Direct Synthesis of Characteristic Polynomials and Practical Topologies for Codesigned Filters With Independent Subband Responses

This work presents a direct synthesis methodology for realizing codesigned filters that integrate low-pass/multi bandpass or high-pass/multi bandpass responses within a unified network. The proposed approach enables independent control over each subband—such as order, bandwidth, and return loss—while supporting flexible placement of transmission zeros (TZs) for enhanced out-of-band selectivity. The synthesis is built upon a new class of characteristic polynomials defined in the nonnormalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega $</tex-math> </inline-formula>-domain, which intrinsically realizes composite low-pass and multi bandpass filtering behavior without requiring frequency transformation. These polynomials are then mapped to a transversal prototype comprising low-pass and bandpass blocks, which can be corresponded to a high-pass/multi bandpass form via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega $</tex-math> </inline-formula>-to-1/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\omega $</tex-math> </inline-formula> inversion. The obtained transversal networks are then simplified into practical topologies through matrix-based manipulations. A series of examples, including synthesis and experimental validations, confirms the effectiveness and flexibility of the method. The proposed technique establishes a legitimate approach toward the integration of complex codesigned filtering functions based on simple resonator and coupling models.