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

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