Mini Metrology Lab resistor matching question

[BradC]

G'day all,

I've been toying with methods in Conrads Mini Metrology Lab article for a while now and using it to learn about my equipment and its limitations (in addition to mine).

One of the things I've been experimenting with is resistor matching and I've been toying with a couple of methods. The obvious method is matching them with direct reading ohm meters of various accuracy and resolution. The most accurate method available to me is as described in the Mini Metrology Lab series, part 3 by using a makeshift bridge. I have a question about the maths though and I think I must have either a beginners mathematical error, or a fundamental misunderstanding of basic principles. My calculations are out by almost exactly a factor of 2.

I'm going to preface this whole bit with "If I'm not mistaken" and then proceed to explain my calculations hoping that someone will point out where I *am* mistaken.

This is based on the most accurate match required. The first decade are 10K resistors and they need to be matched to 37PPM (0.0037%). This would mean a maximum spread of 0.37 Ohms across the resistors (10,000/1,000,000*37). For the purpose of this example I'm going to select 2 resistors of 10,000.00 Ohms and 10,000.37 Ohms.

I'll assume known bridge resistors are all 10,000.00 Ohms. So with a 27V input, the left side of the bridge gives us 13.5V.
With the 10,000.00 Ohm unknown, the right side of the bridge gives us 13.5V. - 10,000/(10,000+10,000)*27
With the 10,000.37 Ohm unknown, the right side of the bridge gives us 13.500249V - 10,000.37/(10,000+10,000.37)*27

So we have roughly a 249uV difference. The Mini Metrology Lab article specifies resistors must be matched to within a window of 1/2mV == 0.5mV == 500uV.

This is almost exactly double the value I came up with. Can someone please point out my error?

[AG7CK]

In order to save other people from wasting their time locating the article website and finding out which page you probably are are talking about: http://conradhoffman.com/MML%20files/3_kvd_p4.jpg

Table 1 says +-0.0037% and +-0.25mV. May be you will get (13.5-0.000249)V if you switch the resistors on the right side. I don't know 

[BradC]

In order to save other people from wasting their time locating the article website and finding out which page you probably are are talking about: http://conradhoffman.com/MML%20files/3_kvd_p4.jpg

Table 1 says +-0.0037% and +-0.25mV. May be you will get (13.5-0.000249)V if you switch the resistors on the right side. I don't know 

Thanks, sometimes I get tunnel vision and forget people aren't actually reading along. It's something I try hard to get better at, but rather seem to get worse as I get older.

Yes, I see +/-0.25mV, but that indicates a window of 500uV (as described in the document). This is where I'm confused and need a bit of a whack with the clue bat please.

If we pretend that the top resistor remains at 10,000.00 Ohms (as it won't change during out matching session). Doesn't that roughly indicate the unknown may have a window of 9,999.63 to 10,000.37 to indicate +/-0.25mV . Isn't that a 74PPM spread rather than 37? 

I guess where I'm confused as I've fixated on "better than 40PPM" as stated at the bottom of column 1 here : http://conradhoffman.com/MML%20files/3_kvd_p3.jpg and taken that as the absolute, then calculated out the 0.0037% as 37PPM and made the assumption "Well, that's under 40PPM, so there we go".

How does +/- 0.0037% relate to "The process of selecting eleven resistors that are matched to better than 40PPM" ? I'm not trying to be a smart-arse, I genuinely can't reconcile this in my head. Is it +/- 40PPM, or is it an absolute 40PPM window?

[The Soulman]

I think the intend/meaning of the ± symbol is a bit unlucky in this case.
But yes a maximum spread of 40 ppm is what you are aiming for.

[Conrad Hoffman]

It's been so long (22 years!) that I've forgotten everything. I do remember something wonky about the bridge and matching description- trust your own math on that one, not mine.

[GigaJoe]

27 Volt ? ; isnt too much , due to thermal coeff. and a power dissipation?

[BradC]

It's been so long (22 years!) that I've forgotten everything. I do remember something wonky about the bridge and matching description- trust your own math on that one, not mine.

Thanks, Conrad, I appreciate that.

Leaning on your experience (and memory), can you give me some insight as to how the 40ppm specification was calculated? I see it is double your original stated target accuracy of 20ppm. Is that related to the overall accuracy vs number of decades, or restricted to the accuracy of the first decade by itself?


 

[Conrad Hoffman]

The only insight I can give is to make a spreadsheet for the divider and include a cell for tolerance. Then you can see what happens as resistors move out of spec. I think I did that, but it's long lost by now.

[BradC]

The only insight I can give is to make a spreadsheet for the divider and include a cell for tolerance. Then you can see what happens as resistors move out of spec. I think I did that, but it's long lost by now.

Funny, that's exactly what I thought of the millisecond after I pressed "post". I will do just that. Thanks.

I will say that series of articles has stood up rather well, and I appreciate you taking the time to make them available.

(edit) :
Well, that was illuminating. Worst possible case is with 9 resistors @ +20ppm and 2 @ -20ppm, results in an output error of ~35ppm using a pathological and unrealistic distribution designed specifically to present the worst possible outcome.

Applying a real world normal distribution of +/- 2 std deviations using a mean of 10.0k and spread of 40PPM results in having to be pretty unlucky to exceed 15ppm error, with most falling under 10ppm worst case first decade. Even with a bad spread of matches across the entire 40PPM, a bit of judicious placement results in average errors under 10ppm.

[Conrad Hoffman]

That somewhat explains why you can build a reasonably serviceable KVD using nothing more than carefully selected resistors from a bag of ordinary 1% metal films. It won't be the equal of a Julie or Fluke, but will suffice for many tasks. Mostly you have to watch for high TC and changes when you solder them- always use heat sinking clips.

If you haven't read my page on the Hamon divider, a spreadsheet on the math for that is also interesting.

This stuff even applies to other things. I'm working on an old Mettler single pan balance right now. The internal weights go in a 1-2-4-8-16 sequence, and are subtracted from the DUT to bring the balance back to center. Resolution is 10 ug and I've got a slight error somewhere. The trick is getting all the weights trimmed so every possible combination is within spec. The only good way to do that is with another, more accurate, balance.

[branadic]

Would be great if Brad could share the spreadsheet and Conrad would link it to his website. Then everyone visiting his website would benefit from that. 

-branadic-

[BradC]

Would be great if Brad could share the spreadsheet and Conrad would link it to his website. Then everyone visiting his website would benefit from that. 

Spent quite a bit of time on it tonight extending it out to more than one decade. It's done in Libreoffice and right now simulates a 6 decade divider modeled on Conrads document. I still have some bugs to iron out of the last decade being a potentiometer rather than a divider, but that's tomorrows issue.

I am *trying* to get it into a state I can run a proper Monte Carlo simulation on it. Right now it just re-calculates all the resistor values any time the spreadsheet re-calculates, but you give each decade a mean value and a tolerance in PPM, input voltage and selected divider value.

The spreadsheet calculates out a set of resistors for each decade based on the mean and a normalized random tolerance, then calculates the two output voltages it feeds into the next decade, and that repeats for all 6 decades. At the end it calculates the theoretical perfect divided value and compares that with the output of the bridge and gives you the difference in ppm.

It's a bit of an unwieldy beast, but it looks like I'll either need to port it to gnumeric, excel or write some OOo python if I want to get a proper Monte Carlo out of it. libreoffice calc can't do it. It is interesting to feed it a set of values and just sit there hitting ctrl-r and watching the output variances. I'd like to be able to let it run a couple of thousand samples and have it spit out the stats on that to be able to see meaningful differences when playing with the tolerance values.

Over the next couple of days I'll get it cleaned up and documented and I'll attach it to this thread for critique and comment. I'm mostly interested to see if I've made any mistakes. The output seems to validate the theory, so it's probably all there.

Conrad, I have read your page on the Hamon dividers a few times. Actually I confess I've trawled your publishing quite a bit over the last year or so.

Having done the simulation, and again basing that on me not having made a giant error in the math, I fully understand how you can make quite a serviceable divider using the methods you outline, and frankly given a bit of care and attention to detail the math would indicate a measurement accuracy that would exceed the meters I have available to me when used with a stable and calibrated reference.

I might have to bite the bullet and build one now.

[branadic]

It's a bit of an unwieldy beast, but it looks like I'll either need to port it to gnumeric, excel or write some OOo python if I want to get a proper Monte Carlo out of it. libreoffice calc can't do it.

What about using GNU Octave? This is a perfect tool for Monte-Carlo analysis.

-branadic-