Coupling matrix synthesis by solving nonlinear equations using Newton's method

This paper presents a new coupling matrix synthesis method. The method synthesizes a coupling matrix by moving poles and zeros to their own target positions in the complex plane. Mathematically speaking, the procedure is to solve a system of nonlinear equations using Newton's method. In addition, a new algorithm for generating the initial values is devised. The method exhibits a lower possibility of falling into local minima and faster convergence than the existing optimization methods. The method verifies its performance by synthesizing high-order asymmetric filters repeatedly in a very short time period without failure.