An analytical technique for the synthesis of cascaded N-tuplets cross-coupled resonators microwave filters using matrix rotations

In this paper, a general simple technique for reducing any canonical n+2 coupling matrix to the more useful modular (i.e., cascaded N-tuplets) form is presented. This is accomplished by performing a suitable sequence of matrix rotations whose angles are not derived through optimization, but are analytically computed from the starting coupling matrix elements and the transmission zeros frequencies. The proposed technique allows the association of a transmission zero to a specific block (i.e., a triplet or a quadruplet) increasing the degree of freedom in the filter design process.