Electronics > Metrology

PCR versus TCR

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There is much discussion here about TCR (Temperature coefficient of Resistivity), as to be expected, but much less about PCR (Power coefficient of Resistivity).
From the point of view of a Metrologist, arguably TCR is more important, as Metrology is only concerned with accurately measuring and comparing resistance values, and to this end, power dissipation and thus self-heating in the resistors is arranged to be as low as possible.
In the Real World though, PCR is often at least as important, sometimes more so. In real world applications, resistors commonly dissipate significant power, and the resultant change in temperature from self-heating often exceeds changes in temperature from the environment.

Just so, I hear you say, but it’s really all just the same thing, isn’t it? If you know the thermal resistance from the resistive element to the environment, and you know the power dissipation, then you can easily calculate the temperature rise of the resistive element for any given power dissipation, or even simpler, you can directly measure the temperature rise for a given power dissipation. Then it’s just a matter of looking at the R-T (resistance versus temperature) curve (obtained from manufacturer or measurement) and you can confidently predict the change in resistance, as a result of the self-heating-induced change in temperature. In other words, the self-heating-induced change is resistance is easily predicted knowing the self-heating-induced change in temperature and the R-T curve. Right?

Well, that’s what I used to think too, but have found that in practice it doesn’t quite work like that, to the point that in some situations, the self-heating-induced change in resistance bears no relationship to the R-T curve. In short, the change in resistance with temperature of the resistive element depends on whether that change in temperature was caused by self-heating, or by changing the temperature of the environment is which the resistor resides, which is how the R-T curve is measured. To put it another way, when the temperature change is as a result of self-heating, there appear to be other mechanisms at work that change the resistance, that have nothing to do with the R-T curve. That is a bold claim, and I will spend some time presenting experimental evidence to justify this claim, and then bounce ideas around with the experienced resistorologists here as to what I believe those other mechanisms are.
This is not merely of academic interest. The application is a 0R1 shunt resistor, used to measure up to 16A, in an ultra-high-precision current driver circuit. To reduce noise and thermoelectric potentials to an acceptably low level requires 1.6V across the shunt at full current of 16A, thus the choice of 0R1. Inevitably though, the shunt dissipation is 16x16x0.1 = 22.5W, leading to self-heating of the shunt. If the application called for a constant current of 16A over a long period of time there would be no particular problem, as the shunt temperature and resistance (and therefore the controlled current) would eventually stabilize.

Unfortunately, the applications call for the controlled current to be stable within a few ppm, on all timescales after the current is abruptly switched from zero to 16A, meaning that the shunt resistance must be stable within ppm immediately after the current is switched from zero up to 16A. Suddenly the application becomes very challenging indeed, and a very low PCR becomes critically important.

The adopted solution is a very large, custom build resistor made from Zeranin sheet, about 0.3mm thick. The Zeranin sheet is first bonded to a 1.6mm thick aluminium plate, using a 0.07mm thick heat-bonding, electrically insulating film. The Zeranin is then etched to the required shape, being a zig-zag pattern, with the conductor being about 25mm wide, and a total conductor length of about 1.4m. Overall dimensions are about 350mm x 100mm x 1.6mm. The thermal resistance from the Zeranin sheet to the aluminium substrate is about 0.01 K/W, and the assembly is firmly bolted/clamped down onto a 12mm thick aluminium heatsinking plate which itself is temperature controlled to within 0.1K, by way of an array of Peltier modules driven by a PID temperature controller. A fairly serious setup, which keeps the Zeranin temperature constant to within 0.3K under all conditions, even when the dissipation is abruptly changed from zero to 22.5W. The R-T curve of the Zeranin bonded to the aluminium substrate has been carefully measured, and the heatsink/resistor are operated at a temperature of 34.0 DegC, where the R-T curve has a minimum slope of about 1ppm/K. Easy-peasy. When the Zeranin temperature changes by 0.3K, then any text book will tell you that the resistance will change by 0.3K x 1.0 ppm/K = 0.3ppm, which I would be more than happy with.

Unfortunately, what is actually observed is very different, and cannot be explained by way of the R-T curve. After the current is abruptly switched from zero to 16A, the shunt resistance drifts downward by about 5ppm over 50 seconds, and thereafter remains stable. Furthermore, it makes not one zot of difference whether I operate the Zeranin resistor at 20 DegC, 34 DegC, or 47 DegC, the 5ppm drift is exactly the same, although the slope of the R-T curve is many times greater at temperatures other than 34 degC. In other words, as I stated early in this posting, in this particular case the measured R-T curve has nothing to do with the self-heating-induced change in resistance – some other mechanism must be responsible.

I have some ides as to what this mechanism might be, but don’t want to pre-empt ideas that others might have. Comments, gentlemen?

Very interesting topic.

Does the downward drifts of 5ppm, although independent of the operate temperatures, depend on the operate current?
That is to say, will the drifts become about 2.5ppm when operate at 8A instead of 16A?

My guess of the possible cause, it got to be heat or temperature related, not electro-mechanical related such as the length or distance/thickness change by electromagnetic, since that change would be instantaneous.

And another related question is, why you design you shunt to operate at 1.6V instead of 0.8V? I'm asking this because it is related to my partially answered topic/question of 'Why output voltages of precision shunts are so high?'

How are you connecting (conductors) to the zeranin? I would look to dis-similar junctions to cause most of the mischief. Mr. Pettis who sometimes posts here and has deep wire wound resister making experience has differentiated his resisters from the others by his proprietary lead welding. Search the forum for his posts and links to his EDN? articles. The other thing is that by gluing the zeranin sheet down you now have to deal mechanical strain and different expansion rates. This is why immersion in a thermal transfer fluid like an oil bath would be better. Let your resistor creep on its own volition.

Nice first post!

I think what you're describing (non-linerarity) is the consequence of the Joule Effect. Check this article out:

I once tore open an Isabellenhütte RUG-Z shunt resistor, 250W, 0R01, 0.1%, TCR 3ppm/K.
They claim the shunt is made of Zeranin too and it seems to me the conducting sheet is about 0.3mm in thickness as well.


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