A Physical Surface Roughness Model and Its Applications

This paper covers the essential aspects of modeling surface roughness for microwave applications based on underlying physics. After a short summary of the relevant field theoretical fundamentals, surface roughness metrology and commonly used roughness parameters are described. Existing models and their limitations are discussed before the recently proposed Gradient Model is introduced. To this purpose, the modeling approach, the derivation from Maxwell's equations, model predictions, and their experimental verification are shown. Reasonable choices for effective material parameters reflecting the electromagnetic effects of surface roughness as well as a corresponding surface impedance concept are derived. Both concepts allow for easy application of the Gradient Model with 3-D field solvers or analytical models. The obtained simulation results illustrate roughness impact on loss and phase delay in typical transmission lines. Comparison to measurement results up to 100 GHz shows that the Gradient Model accurately predicts these quantities for rough conductor surfaces. As it is not limited to transmission lines only, it significantly improves the design process for arbitrary microwave applications with 3-D field solvers for this frequency range.