Riccati matrix differential equation formulation for the analysis of nonuniform multiple-coupled microstrip lines

A Riccati matrix differential equation (RMDE) is formulated for analyzing nonuniform coupled microstrip lines (NCML's) in the Frequency domain, The formulation is based on a reciprocity-related definition in the theory of multiconductor transmission lines under quasi-TEM assumption, The hybrid-mode nature of modal phase velocities and strip characteristic impedances for multiconductor microstrip structure is included, The nonlinear RMDE is first transformed into a first-order linear differential matrix equation which can be efficiently solved using method of moments, A convergence study is performed to investigate the sufficient number of basis Functions used in the method. The voltage-scattering parameters of a tapered microstrip and two three-line structures are presented, The frequency responses of a pair of nonuniform coupled lines are measured and compared with calculated results.