Arrays of isotropic radiators-a field-theoretic justification

Because of their conceptual simplicity and mathematical con- venience, isotropic radiators are all too popular in the analyti- cal treatment of antenna arrays. However, because an isotropic electro-magnetic field is physically impossible, it is legitimate to ask on which ground the assumption of having isotropic ra- diators in the theoretical analysis of radio communications is justi?ed. In this paper, we provide a field-theoretic answer to this question. To this end, we show that a uniform linear array (¶?Z) of isotropic radiators leads qualitatively to the same relative antenna coupling as if the ¶?Z was composed of Hertzian dipoles. This implies that the transmit array gain - That is, the reduction of necessary transmit power to generate the same electric field strength at a given point of interest, compared to using a single antenna of the array - of a ULA of isotropic radiators, is qualitatively the same as of a ULA of Hertzian dipoles. This shows that, albeit isotropic antennas do not exist, their application in theoretical investigation of antenna arrays is legitimate, because they lead to physically reasonable antenna coupling which allows a qualitatively correct analysis of important performance parameters, like array gain.