Analytical Waveguide Model Precisely Predicting Loss and Delay Including Surface Roughness

This paper describes an accurate modeling approach taking into account the impact of surface roughness on both the attenuation and the phase coefficients of the propagating TE
₁₀
mode in rectangular waveguides. The proposed approach is based on a transmission line model for waveguides and a general surface roughness model, which are both derived from physical relations, i.e., Maxwell's equations. Thus, it is neither limited to explicit frequency bands nor to certain surface profiles. Based on the proposed approach, the specific influence on the propagation coefficient and the line impedance of a waveguide is quantified in the typical transmission frequency region and also around the cutoff frequency. Also, the roughness-dependent shift of the cutoff frequency is covered by the proposed model and explained analytically. Propagation characteristics predicted by the proposed approach absolutely coincide with full-wave simulation by CST Microwave Studio with the same input parameters. Furthermore, WR10 waveguide samples are fabricated and their surface profile is characterized using a confocal laser scanning microscope. Model predictions agree with electrical measurements up to 90 GHz for the attenuation coefficient within ≤10% and within 0.08% for the phase coefficient in the transmission region of the waveguides. In addition, the difference between normally distributed and arbitrarily distributed surface profiles is covered by the model and pointed out in this paper at rigorous measurements even at very smooth surfaces with root mean square-roughness of less than 300 nm. Finally, different techniques for utilization of this approach and possible application fields are presented.