skin depth
Skin depth is a measure of the distance an alternating current can penetrate beneath the surface of a conductor.
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 skin depth is a property of the material that varies with the frequency of the applied wave. It can be calculated from the relative permittivity and conductivity of the material and frequency of the wave. (See the article Mathematical descriptions of opacity for relationships with other optical and electrical parameters.) First, find the material's complex permittivity,
where
4π×10-7 H/m
the relative permeability of the medium
the resistivity of the medium in Ωm
the frequency of the wave in Hz
If the resistivity of aluminium is taken as 2.8×10-8 Ωm and its relative permeability is 1, then the skin depth at a frequency of 50 Hz is given by
mm
Iron has a higher resistivity, 1.0×10-7 Ωm, and this will increase the skin depth. However, its relative permeability is typically 90, which will have the opposite effect. At 50 Hz the skin depth in iron is given by
mm
Hence, the higher magnetic permeability of iron more than compensates for the lower resistivity of aluminium and the skin depth in iron is therefore 5 times smaller. This will be true whatever the frequency, assuming the material properties are not themselves frequency-dependent.
Skin depth values for some common good conductors at a frequency of 10GHz (microwave region) are indicated below.
As one can see, in microwave frequencies most of the current in a good conductor flows in an extremely thin region near the surface of the latter. A 10GHz microwave frequency is approximately four times higher than the frequency of most modern devices such as Bluetooth, wireless, microwave ovens, and satellite television which all operate in or around the 2.4GHz band, and therefore have about two times as much penetration as those figures for 10GHz.
The extremely short skin depth at microwave frequencies shows that only surface coating of guiding conductor is important.
A piece of glass with an evaporated silver surface 3µm thick is an excellent conductor at these frequencies
See also
skin effect
References
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