Coupling matrix synthesis for lossy filters by optimization using Fréchet distance

A new cost function definition based on the Fréchet distance used in the process of coupling matrix synthesis by optimization is proposed. Such a definition finds a kind of similarity by direct comparison of an ideal - tuned filter response (template) and filter response obtained from optimized coupling matrix. The numerical experiments of coupling matrix optimizations using proposed cost function for two different sets of scattering parameters, one from ideal simulated filter response and second one as measurement of physical lossy filter, show very good results in sense of optimization time, convergence and accuracy.