Random Rough Surface Effects in Waveguides Using Mode Matching Technique and the Method of Moments

To address the rough surface effects in high speed interconnects on printed circuit boards and microelectronic packages, we study the electromagnetic wave propagation in a parallel plate waveguide with rough surface walls, using a mode matching technique in combination with the method of moments (MoM). In the formulation, a line source in the smooth section of the waveguide excites a summation of modal fields. For each waveguide modal excitation, the modal response fields in the rough surface section of the waveguide are obtained by the solution of a set of coupled surface integral equations through MoM. Results are illustrated for a variety of roughness types including the very rough case based on exponential correlation functions. The results are compared with the previously developed analytical second-order small perturbation method (SPM2) result and the finite element method (FEM). It is shown that for rough surfaces with large slopes, the mode matching MoM model gives a smaller enhancement factor than SPM2. It is also shown that MoM can give accurate solutions even for the very rough case of exponential correlation functions. The MoM method of rough surface simulation in waveguide geometry requires much less computational resources than FEM.