Author Topic: Manufacturing custom high-precision low-TC resistors  (Read 21011 times)

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Offline JoeNTopic starter

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Manufacturing custom high-precision low-TC resistors
« on: January 27, 2018, 02:03:32 am »
Is there a thread for that?  I tried (title only) search for make/manufacture/custom and resistor/resistors and I didn't see anything.

I remember a thread about a board member that does custom low-TC resistors for metrology applications.  Can a normal person manufacture their own resistors?  I am talking about really good ones, rather than going to Vishay for $50 a pop.  Is that completely impractical?
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Offline amspire

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #1 on: January 27, 2018, 02:39:46 am »
Is there a thread for that?  I tried (title only) search for make/manufacture/custom and resistor/resistors and I didn't see anything.
https://www.eevblog.com/forum/metrology/t-c-measurements-on-precision-resistors/msg462296/#msg462296
Quote

I remember a thread about a board member that does custom low-TC resistors for metrology applications.  Can a normal person manufacture their own resistors?  I am talking about really good ones, rather than going to Vishay for $50 a pop.  Is that completely impractical?
Edwin G. Pettis is the person you are thinking of.

Can you make your own resistors? Yes and no. It is not easy sourcing good materials to make the resistors. If you can get Manganin wire, it is solderable so you can make decent resistors, but Manganin does have a significant temperature coefficient. The better resistors are made from Evanohm wire. It can only be welded and it takes a lot of skill to do it right. The process of making zero tempco Evanohm wire is not easy, so if you just went and bought Evanohm wire on the Internet somewhere, chances it would also have a significant tempco and possibly drift.

Edwin explains it in great detail in that thread.
 
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Offline zhtoor

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #2 on: January 27, 2018, 07:21:37 am »
hello,

here is an interesting method for your consideration. (see attached file)

regards.

-zia
 
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Offline ramon

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #3 on: January 27, 2018, 12:58:15 pm »
Is there a thread for that?  I tried (title only) search for make/manufacture/custom and resistor/resistors and I didn't see anything.

I searched that same thread some months ago, and I think Zhtoor once asked that question.

But I remember that most of the replies were negatively biased (something like ... don't even try that ... hard to do ... better to buy one, etc ...).

So, if you don't mind, let's make this thread the thread about 'Manufacturing custom high-precision low-TC resistors'. With a possitive attitude. Something like 'it could be done' (... however I will not dare to say that it will be cheap, easy, or how long it will take to make it.)

Quote
I remember a thread about a board member that does custom low-TC resistors for metrology applications.  Can a normal person manufacture their own resistors?  I am talking about really good ones, rather than going to Vishay for $50 a pop.  Is that completely impractical?

Well, let's do it. We will not know if we don't try first.

But the very first problem you will find is that no single alloy manufacturer will ever sell the wire spools to a normal person.

I asked every single evanohm manufacturer and they completely ignored my (low quantity) requests. But I was able to find one evanohm spool (actually Nikrothal LX) from some auction site. The specs were really impressive : 3 ppm (from -55 to 25C) and -1ppm (from 25-150C).

I made a simple resistor around a TO3P mica sheet and protected with heatshrink tubing. (The picture shows a very first test version with copper instead of Evanohm that i made when I haven't received yet the evanohm spool)

Once I received the evanohm spool, I made the resistor. As I didn't have equipment to properly test the TC of the DIY resistor I asked TiN for help, and he kindly tested the resistor TCR using his HP 3458A and TEC environment. (Thanks again Tin!)

And the first result was a complete disaster, around 400 ppm. You can still check in his website how that 1.82K resistor compares to a Vishay Z202 10K:

  https://xdevs.com/ramon_res_z202_test1/

I am working on my second DIY resistor on my spare time. It will continue ...
 
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Offline amspire

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #4 on: January 27, 2018, 01:38:48 pm »
Ramon, how did you weld the Nikrothal LX wire to the leads?
 

Offline zhtoor

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #5 on: January 27, 2018, 01:49:33 pm »
hello,

a simpler and maybe practical way would be to get hold of YR NEOHM resistors like these:-

https://www.digikey.com/product-detail/en/te-connectivity-passive-product/YR1B10KCC/A105970CT-ND/3477555

and select -ve tempco resistors the absolute value of which would be < 15ppm,
now add a compensating copper-wire resistor (ca .+3930ppm, measure your wire spool first),
voila, you would have a pretty decent temperature compensated resistor.

(long term drift and environmental issues is entirely another matter of course)

regards.

-zia
 

Offline Kleinstein

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #6 on: January 27, 2018, 03:19:09 pm »
To get a really low TC, one has to look at more than just the linear TC, but also have a low second order TC. With 2 coefficients to watch for it gets increasingly difficult to find suitable ones for compensation, as chances are that the second order TC will be similar in one batch of resistors - so not much chance off compensation, but more like a chance of getting at least good TC matching.
 

Offline guenthert

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #7 on: January 27, 2018, 03:20:11 pm »
It's hard to see on the picture, but you don't want to wind the wire like a coil.  You intend to make a resistor, not an inductor after all.  ;)
 

Offline ramon

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #8 on: January 27, 2018, 03:22:42 pm »
Ramon, how did you weld the Nikrothal LX wire to the leads?

I guess that is the second problem, in the top ten list of issues. And this question arise every time evanohm is discussed.

Welding is the way we are supposed to make the resistors. This is the first and only option. And it is like there is no other correct way to do a precision resistor.

And after many tens of hours searching for a cheap, reliable and repetable solution to this issue, didn't find any single commercial device with all those three requirements. If money is not an issue then you just can go to Amada Miyachi website, contact sales and pick any of their machines. Actually, I recommend to visit they website anyway. It is an amazing place to find technical information about how a good welding can be done, and after reading some of their documents I ordered a molybdenum rod and molybdenum plate, and also a copper rod for some experimental DIY welding ... (that was before I found a place where I could buy cheap welding electrodes from a well known manufacturer of resistance welding machines. Those already made electrodes are much better suited for a reliable welding for many reasons described in Amada Miyachi technical notes, and user manuals of other welding manufacturers) ...

But the fact is ... for a DIY resistor do we really need to weld the wire? Why not just crimp?
Yes, why not? Even Mr. Pettis said that could be possible on one of his first posts.
 

Offline ramon

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #9 on: January 27, 2018, 03:36:43 pm »
It's hard to see on the picture, but you don't want to wind the wire like a coil.  You intend to make a resistor, not an inductor after all.  ;)

For DC, that might be in the lower 5 issues of the top ten list.

I could have changed winding direction in the first and second half, or have used a much more complicated ayrton perry winding (not sure if the wire would have keep on the place I wanted), but I am not sure that the TCR would have changed a lot.

TC was what I wanted to test on first place. (If the wire was actually <3 ppm as written on the spool) .
 

Offline Magnificent Bastard

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #10 on: January 27, 2018, 06:11:40 pm »
Ramon, how did you weld the Nikrothal LX wire to the leads?

I guess that is the second problem, in the top ten list of issues. And this question arise every time evanohm is discussed.

Welding is the way we are supposed to make the resistors. This is the first and only option. And it is like there is no other correct way to do a precision resistor.

And after many tens of hours searching for a cheap, reliable and repetable solution to this issue, didn't find any single commercial device with all those three requirements. If money is not an issue then you just can go to Amada Miyachi website, contact sales and pick any of their machines. Actually, I recommend to visit they website anyway. It is an amazing place to find technical information about how a good welding can be done, and after reading some of their documents I ordered a molybdenum rod and molybdenum plate, and also a copper rod for some experimental DIY welding ... (that was before I found a place where I could buy cheap welding electrodes from a well known manufacturer of resistance welding machines. Those already made electrodes are much better suited for a reliable welding for many reasons described in Amada Miyachi technical notes, and user manuals of other welding manufacturers) ...

But the fact is ... for a DIY resistor do we really need to weld the wire? Why not just crimp?
Yes, why not? Even Mr. Pettis said that could be possible on one of his first posts.

The only way I know of to properly weld such dissimilar materials such as copper and Evanohm wire is to use a pulse-arc (pulsed plasma discharge) welder like these:

https://sunstonewelders.com/

If you can't find a good used welder (they are used in the jewelry and dental industries), then there is the possibility to build your own:

https://frikkieg.blogspot.com/2010/11/pulse-arc-welds.html

A shielding gas (Argon) is used during the weld, and once the arc is started, then a regular CD-type discharge is initiated.  The weld energy is controlled either by switching with a high power MOSFET bank, or by allowing the entire capacitor to dump through an SCR (and you would have to control the main capacitor voltage before the weld).

Using the method, you can even weld a metal to a ceramic!  (>8000oK during the plasma arc discharge-- pretty much melts everything except the tungsten electrode).
 

Offline Magnificent Bastard

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #11 on: January 27, 2018, 06:22:00 pm »
It's hard to see on the picture, but you don't want to wind the wire like a coil.  You intend to make a resistor, not an inductor after all.  ;)

For DC, that might be in the lower 5 issues of the top ten list.

I could have changed winding direction in the first and second half, or have used a much more complicated ayrton perry winding (not sure if the wire would have keep on the place I wanted), but I am not sure that the TCR would have changed a lot.

TC was what I wanted to test on first place. (If the wire was actually <3 ppm as written on the spool) .

Winding the resistor as you have done on a mica card results in very low inductance, because there is very low cross sectional area in the "coil"-- so no need for strange wire configurations.  The edges of the mica card cause the wire to be bent on a very tight radius, and this raises the TCR.  To relieve this stress of the wire, you have to heat it in an oven for about 8 hours at 150C, and then plunge it into some alcohol chilled by dry-ice.  Repeat this cycle as many times as needed to get the TCR back down (and it will not fully recover anyway-- but you do what you can).  I would be more concerned about how the heat-shrink is stressing wire over a temperature range-- this might be a good percentage of your TCR change.  Try making a "case" for the resistor with a 3D printer instead-- so that the wire touches nothing except the mica card.
« Last Edit: January 27, 2018, 08:38:23 pm by Magnificent Bastard »
 

Offline David Hess

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #12 on: January 27, 2018, 06:48:31 pm »
ESI made precision resistors by winding the wire around a mica square so I wonder how good their temperature coefficient was.
 

Offline Edwin G. Pettis

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #13 on: January 27, 2018, 06:58:48 pm »
JoeN: "I remember a thread about a board member that does custom low-TC resistors for metrology applications.  Can a normal person manufacture their own resistors?  I am talking about really good ones, rather than going to Vishay for $50 a pop.  Is that completely impractical?"


I presume you are talking about PWW resistors with a TCR of 5PPM/°C or less with high stability, then your answer is not very likely.  On its face, it looks like it would be fairly simple, just wind some wire on a form, attach leads and there you have it....doesn't work that way in most cases.  Manganin (and its derivatives) are indeed solder-able which makes termination much easier but it also has mechanical handling requirements and stress relief needed in order to produce that under 15 PPM/°C TCR spec.  If you really want to play with some relatively low TCR resistors, you could obtain some Cupron alloy which is also solder-able and it doesn't need the pampering that Manganin requires.

You did not say how you attached leads to the Evanohm wire, obviously it was not by welding AND you CANNOT weld Evanohm to copper leads, I've said this several times in different threads.  However you attached the leads, that is the likely cause of your 400PPM/°C TCR, don't blame the wire.

Technically, you can crimp the wire BUT you're not going to get a very good joint, I also said why this wasn't a good idea in the threads, crimping Evanohm to copper leads is going to make for a bad joint with lousy results.

You can make reasonably good resistors to experiment with using Cupron or even Manganin but you are not going to get high performance resistors you're chasing after.  It is not easy, it takes a lot of experience and knowledge and specialized equipment.  If it was so easy, everyone would be making resistance standards.  I can tell you this, any ideas you come up with to try and make a homemade precision metrology grade wire wound resistor has already been tried many times over the years and all have failed.

It is not a case of negative thinking, it is nothing more than reality, you can only go so far with home made resistors and metrology grade is not one of them.  It is much more expensive to set up and make PWW resistors correctly than to just buy good resistors and no you don't need to spend anything like $50 on a resistor to get there.

Let's say you acquire all of the equipment and materials you need, you've already found out a 'simple' capacitive discharge welder plus weld head isn't cheap (I'll even give you a clue, second hand ones aren't cheap either), you've decided on how you're going to attempt to put wire on a form with some kind of terminations, you've got everything you think you need.  How much have you spent, even on the cheap, to get to this point?  Next you're going to start trying to make a resistor, you're going to get frustrated pretty quickly because things aren't going the way you expected.  You experiment with different ways, nothing seems to be working very good.  At this point, how many PWW resistors could you have bought for all the time and money you've invested in trying to make your own?

I encourage you to get some Manganin or Cupron wire and experiment with it on various forms, you will learn from this, have some fun and hopefully realize just how hard it is to make really good resistors.  This wire can be soldered to normal terminations without expensive equipment, you won't get 5 PPM/°C TCR but it should be a fun and learning experience without so much frustration.

Ramon:  No you won't find an alloy supplier that will sell 'small' amounts to anybody, they have their clientele who buys wire is some quantity, in my case, I have minimum line item cost of $550.00, no exceptions.  Your best bet to find wire is just to goggle for it, such as 'Evanohm', 'Cupron', or 'Manganin'.  There is a company in England, Goodfellow Cambridge Limited, that does sell small quantities but they are expensive.

There are differences in PWW resistor construction, it depends on the manufacturer on how they are doing it, but in the end they are all similar, how good the terminations are is the main difference.  Winding the wire on a mica form has been used for decades, it can work very well, if done properly.  Each way of making a PWW resistor requires different techniques and always has compromises and 'flaws' to some degree, there is no 'perfect' way of making a resistor.  The SR-104 comes very close but it entails a whole lot of work and time, that is why it isn't cheap, it isn't easy to make.

If you tried to solder Evanohm to a copper lead, all you ended up with is a cold solder joint and lousy TCR, actual welding is the only way and it has to be done just right or it doesn't work well.
 
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Offline Magnificent Bastard

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #14 on: January 27, 2018, 08:59:35 pm »
"... you CANNOT weld Evanohm to copper leads ..."

YES you CAN.  You cannot "CD Weld" (capacitive discharge welding)-- that won't work, but you CAN "Pulse Arc Weld"-- this is like TIG welding, but with an intense pulse of energy rather than a continuous discharge.  A gas plasma is very hot (greater than 8000oK)-- and will melt almost anything.

Watch THIS (stainless steel weld characteristic is similar to Evanohm):

 

Offline branadic

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #15 on: January 27, 2018, 09:27:29 pm »
Quote
I asked every single evanohm manufacturer and they completely ignored my (low quantity) requests. But I was able to find one evanohm spool (actually Nikrothal LX) from some auction site. The specs were really impressive : 3 ppm (from -55 to 25C) and -1ppm (from 25-150C).

I made a simple resistor around a TO3P mica sheet and protected with heatshrink tubing. (The picture shows a very first test version with copper instead of Evanohm that i made when I haven't received yet the evanohm spool)

Is this bare wire or is it an enameled wire? Could only find wires without coating on the bay.

-branadic-
« Last Edit: January 30, 2018, 07:57:16 pm by branadic »
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Offline Edwin G. Pettis

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #16 on: January 27, 2018, 11:41:15 pm »
To Branadic:  The spool indicates that it is enameled, if you try to make a resistor using the mica card method, if you're careful, you can use bare wire.

To M.M.:  I was replying to JoeN, as he did not mention how he connected the wires to leads (he didn't say what his leads were either), since it was very unlikely that he had an arc welder, my reply was geared to the more common CD welders which are more commonly available and just plain soldering.  If you have read my other postings you'll know exactly what I've said before (many times) about welding resistors.

Specifically to your indicated method; technically you can certainly weld dissimilar metals with an arc welder, that is not in dispute, the problem with your method is that is cannot be successfully used for precision wire wound resistors, the reason being (among others) is that the very high heat of the arc will profoundly and permanently change the TCR of the resistance alloy wire as far as the heat is above ~350°C along the wire for Evanohm.  Yes you certainly can weld Evanohm to a copper wire/slug with the arc but you are going to mess up the TCR of the wire where ever it was above ~350°C, this is undisputable as a known characteristic of Evanohm.  For that reason, Evanohm wire is not welded directly to the copper lead, there is always an intermediary alloy between them.  The intermediary is usually Alloy 180 ribbon which is arc welded into the copper lead and then the Evanohm wire is CD welded to the Alloy 180 (this too is not the best practice).

Sorry if I was not totally clear on the point before.  Your method would also be quite impracticable for production as well.  As a point of interest, my lead assemblies are actually made with a special arc welder setup and that piece of equipment usually goes for around $20,000 new.  It isn't just an arc welder, there is a lot more to it in order to to do it right.  Your method is actually used to fuse incandescent lamps (tungsten) to wire leads for example, in that case the high heat does not cause problems with TCR as that characteristic is not of primary interest like it is with PWW resistors.
 
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Offline amspire

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #17 on: January 28, 2018, 12:42:33 am »
Edwin, could the Evanohm ends be plated with a solderable metal as a method of termination?

Just did a quick search and saw a Dale patent for a Bulk Metal Chip resistor and they used an Evanohm Alloy R plate plated with a nickel undercoat and tin/lead plating on top. This patent was for a process where they plate the whole surface of the Evanohm plate and then use a method such as a laser to selectively burn away the plating to expose the resistive element. The aim of this patent was to be able to make surface mount resistors without the need to involve any copper along with the associated copper temp. coefficient.

Welding is probably fast for production, but as you point out, probably out of the range of the hobbyist. Electroless nickel plating on the other hand is very easily managed. It is probably hoping too much that it could be that simple. This Dale patent was for a mass manufacturing process for low resistance 25ppm/C resistors and not for precision resistors.

https://www.google.com.mx/patents/US5287083

« Last Edit: January 28, 2018, 01:04:40 am by amspire »
 

Offline Edwin G. Pettis

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #18 on: January 28, 2018, 02:03:35 am »
To amspire:

I haven't tried that but I don't see any reason why you couldn't plate Evanohm with nickle...be advised that pure nickle has a TCR of about 6,000PPM/°C so you won't easily get very low TCR even if the wire is under 3 PPM/°C, not counting the tin/lead plating on top of that.  That's why they're carrying a 25PPM/°C TCR.  Always a trade off in play, nothing is for free unfortunately.  I'd give a try just to see what kind of results you get.
 

Offline amspire

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #19 on: January 28, 2018, 05:28:44 am »
I haven't tried that but I don't see any reason why you couldn't plate Evanohm with nickle...be advised that pure nickle has a TCR of about 6,000PPM/°C so you won't easily get very low TCR even if the wire is under 3 PPM/°C, not counting the tin/lead plating on top of that.  That's why they're carrying a 25PPM/°C TCR.  Always a trade off in play, nothing is for free unfortunately.  I'd give a try just to see what kind of results you get.
I thought you would say something like that. :(

Looks like Electroless Nickel will not plate to Evanohm without a Strike - a thin layer of copper plating. So maybe just a thin copper layer is the thing to try.

My main purpose in having a go is more to make a precision voltage divider like a Hamon 10:1 voltage divider rather then a standard resistor. If I could make resistors with a decent coefficient and very little short term drift, I will probably also try a Hamon resistance transfer (need 10- 12 equal resistors matching to better then 0.1%). The Hamon resistance transfers can get expensive with commercial resistors as you don't need just one - you need to make 4 different transfer boxes to span the range from 10 ohms to 1Gohm. The 10M to 1Gohm range is fine if it a lower accuracy - I am planning on using some fairly cheap 100M resistors for that job.

It still means that if I have to buy precision resistors, I will need either 4 or 10 resistors for the voltage divider and 30 for the resistive transfers. It starts to add up.

Richard
 

Offline TiN

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #20 on: January 28, 2018, 10:30:39 am »
The 1.82K resistor in test that Ramon mentioned had ~-10ppm/K, not 400 ppm/K. Total resistance change was -400ppm from temperature delta of 40C.
I crimped the wire ends in the short pieces of clean small copper tube, which in turn soldered to test cable going to meter. Whole assembly was in TEC box setup.
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Offline branadic

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #21 on: January 28, 2018, 11:24:21 am »
I think this single measurement (ramp up from 21°C to 60°C and back) is not representitive for this resistor at all. If you plot resistance over temperature you can see:

1. that the resistor is lagging temperature, visible at 60°C
2. you have same relaxing during first ramp up

This plots with time on x-axis do hide most of the valuable information. I would suggest repeating the measurement over several cycles to get an idea of the real T.C., hysteresis etc.

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« Last Edit: January 28, 2018, 09:44:24 pm by branadic »
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Offline ramon

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #22 on: January 28, 2018, 11:32:19 am »
The spool I have is not enamelled, it is bare wire. I guess that they use the same standard label for all their wires.
If you look again there is nothing written bellow ('Enamel', 'SWG B&S', and 'Net lb' all have empty fields).

About using other alloys: Edwin thanks for suggesting Manganin and Cupron, but no. I have no interest to experiment with wires that have higher TC (more than 5 ppm); or other characteristics that made them unusable: like a high thermal EMF against copper, or permanent change/drift if exposed to more than 140C (this is probably the worst issue of all). All this three requirements (TC, EMF, and maximum usable temperature) exclude almost every other alloy: Zeranin, Constantan, Noventin (CuMn25Ni10), etc ...

Tin, you made my day ! Did you remember that I 'baked' that resistor for you the same morning we meet on Taipei. Burned by lighter!
The very first crappy resistor I made, and I got 10 ppm? Crazy! I am the happy owner of around 5,000 meters of a 10 ppm spool.
That means it could be true that the spool I have is actually a 3 ppm wire? And maybe we could that spec soon.

To celebrate this moment (and accelerate R&D) I want to make an offer to the eevblog metrology community: I can ship some meters of wire for free, just cost of shipment. I am thinking about sending 4 meters per person, maximum 25 persons (a total quantity of 100 meters). I just only ask that the experiment and results are made public on this thread.

Highly desired DIY experts in the fields of micro-crimping and DIY micro-spot-welding machines (but I highly recommend to check the crimping method first, lower cost and great results ;-)

Thanks JoeN for starting this thread!
 

Offline TiN

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #23 on: January 28, 2018, 11:47:45 am »
1. that the resistor is lacking temperature, visible at 60°C

Not sure I get what you mean here.

This plots with time on x-axis do hide most of the valuable information. I would suggest repeating the measurement over several cycles to get an idea of the real T.C., hysteresis etc.

Plot over time does not hide anything (in fact it have more data, than just T vs R curve), it's just different representation (which might be harder to glance, granted on that).

Quote from: ramon
The very first crappy resistor I made, and I got 10 ppm? Crazy! I am the happy owner of around 5,000 meters of a 10 ppm spool.

I can understand the enthusiasm, but it's not that simple, as there is no real world value in short-term tempco over few hours, if the resultant resistor not stay stable/have large hysteresis and affected by mechanical reliability of the joint. With same idea, you can have 0 ppm/K wire, but the moment you actually make a resistor and put it into the board/device, it would have very different characteristics, no matter crimped, or welded or soldered. Wire itself (and it's qualities) is just one little variable in the large big formula of final errors.
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Offline branadic

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Re: Manufacturing custom high-precision low-TC resistors
« Reply #24 on: January 28, 2018, 12:15:04 pm »
Quote
Not sure I get what you mean here.

See picture attached... no change in temperature but change in resistance is a hint for a lack in temperature.

Quote
Plot over time does not hide anything (in fact it have more data, than just T vs R curve), it's just different representation (which might be harder to glance, granted on that).

Okay, we can be pettifogging, but you expect everybody to calculate the valuable information by himself. Where is the problem plotting resistance over temperature, putting some fit on it and show how you calculate your values? Which ramp did you use for your T.C.  calculation, ramp up or ramp down?
It's pretty easy to miscalculate such paramter using the time domain data as high dynamic range of it hides true behavior.

-branadic-
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