PCR versus TCR

[Zeranin]

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?

[zlymex]

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?'

[chickenHeadKnob]

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.

[gilbenl]

Nice first post!

I think what you're describing (non-linerarity) is the consequence of the Joule Effect. Check this article out:
http://www.digikey.com/Web%20Export/Supplier%20Content/VishayPrecisionGroup_804/PDF/vishay-tech-non-linearity-characteristic.pdf

[zlymex]

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.

[gilbenl]

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.

I apologize for hijacking, but zlymex-How are you able to tear apart all of these high end items? You've posted tens of thousands of dollars worth of beneficent destruction. Are the items out of spec/BER?

[zlymex]

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.

I apologize for hijacking, but zlymex-How are you able to tear apart all of these high end items? You've posted tens of thousands of dollars worth of beneficent destruction. Are the items out of spec/BER?

I'm known locally as the detructor, someone send me items for tear apart only such as that VHA518-7, sometime we group-buy the item to be teardown as in the case of a VHP202Z. However in this case, the RUG-Z had already broken(by sheer mechanical force I think, not burnt down, no smell of that sort), I tore open for repair

[Zeranin]

Hi. Yes, the magnitude of the drift scales with the current, and I agree that the effect is thermal, even if the exact explanation is subtle.

As to the choice of 1.6V across the shunt, everything in life is a compromise. On the one hand, I want the largest voltage across the shunt, because this means that noise and thermoelectric effects become less significant. In this design, very low broadband noise is required, set by the Johnson noise of the resistors in the preamplifier that amplifies the voltage across the shunt, so the higher the shunt voltage, the better the SNR. Total hum and noise is around 1 part in 2E7 over a bandwidth of 10 kHz, not achievable if I needed to amplify up a much smaller shunt voltage. Simultaneously, I also want the shunt voltage to be as low as possible, to minimise self-heating induced changes in resistance, as described. In my application, the ‘sweet spot’, for the best trade-off between these conflicting requirements turns out to be with about 1.6V across the shunt. Having 0.8V across the shunt would also be OK, and I have that option, as I have an identical 0R05 shunt.   

[Zeranin]

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.

Hi, I agree that thermoelectric potentials can be a nasty source of error, but I can prove that this is not the case here. A thermoelectric potential produces a fixed offset error, that would also be present in my ‘zero current’ measurement, but there is no drift in my zero current measurements. What I actually do is produce a 16A ‘square wave’, zero current for 100 seconds followed by 16A for 100 seconds, over a number of cycles. If thermoelectric effects were present, they would show up equally in the zero current measurement, and this does not happen. The zero-current measurement is rock-solid, so thermoelectric effects can be ruled out here.

I agree that immersion of naked zeranin in an oil bath would solve this problem, but causes others. The thermal resistance from (temperature controlled) oil bath to the resistive element will be too high unless vigorous stirring or pumped circulation of the oil is employed, and that is complexity and size I want to avoid.

[Zeranin]

Nice first post!

I think what you're describing (non-linerarity) is the consequence of the Joule Effect. Check this article out:
http://www.digikey.com/Web%20Export/Supplier%20Content/VishayPrecisionGroup_804/PDF/vishay-tech-non-linearity-characteristic.pdf

I did indeed check it out, and am familiar with all that is written there. However, what I am observing is specifically not the textbook stuff described there. The Joule Effect simply means I^2R self heating, and yes, we all agree that the observed drift is as a result of self-heating. However, the article speaks only of effects that can be predicted from the R-T curve, whereas the effect I observe specifically can not be predicted from the R-T curve.

[zlymex]

Total hum and noise is around 1 part in 2E7 over a bandwidth of 10 kHz,

Is the noise in peak to peak or in rms?
What kind of preamplifier are you using?

[Zeranin]

The quoted noise is RMS. If you are really interested, I'll look back at my notes to find the exact numbers. Thinking back, although the circuit bandwidth is around 10 kHz, the noise spec is quoted in ~1.5kHz bandwidth, this being the maximum frequency that the Bose Einstein Condensate atoms can 'see'. The current driver drives current through magnetic coils that are part of a Physics experiment producing BECs. The shunt preamp is part of the precision current driver circuit. It uses multiple amplifiers in parallel to get a root(n) noise reduction. To keep resistor noise down, no resistor anywhere in the driver op-amp circuits can be >500 ohms, and the entire circuit is inside a temperature controlled oven. Transformers or fans can't be placed within 1.5m, or the stray AC fields will get into the circuit. As the shunt is inevitably quite large, it forms a loop, so by Faradays Law this induction loop picks up stray AC magnetic fields, that are always present, so this is cancelled by an 'antiphase cancellation loop' that follows the same path as the zeranin. From memory, the mains hum in the output current is down somewhere in the 1E-8 level. As the load is highly inductive, a thumping great magnetic coil, the driver must be able to produce up to 180V at 16A, to maximize current slew rate through the inductive load coils. I'm lucky. I get paid to design and build this stuff.  But I have drifted off topic. The most troublesome part of this project has been the 16A temperature controlled shunt resistor. As far as I'm concerned, if I can measure an imperfection, then it should not be there. 

[Zeranin]

The problem is that you are bonding the resistance element to a substrate [aluminium in this case].  For steady-state [DC] current, you can have an excellent TCR [even zero!], but for pulsed currents, there can be a short period of time where there appears to be a larger-than-should-be-normal change in resistance.  This is due to the fact that the substrate itself affects the resistance of the entire resistor-- because of different strains TCE's between the different materials causing the bonding strain to be different.  This problem also comes up with bulk-metal-foil resistors, that have a resistance element bonded to a ceramic substrate.  During a highly dynamic current profile, the substrate and the resistance element can be at different temperatures-- changing the strain relationship between the element and the substrate, and this in turn will [temporarily] modify the final resistance until the element and the substrate reach thermal equilibrium.  If the element and the substrate have a different thermal impedance, then there can be a situation where they *never* reach thermal equilibrium, and there you have what appears to be a PCR.

To get what you want, you will have to figure out how to use just the Zeranin alloy, suspended in between the large copper contacts-- not bonded with anything.  An oil bath will help a great deal here to keep the element at it's "sweet spot" for TCR [about 40C for Zeranin alloy, +/-5C].

I broadly agree with what you say, but feel that the exact mechanism requires a more detailed explanation. Like others, you refer to the different TCE’s between the different materials causing the bonding strain to be different, but I’m not convinced that this is relevant. Keep in mind that the R-T curve that I measured was with the zeranin sheet already bonded to the aluminium substrate, and mounted in the current driver circuit. It is true that differential expansion between the zeranin and aluminium will modify the zeranin R-T curve, and indeed this is the case, with my measured curve being significantly different to the manufacturer zeranin curve, taken on a ‘naked’ sample of zeranin. Therefore, this different rate of expansion is already accounted for in my measured R-T curve, isn’t it?
 
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 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.

As you would thus appreciate, this is exactly the same physical setup as when the 5ppm drifts in the zeranin resistor are observed. In this case, the current driver is commanded to produce a 16A ‘square wave’, zero current for 100 seconds, followed by 16A for 100 seconds, repeated for a number of cycles. If the resistance of the zeranin shunt resistor within the driver circuit should change, then the current produced by the driver circuit changes, and this is detected by logging the voltage across the L+N master shunt. If I log the voltage across the 0R1 zeranin shunt, then of course I see a perfect square wave of 1.600000V amplitude, with no measurable drift, exactly as we should expect, as the driver circuitry is of very high quality. However, immediately after the current is commanded from zero to 16A, the voltage across the L+N master reference resistor is observed to drift upward about 5ppm, over a time of ~50 seconds, and then stabilize. As the actual current is drifting upward, this means that the resistance of the zeranin shunt within the driver circuit must be drifting downward. Sorry for long explanation, but it’s not fair of me to ask questions without describing details of the equipment.   

So, why is it that my measured R-T curve, taken with the zeranin sheet already bonded to the aluminium substrate and bolted to the temperature controlled heatsinking plate, is not relevant to the situation where the very same resistor, mounted in exactly the same way, is self heated? Differential expansion caused by the different coefficients of expansion of zeranin and aluminium is already accounted for in my measurement of the R-T curve, and yet this R-T curve cannot possibly explain  the observed 5ppm change in resistance. According to my R-T curve we would need a temperature shift of several degrees to get a 5ppm resistance shift, yet nothing changes temperature by more than a few tenths of a degree.

I predict that we would see the same 5ppm drift, even if the zeranin resistive element was bonded to a zeranin substrate, and clamped down onto a zeranin temperature controlled plate, such that everything has the same temperature coefficent of expansion (TCE). Presumably you don’t agree, as you specifically mention the different TCE’s of the zeranin and aluminium but, as I said, this is already accounted for in my R-T measurement, isn’t it? Can you (or anyone) explain your ideas in more detail, in the light of the points raised in this email?

I have a possible (detailed) explanation for what is happening, but do not wish to not pre-empt the ideas of others just yet. I do agree that the problem is caused by having the zeranin bonded to a thick metal substrate.

[Alex Nikitin]

Hi and welcome to the forum!

1) Does the current need to be set quickly at "any" value between 0 and 16A? Or is it an "on/off" situation for a particular current which can be set and just steered in/out of the load?

2) Right now your amplifier noise is equivalent to about 40 Ohm resistor, isn't it?

3) Are you sure that you are not observing a drift in your L+N master shunt?

Cheers

Alex

[zlymex]

The quoted noise is RMS. If you are really interested, I'll look back at my notes to find the exact numbers.

If that is the case, one part in 2E7 times 6, we get about 0.3ppm pp noise, that is not a big deal. There are many precision opamps capable doing the job alone. Take the very old OP27A for example, 0.08uVpp typical noise(0.18uVpp max), if amplifying 0.8V, it will 'add' 0.1ppm pp typical noise, much less than 0.3ppm pp. So it is very safe to use 0.8V shunt voltage instead of 1.6V as far as the noise is concerned.

[Kleinstein]

The difference in temperature between the resistor element and the aluminum backing can have an influence, but the time constant should be rather short, as it does not take  that long for the temperature to equilibrate.

The time constant might be a good hint to locate the problem. It could be as well be the other shunt.

A thermal effect should be proportional to the square of the current - so a test with a smaller current (e.g. 10 A) might help.

[Alex Nikitin]

If that is the case, one part in 2E7 times 6, we get about 0.3ppm pp noise, that is not a big deal. There are many precision opamps capable doing the job alone. Take the very old OP27A for example, 0.08uVpp typical noise(0.18uVpp max), if amplifying 0.8V, it will 'add' 0.1ppm pp typical noise, much less than 0.3ppm pp.

Not in a 0-10kHz bandwidth

Cheers,

Alex

[zlymex]

Not in a 0-10kHz bandwidth

Cheers,

Alex

Thanks for that. I misread for 10 Hz.

Total hum and noise is around 1 part in 2E7 over a bandwidth of 10 kHz,

[Alex Nikitin]

As far as the L&N shunt goes-- a 100A shunt is rated that way to let you know that you will not damage the shunt at a steady-state current of 100A--- it by no means implies that the shunt will not stray from it's specifications at this current.  This shunt should not be operated at more than about 10A if you expect to get halfway decent performance out of it.  You are operating it at 16A which is a bit much.

This 80 seconds time frame sort of hints to the "reference" shunt problem. An easy way to check would be to precondition the L&N shunt at about 16 A (doesn't need to be very accurate) for several minutes and then measure the current from the source.

Cheers

Alex

[Zeranin]

Several have rightly pointed out that the measured drift could be the L+N reference shunt, rather than the zeranin shunt in the current driver. However, I had already performed the following experiment, showing that the L+N shunt is not the cause of the problem.

The current driver is guaranteed to produce a rock-stable current when producing a steady 16A for a long period of time, because all thermal effects in the zeranin shunt will reach an equilibrium after a few minutes, after which no further drift will occur. For this experiment to determine if the L+N shunt is OK, I set the current driver to produce a steady 16A. I installed an SPST switch, that can switch the driver current output either through a 'dummy' 10 mohm resistor, or through the L+N master shunt 10 mohm resistor. Initially, I send the current through the dummy resistor, for 10 minutes or so, until the current stabilizes to better than 1ppm, which it does. Then, I flick the switch, so the current is now sent through the L+N resistor, and I data log the voltage across the L+N. Ignoring the 1st 100ms or so after the switch is settling down, the current pulse sent through the L+N will be perfect, without any drift at all on the leading edge, or thereafter. This we know, because the zeranin shunt in the current driver sees a steady 16A at all time (except for a few ms when the switch is switching), so there cannot be any thermal drift effects occurring in the zeranin shunt, and I know from many measurement that the current stability produced by the Driver is set entirely by the stability of it's shunt resistor - the rest of the current drive circuitry may be regarded as perfect.

The resultant square wave logged across the L+N master shunt, produce by operating the toggle switch, is observed to be perfect, with no drift on the leading edge, after the current is abruptly switched from zero to 16A. I therefore conclude that the L+N master shunt is OK, and that the 5ppm drift issue that I have previously described is caused by resistance drift in the temperature-controlled zeranin shunt in the current driver.

I'll talk more about peoples relies, which I appreciate. It's great to have a bunch of sharp people that find this kind of stuff interesting, that I can bounce ideas off. I think we are all in broad agreement that the problem comes about because the zeranin is mechanically bonded to a metal substrate, and I'll attempt to fill in some details as to exactly why this causes the observed problem.

[Cerebus]

I need to read everything again to be sure I precisely understand what's going on. That said, if my understanding of the 'experimental' setup is correct and the drifts are happening when I think they are I have a suspicion that the problem is caused by creep in the bonding layer. That is, you hit it with a 16A square wave, the shunt heats up, the aluminium heats up and sets up a stress on the bonding layer because of differential expansion of the shunt and aluminium. Then the bonding layer slowly relaxes giving the observed shift as the stress in the shunt changes with movement of the binding layer. Very much a first guess but I think it's consistent with the observed behaviour, if I've understood the observed behaviour properly.

[Alex Nikitin]

I need to read everything again to be sure I precisely understand what's going on. That said, if my understanding of the 'experimental' setup is correct and the drifts are happening when I think they are I have a suspicion that the problem is caused by creep in the bonding layer. That is, you hit it with a 16A square wave, the shunt heats up, the aluminium heats up and sets up a stress on the bonding layer because of differential expansion of the shunt and aluminium. Then the bonding layer slowly relaxes giving the observed shift as the stress in the shunt changes with movement of the binding layer. Very much a first guess but I think it's consistent with the observed behaviour, if I've understood the observed behaviour properly.

A good point, and a possible solution would be to use a heatsink material with the same thermal expansion coefficient as Zeranin (18ppm/C). Silver looks like a perfect match with 18ppm/C and even plain copper (19ppm/C) looks much better than aluminium with 23ppm/C.

Cheers

Alex

[Zeranin]

Hi and welcome to the forum!
1) Does the current need to be set quickly at "any" value between 0 and 16A? Or is it an "on/off" situation for a particular current which can be set and just steered in/out of the load?

I know where you are coming from, but sadly the current needs to be set from any current I1, to any current I2, either in a step, or a linear ramp, or some other form of ramp.

[Zeranin]

The difference in temperature between the resistor element and the aluminum backing can have an influence, but the time constant should be rather short, as it does not take  that long for the temperature to equilibrate.

The time constant might be a good hint to locate the problem. It could be as well be the other shunt.

A thermal effect should be proportional to the square of the current - so a test with a smaller current (e.g. 10 A) might help.

You claim that if the drift effect is thermally induced from self-heating, then the effect would scale as the square of the current. Actually, that is not really right. In ABSOLUTE terms, that is correct, but results and plots of this type are always in units of ppm or ppk/K. If you halve the current, then the ABSOLUTE effect in Amps is reduced by a factor of 4, but the current itself is halved, so the effect when expressed in ppm or ppm/K is halved, in proportion to the current, and this has been confirmed experimentally.

On the time constant, it's more complicated. When the current is switched from zero to 16A, the temperature of the zeranin sheet starts to rise above the constant-temperature substrate. This will not happen instantaneously, because of the thermal mass of the zeranin. In my particular situation, a 12mm thick copper plate is used to clamp the zeranin onto the 12mm thick, constant-temperature heatsinking plate, so the effective thermal mass of the zeranin is considerable, and we would expect the temperature rise of the zeranin to be relatively slow, a few 10’s of seconds. I have a thermistor embedded in the copper block, almost touching the zeranin, so I can confirm that the temperature of the zeranin and the copper block do indeed rise, by about 0.25K, over a few 10’s of seconds.

I explained in another posting the experiment showing that the L+N reference shunt is not at fault.

[Zeranin]

I haven't had my coffee yet, so I hope this makes sense ...

Yes, your posting makes perfect sense, and I thank you for thinking about it. I think the topic still has some way to run though. I am writing up a long explanation of exactly what I think is happening, and hope to post it soon.