A Semianalytical Gradient Model for Characterization of Conductors With Surface Roughness

In this paper, a novel semianalytical gradient model (SAGM) for characterizing conductors with surface roughness is presented. Based on the linear function of conductivity, the governing equation of the magnetic field is reduced to the modified Bessel equation, which has an analytical solution. With the piecewise linear approximation technique, the SAGM is derived to deal with arbitrary functions of conductivity. Three typical distributions, including the uniform, normal, and Rayleigh distributions, are investigated. The proposed SAGM is employed to evaluate the propagation properties of typical transmission line structures with different surface roughness profiles. The simulation results agree well with those from measurements, which confirm the validity and accuracy of the proposed method.