Abstract:Transmission zeros are difficult to achieved by traditional inline filters. In order to handle this problem, a matrix optimization synthesis method was proposed for inline filters with frequency variant couplings. Firstly, the frequency variant coupling matrix of a given topology was transformed into a frequency invariant coupling matrix by matrix transformation. Then, the objective function was constructed by approaching the eigenvalues of the canonical coupling matrix. Finally, the frequency variant coupling matrix with assigned topology can be obtained by gradient optimization algorithm. The influence of the numbers and positions of frequency variant couplings was analyzed by examples of optimization synthesis with different topologies. The results show that the numbers of finite transmission zeros equal the numbers of frequency variant couplings; The N-order inline filters with frequency variant couplings can achieve at most N finite transmission zeros when the direct source-load coupling exists.