Variations in the frequency sensitivity of waveguide horns

Rectangular horns have extra parameters, when our only requirement is to design to a particular gain. We can use these to improve the design in various ways. The author has designed horns with a maximally flat frequency response. To achieve this goal, it is necessary to consider the slope of the phase-error loss. When the sum of the phase-error slopes in the E plane and H planes of the rectangular-aperture horn equals 6 dB/octave, the antenna-gain response is flat. The rate of change of phase-error loss equals the 6 dB/octave rate of increase with frequency of an aperture antenna. The article goes beyond the maximally flat frequency response to help the designer find parameters for any reasonable frequency-response gain slope