Derivation of the Norton Surface Wave Using the Compensation Theorem

This paper presents a tutorial exposition of the derivation of the Norton surface wave using the compensation theorem. Only the case of a vertical electric dipole above an infinite ground plane satisfying an impedance boundary condition is treated. This is the most interesting case in practice, and the one on which applications such as MF AM broadcasting and HF surface-wave radar rely. It is attractive to use the compensation theorem to treat this relatively complex problem. This theorem, itself simply derived starting from Lorentz reciprocity, is easily understood, and the development that follows draws only on ideas already familiar in at least some context to almost all electrical engineers. This makes it for the most part easier to follow than equivalent alternative presentations. While not the first such derivation to have appeared in the literature, and to some extent paralleling these earlier developments to allow direct comparison, the present paper aims to differentiate itself both by being easier to follow and in removing some errors.