Biconical receiving antenna

The modal solution to a biconical receiving antenna with arbitrary arm angles and lengths is presented in the form of sums over special functions; sums which are exact in the sense that no electromagnetic approximations are made. The antenna load is confined within a sphere of small radius centered at the apices of the cones. The analytical formulation is presented, along with solutions for ψ very small and very large, and certain selected numerical data. The general solution permits calculation of all detailed fields near and far, both receiving and transmitting current modes on the antenna arms and caps and the power and the momentum absorbed by the antenna from an incoming plane wave. It is shown that the receiving current modes are necessary for electromagnetic momentum to be conserved during power reception. Detailed calculation of comparative receiving and transmitting admittances confirms that they are identical, as predicted by the reciprocity theorem. The radiation patterns, however, for retransmission during reception and for transmission differ.