A direct derivation of a single-antenna reciprocity relation for the time domain

In this paper, a single-antenna reciprocity relation is derived for the time domain. First, the antenna is considered on transmission; next, the same antenna is considered when it is receiving an incident plane wave. The two states, transmission and reception, are related by the application of a modified form of the reciprocity theorem for electromagnetic fields with general time dependence due to Cheo. The derivation of the reciprocity relation for the antenna makes use of simple geometric arguments to evaluate the spatial/temporal integrals that occur in the theorem. A few extensions of the reciprocity relation are also described.