Synthesizing microwave resonator filters

In this article, analytic and optimization-based methods for the synthesis of dual-passband microwave filters are presented. First, the frequency transformations for synthesizing dual-passband filters is described. For the filters in which the reflection and transmission zeros cannot be found analytically using frequency transformations, an optimization (or trial-and-error) procedure for a systematic approach is described. The reflection and transmission zeros obtained by the frequency transformation were found to be good initial values for the optimization process.