Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>
At 10:13 PM 9/20/2005, you wrote:
Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>
Hi Gerry, Malcolm,
I've considered what you said and also Malcolms reply to you. I
think you are right and I must retract my comments regarding losses
as per sD. As the frequency decreases, sD increases which means a
larger portion of the wire determined by the frequency is available
to carry current, but this doesn't infer the wire size itself needs
to increase. As the wire reaches full density, sD is no longer
valid (sD tends towards zero because sD is at full density). Losses
due to skin effect is not appropriate if the depth is larger than
the wire diameter. This is the part I wasn't getting. However,
thermal losses due making available too much current is still valid.
One other thing to watch out for is that the classic skin depth
formula is for current in a infinite flat sheet, and is more a
computational fiction to allow computation using things like Ohm's
law. It presumes an exponential decay in current density (i.e.
exp(-x/sd)), and by simple integration, the properties are exactly
the same as if you had a uniform current density of depth sd.
This is NOT true in a round conductor unless it is truly huge; as in
many (>5-10) times the skin depth in diameter.
1) The current doesn't suddenly go to zero at the skin depth, it
tapers off. 5 sd away its still about 0.007. If you're looking for
better than 1% accuracies in your calculations, this implies that
you need a thickness(radius)>5*sd, at a minimum, for Rac
proportional to 1/skindepth.
2) It's a round conductor, not a flat plate, so the current doesn't
fall off as exp(-x). It falls off somewhat faster. Only if the
conductor is large enough that the radius is the same as
(radius-skindepth), to your level of precision does the flat plate
assumption hold. (one way to think about it is that current is
squished by adjacent current, and in the middle of the circle, a
filament of current is surrounded by more filaments than at the
edge) I don't have it in front of me, but I'll bet that Bessel
functions come into it somewhere, as they do with lots of things circular.
It's ugly enough that there are tables and charts for the correction
factors, both for solid and tubular conductors.