Resistivity vs Temperature – flatter is better? - Page 1
Forum section: electronics / general

author: Zeranin
author_rank: Regular Contributor
timestamp: April 21, 2016, 11:49:35 pm
content: This is a sister thread to my ‘PCR vs TCR’ thread. We need to agree on the fundamentals, so here I will talk in general about resistance and resistivity. We all know whatresistivityis. Resistivity is a property of the material, but not of the dimensions of the material. Resistance depends upon resistivity, and the dimensions, as per :-R = rho x L / AWhere rho is the resistivity of the material in ohm-meterL is the length of material, in metersA is the cross sectional area of the material, in meters^2R is the resistance, in ohmsI need to briefly mention Temperature Coefficient of Resistance (TCR), typically expressed in units of ppm/K. Frankly, most of the common ways that TCR is expressed are pretty useless and often deliberately misleading, but I think we would all agree that what is fundamentally useful is the plot of Resistance versus Temperature, from which the TCR is always determined anyway. As far as I am concerned, if the term TCR means anything at all, then it is the slope of the R-T curve, which of course should be as small as possible. In my view, its best to leave the vague term ‘TCR’ right out of discussions, and instead talk about the R-T curve, and the slope of that curve, dR/dT. If you know the R-T curve, then you know everything there is to know, whereas ‘TCR’ can mean almost anything and frequently nothing.For many years I assumed without thinking about it that the perfect resistive material would have a resistivity that was rock constant with respect to temperature, yet if you think about it, that is wrong. We don’t actually care if the resistivity is constant with temperature, what we actually want is for theresistanceto be constant with temperature. The resistance depends not only on the resistivity, but also on the length and cross sectional area of the material from which the resistor is constructed.Most materials (including resistive alloys) expand and contract with temperature. For example, Zeranin has a thermal coefficient of expansion (COE) of 18ppm/K. Therefore, if we manufacture a resistor from a round bar of Zeranin, and change the temperature by 1 DegC, then the length will increase by 18ppm, while the diameter will also increase by 18ppm. As the cross sectional area scales as the square of the diameter, this means that the cross sectional area will increase by 36ppm. You can see where this is leading. If the length increases by 18ppm, and the cross sectional area increases by 36ppm, then the net effect is to decrease the resistance by 18ppm/K, quite independently of any change of resistivity with temperature.It follows that if we could concoct a magic alloy whose resistivity did not change with temperature, but had a COE of +18ppm/K, as does Zeranin, then resistors built from this magic alloy would be rubbish, with a linear change in resistance with temperature of -18 ppm/K. Clearly, the name of the game isnotto produce alloys whose resistivity does not change with temperature, at least not unless the alloy also has a zero COE, which is rarely the case.What the resistor alloy alchemist actually does, is to empirically produce an alloy with the flattest resistance-temperature curve. In doing so, what he is actually doing, though may not realize it, is matching the Resistivity-Temperature curve to be equal and opposite to the linear change in resistance with temperature that comes about from the coefficient of expansion. For example, in the case of Zeranin, at the temperature where dR/dT=0, the resistivity of the material must change by +18ppm/k, exactly cancelling the -18ppm/K change in resistance due to thermal expansion. I have not seen this spelled out in any textbook, yet evidently this must be true. The best resistors, with very flat R-T curve, have a resistivity that varies significantly with temperature, and the resistance also varies considerably with temperature on account of the COE, but the two effects have been arrange to cancel. This concept will be important in my discussion on the PCR vs TCR thread.Does anyone disagree with any of this? If no one shoots this posting down in flames, then I’ll continue my discussion on the sister thread, PCR vs TCR.

author: Vgkid
author_rank: Super Contributor
timestamp: April 22, 2016, 12:12:44 am
content: This could be another interesting read. To bad Edwin hasn't been online in almost 2 weeks. You could try sending him a pm/email.

author: uncle_bob
author_rank: Unknown
timestamp: April 22, 2016, 12:25:03 am
content: HiConsider that most modern resistors are *not* made of wire hanging loosely in free space. Once you put a core material under them, or wrap them on a form, you add another variable.One example:Take your magic material and thin film deposit it on a glass substrate. The glass now dominates the X and Y dimensions of the device. The Z is still dependent on the magic material.Yes, it's complicated.Bob

author: Zeranin
author_rank: Regular Contributor
timestamp: April 22, 2016, 12:43:20 am
content: Quote from: uncle_bob on April 22, 2016, 12:25:03 amAll true. It's actually fairly easy to analyse the case of a wire-wound or thin film 'winding' over a cyclindrical substrate. Assuming that the R-T curve of the naked material is parabolic, as it usually is, then the result of winding on a cylinder with different coeffcient of expansion is simply to add an additional linear term in the R-T curve, that has the effect of shifting the temperature of the turning point, which can be even be useful, and resistor manufacturers therefore sometime deliberately choose to have different COE for the wire and former. I don't want to go off on a tangent though, I'll happily go through the theory on another thread some time if you like. This thread refers to a 'naked' resistor.

author: uncle_bob
author_rank: Unknown
timestamp: April 22, 2016, 12:54:38 am
content: HiThe main point is that just as you can't make a bulk part that does not change dimension with temperature, other very similar things quickly get into the mix as well. If you are going to consider one, it's useful to recognize that it's only a part of the whole design problem. The interaction with the "next guy in line" may very well impact you analysis of a free hanging wire.Bob

author: Zeranin
author_rank: Regular Contributor
timestamp: April 22, 2016, 01:02:35 am
content: Quote from: uncle_bob on April 22, 2016, 12:54:38 amAll true, but it is vital to fully understand the simple situation of a naked resistor first. Trust me, when I get back to my discussion on the PCR vs TCR thread, I will then get to analysing 'everything in the mix'. For this thread, I want to discuss naked resistors only.

author: Zeranin
author_rank: Regular Contributor
timestamp: April 23, 2016, 12:53:54 am
content: The response has been underwhelming, so I conclude that everyone agrees with what I wrote. I will return to the PCR vs TCR thread, and present a full analysis of what causes resistance change when the resistive foil self heats above the substrate, where the R-T curve predicts that no change in resistance should occur.

author: uncle_bob
author_rank: Unknown
timestamp: April 23, 2016, 12:59:39 am
content: HiI think that assuming "silence means consent" is often a dangerous thing ....Bob

author: Zeranin
author_rank: Regular Contributor
timestamp: April 23, 2016, 01:14:31 am
content: Quote from: uncle_bob on April 23, 2016, 12:59:39 amPossibly, but in any debate, if no response is provided, then the point is conceded.

author: miguelvp
author_rank: Super Contributor
timestamp: April 23, 2016, 04:36:05 am
content: I Didn't read the other thread, but if you step off the lumped element model then you'll have to use the full Maxwell equations since Kirchhoff's circuit laws apply only if you follow the lumped matter discipline with no change of charge over time inside the conductive elements and no change in magnetic flux outside that element.If you throw away those characterizations, then you are on your own.Edit: well, not really on your own. RF Gurus do it all the time, but that's why we call it voodoo because it does become very complicated.

author: Zeranin
author_rank: Regular Contributor
timestamp: April 23, 2016, 05:22:40 am
content: Quote from: miguelvp on April 23, 2016, 04:36:05 amI understand what your are saying, but unlike impedance for example, resistance and resistivity are DC quantities, so there is no problem.

author: miguelvp
author_rank: Super Contributor
timestamp: April 23, 2016, 07:16:33 am
content: You are changing the rate of charge over time so you can't use the simplified equations, and it does apply to DC.Edit: but I think I misread the OP, are you trying to come up with a thermistor? or make a resistor that is less affected by temperature?

author: Zeranin
author_rank: Regular Contributor
timestamp: April 23, 2016, 07:59:10 am
content: Quote from: miguelvp on April 23, 2016, 07:16:33 amRe this particular thread, I'm not trying to make anything, just asking if others agree with what I wrote in the first posting. The idea that a perfect resistor, one whose resistance does not vary with temperature, would be made from a material whose resistivitydoesvary with temperature, may seem odd, but is apparently true. Carefully read the first post. Do you agree with what was written?

author: miguelvp
author_rank: Super Contributor
timestamp: April 23, 2016, 08:53:27 am
content: Well, a thersmistor varies resistance based on temperature.They all do, but, Faraday was the first to observe that silver sulfide will decrease resistivity as temperature increased.So can a "perfect" resistor be made?I guess it's not impossible, but it will be more costly than your average resistor. There are other factors of course like humidity and even atmospheric pressure, but in theory I guess it would be viable at a cost of course.

author: quantumvolt
author_rank: Frequent Contributor
timestamp: April 23, 2016, 09:42:43 am
content: Quote from: Zeranin on April 23, 2016, 07:59:10 amThe statement is not true if your 'perfect' resistor (bar conductor) does not 'imperfectly' change size or form (by itself or from constraints).If one wants a resistor that is constant in value with changing temperature (i.e. zero TCR), one must either make it insensitive to changes (as in all relevant partial derivatives equals zero) or construct it so that the net effect of all temperature change induced effects is null (positive and negative effects cancel out in sum). Furthermore, if the resistor is 'bounded' by its environment (as in your case) then one will have to include a model for this in the latter case over.Your 'mystery' is not new. Even Vishay thinks in these terms:Manufacturers of precision resistors control the ?R/R= f(T) by matching the physical properties and designof the resistive alloy and pattern (alloy’s temperaturecoefficient of resistivity and of expansion, gage factor, andother properties—see Ref. 1, page 292) with substrate’scoefficient of thermal expansion (see Ref. 2).http://www.vishaypg.com/docs/60108/VFR_TN108.pdfI find the topic very interesting, but I have chosen not to participate. Your presentation has imo the character of some 'Sherlock Shunt' quiz. In my view you would have been better off laying all facts and thoughts on the table in your first post.Finally, you have been talking about 'theory' but most of your statements counts imo as mere opinions as long as there are no (or few/little) 'controlled' experiments/measurements and referencing to solid state physics / (electro-)mechanics.But it was fun for as long as it lasted (and that was quite a while ...)

author: Zeranin
author_rank: Regular Contributor
timestamp: April 23, 2016, 11:45:54 am
content: Quote from: quantumvolt on April 23, 2016, 09:42:43 amI apologize if my style was not to your taste, though am pleased you find the topic interesting. I'll take you comment there on board, as I get the feeling that Diligent may have similar feelings. Personally, I prefer not to express an opinion unless I am fairly sure it is correct, and when I started the thread, I did not feel sufficiently confident in my explanation to present it. The 'mystery' is not new in that I have no doubt that the top design engineers at Vishay precision resistor division know this stuff like the backs of their hand, and I agree that it is mentioned in the Vishay article you reference. That said, some of the key concepts I was discussing are not well known in my experience. For example, the custom-built shunt part of this project has been done in collaboration with a large and well-known resistor company, and their engineers were not aware that the R-T curve was invalid for predicting the change in resistance in my application, and at that time nor was I.Anyway, let's skip the Sherlock Shunt stuff, and I trust we can continue with interesting and fruitful discussions.Re this particular thread, I am talking about 'naked' resistors, whose expansion is not constrained in any way, and I'm still not sure if you agree with my first posting, or not. Do you? Personally I don't regard my first posting on this thread as deep or contentious, more like, 'hmm, I never thought about that, but thinking about it now, it does seem to be true, interesting'. Well, I hope some found it interesting.You wrote:If one wants a resistor that is constant in value with changing temperature (i.e. zero TCR), ....But wait a minute, the very core of the PCR vs TCR article was that zero TCR doesnotguarantee a resistor that is constant in resistance value with changing temperature. Yes? You are correct in saying that all we need to do is make a resistor that is either insensitive to every factor that changes resistance, or make all the effects cancel, though such a statement is of limited use unless we can identify and understand all the factors that cause changes in resistance in the first place, as per my final explanation in the PCR vs TCR thread.You wrote:Furthermore, if the resistor is 'bounded' by its environment (as in your case) then one will have to include a model for this in the latter case over.Yeah, I know I'm thick, but I don't know what you mean byin the latter case over.You wrote:Finally, you have been talking about 'theory' but most of your statements counts imo as mere opinions as long as there are no (or few/little) 'controlled' experiments/measurements and referencing to solid state physics / (electro-)mechanics.If I say that doubling the length of a conductor doubles it's resistance from the well-accepted relation R=rho x L / A, then is that a mere opinion? Do we need a controlled experiment or reference to solid-state physics? Surely not. If you think my final explanation given on the PCR vs TCR thread is wrong, or contains errors in logic or fact, then simply say so, and point out the error - that's what forums are for. I love to be shown wrong, cos that's how I learn.

author: uncle_bob
author_rank: Unknown
timestamp: April 23, 2016, 01:58:54 pm
content: Quote from: Zeranin on April 23, 2016, 01:14:31 amHiThat *assumes* a formal debate setting. There are many settings where it is not a valid assumption.This is not a criticism, simply an observation based on years of seeing that argument used.Bob

author: quantumvolt
author_rank: Frequent Contributor
timestamp: April 23, 2016, 02:20:54 pm
content: Well ... First of all, I have little knowledge of the subject but find it interesting. So I'll jump in with one toe first.I do agree with the principle of the first post. The formula:should be uncontroversial.Also the net cancellation of resistor value change from variation in resistivity, dimension, expansion/contraction, bounding forces etc. should be intuitive and known.Again a Vishay example (TCR here is probably the 'confusing' TCR concept. LCThE - linear coefficient of thermal expansion):'With an increase in temperature the unbonded foil has an inherent increase in resistance (positive TCR). Concurrently, the foil experiences a compressive force because its higher LCThE is pushing it against the restraining force of the substrate. This compressive force drives the resistance down. With an increase in temperature, this perfectly balanced duality works to drive the resistance down (the compressive force) by the exact same amount of inherent increase in resistance (the positive TCR of the unbonded foil), resulting in a near-zero TCR of the finished resistor.'p.5 inhttp://www.digikey.com/Web%20Export/Supplier%20Content/VishayPrecisionGroup_804/PDF/vishay-glance-precision-resistors-for-energy.pdfThe quote illustrates that when seeking cancellation of thermal effects (the 'latter case' in my previous post) one has to include the resistor's environment in the model.Another relevant statement from (p. 2 in) the link in my previous post:'When chip resistors are soldered to a PCB, the differencein coefficients of thermal expansion and temperaturegradients cause additional thermal strains which influenceresistor’s ?R/R = f(T). Mounting a chip resistor on aceramic and on an FR4 PCB will result in a different?R/R = f(T) relationship.'http://www.vishaypg.com/docs/60108/VFR_TN108.pdfI do not have the time or inclination to answer all points now. But you will surely see that I agree with the points concerning resistivity, unconstrained dimension (length and area in the bar model), and strain from bonding and/or spatial bounding.I must reserve the right to comment on other points and your main thread's conclusion at a later time.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: April 23, 2016, 02:44:43 pm
content: While I do agree with the statements in the first post, I think the mysteries and problems are more with language and problem definition than in any underlying physics. Many of the responses here reflect answers to different questions than you were asking.Language - TCR. If you want an ideal resistor for a voltage divider or some similar application you want zero TCR (temperature coefficient of resistance), which as you point out, often requires a non-zero TCR (temperature coefficient of resistivity).Problem definition - "zero" TCResistance. If you want a few percent accuracy in a voltage divider, "zero" is something you can read off spec sheets. The more decimal places you want you will have to define more and more of the problem. For example if the voltage divider is by 2, you may not need "zero" TCR, but will need matched TCR. If the divider is other than by 2, self heating may put additional constraints on the TCR. Making your voltages "slowly" time varying adds other constraints and requires more thorough definition of slowly.In many cases engineering solutions are wrapped around "simplifying" the problem. Using an oven to minimize temperature fluctuations for example. The complexity of the oven simplifies the problem.My general rule is that thought spent defining the true problem is seldom wasted. In some cases after all of that thought a very simple response may be adequate, in other cases lots of "simplification" is required.

author: Zeranin
author_rank: Regular Contributor
timestamp: April 24, 2016, 12:52:36 am
content: Quote from: uncle_bob on April 23, 2016, 01:58:54 pmLet's summarize(a) Because someone does not respond to a claim, does not mean they agree with it. In your words, silence is not consent.(b) In all cases, if someone does not respond to a claim, then their unstated views are irrelevant in the discussion. That is what I meant by saying you 'concede the point'. It doesn't mean that you personally agree with the claim, just that your view on the matter is irrelevant, unless and until you state your view, and provide evidence for it.(c) If someone makes a claim, and others choose not to respond, then it does not necessarily mean that the claim is correct. What it does mean is that the claim is the best available, and that the claim 'stands' unless and until challenged. That said, if a large number of people have read the claim, as here, and no one has provided evidence to refute the claim, then this greatly reinforces the likelihood that the claim is correct. That's how scientific knowledge is gained. Someone proposes a theory, but it only becomes worth something after it is published, and made available for scrutiny, which is what I have done here.As with your posting to me, this is not a criticism in any way. I don't even know if you agree or disagree with all or part of what I've written, because you haven't told us.

author: Zeranin
author_rank: Regular Contributor
timestamp: April 24, 2016, 01:26:40 am
content: Quote from: quantumvolt on April 23, 2016, 02:20:54 pmWe seem to be in complete agreement so far. One of the great things about forums, is that it forces all concerned to think about and research the topic. For example, your Vishay example discusses a little bit of detail about differential expansion of the foil and substrate, and how if the foil attempts to expand relative to the substrate, then in effect the foil is in compression, leading to a decrease in resistance. Deja vu, exactly as in my PCR vs TCR conclusion, except I went a step further and explainedwhythe compression in x and Y leads to a decrease in resistance, via the Poisson effect. This decrease in resistance is the origin of the unwanted PCR, but a zeroTCRis still possible, because the resistivity vs temperature of the foil material is carefully arranged to cancel the effect, which of course is the principle that I was illustrating in this thread.I look forward to your future comments 'on other points and the main thread's conclusion'. Cheers.

author: quantumvolt
author_rank: Frequent Contributor
timestamp: April 25, 2016, 02:39:17 am
content: I have been looking a bit at the Poisson effect (that was unknown to me), strain and elasticity in metals:'Poisson's ratio, named after Siméon Poisson, also known as the coefficient of expansion on the transverse axial, is the negative ratio of transverse to axial strain. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio \nu (nu) is a measure of this effect. The Poisson ratio is the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes.Conversely, if the material is stretched rather than compressed, it usually tends to contract in the directions transverse to the direction of stretching. That is a common observation when a rubber band is stretched, it becomes noticeably thinner. Again, the Poisson ratio will be the ratio of relative contraction to relative expansion and will have the same value as above. In certain rare cases, a material will actually shrink in the transverse direction when compressed (or expand when stretched) which will yield a negative value of the Poisson ratio.'https://en.wikipedia.org/wiki/Poisson%27s_ratioGiven this information I expect that this is the effect observed with the shunt. But of course, I am no expert and I do not have access to the item in question, so I state only my opinion. Furthermore, the value of the constants you use is beyond me to estimate.This topic touches solid state physics, metallurgy / materials science and mechanics. It is still my opinion that it would have landed better with some drawings, tutorial quotes, datasheets (or material constants / parameters) and (quasi-) academic references.I also would have liked if your situation allowed an identical shunt with another mounting material. As a side note, since what you want is similar to a 'strain gauge that does not react to strain' (sic), I read a bit about strain force sensors. It turns out that many situations (including bridges) often use reference or control gauges (often named dummy gauges or Poisson gauges) - some times mounted orthogonally and in some cases protected from strain.I have tried to find a piece of flat zeranin, konstantan, isotan, manganin or whatever on eBay, but found only wire. If I were you I would plan my next building of a precision component like the shunt in question in two different versions and/or with some add-ons that allowed some control monitoring and experimenting.As for the PCR, I like to swallow one subject at the time. So after I read around a bit, I realized that I should dwell more on TCR-related stuff first. However, there is a Vishay patent somewhat related to this topic in the list of some of the links I have read and present to anyone interested.Since you obviously have thought well about your shunt and the mechanisms occurring, and also like to write, I propose that you make some kind of 'lab report' with figures, formulas, measurements, calculations and explanations in the main thread. It could be useful for future reference to have it all in one post.Just my song satang.https://en.wikipedia.org/wiki/Poisson%27s_ratiohttps://en.wikipedia.org/wiki/Deformation_%28mechanics%29https://en.wikipedia.org/wiki/Gauge_factorhttps://books.google.co.th/books?id=I026BAAAQBAJ&pg=PA21&lpg=PA21&dq=resistor+poisson&source=bl&ots=NFJLjQWB_B&sig=PWGiEfRH24XhnOvMoj05-NP7U6U&hl=en&sa=X&ved=0ahUKEwiXwYWIl6bMAhWDWo4KHdBaDMo4ChDoAQg_MAg#v=onepage&q=resistor%20poisson&f=falsehttps://www.google.com/patents/US4677413http://health.uottawa.ca/biomech/courses/apa6903/transducers.pdfhttps://www.transducertechniques.com/wheatstone-bridge.aspxhttp://www.ni.com/white-paper/3642/en/http://www.ing.unp.edu.ar/electronica/asignaturas/ee016/anexo/r-an078.pdf

author: Zeranin
author_rank: Regular Contributor
timestamp: April 25, 2016, 11:46:15 am
content: Quote from: quantumvolt on April 25, 2016, 02:39:17 amVery nice posting. Thank you for your considerable effort. I'm pretty much in agreement with all you wrote, but will make a few comments when I've recovered from my day's bushwalking. I find the Vishay patent that you found to be of particular interest. I've only briefly read the patent at this stage, but it's very similar to what I concluded and wrote, also concluding that for low PCR thesubstrateshould be made from a material with zero or very low expansion coefficient, and that then the resistivity vs temperature of the resistive material needs to be adjusted so as to give a zero TCR. The TCR and PCR stuff no longer bothers me because I'm confident that I understand it, and that what I wrote is correct, but it is reassuring to see the same concepts and conclusions written by people such as Zandman who are pioneers and leaders in the field. I was also impressed by the very clever method described of fine-tuning the resistivity vs temperature curve by plating with small amounts of a different metal. Very neat and clever. I often wondered how they managed to reasonably cheaply and easily tweak the TCR so ridiculously low on their top-end foil resistors, and that's how!

author: Edwin G. Pettis
author_rank: Frequent Contributor
timestamp: April 25, 2016, 05:17:40 pm
content: Another supposedly simple question with not so simple answer. First, TCR is far from useless, it is the actual real world variance of resistance with various real world effects on the resistor. There is the 'raw' TCR, this is essentially what you are talking about here, a piece of resistance alloy just laying there, such as a bar sitting on a table top, this bar will have limited effects placed upon it, dimensional variation with temperature is one of them, humidity and barometric pressure (depending on the alloy) also affects this bar sitting on the table. This bar will also have a raw TCR of a specific value which consists of all of the variables affecting the bar in its present state as measured by a resistance bridge. In the case of alloys such as Manganin and Zeranin, the TCR curve is essentially hyperbolic with near zero TCR adjusted around the cardinal temperature point. Other alloys such as Evanohm have much flatter TCRs with wide temperature variations. All TCR measurements, whether it is 'raw' or from a finished resistor is the total net effect of all of the variables that affect the resistive alloy. In the case of wire wound resistors, the 'raw' TCR of the wire is measured and labeled on the spool of wire, this TCR is usually not what you get when the resistor is manufactured, the end result i.e. the final actual TCR of a finished resistor is the net total effects of all of the physical variables on that resistor, in addition to the ones I mentioned earlier, there is additional sources of stress put of the resistive element by the manufacturing processes, for example the act of drawing alloy through a die to produce a specific wire size or the milling of alloy to make film or foil affects the TCR of the element, the 'raw' TCR in effect.When the alloy is used to make a resistor there are additional mechanical stresses put upon the alloy which further changes the apparent TCR, for wire wound resistors, this is the act of wrapping the wire around a bobbin, in addition to that there is the coefficient of expansion of the bobbin, humidity absorption of the bobbin and encapsulant, ect. all of which affects the overall TCR of the resistor. Of course steps are taken during manufacture to reduce these effects to as low as possible. The end result is a finished TCR which is rarely ever the same as the 'raw' TCR was. The actual TCR of the wire as manufactured can only be changed by very high heat, well above any operating temperatures, in a finished resistor it is physical forces which change the end result TCR, properly made, the TCR itself is very stable long term.Since Vishay's parts were mentioned I'll give some detail about their manufacture, first Felix Zandman was hardly the only person who developed film/foil resistor technology, he had a lot of help over the years and his initial patents were declared invalid in court. Be that as it may, Vishay became the prime mover of film/foil technology over the years. These resistors are both similar and different than wire wounds, while they both use very similar alloys, the manufacturing processes are considerably different because of the physical differences. Vishay, et al, uses very thin sheets of resistance alloy which are etched by various methods and then attached to a substrate, ceramic being the most common. The act of attaching a very thin sheet of alloy to the ceramic creates considerable physical stresses on the alloy by adhesive, temperature, power, humidity and barometric pressure to name a few. These various stresses created extremely non-linear TCR curves and relatively high TCRs. Over the years, the engineers at Vishay and others, gradually reduced the fluctuations of TCR to ever smaller values, this took a lot of time, decades actually to accomplish. As mentioned there was a lot of 'tweaking' going on with various materials and adhesives trying to find a way to flatten out the TCR curve stresses.Today they have some models with very low TCR over limited temperatures, while the curve is still not 'flat' per se it is substantially flatter than it used to be. I might add that Vishay does not guarantee their TCRs are 'zero', they guarantee the maximum limit of TCR and I've found over the years that Vishay tends to make claims that they can't always meet. As to Zeranin's comment, "I often wondered how they managed to reasonably cheaply and easily tweak the TCR so ridiculously low on their top-end foil resistors, and that's how!", the process is neither easy nor particularly 'cheap', in fact the yields of these very low TCR resistors I suspect are not particularly high and are likely selected out of a given batch of resistors.Often, depending on the alloy, the dimensional variance is often one of the smaller variables that affect the overall resistor, Evanohm has a TCE of about 6PPM/°C, the physical variables as I described above have a much more significant effect on the finished resistor and personally I really don't pay much attention to it when I'm making PWW resistors, there are other stresses which are much more important to the finished product and while the dimensional property of the alloy is more important to the film/foil resistor, it also tends to be less of an effect than other stress sources as well.As resistor manufacturers strive to get to that supposedly golden TCR of zero, all of the various effects become more important and even the tiniest sources of stress become increasingly important, in fact they can actually become more difficult than the larger sources of stress to control as the TCR drops below 1PPM/°C, ask me how I know!To more directly answer your question in the initial post, you are mostly correct in your premise about dimensional resistivity vs. resistance.

author: splin
author_rank: Frequent Contributor
timestamp: April 25, 2016, 05:50:57 pm
content: How do you know?

author: splin
author_rank: Frequent Contributor
timestamp: April 25, 2016, 06:43:53 pm
content: Quote from: DiligentMinds.com on April 25, 2016, 06:24:25 pmI was responding to the previous post - a bit of a cheap shot; I wasn't expecting an answer but it sounds like there's an interesting story behind it.Quote from: Edwin G. Pettis on April 25, 2016, 05:17:40 pm

author: babysitter
author_rank: Frequent Contributor
timestamp: April 25, 2016, 08:03:56 pm
content: I can confirm what Kevin said about Edwin!

author: Edwin G. Pettis
author_rank: Frequent Contributor
timestamp: April 25, 2016, 08:29:49 pm
content: How do I know? I manufacture PWW resistors with sub-PPM characteristics, that is something you can't do if you don't understand all of the fundamentals of resistors. This is proven by how many PWW manufacturers can actually make sub-PPM resistors repeatedly, I can count those on somewhat less than five fingers. I've worked in the resistor industry for over 4 decades. I've made ratio sets with tracking TCRs as low as 0.1PPM to 0.2PPM/°C that have actually been verified by measurement not catalog claims. To my knowledge, none of the other folks posting on here has worked in the resistor industry or actually manufactures resistors. I am also quite familiar with the inner workings of film/foil resistors even though I do not personally make them although I worked for a company that made them for a period of time. Most of these discussions are of theoretical origins and as most of us are aware of, theory and the real world reality does not coincide very well. Theory is great for an intellectual discussion but is only a framework for the real world of manufacturing.These days, almost anybody can produce a resistor with a TCR of less than 10 PPM/°C or even 5 PPM/°C, but once you start getting closer to that 1 PPM/°C or less, it becomes much more difficult and it separates out the commodity parts from the truly precision parts and yes there are very few of us who can consistently turn out parts near ±1PPM/°C or less. Those who can do it over more than a narrow temperature range are even fewer in number.I will also admit that I do not know every latest little trick being used by the Vishay group at the moment, that takes time to find out about as Vishay, like everybody else doesn't like to spill their trade secrets to the competition.

author: splin
author_rank: Frequent Contributor
timestamp: April 25, 2016, 09:42:21 pm
content: Oh dear, it seems that apologies are in order; for the avoidance of any further doubt my response was a joke - albeit a very poor one. I am well aware of Edwin's expertise having read most of his writings here and elsewhere and having responded to several of his posts.I know it's easy to inadvertently mislead when posting but I assumed the popcorn emoticon and my 'cheap shot' response would make it obvious but clearly I misjudged that, causing at least two people to spend more than a few minutes responding. Hopefully those responses may at least be of interest to those who were unaware of Edwin's background.So please accept my apologies and promise to make it absolutely clear in future if I am trying to make a joke, however bad.Splin

author: Zeranin
author_rank: Regular Contributor
timestamp: April 25, 2016, 10:22:26 pm
content: Quote from: Edwin G. Pettis on April 25, 2016, 05:17:40 pmHi Edwin, great to have you in on the discussions. You say that my initial post ismostly correct. Can you give us more detail, as in what part is not correct? Also, I don't understand your termdimensional resistivity. I would claim that theresistivityof a material does not vary with dimension, because resistivity is a property of the material, not of it's dimensions.Re my comment about the Vishay method of tweaking the R-T curve (I really must refrain from using the term TCR, which can mean almost anything), when I saidreasonably cheap and easy, this needs to be interpreted relative to the difficulty and cost of making very-high-end resistor in general. As you stress yourself, nothing is easy at this level of performance.

author: Edwin G. Pettis
author_rank: Frequent Contributor
timestamp: April 25, 2016, 11:06:21 pm
content: Sorry if I was a little foggy on the subject, I'm fighting a pinched nerve in my lower back and it can be very distracting to the train of thought. For a bulk material, the resistivity is not strictly dimensional, whether it is a pure metal such as copper or as an alloy such as Zeranin or Evanohm, the resistivity at the bulk level is constant, however if you want to get down to the nitty gritty level, very thin sheets approaching molecular thicknesses can exhibit variations of resistivity, think nanoscale for instance. For all intents and purposes resistivity at the bulk scale is constant. The characteristics of alloys are not particularly constant with dimension, for instance, the finer wire sizes of Evanohm can have a TCR much closer to zero on the whole than for larger wire sizes where it is much more difficult to get very low TCRs even today. I have a very specific specification for wire which produces low TCRs consistently even with the larger sizes, for that I have to pay more for the wire than the average run-of-the-mill resistor house. For the thinnest wire size as an example, 0.0004" diameter, that wire exceeds $50,800/lb (if it hasn't gone up again).Resistance varies with dimension, resistivity, not so much.Splin: explanation accepted, that is enough, no apologies needed, everyone has a flop now and then <grinning>.