Analyzing a grid of resistors 3

[handleman]

Hiya Sparkies!
I am sure this is going to be a very noob-sounding post, but it's been a few years since my Circuits class...

I have what is essentially a ladder-shaped arrangement of resistors. Each "rung" of the ladder is a resistor, and each segment of the "legs" from rung to rung is also a resistor. I can't disconnect any of the junctions, but I'd like to know the resistance of each segment. I can check the resistance from any junction to any other junction pretty easily, but I know that every measurement I can take is going to end up with a bunch of parallel resistors in the path.

I can't assume symmetry of resistance values on any portion of the ladder, so I am guessing that if my ladder has "n" resistors then I need to take at least "n" measurements, but I don't have a great idea how to set up the measurement points and forumulas/algorithms I should use to do this most efficiently. My fear is that it ends up being a huge system of equations with "n" unknowns, and "n" is in the neigborhood of 30.

The other wrinkle is that I am afraid that variability in my measurements may lead to a system of equations that's un-solvable. The resistance values are (ideally) in the 10s of ohms range. Right now the measurements are taken manually with a DMM, and I can't be entirely sure that if I measure from A to B, then A to C that point A was exactly the same point electrically. At some point I hope to build a jig with multiple probes and switches such that I can take every measurement without moving any probe and just switching the electrical paths. I hope that makes sense... any input or guidance to kick this off in the best direction would be appreciated!

 

[handleman]

Hmm, interesting idea. Are there off-the-shelf sensors/meters available for that?

 

[IRstuff]

What's the relative magnitude of the resistance differences? Something that's more than a factor of 10x will be nearly invisible, if you consider them to be parallel to your measurement path --> 10/11 = 9.09

re: eddy current, I've not used them, but there are systems like:

https://www.materialstoday.com/meta...curate-thickness-testing-via-phase-sensitive/

which would seem to have some chance of detecting patches that are different as either material or thickness change.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[Skogsgurra]

First hit:

https://www.balluff.com/en/de/products/sensors/inductive-sensors/

The output is very dependent on distance to target, which is the primary function. But also very dependent on the target's conductivity - or lack thereof.

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[Compositepro]

I starting to sound like you are actually interested in measuring surface resistivity, and are trying to model it with a resistor grid. There are instruments to measure surface resistivity.

http://www.trekinc.com/pdf/1005_Resistivity_Resistance.pdf

 

[sunnysky]

Guarding is the best way on 2 , 4 or more nodes where the average or common-mode signal is driven on the perimeter around the differential measurement. The same method is used on differential instrument amps with low level signals.

You can see by intermediate measurements with a current source , that the voltage or impedance measurements , that the sensitivity is inversely related to the distance from the source.

http://tinyurl.com/yc7py6co

( ladder simulation on java)

Here I used a differential current source (top and bottom) so you can see the intermediate results with symmetry for now. Any value can be changed or duplicated.

It reminds me of a perimeter diffusion bonding system that I added instrumentation in late 70's at an Aerospace co. (Bristol Aero) so the welder could tune the energy around the circumference as the resistance reduced by the previous continuous welding closes the joint. I monitored with a current shunt up to 10kA and voltage in the 4V range as water jets poured on the arc. These 6" Monel Steel tubes being joined with Zirconium shims. So somewhat like a closed loop ladder growing in real-time as short circuit or rising conductance requiring more current from start to finish. The solid copper conductive rollers were on the inner and outer surfaces as it rolled the pipe as it welded it.

 

[zappedagain]

I agree with CP; from your comments measuring surface resistivity or volume resistivity may give you direct answers instead of having to pull the error out of a model.

Z

 

[sunnysky]

The problem is not clearly defined in terms of tolerance error for each step and rise of the "ladder". As a suggestion, maybe you could define the problem in specs better.

Is it the standard deviation or the mean or just the error tolerance in the measurement of the family of steps and rises that is important or a defect not to exceed??

I suspect a "guarded" 2D Kelvin measurement on the surface is appropriate, but we have no idea of the "physical properties".

cheers

Tony
65, retired at 55 but not tired of Electronics
EE since 1975