On Searching All Solutions of Filter Topologies Based on Interval Arithmetic

In this article, the exhaustive numerical Interval Newton algorithm (NINA) is introduced to filter topology synthesis for the first time. NINA is a deterministic method that can identify the existence or nonexistence, uniqueness, or nonuniqueness of the solutions of one customized target topology. Therefore, all real solutions can be derived if there is more than one solution, which enables the selection of the optimal one. Moreover, NINA is independent of the initial variable values, and the global convergence is guaranteed mathematically. The synthesis framework based on NINA that can reconfigure the filter from a canonical topology to a target one is elucidated, including the acceleration process based on parallel computation and database-driven recalculation. To cover the synthesis of extensive filter configurations comprised of cross couplings, frequency-dependent couplings (FDCs), and nonresonating nodes (NRNs), the solving of well-, over-, and under-determined systems are discussed. Specially, NINA can proceed with added limits to only synthesize solutions in a prescribed range that best matches physical reality. Multiple examples are presented, including one fabricated dielectric waveguide filter with parasitic couplings. In the future, NINA will be possibly extended to synthesize nonmodularized high-order filters.