부산대학교 도서관

We have recently formulated a maximum bound of superdirectivity of self-resonant antennas for a given Q (inverse of frequency bandwidth). This article complements the above work treating the influence of the losses. The problem is faced by assuming small losses in terms of surface resistance over the metalized surface of the minimum sphere circumscribing the antenna. The final closed-form formula shows that the maximum gain is obtained by a summation that resembles the well-known Harrington’s sum for maximum directivity, except that the expansion coefficients are weighted by the radiation efficiency of each spherical harmonic. The formulation is then generalized to the case of self-resonant antennas, providing a tighter bound for any losses. For small antennas, we provide a simple interpretation of the field corresponding to the maximum gain in terms of dipolar and quadrupolar source contributions, weighted by the appropriate efficiency, offering a physical insight into the phenomenon. The formulation is then extended to also account for a Q-bound, deriving a final series expression as a function of the loss resistance and the antenna electrical size. This expression seamlessly merges to the previously derived Q-bounded maximum directivity as losses tend to zero and converges to Q-unbounded maximum gain for very large values of Q.