Rapid Coupling Matrix Reduction for Longitudinal and Cascaded-Quadruplet Microwave Filters

To realize standard microwave filter structures, it is necessary to zero some of the elements in a general even-mode coupling matrix. The zeroing process involves solving a nonlinear set of equations, performed here by using the Newton-Raphson method. Thus, intelligence is added to the numerical iteration procedure, to ensure rapid convergence. The reproduced transmission coefficient S(21) from the reduced matrix agrees well with the one synthesized.