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skin depth in round conductors Re: 8 kHz Tesla Coil

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 As the wire reaches full density, sD is no longer valid (sD tends towards zero because sD is at full density).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.