Synthesis of Non-Classic Filter Topologies Based on Orthogonal Matrix Decomposition

In this article, a semi-analytical synthesis method for filters with non-classic topologies is proposed based on orthogonal matrix decomposition. The orthogonal transform matrix of filter topology reconfiguration is decomposed into a product of rotation matrices with different pivots via the analytical Gaussian elimination method. Hence, the path of rotation transform can be obtained from these derived pivots. Once the rotation path is available, the corresponding rotation angles can be easily solved by optimization. Aided with the rotation path already figured out, the synthesis efficiency can be significantly improved. More importantly, once the topology is determined, the rotation path is not affected by the position of transmission zeros and return loss. Therefore, the obtained rotation path can be applied to accelerate the synthesis of the same class of non-classic topologies. Finally, a sixth-order filter with the extended box topology is given as an example to illustrate the effectiveness of the proposed method.