Exact Expression for the Skin Effect (Including Surface Roughness)

This option adds an exact skin effect (which includes the effects of surface roughness) to metallic surfaces and/or wires.

Figure 1. The SK - Add a skin effect (finite conductivity) dialog.
Note: The material parameters for the skin effect are defined with the DI card. The SK card then uses the label defined at the DI card.


Thickness of elements
The thickness d of the surface elements in metres (if an SF card is present, this is always scaled).
Surface roughness (RMS value in m)
The surface roughness of the metal specified as a RMS value in m.
Material label
Label of the material which will be used (as specified in the DI card).

The required parameters are μ r , tan δ u and σ (defined with the DI card). If applied to surfaces then also the thickness d is required.

The following restrictions apply:
  • A good conductivity is required, satisfying the condition σω ε 0 .
  • For wires with wire radius ϱ the surface impedance is given by
    (1) Z s = 1j 2πϱσ δ skin J 0 [(1j) ϱ δ skin ] J 1 [(1j) ϱ δ skin ]
    where J0 and J1 are Bessel functions.
  • For a sheet of thickness, d, with properties ε c , μ c with ε c =ε+ σ jω the wave propagation constant in the sheet is given by β c =ω μ c ε c and the wave impedance in the sheet by η c = μ c ε c . The reflection coefficient at the interface between the sheet and the environment is defined as Γ= E E + = η o η c η o + η c . The surface impedance is given by
    (2) Z s = η c 1+Γ e j2 β c d 1Γ e j2 β c d +(Γ1) e j β c d