RF and Microwave Engineering: Fundamentals of Wireless Communications

2.4 Skin Effect

In order to mathematically analyse the skin effect we start with Maxwell's first and second equation in differential form which are repeated here for convenience

2.76

2.77

Since skin effect takes place in good conductors we are interested in the electric fields in conductors with high values of the conductivity σ. Let's further assume non-dielectric non-magnetic material (ε_r = μ_r = 1). In these conductors current flow is mainly due to conduction current density . The displacement current density is of minor significance. We will consider a conductive halfspace (z ≥ 0) in order to ease our calculations by having a simple geometry. First we apply the curl operator¹² and the constitutive relation on Equation 2.77

2.78

Next, we will insert Equation 2.76 and Ohm's law in Equation ...