Poor Man's Resistive Ring 10K Standard

[zhtoor]

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[BNElecEng]

I remember reading about something like this in a NIST paper I found online. Any further reading you can link to?

[BNElecEng]

See link below to the paper I mentioned:

https://www.nist.gov/sites/default/files/documents/calibrations/tn1458.pdf

relevant section can be found by searching for the term "Ring Method", or by going to page 25

[BNElecEng]

No worries. Could you post a diagram of your concept please? I'm having a slow day and can't picture it in my head.

[BNElecEng]

Thanks for the diagram, it makes sense to me now. It's given me something to think about over the weekend, thanks.

[Jay_Diddy_B]

Hi,

Not a mathematical analysis, but a quick LTspice model:


The {mc{value, tolerance)} feature is used to simulate resistors with 1% tolerance. The distribution is rectangular, that is equal probability of any value in the +/-1% from the nominal.



A current source is used to measure the resistance.

I am comparing the ring against 5x 50k resistors in parallel.

Results from 100 runs:



It is obvious that the 5x 50K resistors in parallel is better than the ring. Each resistor makes an equal contribution. In the ring the configuration, there is a dominant resistor and the other resistors have a smaller influence.

Regards,

Jay_Diddy_B

[Jay_Diddy_B]

thanks.

but if you note, there are 5 ways to measure 10K on a 5-resistor-ring, so you have the possility
available to you to do a (geometric) mean of all the readings, has that factor been addressed?

snip

regards and thanks again.

-zia

OK.

Here is a modified model. This model selects 5 resistors with 1% tolerance, rectangular distribution. 5 resistance measurements are made using pulsed current sources and differential voltage measurements. The individual resistances are recorded and the average of the 5 resistances is recorded.

Model



Results



I have attached the model.

Regards,

Jay_Diddy_B

[ebastler]

but if you note, there are 5 ways to measure 10K on a 5-resistor-ring, so you have the possility
available to you to do a (geometric) mean of all the readings, has that factor been addressed?

moreover, there is another set of 5 - 15K measurement available which can further enhance
our estimates of the original 10K standard.

ie; in case of 5 - paralleled 50K resistors, only one measurement is available with all resistors having equal weight
both the resistance and tolerance wise, whereas in the ring method 5 measurements are available with a dominant
weight resistor.

I don't get it. How is all this statistically better than just measuring N 10k resistors separately and averaging the results?

You may be able to conduct N(N-1) different measurements, but they will obviously not be statistically independent. With a set of N resistors there are only N independent variables. Why not measure them separately, each with equal statistical weight, without complex dependencies and double-counting? Am I overlooking something?

[anymouse]

for starters there are a total of N-terminals in a ring vs. 2N-terminals for independent resistors.
having N(N-1) measurements which are measuring the same aggregate parameter (the reference value) in a ring
vs. having N measurements which are just measuring the independent resistors does not lower the uncertainty of
measurement.

You got your math wrong: In the ring, each terminal has only one "next terminal", therefore you have the same N measurements as terminals
(reverse order excluded in both cases).

So no better.

[ebastler]

intuitively: the more ways you have to measure a parameter, the more accuracy / resolution of measurement can be achieved.

example: contrast having 1 measurement method to measure a value, then N measurement methods to measure a value, and
then having N^2 measurement methods to measure a value, which of the three cases will give you a better uncertainty of measurement?

Let me try to paraphrase, to see whether I got your point.

There are two sources of variation or uncertainty in the measurement: (a) the individual resistor values will deviate from the nominal value, and (b) the measurement step itself will bring uncertainty -- due to variations in contacting the resistors, shot noise etc.. 

I think we are in agreement that there is nothing to be gained regarding aspect (a). If you have N resistors, that's the number of independent samples you have available, and it does not matter how you group or connect them -- right?

So is your argument that the ring geometry will enable you to improve your statistics on aspect (b)? If that's the goal -- why not simply repeat the measurement of each separate resistor multiple times? What is the benefit of your method over taking N separate resistors and measuring each of them N-1 times ?

[ArthurDent]

…so instead of purchasing 5 or more odd value resistors to string together and worrying about interconnections and possible math errors in averaging, I can just buy a single higher quality standard value and keep it simple. I quickly tired of solving those infinite number of resistor puzzles long ago.

As a hobbyist I don’t see any advantage to needlessly complicating testing procedure, NIST, maybe. It is an interesting concept however. I don't know if the effort is worth whatever slight gain there might be.

[Jay_Diddy_B]

Hi,

There are couple of ways to think of this ring arrangement. The first way is to think about conductance, which is the reciprocal of resistance.


1/R = 1/1.1R + 1/(1.1R + 1.1R + 1.1R ... + 1.1R)

You can see, by inspection, that the total is dominated by the first term.

In fact 10x more current flows in the first term.

In fact the resistors in the ring have 1/10 the current and 1/10 the voltage.

So the first resistor is 100x more important.

The larger the ring, the less impact the ring has on the dominant resistor.



If I change R3 by 1% the total resistance only changes by 0.009%

The other way to look at this is, simply measure and record the value of each of the individual resistors. Any combination that you do after that can be done mathematically, it does not need to be done electrically.

If the resistors are all 1% high, no matter how you combine them, mathematically or electrically, the results will be 1% high. So the worst case values are the same.

If you assume that the resistors are randomly distributed within in the tolerance band, a wild assumption, then there is some statistical benefit from averaging. But it is a bold assumption that the are truly random.

Regards,

Jay_Diddy_B

[CopperCone]

why is everyone focused on summing demons ?