Using Coupling Matrix in Band-Pass Filters Design

Abstract

This article shows that the capabilities of the coupling matrix [m] for describing microwave band-pass filters (BPF) are limited. The existing procedure for calculating frequency characteristics, based on the coupling matrix, inaccurately describes the physical processes in real BPF with one or several transmission-type resonators. Moreover, these filters can have both simple (magnetic and electrical) and mixed coupling coefficients between the resonators. This fact is confirmed on four experimental microstrip BPF samples. A third-order filter with two direct and one magnetic cross-coupling has a left-hand transmission zero, while the matrix [m] predicts a right-hand transmission zero. A fourth-order filter with three direct and three magnetic cross-couplings has two different transmission zeros, while the matrix [m] predicts one right-hand transmission zero. A fifth-order filter with four direct and six magnetic cross-couplings has a frequency response close to symmetric, if an attenuation level is limited to 40 dB. At the same time, the matrix [m] leads to an asymmetric frequency response of this filter with a right-hand transmission zero. The experimental microstrip three-resonator BPF with mixed cross-coupling has a symmetrical frequency response with two transmission zeros, which are equidistant from the center band-pass frequency. Using coupling matrix leads to a symmetric frequency response with low selectivity, which has no transmission zeros. An explanation of the discrepancies between the measured characteristics of real filters and calculated with the coupling matrix filters is provided in this study.