This article presents an analytical method for the synthesis of a low-pass prototype filter constituted by cascaded ${n}$ -tuplets, including resonant node (RN) and nonresonant node (NRN). The method extends the features of previously published solutions, limited to RNs only or that allow the inclusion of NRNs but in rigid configurations. The method begins with extracted-pole synthesis, arbitrarily defining the transmission zeros (TZs). Then, a filter topology transformation is applied by grouped node blocks to obtain the desired topology, with each ${n}$ -tuplet characterized by the assigned TZs. The procedure overcomes the ad hoc techniques currently available in the literature. Moreover, the novel filter transformation presented here (from extracted-pole to cross-coupled topology) provides an additional degree of freedom for filter synthesis, which can be further exploited by filter designers. Several examples are presented to validate the novel synthesis procedure.

中文翻译：

---

级联的统一分析综合 n- 包含非共振节点的连音滤波器

本文提出了一种合成由级联构成的低通原型滤波器的分析方法。 ${n}$ -tuplets，包括共振节点 (RN) 和非共振节点 (NRN)。该方法扩展了先前发布的解决方案的功能，仅限于 RNs 或允许包含 NRNs 但在刚性配置中。该方法从提取极点合成开始，任意定义传输零点 (TZ)。然后，通过分组节点块应用过滤器拓扑变换以获得所需的拓扑，每个 ${n}$ -以指定的 TZ 为特征的连音。该程序克服了特设目前文献中可用的技术。此外，此处介绍的新型滤波器转换（从提取极点到交叉耦合拓扑）为滤波器合成提供了额外的自由度，滤波器设计人员可以进一步利用该自由度。提供了几个例子来验证新的合成程序。