Closed-Form Solution of Rough Conductor Surface Impedance

摘要

This paper presents a closed-form solution of rough conductor surface impedance in terms of material DC conductivity and RMS roughness. Surface roughness is modeled by position-dependent conductivity at conductor-dielectric boundary to account for protrusion of rough conductor into dielectric, which was first proposed in the Gradient model. Analytic solution is obtained by approximating the Gauss cumulative distribution function, used to model the position-dependent conductivity in the Gradient model, with a square of hyperbolic tangent. Closed-form solutions are compared with numerical solutions of the Gradient model and are in good agreement up to a frequency of 100 GHz. Derived surface impedance is causal, which has been shown by numerical Hilbert transform.