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Microstrip bandpass filters designed with various types of transmission-line resonators are newly proposed in this study. The connected-coupling mechanisms are theoretically analyzed and then appropriately applied in the design of an all-connected-coupling basic filter for preliminary validation. With the simultaneous utilization of conventional edge-coupling and the proposed connected-coupling mechanisms, a fifth-order stopband-extended filter with half- and quarter-wave resonators is then accomplished based on resonance misalignment. After that, the newly proposed three-way resonators made possible by the proposed coupling schemes have been employed as the frequency-selective power-splitting/combing elements for design of dual-band filters and diplexers. Specifically, in the constructed dual-band filter, the three-way resonators not only serve as a power splitter/combiner, but also play the important role of resonant components among filters. As for the presented diplexer, the three-way resonator splits the signal to two channels without necessitating extra matching circuits and thereby economizes the occupied area. The proposed approaches have been validated by experimental results that are well predicted by simulations.