Theoretical bounds on the directivity and bandwidth of electrically small and wideband antennas

Since the introduction of the pioneering ideas by Chu and Fano in Refs. 1 and 2 more than half a century ago, a priori bounds on the directivity and bandwidth of electrically small antennas have attracted great attention in the scientific community. The classical bounds by Chu (and many subsequent authors) are based on the lowest order partial waves to estimate the ratio between the stored electromagnetic energy and the radiated power. There are several problems associated with this approach, and the final inequality for the directivity and bandwidth is somewhat misleading since it only relates to the smallest circumscribing sphere. A new set of bounds that apply to enclosing regions of arbitrary shape are derived in Refs. 3 and 4 based on the optical theorem and the holomorphic properties of the forward scattering dyadic. These new bounds resemble the classical results of Chu for a spherical region but yields considerable sharper estimates for non-spherical geometries and non-degenerate polarizations.