An FOM for Gauging Numerical Synthesis Methods of Microwave Bandpass Filters

Various numerical methods for synthesizing microwave bandpass filters have been proposed in the past to explore new coupling topologies. However, the community lacks a figure of merit (FOM) for evaluating the superiority of the methods. To fill this gap and provide guidance for a better formulation, this letter will propose a general FOM for assessing the generality, completeness, and robustness of a numerical method when multiple solutions exist for a given coupling topology. The proposed FOM is based on the statistical distribution of the condition number of the Jacobian matrix. The performance of a numerical method is gauged by the convergence rate of the number of solutions. Different numerical solvers and ranges of initial values are also investigated to check the robustness of the FOM. Several well-received methods are studied, and their numerical performance is compared. In conclusion, the proposed FOM renders a general assessment for the formulations of numerical synthesis methods, which will lead to more powerful synthesis methods of microwave bandpass filters.