Abstract
A sum rule valid for a large class of linear and reciprocal antennas is presented in terms of the electric and magnetic polarizability dyadics. The identity is based on the holomorphic properties of the forward scattering dyadic and includes arbitrarily shaped antennas modelled by linear and time-translational invariant constitutive relations. In particular, a priori estimates on the partial realized gain are introduced, and lower bounds on the onset frequency are derived for two important archetypes of ultra-wideband antennas: those with a constant partial realized gain and those with a constant effective antenna aperture. The theoretical findings are illustrated by an equiangular spiral antenna, and comparison with numerical simulations show great potential for future applications in antenna design.
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