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Re: Subject: Calculating inductance, capacitance, and resistance of 3D objects

Tesla List wrote:
> 
> Original Poster: Scott Stephens <Scott2-at-mediaone-dot-net>
> 
> At 02:19 AM 12/15/98 -0700, you wrote:
> 
> >Original Poster: Jim Lux <jimlux-at-jpl.nasa.gov>
> >
> >I've just run across some interesting free software from MIT which
> >calculates the capacitance, inductance, and resistance of arbitrary
> >objects by numerical methods.
> 
> A 'field solver'. A web search of electromagnetics will turn up a NASA page
> that references many free & commercial codes.

That would be http://emlib.jpl.nasa.gov/  here at work....  Actually,
the ACES web site, and the University of Missouri sites are also pretty
good.

 There are even plasma
> simulation codes available free. Siglo web page has one, but its 2
> dimensional (as are many of these codes).
> 
> > I haven't had a chance to work with it
> >yet, but, it might prove useful to some for calculating Cself and Ctop
> >for all those weird toroid shapes, etc... It's at:
> >
> >ftp://rle-vlsi.mit.edu/pub/
> 
> I would use book equations for such things. A field solver is over-kill.

But there isn't a good book equation for the capacitance of a cylinder
over a ground plane or for a toroid on top of a cylinder. All you have
are empirical approximations for parts of the problem such as those of
Medhurst. I think it would be useful to run a field solver with a very
large number of cases of various combinations of "top load" and
cylinder, etc. then derive some empirical relations. 

I recognize that for practical construction, the model doesn't have to
be very good (say, within 10%), because you'll need to tune it anyway,
but it would be nice to have an understanding in a sort of
semiquantitative way of the effects of toroid size/spacing above the
secondary, working against a flat primary of various sizes, etc.

I think that the real value would be in confirming that the the quick
and dirty expressions we use for design and construction(which make some
dramatic simplifying assumptions) are valid. For instance, the Medhurst
approximation is against an infinite ground plane at the base of the
cylinder. The commonly used toroid capacitance equation is in free
space. Neither of these are true in a typical tesla coil, but, the
equations are probably valid anyway (at least to 10%). With a lot of
work (computational, not human) a field solver could confirm this.

I, for one, would be interested to know the effects of ground planes and
counterpoises of various configurations over various substrates.
Concrete floors aren't infinitely conducting groundplanes....

> 
> >On a related note, has anyone done any modelling of TC's and their
> >environment using a tool like NEC? NEC supports helices, and does
> >calculate the turn to turn interactions, etc.
> 
> That would give you an excellent theoretical analysis. Field solvers analyze
> a structure as if it were a very large array or mesh of inductors,
> capacitors and resistors. Conductor thickness is even modeled in NEC.
> 
> But once again, the list has fairly well flogged that horse with empirical
> measurements too. I gather from the list's posts, that the TC is much better
> modeled as lumped rather than distributed (transmission line) with a large
> top terminal capacitance. And the big terminal is necessary to store enough
> charge for good discharge formation.

You bet, lumped is the way to go... That's why I had the word
"environment" in my original statement. We need more work understanding
how the surroundings of the coil affect its behavior. I think the
mechanics of exciting, winding, and so forth are pretty well thrashed
out by now. [A change in the dissipation factor of the coil form of 0.1%
isn't going to make any difference: wind it on whatever will stand the
voltage and meet the structural requirements.]
> 
> After 20 hours of tedious work, you may not learn much you don't already
> know. I've tried NEC example files and some of the free & cripple ware for
> it, which I'll dredge up references for if you want. It seems to have been
> developed by people comfortable with hollerith cards, as conductor
> structures are specified by netlists & lists of commands on 'cards'. But
> others have made nice Windows GUI interfaces to it, so its not so
> cumbersome. Their is another public domain University - sponsored code (I'll
> forget) that would probably do a faster job of simulation.

Yes, indeedy, it was developed back in the days of card input. Which
isn't all that bad for something that is highly compute intensive. Some
of the larger field problems take minutes on a supercomputer, and if you
are going to run a whole series of them for a parametric study, you
don't really want to spend your valuable human analysts time writing a
cool GUI.

> 
> I've been researching writing my own field solver, as I want to model
> microwave cavity heated plasma loops. But 3-dimesional (rather, 4-dimension
> including time) is computation intensive. Especialy when algorithms require
> iteritive solutions. To make full use of the power of the pipelining and
> cacheing in pentium processors, and the power of the MMX matrix processor,
> code must be optimized. Otherwise performance is no better than 386 class.
Which is why the higher performance codes are commercial and cost a
bunch...

A better answer may be to develop a solver that can run on a distributed
network of PC's (much like the digits of PI or prime number searches). I
did this for a Computational Fluid Dynamics code based on numerical
integration of the Navier-Stokes equation. Let it run for a week as a
screen saver on 30 PCs...

Then, make a cool visualizer to look at the output, if one doesn't
already exist.

> Which I bet is the case for the University codes. And the net field solvers
> typicaly give you complex impedance at a point or radiation patterns. My
> ideal is to have an Open-GL based 3-D animation, with colored fog
> visualizing the potentials and currents.
> 
-- 
Jim Lux                               Jet Propulsion Laboratory
ofc: 818/354-2075     114-B16         Mail Stop 161-213
lab: 818/354-2954     161-110         4800 Oak Grove Drive
fax: 818/393-6875                     Pasadena CA 91109