Transients on lossless terminated transmission lines

This work contains a general exposition of the methods which are available in analyzing the transients on a lossless terminated line. After reviewing the well-known method based on theΓ-series expansion, we present two alternative methods: one in the form of a Volterra integral equation, and another corresponding to the so-called singularity expansion method. For a resistively terminated line, we have proved the identity between theΓ-series solution and the one obtained by the singularity expansion method. The application of these methods to more complicated terminations is illustrated by the case of a series RL termination. Weber's solution for a short-circuited line is compared with our solution. The importance of injecting the causality condition in our formulation for this class of problems is emphasized. The application of these methods to the treatment of the input current response of a thin biconical antenna is briefly outlined.