WAVE-FORM RELAXATION SOLUTION OF THE ABCD MATRICES OF NONUNIFORM TRANSMISSION-LINES FOR TRANSIENT ANALYSIS

In this paper, the transient response of arbitrarily terminated nonuni form transmission lines with frequency-dependent parameters is analyze d by introduction of ABCD matrices and waveform relaxation (WR) method . A differential equation describing the ABCD matrices of nonuniform t ransmission lines is derived and then solved efficiently with the WR m ethod. A convergence theorem is proven, according to which the nonunif orm transmission line is segmented into a number of cascaded subnetwor ks to increase the convergence speed. An example of nonuniform transmi ssion system is analyzed. The results are comparable to that of the co nvolution-characteristics method.