A Modified Gradient Model to Determine Surface Impedance from Measured Roughness Profiles with Printed Circuit Board Emphasis

A modified version of the Gradient Model is presented. With the formulation of the electric field inside a rough conductor, real roughness profiles can numerically be analyzed without mathematical issues. It is also outlined how to determine the surface impedance of roughness profiles not having the symmetry of a gaussian cumulative density function. Theoretical results are compared to basic findings of scattering simulations and confirmed by measured insertion loss of microstrip lines.