Coupling Matrix Modification for Bandpass Filters With Through-Type Resonators and Simple Couplings

In this brief, the problem of modifying the coupling matrix [ ${m}$ ] is solved, which makes it possible to use it in BPFs with reflective and through-type resonators. The matrix [ ${m}$ ] is not applicable to bandpass filters (BPF) containing through-type resonators. This matrix [ ${m}$ ] is formed from impedance matrix [ ${Z}$ ] or admittance matrix [ ${Y}$ ]. In turn, these matrices present the Kirchhoff’s laws for electrical circuits with lumped elements. Therefore matrix [ ${m}$ ] is applicable to BPFs with reflective-type resonators, which are included in BPF as one-port network. However, through-type resonators carry out the impedance transformation, it’s are included in BPF as two-port network, and not described by Kirchhoff’s laws. Its limits the use of [ ${m}$ ] matrix in BPFs with such resonators. The modification of matrix [ ${m}$ ] consists in sign changing of some coupling coefficients $m_{ij}$ according to established rules. These rules are based on specific features of the BPF coupling structure.