Inline Microwave Filters With N + 1 Transmission Zeros Generated by Frequency-Variant Couplings: Coupling-Matrix-Based Synthesis and Design

Abstract

A general coupling-matrix-based synthesis methodology for inline <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> th-order microwave bandpass filters (BPFs) with frequency-variant reactive-type couplings that generate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N+1}$ </tex-math></inline-formula> transmission zeros (TZs) is presented in this brief. The proposed approach exploits the formulation of the synthesis problem as three inverse nonlinear eigenvalue problems (INEVPs) so that the coupling matrix is built from their sets of eigenvalues. For this purpose, an optimization nonlinear least-squares procedure is employed. The theoretical foundations of the engineered INEVP coupling-matrix-based synthesis framework are described. In addition, its effectiveness is verified through various synthesis examples of a third-order BPF with four TZs based on different circuit models. Moreover, as experimental validation, a 2.4-GHz microstrip prototype of the distributed-element BPF synthesis example is built and measured.