Rough surface effects in parallel plate waveguide at gigahertz frequencies

We consider a parallel plate waveguide model excited by a line source to address the rough surface effect in an environment more directly applicable to package substrates and PCBs. The problem is solved by the finite element method (FEM). The FEM is applied to the region between the metal plates of the waveguide. The excitation line source is outside the numerical modeling region. Modal basis functions are used in the input plane and the numerical modeling area is discretized by the finite element method. Each modal basis function acts as the excitation source for the FEM model and yields linear algebraic equations that are solved by direct sparse symmetric matrix inversion. Convergence of the model is demonstrated by varying the realization number. The numerical model accuracy is validated by comparing the numerical simulation result and analytical result of smooth parallel plate waveguide structure. Numerical results are illustrated to show the power loss due to the rough surface as a function of the surface parameters RMS height and correlation length. Comparisons are made between the absorption enhancement factor obtained from the numerical FEM model and SPM result of the previous plane wave model and the waveguide model.