Waveform relaxation analysis of nonuniform lossy transmission lines characterized with frequency-dependent parameters

An efficient method for the transient simulation of nonuniform frequency-dependent transmission lines is presented. The method consists of iterative waveform relaxation analyses of asymmetric disjoint two-port networks constructed with FFT waveform generators and characteristic impedances synthesized by applying the Gauss-Marquardt optimization technique. The method can also be adapted for discrete-time analysis by replacing the FFT waveform generators with ideal transmission lines connected with waveshaping networks. Transient responses of uniform and nonuniform transmission lines with and without skin-effect parameters and terminated with linear and nonlinear loads are simulated for illustrations. The accuracy and efficiency of the relaxation technique are substantiated with exact analytical solutions and experimental data.>