Discussion
Why does the gain of a horn not increase indefinitely with flare angle?
Answer: D
Opening the flare enlarges the aperture, which raises gain, but the path from the apex to the rim grows longer than to the centre, and that phase error eventually costs more than the extra area gains. The optimum sits where the edge phase error is about a quarter to half a wavelength. Wall loss is negligible, the guide supplies whatever power is fed to it, and higher order modes are a secondary effect. Balancing an area gain against a phase loss is the whole of horn proportioning.
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