General method for synthesizing dispersive coupling matrix of microwave bandpass filters

In this paper, a general method for synthesizing dispersive coupling matrix (DCM) of coupled-resonator bandpass filters with the general dispersion is proposed. Compared to the dispersion-less coupling matrix synthesized by classic approaches, the DCM incorporates the identity of the physical realization and provides an accurate description of the filter. Moreover, the DCM can accurately describe the complex resonators and coupling elements with intentional strong dispersion. A DCM consists of two parts: the frequency-invariant part that corresponds to the coupling matrix at the center frequency and the frequency-variant part that reflects the dispersion of the physical realization. By iteratively adjusting the transmission zeros governed by the given filter topology and ignoring the transmission zeros brought by the dispersion, the synthesis method can directly obtain the frequency-invariant part so that the overall DCM leads to an equal-ripple response. To illustrate the general synthesis method, two design examples are presented, which include a filter with unintentional weak dispersion and a filter with intentional strong dispersion. The examples are validated by EM simulation, demonstrating the effectiveness, accuracy, and generality of the proposed synthesis framework. Key words: dispersive coupling matrix, filter synthesis, microwave bandpass filter