Resistances of 3 Dimensional Objects

[wagnerc]

Greetings. I have a very interesting problem that I don't even know where to begin to look for info. Or even what to type into Google. Good thing I found this forum. Very informative discussions. What I'm looking for is information on calculating the resistance through large objects. It's tricky because there's no regular current path like in the trivial case of a wire. For example, if you had a 3 inch square cube of some uniform substance, all of whose properties were known, figure out the resistance between any two points on that cube. Obviously the closer the test leads are the lower the resistance and vice versa. It reminds me of the force trajectories in stress analysis of metals. I have thought about simulating the cube as a very very large array of resistors in ultra series/parallel combo and writing a program to compute it but there's got to be some really cool way to derive it with calculus or differential equations. Anything appreciated, thanks.

Chris

 

[VEBill]

The average patent probably has a worse ROI than a lottery ticket. But I digress...

There are some good ideas posted above. For example, if you can program a simple routine to convert a 3-D shape into a list of 3-D coordinates (at a given spacing) [easy], then you could automatically create a Spice network (resistor grid) by simply looking for the up-to-6-maybe-less adjacent nodes (+/- 1 in X, Y, and Z). Then let Spice execute and any point-to-point R will fall out. Maybe run the method at several increasingly tight grid spacings to see where it trends. As with EMI models, you could tighten the grid where it most matters (directly between the contacts), and widen the grid at the extremities.

If the material is solid (no voids) between the contacts, then I suspect that the extremities at any significant distance from the contacts would have a small effect. In other words, if your 3-D object was infinitely large with the contacts an inch apart, I suspect that you'd get almost the same answer modeling just a few cubic inches.

This might be one of those topics that was fully explored a hundred years ago, and that's why you're not finding much on Google.

 

[wagnerc]

I've been thinking about various modeling techniques. I'm pretty sure I can eliminate the the 3rd D because the shape I need shouldn't have any voltage drops in that dimension. It's planar, meaning I can divide it up into as many planes as I want and each plane will be receiving the exact same current. I've been searching for resistor reduction algorithms and I can't find one, or think of one, for reducing cubic arrays. That is, where each resistor is connected to 6 adjacent ones. But since it's planar I can use the triangle-star transform on a triangular array. Though it would be nice if Spice could do the cubic. Of course I would have to aquire a copy of it. Another way I was thinking of doing it is by dividing each plane up into lines of conductance, whose resistance can be determined by their length and the resistivity of the material. Then evaluate all the lines in parallel. Think isobars on a weather map. I'm not sure this will work because I haven't accounted for voltage drops between the lines causing current to leak out. Hmm. Now, I have been thinking about how I would build a model to do the fluid filled tank and to hell with the calculations. :-D

 

[VEBill]

"...aquire a copy of it."

http://www.google.com/search?q=freeware+Spice

"...be nice if Spice could do the cubic."

(Is this what you mean? ...)

Spice doesn't have to realize that it is a 3-D grid. You simply labled the nodes with a WagnerC-derived 3-D nomenclaturism (based on XYZ coordinates) and to Spice, they're simply a list of nodes.

By way of a simple example, Node AAA (on the outside corner) has resistor segments to three nodes: Nodes BAA, ABA, and AAB (one step in each dimension). Node JJJ would have resistor segments to six adjacent nodes: Nodes IJJ, JIJ, JJI, KJJ, JKJ, and JJK. Etc. This adventure in nomenclaturism can be expanded to multiple characters per unit step (if required) and into even N-Dimensional hyper-space if required (until you run into the limits of Node Naming in your copy of Spice).

So, Shhhhh! Don't tell Spice that it is a 3-D structure. It doesn't need to know that the stepped-on flatten mess of a schematic could be pulled out into a neat 3-D grid.

So, of course Spice can deal with a 3-D grid.

 

[IRstuff]

http://electron.mit.edu/~gsteele/vanderpauw/vanderpauw.pdf

TTFN

 

[lighterup]

This measurement is done routinely in the oil patch to measure the resistivity of formations around the borehole to see if they have characteristics which indicate a high probability for the presence of hydrocarbons (oil). One of the techniques the guys in the resistivity sonde group used was the so-called van der Pauw method, which is a combination sheet resistivity and Hall measurement. A description of this method is nicely illustrated on the tax payer-funded NIST website below:

http://www.eeel.nist.gov/812/effe.htm#vand

This description is highly schematic, and I am sure there are many pitfalls not described therein, but the theory is there. Wish I could be of more practical help, but my field was acoustic measurements during my oil patch incarnation.
Havagudun,
Larry

 

[wagnerc]

Thanks for those links. I downloaded Spice+ but it's a command line program and there's no documentation on how to use it. I have no idea how to make a Spice file. I got Aim-Spice too but it also seems to want a spice file. I was hoping for something with a CAD like drawing interface to get started. IR, *great* old file. Lighter, thanks too. Maybe I should restate want I want to do. I'm looking for a mathematical model of a resistive body that will let u calculate the resultant resistance between two terminals from it's shape and the terminal locations. Every propery and parameter will be known.

 

[wagnerc]

Sorry I've been away a bit. Been having computer trouble. Anyway, does anybody know of a good tuturial on how to use Spice? I didn't find anything with the software links. It's like they all assume u already know how to use it or why else would u be downloading it. Once I get it working I'll definately have the power to churn through the model. I just upgraded to dual Athlon 2800's.