Abstract

The paper introduces the concept of hyperbolic reflections in order to complement the hyperbolic rotation matrices used in the lossy coupling matrix filter synthesis. A complex transversal coupling matrix representing a lossy filter is chosen and it is seen how by applying a succession of similarity transformations based also on hyperbolic reflections one obtains different results than by using hyperbolic rotations which are nowadays used in the coupling matrix reconfiguration. Finally a lossy symmetrical filter is designed and simulated based on a folded coupling matrix by shifting the losses into the first and last resonators of the filter.

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