A Design Method of Multimode Multiband Bandpass Filters

In this paper, a general design method for multiband filters is proposed. First, the frequency and element transformations from a low-pass prototype filter to a practical multiband bandpass filter is derived. Afterwards, formulas for extracting the coupling coefficient $k$ between coupled multimode resonators and the external quality factor $Q_{e}$ are also obtained. Thereafter, the design procedure of coupled multiresonator multiband filters is similar to that of single-band filters. A tri-band microstrip filter with tri-mode resonators is successfully designed with the proposed method and fabricated, which validates this theory.