very first post of this thread). And if I meet the figures between 0.9 and 2.1 ppm / K with about 10% relative error this will be "good enough" for me to get a factor 10 improvement for the divider.
Of course I will also have do some estimation on the error of my setup. For the T.C. I am confident that it will be ok.

Hysteresis is the much more difficult to measure.
And I fear that there is still some hysteresis at the UPW50 resistor which has nothing to do with the temperature measurement error.
Edit: See also updated measurements on page 1 for UPW50 from 22.06.2014.
https://www.eevblog.com/forum/projects/t-c-measurements-on-precision-resistors/msg462300/#msg462300
But since the hysteresis of about 2 ppm for my temperature range is much less than a 18-32 degree shift with 0.9-2.1 ppm/K it will be negligible.

With best regards

Andreas

[Galaxyrise]

I suppose if I use the marketing method that Vishay and others use, I could validly claim that my typical TCR is 0 +/-1 PPM/°C since the majority of my resistors fall into that spec and I wouldn't be lying.

But it's one thing to complain about specs given in datasheets by competitor but to not have an own datasheet of resistors that are fabricated by you for long time. That is somewhat strange, won't you agree?

He posted his specifications sheet, dated 2001, which states "60% of units will be 0+/-1 PPM".  That's actually more specific than just the word "typical".

[branadic]

He posted his specifications sheet, dated 2001, which states "60% of units will be 0+/-1 PPM".  That's actually more specific than just the word "typical".

Please allow that I'm another opinion. This is just a "specification", some words printed on white paper, nothing more. Is it now task of the end user to verify if his ensured specs are fullfilled?
All I'm asking for is a database made by measurements on his own resistors to prove his written words, that's it. As I said, I can't claim others datasheet if I haven't one myself.

[Edwin G. Pettis]

To Branadic (reply #73)

I would argue that Vishay has not posted actual test results as such only graphs with said claimed performance on them, usually with no 'window' of minimum and maximum except as a brief blurb somewhere on the data sheet.  Vishay, in my opinion, does need graphs (even if they are 'fudged' a bit) because none of their TCR curves are linear, never have been and never will be.  To my knowledge, I rarely, if ever, have seen any 'official' test data put out by Vishay in the manner I believe you are asking for.  Their data sheets are pretty much it, there are no measurement "data bases" in any other data sheets.  It makes me wonder why you are being so fussy about my resistors?  Would you be so fussy if I was only claiming similar performance to the other resistor manufacturers?

I/we have never bothered to put a graph in the data sheet because it is simply a straight line of the TCR with very slight deviations at the far ends and 25°C as the reference point.  It is linear, in that respect a graph is redundant, words describe it accurately.  The other specifications are simply called out as they are, simplicity as needed.  A graph would be a bit redundant here as well.

To accede to Branadic's request for data, here is a test report for our standard parts, no special preconditioning and it includes the 'warts' as well.  A mistake was made with the wire size in one of the bobbins which caused an aberration in the test results, a tear-down was done and the cause of the aberration found.

[babysitter]

I consider Edwins Information very accomodating compared to Vishay (the publicly available stuff.) Vishay might - at least I guess so - just say go away or have you signing a NDA if you want the answer to such questions.

Isn't it right that you usually get either the exact measurement data of the part you bought or a collective datasheet with anything, where statistics is used to tell you typical or guaranteed values?

@Edwin: How many revisions are in your recent resistor design compared to the first sold, either forced due to supplier problems or due to new insight ? At least how many digits does this count have ?

[Edwin G. Pettis]

Hello Babysitter,

Since we first went into full production back in the mid-1980s, there has been no 'revisions' to the basic specifications of the standard line parts since the design was up and 'running'.  During the design phase, there was some testing of different materials and different manufacturing procedures of course.  The specific materials and procedures, from start to finish, is what produced this resistor which has proven to be a very robust design.  We did end up having to change one material supplier whose pricing became excessive, apparently they didn't want to deal with this kind of product anymore and just priced it skyhigh.  We were able to find another material that worked just like the original so we did not do a revision to the resistor specifications, only the supplier list and material type.  There has been minor revisions to manufacturing procedures when we found an unexpected omission in a procedure.

For instance; an operator was welding 1 Meg resistors which uses a very small wire size (they were expensive back then too), at one point in welding the batch of resistors, the wire was being 'burned' off instead of welded like it should be.  Since the resistors were expensive, the operator tried to 'save' them; there was just enough wire left to make a second weld joint right next to the first joint.  In this manner she finished the batch, 'saving' a number of resistors from being junked.

At this time, we were no longer TCing entire batches but just doing a small sampling for TCR, none of the 'saved' resistors managed to get into the small sample and the finished resistors were sent to the production line.  A few days later, we received the entire batch of resistors back and were told they were out of tolerance on TCR which was 0 +/- 1 PPM/°C.  We immediately ran the entire batch for TCR and found that the 'saved' resistors had a TCR of 3 to 4 PPM/°C.  Mike tore down one of the 'faulty' resistors and the cause was immediately clear.  The 'double' weld had caused a line contact in the weld area instead of a point contact, throwing the TCR off.  The procedure handbook was amended to correct the welding procedure and the problem never appeared again.

I am working on a new design which would require a major revision of the original, which would be the first time but until that happens, no revisions.

[Andreas]

Hello,

I checked some of the error sources:

For the convex curves of the resistors I checked NTC linearity.

Usually I use my NTC-configuration 33K NTC with 27K pull up in a 10-40 degree range.
I optimized the pull up for linearity in this range (0.2 - 0.3 K maximum nominal deviation).
the equation for the temperature is: 75.95614516 deg C  -0.018517152 * ADC value in mV (5000mV ratiometric end value)

In this setup before I used the FAN I had problems to reach the upper temperature limit.
So I increased the setpoint without checking linearity. With fatal result: up to 1 K error on 46 degree C.
see 20140625_NTC_linearity.PNG

I generated a correction curve to correct the nominal error:
So non linearity from Steinhart + Hart equations is reduced to 0.02 deg.
see 20140625_NTC_linearity_corr.PNG

I recalculated one of my T.C. curves of UPW50 to see the difference:
20140621_TC_UPW50_1K_1_raw_temp.PNG shows the uncorrected diagram
20140621_TC_UPW50_1K_1_raw_temp_corr.PNG is the NTC linearity corrected diagram

The main difference is that the corrected x-axis reaches 1 degree higher temperature and 0.3 degree lower minimum temperature.
so the average tempco after box method decreases by 3.5% from 2.05 ppm/K to 1.98 ppm/K
The temperature gradient at 25 degrees changes from 2.06ppm/K to 2.10ppm/K. (2%)

And: The NTC linearity is not the reason for the non-linear T.C. curve.

corrected LMS curve for UPW50 #1 T.C.

T.C. Curve = A0 + A1 * t + A2 * t * t + A3 * t * t * t   with: t = (Temp - 25 deg)

A 0 =  7.3038543243537982E-0001
A 1 =  2.0971377460001767E+0000
A 2 = -2.2197393589624226E-0002
A 3 = -1.0659158556926091E-0004

max. deviation to regression curve 1.6871989574339004E+0000 ppm

Edit: the story reminds me of another story of Josella Playton:
http://www.josella-simone-playton.com/solarpow.html
Sorry only in german.
The quintessence is: never leave proven limits.

With best regards

Andreas

[Edwin G. Pettis]

Assuming (that almost always gets you into trouble) that all external sources of error have been accurately accounted for (careful how many digits of resolution you're using in the calculations, most of those digits are really useless) that leaves the resistor's sources of error.

A precision wire wound resistor should have a nearly ruler flat TCR 'curve' (that's a misnomer! as it is flat, no curve) throughout its operating range with the possibility of slight deviations from flat at the temperature extremes.  The cause of stresses which account for a non-linear TCR curve comes from multiple sources.  The interaction of the bobbin material with the windings, incorrect choice of wire size for the given resistance, insufficient rubber coating of the windings and quality of the welds to name a few of the possible sources.

A TCR curve which shows hysteresis with temperature changes is a guarantee that there are problems with the resistor's design and construction.  This further leads to more instability with time, it is the mistaken assumption that baking these unstable resistors gets rid of or minimizes the long term drift factors, it doesn't, an incorrectly designed resistor is just naturally more unstable with time than a properly designed and built resistor.

Rhopoint says that they age their resistors for a full week to completely stabilise their resistors before final calibration, what a load of rubbish, if they were "completely stabilised" (no resistor is completely stabilised!) their drift specs would be about five times better and running them for a full week in an oven is a huge waste of time and energy, those resistors should reach a stabilised condition in less than a day if they were built correctly.

Neohm (UPW series) is a bit more tight lipped about their manufacturing process except to extol the RTV coating on the windings but their long term drift is even worse than Rhopoint's, so much for  exceptional resistor claims, pretty much another 'me too' resistor shop.  What little else they mention about their resistors is just average, me too manufacturing.

Just in case our friend Branadic is peering in over my shoulder, yes I am whacking on all these me too resistor operations.  They have not bothered to take the time to ferret out the flaws in their manufacturing and fix them, they have just copied everything they can find out about resistors from their competitors who have the same flaws.  It took a lot of time and effort to design a damn good resistor and from that standpoint, I have earned the right to whack on my inferior competitors with a big stick.