Analytical Modeling of Three-Section Coaxial Stepped Impedance Resonators for the Design of Compact Tx Bandpass Filters

This article focuses on the synthesis equations of three-section coaxial stepped impedance resonators (SIRs) for the design of Tx bandpass filters and on the benefits of adding a third section compared with using a two-section SIR. In this topology, the three coaxial structures fit inside ones another. In terms of the electrical scheme, the model is a succession of coaxial sections in a cascade, where the ground conductor of one becomes the central core of the next and vice versa. An advantageous property of SIRs is that they allow the size and the distance from the next harmonic to be controlled. The SIR effect depends on the ratio of the characteristic impedances of two adjacent coaxial TEM sections. For a resonator based on three sections, two impedance ratios need to be considered to electrically characterize the resonator in terms of fundamental resonant frequency and transmission zeros. Thanks to the equations obtained by modeling its frequency behavior, we are able to show the added value of changing such a resonator from two to three sections. This makes it possible to enlarge the minimal gap between the cylinders, decreasing the sensitivity to technological variations in manufacture and improving immunity to multipactor phenomena under constrained conditions of height and bandwidth. It also makes the first transmission zero frequency and fundamental frequency independent, as the relative proximity of these two frequencies has an impact on the quality factor and the power handling of the structure. To demonstrate the advantages, we designed an example of a three-section fourth-order filter in the L-band. This was compared with equivalent two-section filters, considering electrical performances and power handling, particularly the multipactor effect. This filter was fabricated in aluminum and tested. The experimental results are presented and discussed.