Surface impedance concept for modeling conductor roughness

The Gradient Model describes skin effect in rough surfaces even at frequencies, where classical skin depth decreases to the order of surface roughness. It models microscopic roughness as a continous transition of conductivity perpendicular to the mean surface. This is justified by the fact, that roughness feature sizes are much smaller than the wavelength, so a propagating wave effectively interacts with a surface showing a conductivity gradient. As this interaction can be quantitatively described by field theory, the Gradient Model not only correctly predicts the loss increased due to surface roughness, but also roughness impact on phase velocity and characteristic impedance of transmission lines. The new concept presented here derives a complex surface impedance from the Gradient Model, reflecting both loss and propagation effects. This surface impedance can easily be applied as boundary condition in commercial field solvers and significantly increases their prediction power.