PCR versus TCR

[Zeranin]

And YES I do consider the mystery solved.  When the resistor self-heats, there is a temperature difference, and that explains the PCR.  What is actually happening is probably a very complex interaction between the TCE of the various materials, and the TCR of the Zeranin-30 element, combined with less than 100% efficiency in transferring  the heat from the element ...

And I maintain that you are 'hand-waving', without understanding what is actually going on. 

It's time for me to stick my neck out. I have always claimed to know what was going on, and that I would get around to explaining my ideas. What I have been doing so far is shamelessly using the excellent brains here to see what ideas others would come up with, which helps crystallize my own thoughts. I now feel sufficiently confident to present what I believe is happening, in full detail. Any detailed explanation will need to correctly predict the observed direction of resistance shift, as well as get the magnitude approximately right. I welcome critical scrutiny, that is one of the great benefits of presenting ideas on a forum.

 

[Zeranin]

Zeranin - Thanks for bringing your problem to the forum and for your detailed descriptions and responses.  Everyone loves a mystery!

I would like to question your assumption that the Zeranin is constrained in the X and Y axis.  As-built, the Aluminum X & Y are locked to the Zeranin X & Y through the heat-bonding, electrically insulating film.  But that film has mechanical compliance and its own TCE (which is safe to ignore).  The mechanical compliance can be thought of as an array of stiff springs connecting each Al X-Y coordinate to the same Zeranin X-Y coordinate at room temperature (as-built).  Now when heated uniformly in an oven (no current), the Al and Zeranin want to grow to two different sizes because of the differing TCEs but they can't because they are constrained by all these stiff springs.  So, does the Al get compressed to match the Zeranin hot dimensions or does the Zeranin get stretched to match the Al hot dimensions?  My guess is that the Al, even though it's softer, is thicker and ultimately has the higher stiffness.  So the Zeranin gets stretched when the assembly is heated.  But the springs of the insulating film also get stretched such that the hot X-Y coordinates no longer match; the Zeranin is stretched to slightly smaller X-Y dimensions than the Al.  In this regard, the rubbery thermal interface may have and advantage because it has more "give" (weaker springs).

Also recognize that in the dimension of the zig-zags of the Zeranin, there are gaps which will take up a lot of the differential TCE in that dimension.  However, these put additional strain on the corners where the zig bends to become a zag.  But I agree, that within each 25mm zig and zag the Zeranin is still getting stretched in both dimensions.

Now apply current.  The Zeranin gets 0.25K warmer and would have slightly larger dimensions, if it weren't constrained, by an amount I'll call dx and dy.  In this case, the Al X-Y coordinates stay the same (assumed constant temperature) but what will the Zeranin's X&Y's become?  I assume the spring constant of the insulating film remains constant and stretches the Zeranin by the same amount.  It follows then that the differential heated dimensional difference of dx and dy shows up as Zeranin's X&Y coordinates growing by dx and dy (in reality, slightly less than dx & dy due to slightly less spring force).

I believe there is also a slight temperature difference between the cooled side/face of the Zeranin and the top clamp side of the Zeranin.  This means the clamped face area expands slightly more than the cooled face causing the Zeranin to want to curl or cup (convex on the warm side, concave on the cool side).  Given the thinness and good thermal conductivity of the Zeranin, this is probably a second-order effect at best.  But it also results in different stress/strain and dimensional changes that may explain the powered vs un-powered difference in R-T.

I also love a technical/engineering mystery, and glad others do too. Personally I need to understand everything I observe and measure, otherwise I would go mad, even if it means considerable head-bashing and lost sleep until I see the light.

Thank you for thinking in detail about the stresses and strains that we would expect. I take your point that the thin bonding film will be very slightly compliant, so that the zeranin does not exactly follow the movement of the aluminium substrate. It remains my belief though, that for all practical purposes, the two are completely bonded together. The full explanation of what I believe is happening is rather long and subtle, and so far I have been flat out reading and responding to the many replies on this topic. Time has come for me to give my explanation, which does completely explain all observations, and I hope you will be convinced by it. Cheers.

 

[Zeranin]

I have started a sister thread entitled Resistivity vs Temperature – flatter is better?, as a precursor to explaining what I believe is going on to produce the 5ppm drift that I observe immediately after the current through my Zeranin 30 shunt is switched from zero to 16A, and why the R-T curve does not apply.

If and when we have agreement on the sister thread, I'll resume my discussion here.

[Zeranin]

You stated earlier that it is time to deliver to your client, and so there is nothing drastic that can be done, so you have to work with what you have [which, is pretty good-- so what's all the complaining about?]  That is why I suggested compensation at this stage of the design cycle.  Since the laws of physics are not going to change for your project, you will *never* reduce the natural PCR to zero, and if you need it to be zero, then compensation is the only way to make that happen.  5ppm is not that awful to compensate for as long as the PCR is predictable and reproducible.

If I were designing such a thing, I think I would start with Evanohm-R instead of Zeranin-30.  Very thick Evanohm bar [or "strap" or "sheet" or whatever].  This would be TIG welded to a heavy copper bar on each end.  The whole thing would be bent into the familiar "potato masher" shape, and then gold plated.  Then, a heat treatment process would begin by measuring the TCR, and heat treat again [iterate until the TCR becomes immeasurable].  Then, place the whole thing in an oil bath that is controlled to +/-0.01C ...  End of problem, but considering the labor involved, quite expensive.  This kind of shunt would be extremely stable [less than 0.1ppm/a drift].  If you were to contract with a supplier for a few of these, I would guess that it would end up costing you between US$5K and US$10K per shunt-- [most of which is labor].

*** EDIT ***
Almost all high-end DMMs compensate for internal shunt PCR [and some even compensate for the TCR]; and they do this in software.

I agree with all of that. I am not in a position to make major changes at this stage, though it would make sense for me to make an effort to reduce thermal resistance from zeranin to constant-temperature heatsink. I still have time and budget to at least have a go at that, and conceivably could gain a factor of x2 improvemnt. I hear what you are saying re compensation. Can't do it in software, as there is no software in this current driver. As the effect is non-linear because the heating goes as I^2, hardware compensation would be ugly and messy, and I have no intention of re-designig and re-building the current driver PCB.

Your suggested shunt design would perform superbly. To properly eliminate PCR effects, we agree that you really need to go naked.   

[Zeranin]

Here is what I believe is going on.

When the current is switched from zero to 16A, the temperature of the zeranin sheet rises above the constant-temperature substrate, changing the resistance for reasons as yet unexplained. This small 0.25K rise in zeranin temperature won’t produce any measurable change in resistance by way of the measured R-T curve, because I’m operating on the flat part of the curve where dR/dT=0. As it is only the temperature difference between zeranin and substrate that produces a resistance change, I can equally well consider a drop in temperature of the substrate of 0.25K, an approach that simplifies the analysis. Therefore I will analyse what happens to the zeranin resistance when the substrate temperature falls by 0.25K, realizing that the result will be the same as if the zeranin temperature was to rise by 0.25K.

The aluminium substrate is much thicker than the zeranin, and they are bonded together, so any dimensional change in the substrate in the X-Y direction will be forced to also occur to the Zeranin. The expansion coefficient of aluminium is +22 ppm/K. If the substrate temperature falls, then it will contract by 22 ppm/K equally in all directions. The substrate contraction in the Z-direction will do nothing, because nothing is constrained in the Z-direction, as discussed in previous postings. However, the zeranin will be forced to follow the substrate in X and Y, with the result that the zeranin dimensions will contract by 22ppm/K in X and Y, but this will result in no change in resistance, because these two dimensional changes cancel, one being a Length term, and the other a Width term.

I am confident that the explanation so far is correct, predicting that an increase in the zeranin temperature above the substrate (or fall in substrate temperature relative to zeranin, same thing) will produce no change in resistance, darn it. That is not the answer we wanted, because we observe that the resistance damned well DOES change, that’s the whole problem.

Clearly there is some other dimensional effect going on in addition, that has not yet been considered, that causes the observed decrease in zeranin resistance, when the zeranin temperature rises relative to the substrate.

The explanation is found in the ‘Poisson effect’. Imagine elastically stretching a length of wire. Of course, the resistance increases because the length is increased. However, what also happens is that the diameter elastically decreases, thus increasing the resistance even further. This is called the Poisson effect, and Poisson’s Ratio is the ratio between the ppm change in length, and the ppm change in diameter, with a value of 0.5 corresponding to an overall conservation of volume. Now apply this to our case where the zeranin has been compressed by 22 ppm/K in X and Y, resulting in an increase in thickness in the Z-direction. In effect, when the zeranin is compressed in X and Y, it responds by ‘popping out’ in the Z-direction, in an attempt to maintain the original volume.
 
The maximum possible extent of this effect would be an increase in zeranin thickness of 44 ppm/K, being a 22 ppm/K contribution from X and Y. However, for typical values of Poisson’s ratio, the actual increase in thickness will be less than that, say around half, leading to an increase in zeranin thickness of 22 ppm/K. The observed rise in temperature is 0.25K, so this would lead to a decrease in resistance of 0.25 x 22 = 5.5 ppm, which is remarkably close to the ~5ppm decrease that is observed.

This analysis explains why the zeranin resistance does not change when the zeranin and substrate are heated in unison ( dR/dT=0 on R-T curve), but the resistance does change when the zeranin self-heats above the substrate, and both the direction and magnitude of the resistance change are correctly predicted. I feel confident that this explanation is correct.

If we translate the above analysis into a formula, we get :-

dR  = P x Rth x B x EC  (equation 1)
     
where
dR is the decrease in resistance, in ppm, as a result of self-heating
P is the power dissipation in Watts, self-heating the zeranin
Rth is the thermal resistance from zeranin to substrate, in K/W
B is a constant related to Poisson’s Ratio, ~1.0, but <2.0
EC is the thermal expansion coefficient of the substrate, in ppm/K

For my zeranin shunt example :-
dR = 25 x 0.01 x 1.0 x 22 =  5.5ppm

One can also rearrange equation 1, to give an expression for the Power Coeffcient of Resistance (PCR), in units of (ppm/K) per watt of dissipation.

dR/P = PCR = Rth x B x EC   (equation 2)


Knowledge is power. Now we can clearly see exactly what will help in reducing the self-heating-induced resistance drift, and what will not.

From equation1, we can reduce the resistance drift, dR, by reducing the dissipated power, P, or the thermal resistance from foil to substrate, Rth. No surprises there, we knew that already.

Some people suspected that the resistance drift was caused by difference in expansion coefficient, EC, of the zeranin and substrate, but not so. The EC of the zeranin foil doesn’t show up in the analysis or equations at all, and therefore there is nothing to be gained from choosing a substrate material that matches the EC of the resistive foil, at least as far as minimizing PCR is concerned. The formula clearly shows the only thing that matters for PCR is the EC of the substrate.

The self-heating-induced resistance drift scales directly with the EC of the substrate. Thus, an aluminium substrate (22ppm/K ) is a poor choice. Copper would be better, and steel significantly better, though the thermal conductivity of steel is less than ideal. Invar would be best, except that the thermal conductivity is so low as to be useless. The resistor manufacturer has further options with ceramics.

Note that whatever substrate material is chosen, it will always be necessary to arrange for dR/dT to be zero or small at the foil operating temperature. If the ECs are not matched, this will modify the ‘naked’ R-T curve which in my case I can account for (within reason) by operating at whatever temperature the sweet spot (dR/dT=0) happens to be at. The resistor manufacturer can account for this by tweaking the resistive alloy.
 
Please tear this explanation apart, and/or offer an alternative explanation that fits the measurements. Comments, please. If the explanation withstands scrutiny, then the mystery is solved and understood.

[zlymex]

I'm wondering how your ‘naked’ R-T curve is measured.

[Zeranin]

I'm wondering how your ‘naked’ R-T curve is measured.

I have not personally measured the 'naked' R-T curve for the zeranin, firstly because it came to me already bonded to an aluminium substrate, and secondly because the only R-T curve that matters in this case is the curve measured with the zeranin already bonded to the substrate, as that is how it will be used. When I speak of my measured R-T curve, I mean the curve with the zeranin already bonded to the substrate, and mounted in the current driver, clamped against the constant-temperature heatsinking aluminium plate. I explained how my R-T curve was measured, in my posting #13, the relevant part copied below :-

Let me explain how my R-T curve was measured. As explained, the zeranin sheet is pre-bonded to a 1.6mm thick aluminium substrate and clamped/bolted down to a Peltier-temperature-controlled 12mm thick heatsinking aluminium plate. This zeranin shunt is the current measuring element in a precision current driver circuit, that for measuring the R-T curve is set to produce a steady 16A. In series with the same current is my massive (100A rated) Leeds&Northrup (L+N) naked master-reference-shunt, temperature controlled to 0.02K. If the resistance of the zeranin shunt in the current driver should change, then the controlled current changes, and this is detected via the voltage across the L+N master shunt. The zeranin shunt is clamped down onto the temperature-controlled aluminium plate with a 12mm thick plate of copper, and a thermistor is embedded deep within this copper plate, essentially touching the zeranin sheet, so the thermistor therefore accurately measures the zeranin temperature, say within 0.1K. The heat flux flows from the zeranin to the temperature controlled aluminium plate, with a thermal resistance of around 0.01K/W, so at full dissipation of 25.6W, the zeranin temperature rises by ~0.25K with respect to the 12mm thick aluminium plate to which it is clamped, not much at all, and completely negligible on the R-T curve. Measuring the R-T curve is real easy. The heatsink temperature (and therefore the Zeranin temperature) is ‘dialled up’ on the Peltier temperature controller setpoint to values between 20 and 50 DegC. At each zeranin temperature, the voltage across the L+N master shunt is recorded, being an accurate measure of the zeranin resistance.

The 'naked' R-T curve can be found on the website of the zeranin manufacturer, Isabellenhutte. In this case, the resistance of a naked sample of zeranin is accurately measured as a function of the zeranin temperature, probably with the zeranin sample in a variable-temperature controlled oven.

[Zeranin]

All of the discussions here predict that my PCR problems scale with the rise in temperature of the zeranin foil, and that therefore I should be able to reduce the problem by reducing the thermal resistance from foil to constant-temperature heatsinking plate.

To this end, I have ordered an 18” x 18” sheet of 0.003” thick Tpcm 580 Series Phase Change Material, part number Tcpm583, manufactured by Laird Technologies, priced at US $49.81 from Digikey, the highest performance thermal interface material that I have been able to find.

I have started a thread about on the Technical Stuff forum for a general discussion about the best thermal interface materials available. That thread has the calculation showing that the temperature rise of the zeranin should be reduced from ~0.25K down to 0.037K, a x6 improvement.

I will report back on this thread as to what improvement this gives to my 5ppm drift in shunt resistance, after the current is switched from zero to 16A. I’m not expecting a x6 improvement because there are other imperfections such as the constant temperature plate is not at exactly constant temperature under transient conditions, and there is still a thermal ‘contact resistance’ on each side of the thermal interface material, but I do expect a measurable improvement in my PCR induced drift of 5ppm. The result will be interesting.

[sarepairman2]

 

[Zeranin]

There is a wise old saying, that if something appears too good to be true, then it probably is. As it turns out, the Laird Tcpm-583 thermal interface product that I ordered is utterly useless, being merely an expensive and inferior alternative to thermal grease.

Despite being an electrical insulator, this material (as it turns out) is apparently not intended to provide electrical isolation, though nowhere do Laird actually say this. The ‘film’ is supplied between 2 transparent protective plastic sheets. To use the material, you peel off the top plastic sheet, then press the sticky surface of the grey ‘thermal interface material’ onto one surface.  Then you peel off the other protective plastic sheet, and finally, press your second surface down onto the tacky grey material. The interface ‘film’ has no mechanical strength or integrity whatsoever. I tried a 25mm square test sample of the material, clamped between 2 metal surfaces and heated to 65 DegC, and just as predicted, a few 10’s of volts was enough to break down the film, with the 2 metal surfaces thereafter shorted together. Oh, and once assembled, you can’t get the surfaces apart again, another great ‘feature’ of the product.

Apparently, the purpose of this material is simply to provide good thermal contact between two metal surfaces, but provide no electrical isolation. That being so, it is difficult to comprehend why they make the material electrically insulating in the first place, as better thermal conductivity can be obtained by using thermal grease loaded with microfine copper or silver particles. Furthermore, a metal-loaded grease will provide a thinner interface, as the excess grease is squeezed out under pressure, while with the Laird product you are lumbered with the thickness of the thermal interface material, 0.003” in this case, and much thicker again for most of their Tcpm-580 products. No thanks.

In summary, what we have here is an expensive and inferior alternative to a high-quality, metal-loaded thermal grease. I am extremely unimpressed with both the product and the company. As described in detail in a previous posting, the published thermal resistance specifications are nonsense. I sent two emails to Laird, to 2 different enquiry email addresses, seeking clarification, and still have received no reply to either. Their documentation, product, and customer service are all complete rubbish as far as I am concerned, and I won’t be buying anything from Laird again. I am seriously unimpressed. 

My conclusion from all of this, is that the only advantage of the modern thermal interface materials is ease of use. Sure, some of the modern insulating interface materials have quite good thermal conductivity (W/mK), but in order to get useable mechanical integrity and electrical isolation, the thickness is so great that the resultant thermal resistance is at best as good, and generally inferior, to the old-fashioned approach of using a thin film of Kapton or similar, with thermal grease. My original plan was to use the thermally conductive grade of Kapton, known as ‘Kapton MT’, and it looks like that would still be the best solution. The only reason that I didn’t do it that way in the first place was because I could not obtain a sample sheet of Kapton MT bigger than A4 size, which is too small.

Maybe I need to spend $500 or so on to get the minium order quantity of 37 mictron Kapton MT. At least I would have plenty left over for the next job.