Unified Analytical Synthesis of Cascaded n-Tuplets Filters Including Nonresonant Nodes

• Published in: IEEE transactions on microwave theory and techniques Vol. 69; no. 7; pp. 3275 - 3286
• Main Authors: Caicedo Mejillones, Steven, Oldoni, Matteo, Moscato, Stefano, Macchiarella, Giuseppe, D'Amico, Michele, Gentili, Gian Guido, Biscevic, Goran
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cascaded-block synthesis; elliptic filters; filter topology transformation; Inverters; Low pass filters; Mathematical analysis; Microwave theory and techniques; mixed topology filters; Network topology; Nodes; Prototypes; Research and development; Silver; Synthesis; Topology; tuplets
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2021.3073481

This article presents an analytical method for the synthesis of a low-pass prototype filter constituted by cascaded <inline-formula> <tex-math notation="LaTeX">{n} </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">{n} </tex-math></inline-formula>-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.