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In page Feed horn:

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When used with a offset, parabolic or lens antenna, the phase center of the horn is placed at the focal point of the reflector. The characteristic of the feed horn is usually selected with the 3 dB points of the horn's radiation pattern falling on the edge of the reflector (the beamwidth of the horn matching the F/D ratio of the dish).[citation needed] When the shape of the antenna deviates from a circular dish, the feedhorn needs to be shaped accordingly to illuminate the antenna properly.