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

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

Hi Terry,

I agree with everything you said with exception to the last opinion. This topic was brought up due to the 8 kHz post. Using the recommendation, an 8 kHz coil should use a wire size that is getting ridiculously large. Malcolm has recommended wire diameter to be 3 x sD for spacewound coils and 6 x sD for closewound coils. I've used this evaluation in Javatc for a recommended wire size for some time now. Jim has also recommended similar.

Obviously, there should be a recommended wire size evaluating skin depth among other bits and pieces of the pie. I'd just like to understand the theory for the recommendation better. The more I learn about skin depth, the more it appears there may be an unrealized problem with the recommendation.

Take care,

Tesla list wrote:

Original poster: Terry Fritz <vardin@xxxxxxxxxxxxxxxxxxxxxxx>


Used to work with 13.56 MHz at up to "thousands" of amps. Skin depth is VERY real ;-) But there are other factors too like diameters and especially stray inductances of the conductors affecting impedances and altering current paths in none obvious ways. RF currents happily follow all the laws of physics, but at higher frequencies, there are MANY laws to be considered aside from simple conduction. At very high current levels, unbalanced currents cause dramatic fires so things are a little more obvious there.

But in general and at low frequencies, skin depth is a fairly good estimate of where the current is at with maybe a +- 300% tolerance ;-) The important part is just to realize that RF currents flow on the outer skin of inductors. Also, ferrous metals are terrible RF conductors due to their high permeability. Replacing a cool running brass screw with a steel one can result in a small explosion! Also, aluminum has a very thick resistive oxide layer which can also be devastating in many cases. For human "flesh" at around 200kHz, the skin depth is about 2 meters, so don't think skin depth is going to protect you from RF Tesla coil currents in any way...

So I think it is most important just to understand the general idea of skin depth without getting into too much math or exact numbers. There are some on the list that certainly can do the math, but for most of us, it is just not that important.



At 11:26 PM 9/22/2005, you wrote:

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.

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. Once the conductor is small enough that the conductor no longer has a ratio less than the wire diameter, there can be no losses associated with skin depth. This does not mean there are no losses associated with AC currents. But, to apply those losses to skin depth is no longer appropriate. Proximity losses, absolutely!

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.

It should be noted that the current is not uniform around the wire. The current density will occur adjacent to magnetic fields. In an iron core transformer, the current flow through a conductor is drawn to the high permeability core side of the winding. In an air core transformer, it's toward adjacent wires. In a helical single layer coil, toward the 2 adjacent wires. In transformer design, the designer decrease the layers to minimize losses which is why novel winding techniques are thought of because of the huge losses with adjacent currents (high frequency or low).

For an air core transformer at a high frequency where depth penetration crowds toward the surface, the self inductance of the wire must also change due to the changing flux and portion of the conductor which is effectively conducting current, and which is also crowded toward adjacent wires. Thus, as frequency increases, the coil inductance must also move away from the DC inductance. We certainly know this to be true in our measurements.

But at low frequency, where sD is no longer valid, Rac must be due to proximity losses in the conductors and to dielectric heating. Out of all the study which has been done on RF from pcb traces operating in the GHz to antenna theory, I just can't bite on why the conductor must be large in size. In everything I'm reading, it is actually typical to reduce losses by reducing the wire size until the skin depth is no longer affecting the conductor and then to add multiple conductors for the "same" current flow to minimize proximity losses and power losses. I think this is where the 5 x recommendation is appropriate, I do not believe it was meant to show the conductor itself should be 5 x the penetration depth. That should actually create a problem because it causes the sD induced eddy's I discussed earlier.

Sorry for the long post, but it's one of the area's I think I understand, then I don't, then I do, then I don't, ... Are there any references anyone can point me to for the 5 x sd recommendation for a "single" conductor wire size or similar recommendation?

Take care,

Tesla list wrote:

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 07:43 AM 9/22/2005, Tesla list wrote:

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Jim,

Lets say that the skin depth is 10 mils as calculated from the flat plane formula. Are you saying the skin depth in a round conductor (at the same frequency) is smaller than the 10 mils???

Yes, that's exactly what it is.. (bearing in mind that skin depth is a mathematical fiction to use to calculate Rac from geometry and the resitivity of the material)

If so, by how much approximately??

Depends on the diameter of the conductor. There's a table in the "Reference data for radio engineers" book, as well as others.

Also, does the current fall exponentially???

Yes, in a flat plate.