Paradoxical behaviour of an infinitely long lossless transmission line

Abstract

An infinitely long loss-less transmission line presents a pure resistance at its input. This is a paradox because a purely reactive network - lumped or distributed - should present only a pure reactance at its input. One possible explanation is that an infinitely long line should radiate energy at any finite wavelength, and, consequently, the resistive input impedance can be identified with the radiation resistance of the line. However, this logic runs into trouble when the line is lossy, because, as shown in the paper, all the energy fed to the line is then dissipated in its distributed resistance and conductance. The infinite line paradox thus remains an outstanding problem in electromagnetics.