A Compact 2-D Beamforming Using Multilayer 4×4 Butler Matrices

This paper presents a two-dimensional (2-D) beam- forming network (BFN) constructed using eight 4×4 Butler matrices for C-band operation. A newly designed 4×4 Butler matrix using a multilayer printed circuit board is introduced to achieve system compactness. It offers a small size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(1.3\lambda_{g}\times 1.3\lambda_{g})$</tex> while maintaining high-quality signal integrity and reliability. The paper demonstrates 2-D beamforming capability using eight 4×4 Butler matrices, stacked and cascaded to get the 4×4 multibeam phased array system. Such a configuration ensures efficient and versatile beam steering capabilities, making it suitable for a variety of applications requiring targeted signal transmission or reception across different spatial dimensions.