A hybrid optimization method that synthesizes coupling matrices for cross-coupled microwave filters is presented. This method consists of a general solvopt algorithm and fmincon algorithm, respectively. To avoid divergence from the coupling matrix, two cost functions are built, where the first one is constructed from the eigenvalues of the coupling matrix and its principal sub-matrices, while another one is dependent on the determinant of the coupling matrix and one of its cofactors. The values of non-zero elements of the coupling matrix serve as the independent variables to minimize the cost functions by using solvopt and fmincon. Although the stochastic initial values are not sufficiently close to the global optimum, the hybrid optimization procedure is still robust to find multiple coupling matrices to overcome the initial problem. It is significant that the suitable coupling matrix can be chosen from the multiple solutions to meet the given requirements in practice. For demonstrating the proposed hybrid optimization algorithm, some extraordinary prototype topologies are provided which validate the efficiency of the proposed synthesis procedure.
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