Inverse Problem of Triplet BPF with All Mixed Couplings

In this article, using the inverse problem method, an analysis of a third-order bandpass filter (triplet BPF) with all mixed couplings was carried out. These filters have advantages over simpler triplet BPFs with partially used mixed couplings. The inverse problem method determines the mixed coupling coefficients of a triplet BPF from a given location of two transmission zeros (TZ) on the complex plane s = σ + jΩ. As a result of the analysis, it was found that triplet BPFs with all mixed couplings more effectively bring together TZs located on the σ or jΩ axis, which leads to an increase of flat group delay or BPF selectivity. Microstrip triplet BPFs with all mixed couplings use stepped-impedance resonators (SIR) located a short distance from each other. This results in very compact filters formed according to the “close-packed” principle. In such microstrip filters, increasing the thickness of the dielectric substrate makes it possible to increase the unloaded quality factor Q_u of the resonator and realize narrow passbands without increasing the area occupied by the filter. A universal microstrip triplet BPF with all mixed couplings is considered. It combines the properties of symmetric and asymmetric triplet BPF and provides 10 different locations of two TZs on the s-plane and forms significant variety of frequency responses.