Modeling of 3-D Surface Roughness Effects With Application to $\mu$-Coaxial Lines

Effects of 3-D surface roughness on the propagation constant of transverse electromagnetic transmission lines are calculated using finite-element method software by solving for the fields inside conductors. The modeling is validated by comparison with available literature results for the special case of 2-D surface roughness and by simulations using the finite-integration technique. Results for cubical, semiellipsoidal, and pyramidal indentations, as well as rectangular, semicircular, and triangular grooves in conductor surfaces are presented. A developed surface roughness model is applied to rectangular mu-coaxial lines. It is shown that roughness contributes up to 9.2% to their overall loss for frequencies below 40 GHz