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

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Malcolm Watts" <m.j.watts@xxxxxxxxxxxx>

Hi Bart,

On 23 Sep 2005, at 10:56, 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.
>
> 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,
> Bart

That figure probably came from me. A bunch of measurements I did on a
range of coils (I recently re-sent this to Terry to put on hot-
streamer) suggested this was a useful guide for producing high Q
closewound secondaries with 3 sd being a useful guide to achieve the
same result with a 1:1 spacewind. I seems to work in practice but I
wouldn't like to claim this as being the last word on the subject.

Malcolm