Synthesis of Generalized Strongly Coupled Resonator Triplet Filters by Regulating Redundant Resonant Modes

This article proposed an analytical synthesis approach of generalized strongly coupled resonator triplet (GSCRT) filters, which eliminates the need for negative couplings regardless of the location of transmission zeros (TZs). The principle of removing negative couplings in GSCRTs is explained from circuit level for the first time. In contrast with conventional filter function synthesis with all in-band reflection zeros (RZs), some RZs are preassigned out of the passband, which are named redundant resonant modes (or even modes). By regulating the frequency of the redundant modes, flexible synthesis solutions can be achieved and the previously published strongly coupled resonator triplet (SCRT) becomes a special case of this new generalized version. Besides, a novel physical interpretation of GSCRT from the basis of modes is presented, which shows the modes routing clearly within the coupling matrix framework. Due to the proposed theories, additional approximation and optimization can be avoided during the synthesis procedure. Due to the redundant mode, all couplings in the GSCRT are positive, thus easing the design and manufacturing process. Also, GSCRT brings compact and in-line configuration of filters. Moreover, due to the higher flexibility provided by redundant resonant modes, reasonable synthesis solutions can be selected depending on the specifications or other physical limitations, such as bandwidth and size. A group of synthesis examples with simulations are elucidated. The simulated results show a good agreement with the synthesis theories. The simulated and measured results of an anti-interference C-band eight-pole filter with four TZs below the passband further validate the effectiveness of the proposed theories.