Discussion
Why is the aperture efficiency of an optimum pyramidal horn only about 50 per cent?
Answer: C
The dominant waveguide mode supplies a half sine taper in one plane, and the flare leaves a quarter to half wavelength of phase error at the rim, and the two together cost about half the aperture. Neither absorption nor reflection accounts for anything like that much, and a horn radiates forward. Corrugated and dual mode horns improve on the figure by attacking the amplitude and phase distributions directly, which is what makes them worth their extra manufacturing cost.
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