Unified Framework for Coupling Matrix Reconfiguration Through Sequential Householder Transformation

This article proposes a universal framework for coupling matrix (CM) reconfiguration, offering exceptional adaptability and efficiency. Leveraging Householder transformation (HT), the proposed method enables the attainment of any desired configuration within a maximum of N (the filter's degree) steps. Analytical derivations of N-step Householder matrices tailored to conventional topologies such as folded, arrow, and N-tuplets are provided, streamlining the synthesis process. Additionally, an innovative optimization process applicable to arbitrary topologies is developed, ensuring flexibility across various design requirements. By employing the universal N-step approach, HT matrices can be updated using analytical gradients while preserving orthogonality, ensuring precise and reliable outcomes. To validate the effectiveness of the approach, a complex dual-band filter example with a 16 ^{\circ} extended box (EB) CM is utilized, demonstrating accuracy and efficiency through synthesized and measured results.