Skin depth

Encyclopedia : S : SK : SKI : Skin depth

Skin depth is a term used for the depth at which the amplitude of an electromagnetic wave attenuates to 1/e of its original value. It also has applications in numerous other areas, such as seismic exploration.

The skin depth can be calculated from the relative permittivity and conductivity of the material and frequency of the wave. First, find the material's complex permittivity, [\varepsilon_c]

[\varepsilon_c=\right)}]

where:

[\varepsilon] = permittivity of the material of propagation

[\omega] = angular frequency of the wave

[\sigma] = conductivity of the material of propagation

Thus, the propagation constant, k, will also be a complex number, and can be separated into real and imaginary parts.

[k_c = \sqrt = \beta + j\alpha]

[ \alpha = \sqrt = }].

It can be seen that the imaginary part of the complex permittivity increases with conductivity, implying that the attenuation constant also increases with in conductive materials. Therefore, a high frequency wave will only flow through a very small region of the conductor (much smaller than in the case of a lower frequency current), and will therefore encounter more electrical resistance (due to the decreased surface area).

The term "skin depth" traditionally assumes ω real. This is not necessarily the case; the imaginary part of ω characterizes' the waves attenuation in time. This would make the above definitions for α and β complex, and so they would need to be redefined so that [ Im\ = \alpha ].

The same equations also apply to a lossy dielectric. Defining

[\varepsilon_c= - j\right)} ]

replace [ \varepsilon ] with [\varepsilon' ], and [} ]with [ \varepsilon''\over ]

References

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.