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.

中文翻译：

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用于设计紧凑型 Tx 带通滤波器的三段同轴阶梯阻抗谐振器的分析建模

本文重点介绍用于 Tx 带通滤波器设计的三段同轴阶梯阻抗谐振器 (SIR) 的合成方程，以及与使用两段 SIR 相比添加第三段的好处。在这种拓扑结构中，三个同轴结构相互配合。在电气方案方面，该模型是级联中的一系列同轴部分，其中一个的接地导体成为下一个的中心核心，反之亦然。SIR 的一个有利特性是它们允许控制与下一个谐波的大小和距离。SIR 效应取决于两个相邻同轴 TEM 截面的特性阻抗之比。对于基于三个部分的谐振器，需要考虑两个阻抗比，以根据基本谐振频率和传输零点对谐振器进行电气表征。由于通过对其频率行为建模而获得的方程，我们能够显示将这种谐振器从两个部分更改为三个部分的附加值。这使得扩大圆柱之间的最小间隙成为可能，降低了对制造技术变化的敏感性，并提高了在高度和带宽受限条件下对多核现象的抵抗力。它还使第一次传输零频率和基频独立，因为这两个频率的相对接近度对质量因数和结构的功率处理有影响。为了展示优势，我们在 L 波段设计了一个三段式四阶滤波器的示例。这与等效的两段式滤波器进行了比较，考虑了电气性能和功率处理，特别是多因子效应。该过滤器由铝制成并经过测试。给出并讨论了实验结果。