Lossy Microwave Filters With Active Shape Correction

Abstract

Obtaining the prescribed microwave filter response is highly desirable for proper frequency selectivity in RF transceivers. As the traditional microwave filter design methods do not take into account finite unloaded quality factors, lossy resonators cause significant deviations from the prescribed filter response, especially in filters with narrow bandwidths or of high orders. This deviation gets more severe as the resonator losses increase. Building on the lossy filter design techniques by using an active shape correction mechanism, this paper proposes a new approach to recover the filter response when the filter has moderately-to-highly lossy resonators. Being different than most active filter topologies, where all of the resonators are loss-compensated, this study aims at achieving the shape correction with $N-2$ active elements. To characterize the design, a novel lossy-active coupling matrix is introduced by extending the $(N+2) \times (N+2)$ lossy coupling matrix. The proposed theory is verified with the design and fabrication of two $3^{rd}$ order 5 % bandwidth filters operating at 1 GHz and employing resonators with quality factors of 100 and 28, respectively. It has been shown that the method can recover the response in both designs and the theoretical and measured responses are in good agreement.