Compact cross‐coupled filters based on isosceles right triangular and equilateral triangular SIW cavities

Abstract

Two kinds of classical triangular metric resonant cavities including the isosceles right triangular and equilateral triangular metric cavities are investigated carefully. A comprehensive and rigorous derivation process of these two resonant cavities is proposed. Based on this, the mode function and the transverse field components for the modes in the triangular substrate-integrated waveguide (SIW) cavities can be provided. Then the resonant frequency of both kinds of triangular SIW cavities can be calculated. Combined it with the coupling matrix, a fourth-degree filter implemented of isosceles right triangular SIW cavities and a sixth-degree filter formed by equilateral triangular SIW cavities are designed, fabricated and measured in detail. The measured results are in line with the simulated ones. The frequency responses of both filters show a pair of transmission zeroes at each side of the pass band due to the cross-coupling structure. It also verifies the validity of the derivation in this study. Compared with the rectangular and circular resonant ones, the construct of the triangular cavity has the advantage of much more compact. Besides, the proposed filters based on the triangular cavity also have their own advantages of low cost, good selectivity and easy integration with other planar circuits.