Coupling Matrix Synthesis for Asymmetric Filter Topologies

An easy to follow general procedure is given here to synthesize a coupling matrix for a physically asymmetric or/and asynchronously tuned network exhibiting the generalized Chebyshev frequency characteristics. In this procedure we show that a physically realizable coupling matrix can be obtained for a given S₂₁(s) by first choosing a suitable structure that can support the required number of transmission zeros with a sufficient number of non-zero couplings. Then a system of non-linear equations can be written to find the elements of the coupling matrix of the selected structure using the Newton-Raphson method, which guarantees rapid convergence.