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Re: skin depth in round conductors Re: 8 kHz Tesla Coil

Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Jim,

I have Terman documents, so I'll go and investigate what is said on the subject. Agree with your statement about proximity losses. That is actually my point here. Depth penetration at the kHz ranges we run our coils at is in no way going to require a 5 awg wire size. The 8 kHz coil was outside our norm, so it stood out and showed me there is a problem with the sD recommendation. In design programming, more emphasis should probably be put on proximity, power, and dielectric losses.

Those are my main points with this discussion. Yes, problems with skin depth are real, however, those losses are not being put into perspective and the sD recommendation is probably doing more to minimize basic power losses than actual sD losses. Q would still go up, but the reason may not have actually been sD losses.

Regarding proximity losses in round conductors, this paper may be of interest:
http://www.classictesla.com/download/Proximity_Effect_Loss_Calculation.pdf

"An Improved Calculation of Proximity-Effect Loss
in High-Frequency Windings of Round Conductors"
Xi Nan and Charles R. Sullivan

Take care,
Bart

Tesla list wrote:

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 09:56 AM 9/23/2005, Tesla list wrote:

Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Jim, All,

In every reference I've been reading regarding skin depth, I can find nothing stating round conductors and sheet conductors have a difference in depth penetration due to frequency, and it just doesn't make sense that they would (at least, I'm not getting it). The only difference I can find is that for round conductors, the math gets messy to define exactly when the abrupt change occurs and tails off toward zero.


I think Terman has a discussion of this. I don't have a copy here, so I'll have to check with someone else who does.

In any event, there is never an "abrupt" change. It's always a gradual decrease (exponential in the infinite flat plate case)


Skin depth is defined as the distance from the surface of a conductor where the current density is 1/e times the surface current density. This is nothing more than a density ratio used to describe the effective conducting area.


I'll agree with this, because it happens that the integral of exp(-x) from 0 to infinity is = exp(-1).



Skin depth occurs because a changing flux induces a voltage loop or eddy current which is coincident with the voltage. This eddy reinforces the main current at the surface and opposes the current in the center of the conductor. The result is that as frequency rises, current density increases at the surface and tails off exponentially toward zero at the center because of these frequency dependent eddy currents.


In a conductor, the eddy current at some depth is affected by not only the current directly above it, but also by the current on either side. Imagine a bunch of filaments with equal current all laid next to each other. In the flat plate case, this winds up giving you the exp(-x) characteristic. In the round conductor case, the filaments next to the one directly above are closer than they are in the flat plate case, so the current decays faster.


It should be noted that the current is not uniform around the wire. The current density will occur adjacent to magnetic fields.


That's an entirely different (proximity) effect. Even for single straight wires, round conductors have an AC resistance greater than you'd get from circumference*flat plate skin depth.