Synthesis of Cross-Coupled Prototype Filters Including Resonant and Non-Resonant Nodes

In this paper, we present an approach to the synthesis of canonical cross-coupled prototype filters including resonant and non-resonant nodes (NRNs). The family of realizable topologies (including the folded and wheel configurations) is obtained through a recursive extraction technique and is characterized by all the couplings between adjacent nodes plus a number of cross-couplings between non-adjacent nodes (either resonant or non-resonant). The total number of distinct topologies that can be realized is 2^(np-2) with np order of the filter (i.e., number of poles). Some examples of synthesis are reported for illustrating the capabilities of the new proposed procedure. It is also shown how to de-normalize the synthesized low-pass prototype by means of the generalized coupling coefficients, which allow to extend the usual de-normalization procedure also to networks with NRNs.