Spectral Theory of Transmission Lines in Presence of External Electromagnetic Sources

ABSTRACT The analysis of the coupling of electromagnetic pulses with transmission lines is rigorously formulated in the spectral domain by means of a Fourier transform, on the line axis, of the currents and of the total electromagnetic field. By means of this formulation, the validity of the telegrapher model and its limitations are clearly assessed; and the spectral domain counterpart of the telegrapher model is presented along with the modifications required to deal with transmission lines over an unperfectly conducting ground. To demonstrate the usefulness of the spectral theory on a practical case that cannot be studied by the telegrapher model, the formal solutions of the problem of a single buried wire of arbitrary length are obtained, by means of the Wiener-Hopf technique. A discussion of the numerical methods that can be used to solve the general equations obtained by the spectral theory is also included.