Fast synthesis of coupled-resonator filters

This letter proposes a new quickly converging technique for the synthesis of coupling matrix of cross-coupled resonator filters. The method formulates the synthesis as a nonlinear least squares problem involving the zeroes and poles of short circuit input and output admittances, as well as eigenvalues of the coupling matrix and its principal sub-matrices. The solution is found via a damped Levenberg-Marquardt method with analytically computed gradients. Numerical tests show that coupling matrices for high order pseudo-elliptical filters can be found in surprisingly few optimization steps.