On Searching All Solutions of Microwave Filter Synthesis Based on Interval Arithmetic

In this letter, the numerical interval Newton algorithm (NINA) is introduced into coupling matrix (CM) synthesis (reconfiguration) for the first time. In particular, all existing real solutions to microwave filter CM can be found with mathematical certainty, which provides designers with the flexibility to select the most suitable configuration. Also, CM limits can be directly imposed in the synthesis process to only compute solutions in the specified range. This synthesis process is independent of initial variable values, and the global convergence is theoretically guaranteed. Moreover, NINA is a deterministic method that can verify the existence or nonexistence, uniqueness or non-uniqueness of a given CM topology with the desired filtering performance. Furthermore, the processes dealing with both well-determined and over-determined systems are discussed to cover the synthesis of CMs with diverse configurations. One practical sixth-order dielectric filter with parasitic couplings is exemplified to validate the effectiveness of the presented synthesis approach.