Preliminary design of paraboloidal reflectors with flat facets

Based on the concept of approximating antenna surfaces using flat facets or triangulated cable networks, a geometric scheme to subdivide a parabolic surface is discussed. According to the proposed scheme, the paraboloid is divided at the aperture circle into six equal segments first, which form a regular hexagon. Then the regular hexagon is subdivided into equal regular triangles to form subelements. Finally, the points of intersection of these triangles are projected or mapped on the paraboloid surface using a suitable origin of coordinates to obtain the final nodal coordinates of the members along the revolution axis direction. An expression for the relation between the systematic deviation of the actual surface from the desired surface and the side length of the regular triangles on the antenna's aperture surface is developed, which can be used to determine the side length of the regular triangles, and in turn to determine the size of the reflector surface facets necessary to meet antenna surface accuracy requirements. Application on a 0.6-m offset reflector is described and the simulation results demonstrate the effectiveness of the proposed technique in design of paraboloidal reflectors with flat facets. •A preliminary design technique is presented.•An expression between RMS and side length is developed.•Simulation results demonstrate the effectiveness of the proposed technique.