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Skin Effect - What is it?

Skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. That is, the electric current tends to flow at the "skin" of the conductor, at an average depth called the skin depth. The skin effect causes the effective resistance of the conductor to increase with the frequency of the current because much of the conductor does little. Skin effect is due to eddy currents set up by the AC current. At 60 Hz in copper, skin depth is about a centimetre. At high frequencies skin depth is much smaller.

Methods to minimise skin effect include using specially woven wire and using hollow pipe-shaped conductors.

Skin Effect Calculator

Frequency

Skin Depth

When an electromagnetic wave interacts with a conductive material, mobile charges within the material are made to oscillate back and forth with the same frequency as the impinging fields. The movement of these charges, usually electrons, constitutes an alternating electric current, the magnitude of which is greatest at the conductor's surface. The decline in current density versus depth is known as the skin effect and the skin depth is a measure of the distance over which the current falls to 1/e of its original value. A gradual change in phase accompanies the change in magnitude, so that, at a given time and at appropriate depths, the current can be flowing in the opposite direction to that at the surface.

The effect was first described in a paper by Horace Lamb in 1883 for the case of spherical conductors, and was generalised to conductors of any shape by Oliver Heaviside in 1885. The skin effect has practical consequences in the design of radio-frequency and microwave circuits and to some extent in AC electrical power transmission and distribution systems. Also, it is of considerable importance when designing discharge tube circuits.

The current density J in an infinitely thick plane conductor decreases exponentially with depth d from the surface, as follows:

$J=J_\mathrm{S} \,e^{-{d/\delta }}$

where δ is a constant called the skin depth. This is defined as the depth below the surface of the conductor at which the current density decays to 1/e (about 0.37) of the current density at the surface (JS). It can be calculated as follows:

$\delta=\sqrt{{2\rho }\over{\omega\mu}}$

where

ρ = resistivity of conductor

ω = angular frequency of current = 2π × frequency

μ = absolute magnetic permeability of conductor $= \mu_0 \cdot \mu_r$ , where μ0 is the permeability of free space (4π×10−7 N/A2) and μr is the relative permeability of the conductor.

The resistance of a flat slab (much thicker than δ) to alternating current is exactly equal to the resistance of a plate of thickness δ to direct current. For long, cylindrical conductors such as wires, with diameter D large compared to δ, the resistance is approximately that of a hollow tube with wall thickness δ carrying direct current. That is, the AC resistance is approximately:

$R={{\rho \over \delta}\left({L\over{\pi (D-2\delta)}}\right)}\approx{{\rho \over \delta}\left({L\over{\pi D}}\right)}$

where

L = length of conductor

D = diameter of conductor

The final approximation above is accurate if D >> δ.

A convenient formula (attributed to F.E. Terman) for the diameter DW of a wire of circular cross-section whose resistance will increase by 10% at frequency f is:

$D_\mathrm{W} = {\frac{200~\mathrm{mm}}{\sqrt{f/\mathrm{Hz}}}}$

The increase in AC resistance described above is accurate only for an isolated wire. For a wire close to other wires, e.g. in a cable or a coil, the ac resistance is also affected by proximity effect, which often causes a much more severe increase in ac resistance.

To read more about Skin Effects and how it works, refer to Wikipedia please.