Analytical expressions of the Q ‐factor for the complete resonant mode spectrum of the equilateral triangular waveguide cavity

Abstract

This Letter presents the closed-form expressions of the unloaded Q-factor in metallic cavities with equilateral triangular cross section, computed from its analytical resonant mode solutions. The obtained analytical formulas for the Q-factor extend the very restricted range of problems with closed-form solutions, complementing the classic cases of the rectangular and circular cavities found in the literature. The presented derivation provides extremely rapid reference solutions for diverse applications such as filter design by test cases for microwave characterisation systems or numerical full-wave solvers. A universal Q-chart, valid for any aspect ratio, is given and the achieved analytical results for the first resonant modes are tested with numerical commercial software, showing excellent agreement.