Compact In-Line Frequency-Variant Coupling Filters Design Using Fan-Shaped Folded Waveguide Resonator

This article introduces a modified fan-shaped folded waveguide resonator (FWGR) that exhibits a lower fundamental frequency, improved unloaded quality factors ( Q_u ), and a unique field distribution. Notably, the field distribution enables mixed coupling without requiring any additional structures, which is essential for realizing in-line frequency-variant coupling (FVC) filters with transmission zeros (TZs). Based on the resonator, two coupling schemes, slot coupling and gap coupling, are proposed for constructing higher-order in-line FVC filters. Comprehensive analysis, including the extraction procedure for determining the FVC coefficient and the corresponding TZs, is also presented. Three third-order in-line filters with the same in-band responses are first designed using slot coupling to demonstrate superior control of TZs, where each filter generates two independently controlled TZs due to asymmetrical structures. A fourth-order filter with three TZs is implemented based on symmetrical slots coupling further. To explore additional design possibilities, a novel kind of coupling topology integrating slots and gap couplings is proposed. One four-pole and one six-pole in-line FVC filters with a similar volume are developed for validation. In general, all developed filters in the work can achieve compact volumes and N -1 TZs with simple physical structures. For experimental validation, demonstration, fourth- and sixth-order filters were selected for fabrication using 3-D metal printing technology. All prototypes were printed well, so the test results were consistent with the simulated results.