Time domain analysis of transmission lines

A simple numerical method is developed for the determination of the transient response of lossy transmission lines with a general impedance loading to a general voltage excitation. First, the transient response of the lossless transmission line with a load impedance to a voltage excitation is formulated. The steady state response of the line is then derived from its transient response. A recursive relation for determining the transient response is also given. Reflection coefficient at the load is determined by deriving differential equations directly and also by the use of the Thevenin´s equivalent circuits. A computer program for the implementation of the numerical method together with several examples of the transient response of lossless/lossy transmission lines with passive/reactive loadings are presented. This numerical method has both practical engineering applications and pedagogical value.