Direct Synthesis and Design of Dispersive Waveguide Bandpass Filters

In this article, a direct synthesis and dimensional design method for narrowband waveguide bandpass filters with a general dispersive coupling element is proposed. Comparing with the dispersion-less filter synthesis approaches, the general dispersive coupling matrix (DCM) that incorporates unique dispersive characteristics of a physical realization is introduced to provide an accurate description of the filter to be designed. Moreover, the DCM can describe not only strong dispersive coupling elements for realizing transmission zeros (TZs), but also dispersive resonators. A DCM consists of a frequency-invariant part and a dispersive part. For a given dispersive part, by iteratively remedying the characteristic polynomials, the frequency-invariant part for an equal-ripple response can be directly obtained. Consequently, according to the synthesized frequency-invariant coupling matrix, the filter dimensions can be designed only by electromagnetic (EM) simulation of each individual coupling element at the center frequency. Two design examples are presented, including a four-pole filter with two TZs and an eight-pole filter with four TZs. The examples are validated either by hardware prototyping or by EM simulation, demonstrating the effectiveness, accuracy, and generality of the proposed synthesis and design framework.