Excitation of a surface wave along an infinite yagi-uda array

The fundamental integral equations defining the current along the dipoles of an infinitely long Yagi-Uda array excited by a single delta function voltage source are reduced to a system of simultaneous algebraic equations by the use of the King-Sandler array theory. This system is solved by identifying it with a summation equation and applying a technique analogous to the use of Fourier transforms on integral equations. The resulting solution is made up of a term associated with a surface wave, and terms which decay with increasing distance from the source dipole. The wave term is found explicitly from this summation equation solution and the remaining terms are evaluated approximately by reverting back to the original matrix equation. Finally, a variational procedure is developed and yields an accurate stationary solution for the input impedance when the approximate dipole currents are used as trial functions.