A Novel 2-D $3\times3$ Nolen Matrix for 2-D Beamforming Applications

In this paper, a 2-D beamforming phased array using a novel 2-D Nolen matrix network is presented. The Nolen matrix is a novel antenna feeding network composed of only couplers with dedicated coupling ratios and phase shifters. It does not require crossover and load termination compared to other networks based on Butler and Blass matrix. To be specific, the closed-form equations are derived first for uniplanar single $3 \times 3$ Nolen matrix, which is composed of three couplers and three phase delay lines. Most importantly, it is found that the proposed Nolen matrix can employ couplers with arbitrary phase differences to achieve relatively flexible progressive phase delays across the radiating elements, presenting a high degree of freedom on circuit topology and beamforming performance. Then, a 2-D antenna feeding network is designed by stacking and cascading six $3 \times 3$ Nolen matrices, and a 2-D patch antenna array is integrated with the proposed feeding network to generate nine radiation beams with unique directions on azimuth and elevation planes, realizing the 2-D beamforming function. To verify the proposed design concept, a prototype of 2-D beamforming phased array operating at 5.8 GHz is designed, fabricated, and measured, and the experimental results agree well with simulation and theoretical analysis.