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The influence of skin effect on eddy current losses

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Dr. Dark Current
Mon May 21 2012, 12:30PM Print
Dr. Dark Current Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384
Hi,
I came across a formula for eddy current losses in thin sheets or wires, at Link2 [Strength of eddy currents].
They say the formula is simplified for no skin effect influence. When there is a skin effect, will the losses be lower or higher? Do you think I can multiply the answer by the DC to AC resistance ratio of the conductor, as calculated eg. by JAVATC to get closer to the real world value?

Thanks for any ideas.
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Steve Conner
Mon May 21 2012, 03:19PM
Steve Conner Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
I guess the skin effect will make the thickness parameter in the formula seem smaller than it really is.

So, since the skin depth in conductors is proportional to 1/sqrt(f), we could say d is proportional to d'/sqrt(f), and substitute into the equation.

Then the eddy current losses would be proportional to the three-halves power of the frequency, instead of the square.

To calculate losses at a given frequency, you could use the skin depth for d instead of the actual thickness of the material.
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Dr. Dark Current
Mon May 21 2012, 10:51PM
Dr. Dark Current Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384
Hmm, but the current path no longer represents a conductor with its diameter equivalent to the skin depth, but rather a hollow tube where the currents can flow a larger diameter than the skin depth - if I get this right...
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klugesmith
Tue May 22 2012, 12:35AM
klugesmith Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
You can't really separate eddy currents from skin effect.
As the Wikipedia artice cited in OP says:
Self-induced eddy currents are responsible for the skin effect in conductors

[edit]
Anyone here got time & inclination to study that formula in the Wiki article,
"eddy current loss without skin effect", and figure how it is derived?

I will guess that in the case of, say, steel core laminations much thicker than the skin depth,
the per-pound losses will be lower than those calculated by the f^2 formula.
In fact will agree with Steve C, that they will (in the limit) go up as f^1.5.

Dr.DC: can you give us the specific application of interest?
For more detailed, more distracting study?
Note that skin effect theory seems to invariably use a linear model,
while the magnetization of transformer steel is extremely nonlinear in ordinary operation.



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Dr. Dark Current
Tue May 22 2012, 09:48AM
Dr. Dark Current Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384
klugesmith: It is for the calculation of eddy current losses in a Tesla coil secondary with single layer solenoid primary and secondary coils. The primary induces a high frequency magnetic field B, which induces eddy currents in the copper wire of the secondary winding. The purpose is to calculate the eddy losses per cm2 of the secondary winding with sufficient accuracy. This is just for the calculation of eddy current losses alone, not the IIR losses in the wire from the actual winding current passing through it.
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Steve Conner
Tue May 22 2012, 09:57AM
Steve Conner Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
Hmm. I think this is better analysed in terms of proximity effect and skin effect, than by using the eddy current loss formula. Could be a job for FEMM.
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