[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: skin depth



Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

It has been done, but it's ugly.. The usual scheme for practical use is to
look it up in a table. There are tables of correction factors for Rac vs Rdc
for solid and tubular conductors.

Unlike for the infinite flat plate situation, where you get a nice equation
(because you're essentially solving a simple low order linear differential
equation.. the current goes as e^(-kx)), when the geometry isn't so uniform
(i.e. it's a circle or a bar), life becomes tougher.

The circular case is actually an easy one, although, the integrals you wind
up with don't have nice analytical solutions, but tend to be infinite series
(Hey, any time something is round in an EM problem you can count on either
elliptic integrals or Bessel functions being involved!)

There are some approximations which are convenient for evaluating, for
instance, the current induced in one wire by a parallel one. Often times,
though, you make some basic assumption like the current in some of the wires
is an infintely thin filament, and then go through some math gyrations to
show that the difference between that and the "real thing" is insignificant.
Of such is a variety of thesis topics and little papers in things like IEEE
Transactions in Antennas and Propagation made.  If you're talking about
analysis of conductors in layered or inhomogenous media, it gets even more
complex, and a gentleman named J.R. Wait has a whole raft of papers on this
at all levels from highly theoretical to practical.

For square or rectangular conductors it's much worse, and one usually
resorts to FEM techniques, or some approximation.

This is actually a topic of quite some interest in the IC design business,
because 2 GHz clock speeds imply harmonics up to at least 6-10 GHz, and skin
depth is quite small, even in good conductors. (1.5 micron in Al, a lot more
in silicon). That's in the same general magnitude as the features on your
run of the mill IC, and even closer to the size of the bond wires (25
micron/1 mil wide ribbon, for instance).
----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Tuesday, September 23, 2003 6:56 AM
Subject: Re: skin depth


 > Original poster: Peter Lawrence <Peter.Lawrence-at-Sun.COM>
 >
 >
 > I still find it very odd that apparently no one has done skin depth calcs
 > for cylindrical wire, only for hypothetical infinitely wide infinitely
deep
 > flat plane conductors...
 >
 > Sounds like a good problem for a math-physics type, or even a
 > physical-simulation type.
 >
 > -Pete Lawrence.
 >
 >  >
 >  >Original poster: Jim Lux <jimlux-at-earthlink-dot-net>
 >  >
 >  >The handy thing to do is to remember the skin depth at a standard
frequency
 >  >(100 kHz is good for TC work), and then remember it scales as the square
 > root..
 >  >So.. reading off the chart..
 >  >Ti ->1.2mm
 >  >Al ->.5 mm
 >  >Cu -> .15 mm
 >  >showing the usual progression as conductivity gets better, the skin
depth
 >  >decreases...
 >  >
 >  >Fe(+C) -> .06 mm
 >  >showing that ferrous/magnetic materials have very shallow skin depths...
 >  >
 >  >Double the frequency, skin depth multiplied by .707
 >  >Quadruple the frequency, skin depth is halved.
 >  >
 >  >Etc...
 >  >
 >  >By the way, Chris, if you scanned that chart or copied it from
somewhere,
 >  >you should credit the source.
 >  >
 >  >At 11:55 AM 9/22/2003 -0600, you wrote:
 >  >>Original poster: "chris swinson" <exxos-at-cps-games.co.uk>
 >  >>Hi all,
 >  >>
 >  >>In addiction to my previous post, I have come across a nice chart which
I
 >  >>have uploaded to my space at
 >  >><http://hot-streamer-dot-com/exxos/>http://hot-streamer-dot-com/exxos/
 >  >>
 >  >>enjoy!
 >  >>Chris
 >  >>
 >  >
 >  >
 >  >
 >
 >