Synthesis of Annular Sum and Difference Patterns Produced by Array-Fed Ring-Focus Reflector

Annular sum and difference beam patterns, produced by an array-fed ring-focus reflector (RFR), are synthesized using three different methods. An ideal planar source that produces an annular beam with the maximum possible gain is determined. The first method places the above ideal planar source in front of the RFR’s aperture. The radiated electromagnetic (EM) fields produced by the induced current on the RFR’s surface determine the feed-array source distribution. The second method directly projects the ideal planar source onto the RFR’s surface with phase adjustment. The EM fields radiated by the surface current are then employed to synthesize the source distribution of the feed array. The third method employs conjugate field matching optimization to determine the array source distribution. The difference beams are synthesized by employing Gram–Schmidt’s orthogonalization method. The second and third methods show improved performance over the first method. The array-fed RFR is advantageous over direct radiating mechanically scanned arrays, typically used in mobile receiving systems, in terms of complexity and implementation cost.