Resistances of 3 Dimensional Objects
Resistances of 3 Dimensional Objects
(OP)
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
Chris





RE: Resistances of 3 Dimensional Objects
I think you could google for "bulk resistance"
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
Not sure about that. In 2D, sheet resistance is measured in ohms per square (distance between the test points doesn't matter). I don't know off-hand about 3D bulk resistance, but I wouldn't say it is obvious. Google is your friend.
Contact resistance only matters if the material under test is relatively low resistance. Four wire measurements are one option for dealing with that if required.
RE: Resistances of 3 Dimensional Objects
and use AC !!!
<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032
RE: Resistances of 3 Dimensional Objects
For a 3-D object, there would be a similar treatment, but would require you to do the transformation for the 3-D spreading resistance. I can't remember the original source, perhaps Van der Pauw, himself? The original article describes the mathematical approach for determining the mathematical treatment of 4-point probe measurements, where the probes are arbitrarily positioned. I haven't even looked at my hardcopy in probably 10 yrs, so my recollection is somewhat hazy.
TTFN
RE: Resistances of 3 Dimensional Objects
I vaguely remember reading an article on same
that delved fairly deep into the subject, and
the treatment of 3D objects was one of the
subjects. Sorry that I cannot recall more.
<als>
RE: Resistances of 3 Dimensional Objects
http://www.esdjournal.com/techpapr/ohmmtr/ohm.htm
Back to original question, see this Googled-nugget:
http://www.jandel.co.uk/faq.htm
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
"...if one already knows the sheet resistance, bulk resistivity can be calculated by multiplying the sheet resistance in Ohms-per-square by the thickness of the material in centimeters."
RE: Resistances of 3 Dimensional Objects
how much accuracy do you need?
I suggest the following approach: make a math. model,
integrate it and check it with the liquid tank.
<nbucska@pcperipherals DOT com> subj: eng-tips
read FAQ240-1032
RE: Resistances of 3 Dimensional Objects
What is referred to in the reverse calculation is the bulk resistivity of a LAYER, not a bulk material.
TTFN
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
TTFN
RE: Resistances of 3 Dimensional Objects
What is the practical real world application?
My first thought when I read this was calculating the resistance of bus work.
Dan Bentler
RE: Resistances of 3 Dimensional Objects
chris
RE: Resistances of 3 Dimensional Objects
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.
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects
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.
RE: Resistances of 3 Dimensional Objects
TTFN
RE: Resistances of 3 Dimensional Objects
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
RE: Resistances of 3 Dimensional Objects
RE: Resistances of 3 Dimensional Objects