Beam steering using feed displacement with a paraboloidal reflector

The field in an aperture plane for a symmetrical paraboloidal reflector with its feed displaced from the axis is obtained as a polynomial expansion in coordinates in that plane. From this expansion, the loci of feed positions for maximum gain and for narrowest beamwidths in the radial and tangential directions are found to be on spheres passing through the focus and with their centers near to the vertex, near midway between the focus and the vertex, and near infinity in the direction of the vertex, respectively. Expressions for the variation of the gain with offset are obtained, and are found to be consistent with results obtained by other workers by extensive computer modeling for - numbers greater than one (the range that was covered in their models).