sheet resistor simulator

Sheet_Resistor.JPG

Femm is free but I wouldn't call it easy to use:

I have to admit, cutting sheets of resistive paper actually sounds like good fun to me.

...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142     Skype: skypeanalog  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
I love to cook with wine.     Sometimes I even put it in the food.

It's exactly calculable, by applying shape-changing but analytic transformations in the complex plane. You just apply transformations until the shape is a simple (rectangle) easy-to-calculate case. There are tabulations of common shapes, for the end-to-end resistance.

After getting to a rectangle, for which you KNOW where the equipotentials are, reversing those shape-changing transformations gives the equipotential curve in the original shape. From there, you ought to be able to find point-solutions to the current density.

Searching on 'conformal map shape resistor' gives lots of hits...

It looks like Sonnet will do it:

There's lots of tutorials and such, and it doesn't look hard to drive. I'm not sure about current density, but that's a secondary issue.

I might have one of my young things download the free Lite version and give it a try.

Cutting resistive paper is appealing, but it would be clumsy, hard to tune things.

D

use a script/program to make an LTspice netlist with a resistor grid in the ~right shape?

-Lasse

With a little care, you can draw a small block of resistors and then cascade copy into huge arrays, all connected. Then start deleting things to make shapes, and add connections for terminals.

That works, but it's a little klunky. And pretty ugly. Turning off Rxx and value visibility helps a lot.

I second that. It's not easy, but I've generally been able to struggle through it effectively. I suspect that the sheet resistance model is a fairly easy one to get right.

It would certainly be a good thing to do as a final check on any numerical result, no matter how it's arrived at.

--
www.wescottdesign.com

+1. When maths limits are reached, draw it on squared paper and count the squares. I expect you could easily write a little routine to do it.

NT

Whats nice is a hi-res camera shot of the material, calculate the X,Y of the overall surface of the image and then sum the pixels of interest.

So instead of doing the (I) math, one could simply get a quick sum of the surface area via some basic graphics software.

I made something like this using cheap USB camera's to take a snap shot of a piece of wire/cable insulation so that concentricity and material usage could be calculated and printed for inspection reports.

Jamie

I get by with the larger shape broken down into simple Length/Width ratios. Their sum is multiplied by K - the material thickness and resistivity constant for the conductive material.

Copper Resistance: Rc= r . L/HW r = 1.7241E-6.ohm.cm or 6.786E-7.ohm.in

R = K L/W R= resistance ohms L= length in same units as W W= width in same units as L

K @ 1oz cu (H=.0014in or .035mm) = 4.84E-4 @ 2oz cu (H=.0028in or .070mm) = 2.43E-4 @ 3oz cu (H=.0042in or .105mm) = 1.61E-4 @ 4oz cu (H=.0056in or .140mm) = 1.21E-4 @ cu foil .01in = 6.79E-5 @ cu foil .02in = 3.39E-5 @ cu foil .05in = 1.37E-5 @ cu bar .10in = 6.8E-6

Note: K is traditionally expressed as ohms/square, as L/W of the 'printed' square is 1. The resistivity of 1oz copper can therefore be considered as 0.48 milliohms/sq.

L/W 2oz 3oz 4oz

1 .243 .16 .121 mR 10 2.43 1.61 1.21 mR 100 24.3 16.1 12.1 mR

1oz PTH .062L .0017H

dia. 0.02 W=0.0613 R=0.48mR dia. 0.04 W=0.1257 R=0.24mR dia. 0.06 W=0.1885 R=0.159mR

If you feel like writing something, Laplace solvers are pretty easy: you put in the boundary conditions, and then iteratively replace the potential in each box by the average of its nearest neighbours. You get the current density from the potential gradient and resistivity.

You can do I/O by taking apart a.BMP file that you draw in Paint. (Bumpfiles are pretty simple.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Conformal mapping is conceptually nice but the integrals get super ugly if the geometry is complicated. Bolting together small conformal maps (so that corners get treated correctly) with analytic solutions for the simple bits would be easier. That's sort of how the Keller/Ufimtsev diffraction theory works. (Stealth aircraft were designed that way.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

If a first order approximation is all that's requred, all you need is average L/W, without major 'breakdown' of bulk shape.

RL

Year, sheet resistors are easy. The hard part is the graphical interface, mouse, shape entry, display, all that.

ATLC is a transmission line analyzer that uses BMP input and output, which simplifies the graphics part but is still pretty clumsy to use. Not very interactive.

I'm also considering multiple layers and vias and such. I think we'll try Sonnet.

It would be great to import PCB layouts and Autocad/Solidworks too.

Sadly, the world is not made of rectangles. Counting squares is fine for long skinny traces. It won't handle arbitrary shapes or circular contacts, like vias. Like, say, computing the resistance of a square of copper with four via contacts in each of two corners.

Sure it will. You just need to adjust the size of the squares.

How does manually counting squares handle a via, a circular contact near one corner of a copper pour?

Yeah, it only works if you can start with the isopotential curves, and work with subregions which are kinda rectangular.

So, get some teledeltos paper, cut to shape, apply AC, and use a Wheatstone-like circuit, with a probe. Put a lamp on the probe that only lights when the bridge is balanced (window detector on difference absolute value, latch, and you wait one cycle before reading out the latch to the lamp), and scan the paper, raster-style. A time exposure will show the equipotential as an illuminated curve. Graph as many equipotentials as you want; I'd think ten divisions (1/11 to 10/11) would be enough. Or, just calibrate the teledeltos sheet resistivity and use an ohmmeter, then scale.

You make the squares small compared to the circles, of course. Of course you many need your toes, too. ;-)