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

Abstract

This paper presents an analytical method for the synthesis of a low-pass prototype filter constituted by cascaded n-tuplets including resonant and non-resonant nodes. The method extends the features of previous published solutions, limited to resonant nodes only or that allow the inclusion of non-resonant nodes but in rigid configurations. The method begins with extracted-pole synthesis, arbitrarily defining the transmission zeros. Then, a filter topology transformation is applied by grouped node blocks to obtain the desired topology, with each n-tuplet characterized by the assigned transmission zeros. 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.

Analytical Derivation of Scattering and Admittance Rational Functions From Coupling Matrix

“…The coupling matrix can be manipulated according to a number of operations which do not affect the response observed at the ports, but which correspond to different topologies, more or less suitable for practical implementation (i.e. waveguide, planar, micromachining...); available operations [3], [4] include rotations, scaling and others descending from circuital transformations [5].…”

The MTT-S Technical Coordinating and Future Directions Committee: Promoting Our Technical Communities-2022

“…Today, with a wealth of EM software and insightful field knowledge, those barriers tend to be broken, and filter synthesis is developing toward a better reflection of the real physical world. After the modern coupling matrix theory framework was established [14]- [16], extensive realistic factors were incorporated into circuit models, including losses [17], dispersive couplings [18]- [20], network redundancies [21], [22], nonresonating nodes [23]- [25], singlets [26], and doublets [27]. Meanwhile, filter topologies have begun to diversify from classic forms to configurations more closely related to physical reality.…”