resistor temperature coefficient revisited

[uwezi]

Last week I let my students (first year engineering physics) make a simple experiment to show them that the resistance of a resistor does not need to be constant.

I let them wire up a Wheatstone bridge with 3 metal film 1 kohm 1% resistors and 1 carbon film 1 kohm 5% resistor. Then they were supposed to touch the carbon film resistor with their fingers to warm it up and determine the sign and magnitude of the carbon film resistor's temperature coefficient. 

Apart from getting the signs right when connecting and reading the multimeter, there was no big doubt or mystery here. The resistors showed a negative tempco as they should... 

Next they were supposed to warm one of the metal film resistors instead. I had done this experiment before with metal film resistors from a different (older, European) batch and the result was positive as it should be according to the text book for a metal. However, the students found - to my surprise - both positive and negative temperature coefficients from the very same batch of (Chinese) metal film resistors.

I repeated the experiment under very controlled conditions at home and found both positive and negative tempcos for different metal film resistors.

I then also noticed that many modern datasheets for metal film resistors specify +/- some ppm as tempco for metal film resistors.

Of course I know that there are metal alloys with different temperature coeffcients of their resistivity - but am I the only one who has been ignorant and always just assumed that metal film resistors would have positive temperature coefficients?

[SArepairman]

 is it possible for the resistor to change direction of drift due to age/over heating/other factors?

[Edwin G. Pettis]

Hi uwezi,

Most resistors, particularly of more modern manufacture produce TCRs of both polarities, it is quite likely that the same batch of resistors can have both polarities or just positive or just negative.  It has to do with the type of material used to make the resistor and the manufacturing methods.  In the precision wire wound resistors that I manufacture, both polarities are quite normal as this is a characteristic of the Evanohm alloy and the manufacturing processes, it is also very similar for metal film resistors as well.  This is mainly because the nominal TCR of the alloy is close to zero and the TCR tolerance of the alloy can make the final TCR negative as well as positive.   Some of the much older resistor types such as carbon or cracked carbon had only a single polarity (negative).  Other resistive alloys can have a positive TCR with a ± tolerance on the TCR, particularly alloys with higher TCRs.  Cermetic resistors can have both TCR polarities as well.  It just depends on the resistor.

For example:

Cermetic: 0 ±100 PPM/°C
Metal film: 0±50PPM/°C, 0±25PPM/°C, 0±10PPM/°C orlower
Precision wire wound: 0±20PPM/°C, 0±10°C, 0±5PPM/°C or lower
Power resistors: +350PPM/°C

These are just a few examples, resistors can be found with TCRs of up to 6,000PPM/°C depending on the alloy

[T3sl4co1l]

I then also noticed that many modern datasheets for metal film resistors specify +/- some ppm as tempco for metal film resistors.

Of course I know that there are metal alloys with different temperature coeffcients of their resistivity - but am I the only one who has been ignorant and always just assumed that metal film resistors would have positive temperature coefficients?

No, it's just you.

But yeah, like they said, check the datasheet.. all sorts of things are available these days.



Oh- brings to mind another classroom experience I had.  Inorganic chemistry lab.  Band gap.  Involves a big Box O' LEDs, cells to light them with, and a dewar of LN2 to chill the lights with.

Chill the LED, record the shift.  Plot and write up.

The hypothesis was, well, take this red one here.. chill it and it goes yellow, and green!  The blue goes violet then invisible (ultraviolet)!  So, clearly, the bandgap is increasing with reduced temperature!

So, being a rebel as always, I grabbed a green (which is GaP, rather than the GaInAsP alloys constituting the red, orange and yellow emitters, or GaN for blue) from the box.  Which started green, then got yellow and red under LN2.  Response from the instructor?  "Uh let's not use that one, it's a bad example..."

I won't say the moral of the story is, some instructors are bad (ignorant?).  I would rather say, it is two things:
One, just... research what you're doing, before doing it (ah, I've had more than a few unprepared labs, yes...).  So, don't be unprepared, whether for the work itself, or the immediate questions/facts concerning it.  Ok, so, "don't be ignorant" kind of IS saying the same thing...
Two, PLEASE, PUUUHHHLEASE don't mislead your students about "X is always this way", when you damned well sure know it's not anyway!  (In your example: that would be generalizing bulk properties of real materials, which are notoriously variable even among the pure metallic elements.  Bismuth or gallium's TCE for example.)  Just allow that, what you're teaching is an approximation, and that there's always "something more at the bottom" to be found.  At worst, you'll have a few bothersome students asking you "why" incessantly (and I would dare say, that's not a bad thing!), at best you'll have inspired a few excellent future scientists.

is it possible for the resistor to change direction of drift due to age/over heating/other factors?

Sure.

I don't have any particular examples or articles to go on, but from what I know of resistance, it should be more than possible, especially if you're rooting around for changes at the ppm level!
- Oxidation of the surface coating (epoxy / enamel / ), leading to decreased resistance, increased humidity sensitivity
- Oxidation of the alloy, reducing resistance, increasing humidity sensitivity
- Diffusion of alloy components; crystallization and segregation; in the element, or in the terminals and junctions as well
- Inhomogeneity due to crystallization, unbalanced thermocouple voltages (also shows up as a voltage error, not purely resistance), corrosion, humidity
- Electrochemical offsets (voltage rather than pure resistance error) due to humidity

The amount of shift in resistance and TCR due to any of these will vary widely by material, design and sealing process, just as the characteristics of different materials differ quite strongly.  Recall the basic mechanism at work here: most low-TCR alloys are formulated to have a conspicuous bump in their resistivity, which just so happens to coincide with room temperature (or something near there), either near a peak, valley or inflection point.  These parameters are all dependent on tight alloy percentages and uniformity, so to some extent or another, they'll vary even just from crystal shape and such.

Worth keeping in mind, also: even if a resistor is rated for "precision", and up to a 150C or whatever operating limit... that doesn't mean its specs are anywhere near sane at that temperature.  Even/especially for low-TC types, this is good reason to keep the temp rise (power dissipation, etc.) as low as possible.

[uwezi]

I would rather say, it is two things:
One, just... research what you're doing, before doing it (ah, I've had more than a few unprepared labs, yes...).  So, don't be unprepared, whether for the work itself, or the immediate questions/facts concerning it.  Ok, so, "don't be ignorant" kind of IS saying the same thing...
Two, PLEASE, PUUUHHHLEASE don't mislead your students about "X is always this way", when you damned well sure know it's not anyway! 

Points taken  - I normally don't try to mislead my students...

By the way I am very well aware of the green-LED anomaly and would like to test this for my own...

Just allow that, what you're teaching is an approximation, and that there's always "something more at the bottom" to be found.  At worst, you'll have a few bothersome students asking you "why" incessantly (and I would dare say, that's not a bad thing!), at best you'll have inspired a few excellent future scientists.

From the students' general reaction to me and my lectures I am quite sure I'm generally on the right track

[uwezi]

...both polarities are quite normal as this is a characteristic of the Evanohm alloy and the manufacturing processes, it is also very similar for metal film resistors as well...

This would have been my next question: the alloys used... Thanks for the detailed answer!
It's never to learn new stuff and throw the old textbooks overboard!

[paulie]

most low-TCR alloys are formulated to have a conspicuous bump in their resistivity, which just so happens to coincide with room temperature (or something near there), either near a peak, valley or inflection point.

I'm confused. Why would anyone put a bump in a temperature compensated device? Specially near a nominal temperature point. Wouldn't it be better if things were flatter around there? What am I missing?

[T3sl4co1l]

most low-TCR alloys are formulated to have a conspicuous bump in their resistivity, which just so happens to coincide with room temperature (or something near there), either near a peak, valley or inflection point.

I'm confused. Why would anyone put a bump in a temperature compensated device? Specially near a nominal temperature point. Wouldn't it be better if things were flatter around there? What am I missing?

That's exactly what I said.

The general idea is;

Metals have positive TC.
Some combinations have a dip, or inflection point, or something like that.  Because magic.
By varying the alloy, we can adjust the coordinate of this dip until it's in a useful range around room temperature.
The asymptotic behavior (i.e., the TC at temperatures very different from 300K) still tends to be near the prototypical case ("metals have positive TC"), but we locally have a much more stable value (i.e., R'(T) ~= 0, even though R'(T) is asymptotically nonzero).

I don't know how true that is for a large number of metals, what their rho(T) does for wide ranges of T.  It's pretty straightforward (rising, as a power law I think?) for simple(?) cases, like iron and copper.

Further optimization comes when you can adjust more than one parameter and corresponding factor, and instead of a peak or valley (with a local quadratic approximation), you get an inflection point (with a local cubic approximation).  I believe that's the special sauce behind Manganin, as opposed to slightly more conventional (Constantan, I think?) alloys.

You can also make it "minimally bad", by manipulating the double root at the inflection point, kicking the points just barely apart, so you get a +100ppm peak followed by a -100ppm valley, so that instead of a narrow band of frickin' sweet 10ppm, it's dirty but it's 100ppm over a much wider temperature range.

The connection between metals, mixtures and curves is going to be weird (when it comes to condensed matter physics, who knows ), but the general approach with polynomials is always relevant.  Hence the caution to be careful generalizing the performance of a resistor to temperatures other than the one the TC is measured at -- the derivative might be small at one point, but that's no guarantee of tolerance bands or useful range away from that point.

Tim

[SArepairman]

I think there is a misunderstanding between you two because of the curves imagined.



near X = 0 its "flat" i guess kinda like a horizontal asymptote (good for your miliamp current set resistor).

versicle vs horizontal asymptote, I think thats where your confusion lies.

-2/+2 has a true vertical asymptote, which would be good sensor resistors of some kind.

and I wanna say the higher the order the "flatter" the flat part is and the nastier the vertical assymptotes are, like a X^2 parabola is not nearly as nice around x=0 as a X^3, I think... but also it does not have quite as nasty non linearity once you go outside you "metrological operating temperature zone" like X^3




*it's hard to imagine a horizontal "pseudo" asymptote on a X^2 then a x^3

[uwezi]

This is a not-so-widely known phenomena. With a particular case : This effect is used in electrical bonded strain gauges, to measure elongations in experimental mechanics.

Strain gauges are not only used in experimental mechanics but in all modern electronic scales. Close to our resistor measurement setup we actually also have two strain gauge setups and a disassembled luggage scale exposing the miniature strain gauge load cell inside.

And you are absolutely right to point out this higher-order effects as additional sources of measurement error - the metal film resistors I was investigating have, however, TCRs in the order of +/- 50 ppm and I judge that the aforementioned different resistance alloys are the main reason for their behaviour.

I also built a Wheatstone bridge test unit with an instrumentation amplifier to quickly and controllably test 1 kohm resistors for their temperature coefficient. Then I went through my boxes of resistors at home and at the university:

• All vintage 1% metal film resistors (pre-2000) which I tested, both western and Soviet origin, show positive TCRs for temperatures between 20°C and 30°C. ONE single exception: a Vitrohm HSS 1000ohm 1% resistor with a TCR of -200ppm/K.
• All more recently purchased 1% and 0.1% resistors from different sources (known manufacturers are Vishay and Firstronics) show mostly negative TCRs in the same temperature range, at least one order of magnitude smaller than the vintage ones.

All tested resistors so far were through-the-hole resistors.


Thank you all for your input and contributions!

[SArepairman]

This is a not-so-widely known phenomena. With a particular case : This effect is used in electrical bonded strain gauges, to measure elongations in experimental mechanics.

Strain gauges are not only used in experimental mechanics but in all modern electronic scales. Close to our resistor measurement setup we actually also have two strain gauge setups and a disassembled luggage scale exposing the miniature strain gauge load cell inside.

And you are absolutely right to point out this higher-order effects as additional sources of measurement error - the metal film resistors I was investigating have, however, TCRs in the order of +/- 50 ppm and I judge that the aforementioned different resistance alloys are the main reason for their behaviour.

I also built a Wheatstone bridge test unit with an instrumentation amplifier to quickly and controllably test 1 kohm resistors for their temperature coefficient. Then I went through my boxes of resistors at home and at the university:

• All vintage 1% metal film resistors (pre-2000) which I tested, both western and Soviet origin, show positive TCRs for temperatures between 20°C and 30°C. ONE single exception: a Vitrohm HSS 1000ohm 1% resistor with a TCR of -200ppm/K.
• All more recently purchased 1% and 0.1% resistors from different sources (known manufacturers are Vishay and Firstronics) show mostly negative TCRs in the same temperature range, at least one order of magnitude smaller than the vintage ones.

All tested resistors so far were through-the-hole resistors.


Thank you all for your input and contributions!

there are other ways to weigh things that are less drifty then sprain gauges.

http://www.accurateshooter.com/gear-reviews/sartorius-magnetic-scale-is-fast-ultra-precise/

[uwezi]

there are other ways to weigh things that are less drifty then sprain gauges.

http://www.accurateshooter.com/gear-reviews/sartorius-magnetic-scale-is-fast-ultra-precise/

thanks for pointing that out, but certainly strain-gauge type scales are (a) cheaper and therefore (b) more common...

You can also measure weight with a quartz microbalance (QCM) utilizing the change in resonance frequency of a quartz crystal - very fast and very accurate for very tiny weights. We use these in some of our lab equipment.