Step approximations for curved corners in mode-matching waveguide analysis

Step approximations for fillets (curved corners) in rectangular waveguide resonators are presented. TE_n0 propagation is considered, and the fillets are parallel to the electric field. The step dimensions are intended for direct insertion into those mode-matching computer programs which cannot handle curved surfaces. The step dimensions are found by the low-frequency technique of conformal mapping, which is much more accurate than an approximation based on equal areas of the cavity cross-section. 100 parts in 10⁶ accuracy is typical for the fundamental resonant frequencies, taking only two steps per 90° arc. To facilitate comparisons, the method of moments has been developed, so that curved surfaces can be represented very simply