Convergence of the Q-Bounded Maximum Gain to Q-Bounded Maximum Directivity

uthors of this paper have recently formulated a maximum bound of directivity (super-directivity) of self-resonant antennas constrained by a maximum value of quality factor Q (defined in such a way to be the inverse of the relative bandwidth) [L. Passalacqua, et al., “Q-Bounded Maximum Directivity of Self-Resonant Antennas,” in IEEE TAP, vol. 71, no. 12, pp. 9549–9558, Dec. 2023]. The above paper does not address the extent to which small losses can affect the performance of super-directive antennas. Indeed, it is widely acknowledged that super-directivity does not always translate into “super-gain” even for small losses, especially in cases involving high Q factors. The relationship between super-gain and super-directivity has been a highly debated issue in antenna theory, prompting extensive research and numerous publications. The purpose of this paper is to assess the general impact of losses on the maximum super-directivity and, more specifically, to identify the ranges of Q and losses for which the Q-bounded super-directivity corresponds to a Q-bounded super-gain.