Time-domain analysis of lossy transmission lines with arbitrary terminal networks

A numerical method based on traveling wave theory is presented for the transient analysis of lossy transmission lines with arbitrary terminal networks. The method is well suited to computer programming. By introducing the imaginary transmission line, the network is portioned into two parts. An approach by the S-matrix and the z-transform is applied to the arbitrary terminal networks and time convolution is applied to the lossy transmission lines. The time domain S-matrix required for the convolution is obtained by the use of a fast inversion of a Laplace transform. A time-domain wave flow for the network is considered. The voltage waves at the lumped part are obtained by the S-z method, and the time-domain S -matrix is convolved with the voltage waves on the imaginary and lossy transmission lines to obtain a time-stepping solution. Three numerical examples are presented to illustrate the application of the method