Geometric interpretation of synthesis of a quasi-optical distribution system for multibeam phased array antennas

A geometric interpretation is proposed for synthesis of a quasi-optical system employed in multi-beam active phased array antennas (APAAs). Relationships are obtained for the angles of deflections of APAA beams and for optimum positions of the probes of the distribution system. The optimization is performed according to two criteria: the minimum mean deflection and the minimum local deflection. The example of construction of a quasi-optical distribution system for a five-beam APAA is presented. Dependences of phase errors on the positions of radiators and patterns of an APAA with a sidelobe level not exceeding 40 dB are obtained.