# Does skin effect increase the eddy current losses inside magnetic core?

From wikipedia -Ref1

• The skin effect also reduces the effective thickness of laminations in power transformers, increasing their losses.

From eddy current article in wikipedia-Ref2

• "Eddy currents are minimized in these devices by selecting magnetic core materials that have low electrical conductivity (e.g., ferrites) or by using thin sheets of magnetic material, known as laminations.
• The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents

As per theory, as the resistance increases , eddy currents and corresponding losses are minimized $$Losses= V^2/R$$ (V is the induced EMF in magnetic core due to magnetic field variations)

Due to skin effect, the ac resistance of magnetic core is higher. Hence shouldn't it cause a decrease in eddy current and corresponding losses in magnetic core? Then how does Ref1 statement hold good?

Please note that Iam talking about eddy current and skin effect in magnetic core and not in conducting wires (Ref 1 talks about magnetic core laminations).

• Wikipedia can be edited by anyone so is not rigorous. So read it for broad strokes only and don't treat every little nuance mentioned as being rigorous and accurate, especially if it seems off. Read section II.A "Eddy Current Loss": spectrum.library.concordia.ca/977954/1/Pillay2013a.pdf Commented Apr 30, 2022 at 18:26

The confusion arises from a category error, I think -- skin effect is core loss!

If there were no skin effect, we would know that the conductivity of the core is zero, and thus core loss is zero.

For any nonzero core loss, there is some eddy current flowing in it, and thus opposition to applied magnetic field, thus some shielding effect, and some dissipation. Indeed, this applies even when the loss is not due to eddy currents as such: steel and ferrites also exhibit skin effect due to hysteresis losses. Both loss mechanisms have the same effect on the amplitude and phase of the fields within them, so skin effect still applies. Cool, huh?

This means core loss is a matter of scale: at a given frequency, a thicker core will have higher losses. Which is indeed the observed effect: we use thinner steel laminations to work at higher frequencies, or much lower loss materials like ferrite. And among ferrites, "low loss" simply means lower conductivity and hysteresis loss -- compare common MnZn ferrites, to high-frequency NiZn ferrites with substantially lower conductivity.

Ferrites have losses low enough that we don't usually think of them in terms of skin effect at all, though there are still circumstances where it applies. Large transformers for industrial power supplies can run out of effective core area / incur excessive core losses, when very large cores are needed. We can calculate the skin depth: it's 10s of cm for typical materials and frequencies. Large stuff indeed! (I've personally worked with power transformers in induction heating applications, which are constructed using bricks of ferrite -- partly because you can't get massive core shapes in small quantities to begin with, and partly because the air gap between bricks lets some field pass alongside them, to the same effect as laminated steel.)

Note the other effect I just mentioned: skin effect is a shielding effect. It prevents magnetic field from penetrating the full cross-section of the core, so reduces the total cross section available for use. You might naively expect that a transformer can handle proportionally more voltage at higher frequency -- assuming you have means to dissipate the extra core loss -- but in fact, as skin effect begins to dominate, the core will begin to saturate as only the outer layer is carrying full flux density. Since skin effect goes as $$\\sqrt{f}\$$, so too Vmax goes as $$\\sqrt{f}\$$. (In the skin effect limit, that is; it is still proportional for lower frequencies, where the full cross section of the core is available to the field.)

We can generalize still further, and consider what it means when EM waves decay over distance through any lossy medium. We can express bulk resistivity as complex permeability or permittivity, and find that metals simply have an extraordinarily high index of refraction; which is to say, waves travel very slow in it, which makes sense why the skin depth is rather shallow in relation to the [free space] wavelength.

At around 50 Hz, skin effect, which increases in proportion with frequency is considered to be negligible in conductors of less than centimeter or so. Eddy current lamination loss predominates and is roughly proportional to frequency squared. Therefore this loss is all that is usually considered in a silicon iron power transformer cores along with hysteresis loss. At higher frequencies, in say for example a nickel iron cored audio transformer operating at 15kHz, skin effect definitely comes into play. It effectively reduces the thickness of the laminations and actually considerably reduces eddy current loss, but at the expense of core permeability and flux saturation. The expert in this subject, GAV Sowter, doesn't even mention eddy current loss in his audio frequency transformer write up. See https://www.sowter.co.uk/pdf/GAVS.pdf