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Lower bounds on Q for dipole antennas in an arbitrary volume

Past expressions for lower bounds on the quality factor of antennas have generally applied to spherical volumes [1], [2]. Although, the lower-bound expressions on quality factor divided by directivity of Gustafsson et al. [3] based on their “sum rule” can be applied to dipole antennas confined to arbitrarily shaped volumes, they require a “generalized absorption efficiency” that must be computed or estimated for each antenna and whose value changes by an unknown amount depending upon whether the antenna is excited by general sources or by global electric-current sources alone [4]. Therefore, the primary purpose of the present paper is to obtain through direct derivation, using surface current equivalence principles, simple general expressions for the lower bounds on the Q of electric- and magnetic-dipole antennas, in arbitrarily shaped electrically small volumes, excited by general sources or by global electric-current sources alone.