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

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

Hi Mike,

Yes, that is the idea. The paper shows a calculation technique to reduce large error.

Litz wire is used to reduce skin effect losses at RF applications by packing several small insulated wires into a bundle. The insulation prevents the current from moving toward the outer conductors of the bundle (as the current would at high frequency if the wires were not insulated). The individual insulated strands are picked to be much smaller than the skin depth of the frequency used. This ensures all the strands are effectively conducting current. The end result is that the bundle is capable of delivering power equivalent to a single conductor which would be the same size area as the entire bundle, but with a large reduction in skin effect losses. And of course they try to reduce internal proximity effects by weaving and bundling techniques.

38 awg for 50-100 kHz is recommended for a Litz strand. The number of strands to use for a given power is the other part of the equation. Note how small the strand size is for the skin depth at 100 kHz. As the frequency increases, we see the recommended strand sizes getting smaller and smaller. 38 awg is 4 mils and 100 kHz has a depth of 8.2 mils. Just wanted to point that out since it is in line with what I've been trying to point out.

It would certainly be interesting to measure the Q of a TC solenoid wound with Litz wire and an equivalent single conductor solenoid to do a side by side comparison. In our situation, I don't know if we would see much of benefit. But then that's what experiment is suppose to sort out for us.

Take care,
Bart


Tesla list wrote:

Original poster: "Mike" <mike.marcum@xxxxxxxxxxxx>

Interesting paper, tho the math formulas kinda freaked me out and gave me a headache. Any mathmetician out there wanna simplify that? As is it covers every conductor, when 99% of the time copper is used. Probably not important when running regular TC's, but would come in handy when building giant ferrite-cored transformers running at 20 kW. But then again, doesn't litz wire cancel most of these effects to the point the remainder can be ignored assuming you use the recommended strand size (38awg for 50-100 kHz)?

Mike
----- Original Message ----- From: "Tesla list" <tesla@xxxxxxxxxx>
To: <tesla@xxxxxxxxxx>
Sent: Sunday, September 25, 2005 5:29 AM
Subject: 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.