Fundamentals of a 3-D “snowball” model for surface roughness power losses

SEM photographs of a typical copper conductors prepared by the PCB industry exhibit a 3-D "snowball" structure of copper surface distortions. We have developed an analytical basis for the electromagnetic scattering by the copper "snowballs" to predict additional power losses to those presented by the propagating medium that compare well with the observed measurements for a set of rough microstrip lines. In this paper we describe the fundamental concepts involved with the 3D scattering theory of our analysis.