Direct Band-Pass Synthesis of Wideband Reactive Filter based on Matrix Rotations

A synthesis method of wideband filter based on reactive components is presented using the Coupling Matrix (CM) through direct bandpass synthesis. Leveraged in the classical nodal representation of the CM, different topologies can be explored by applying matrix operations such as inversion, similarity transformations and partitioning. In order to easily understand the couplings interactions in a topology, it is convenient to associate these lumped elements with their nodal representation. Applying the proposed synthesis method, all the values of the lumped elements can be successfully extracted without any optimization in the prototype model. Then, the obtained values are scaled in frequency and subsequently adjusted to be able to manufacture the filter. In this scenario, a third-order bandpass filter with a fractional bandwidth (FBW) around 40 % and two transmission zeros (TZ) in the upper band are synthesized in order to validate the proposed method.