Derivation of Conditions for the Normal Gain Behavior of Conical Horns

Monotonically increasing gain-versus-frequency pattern is in general expected to be a characteristic of aperture antennas that include the smooth-wall conical horn. While optimum gain conical horns do naturally exhibit this behavior, nonoptimum horns need to meet certain criterion: a minimum axial length for given aperture diameter, or, alternatively, a maximum aperture diameter for the given axial length. In this paper, approximate expressions are derived to determine these parameters.