On Evaluation of Beamforming Networks

An approach is presented to characterize a beamforming network by means of a single quantity. It is based on a comparison of the actual output signal vector to the desired output signal vector. The formulation can be concisely written in matrix notation and allows for a characterization over frequency, accounting for absolute offsets. By expressing the characteristics of a beamforming network by a single quantity, subsequent iterations of one network or different network implementations can be compared to each other. The formulation is applied to the evaluation of a 4 × 4 Butler matrix implemented in three different ways.