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 [1]. 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 [2] 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 3-D scattering theory of our analysis.