Coupling matrix synthesis of cross-coupled microwave filters using a hybrid optimisation algorithm

A hybrid optimisation algorithm that synthesises coupling matrices for cross-coupled microwave filters is presented. A binary encoded genetic algorithm is combined at regular intervals with a sequential quadratic programming local search method to form a hybrid, exploiting the speed of the local search, while maintaining diversity with the genetic algorithm. The genetic algorithm uses the stochastic uniform selection technique and a multiple point crossover operator. A compact, efficient cost function requiring only the determinant and a cofactor of the coupling matrix is used as the basis of the optimisation algorithm. Optimisation algorithms simplify the process of synthesising coupling matrices, compared with analytical synthesis. However, algorithms that use only local search methods cannot be guaranteed to find a global minimum. This hybrid method aims to extend the range of coupling matrices that can be synthesised by optimisation, while maintaining the speed of search. A coupling matrix for a tenth order coupling matrix for a dual band symmetric filter and a seventh order asymmetric filter are synthesised to verify the method.