Simple and Accurate Approximation of Rough Conductor Surface Impedance

This article presents a simple but accurate approximation of the surface impedance of rough conductors. The approximation uses insights about properties of magnetic field and surface impedance observed from the finite-difference numerical solution of gradient model. The key insight is that surface impedance calculated by the gradient model is essentially only a function of frequency. This property allows the design of approximating function that depends only on frequency but can be used to calculate the surface impedance of conductors with any conductance and roughness. Coefficients for Gauss and Rayleigh distribution of position-dependent conductance are given, and approximations are compared to numerical solutions. The relative error of both approximations is below 0.1% at all frequencies of interest. Approximating function is causal by design and is simple enough that it could be evaluated with a scientific calculator.