ABSTRACT

An electromagnetic field can penetrate into a conductor only a minute distance at microwave frequencies. The field amplitude decays exponentially from its surface value according to

A = e−x/δs (26.4)

where x is the normal distance into the conductor measured from the surface, and δs is the skin depth. The skin depth or depth of penetration into a metal is defined as the distance the wave must travel in order to decay by an amount equal to e−1 = 0.368 or 8.686 dB. The skin depth δs is given by

δs = 1√ π f µσ

(26.5)

where f is the frequency, σ is the metal conductivity, and µ is the permeability of the metal given as

µ = µ0µr (26.6)

with µ0 equal to the permeability of free space and µr the relative permeability of the metal. For most metals used as conductors for microwave and RF applications, the relative permeability, µr = 1. The relative permeability of ferroelectric materials such as iron and steel are typically on the order of several hundred.