2-D Butler Matrix and Phase-Shifter Group

The principles and design methods of two novel devices, 2-D Butler matrix (2-D-BM) and phase-shifter group, are presented. The 2-D-BM has 2M+N × 2M+N configurations that can be built based on the traditional 2M × 2M and a 2N × 2N BMs, and all the output ports can be arranged into a parallelogram configuration to fit the planar array. The major merits from traditional BMs, such as perfect matching, lossless transmission, spatially orthogonal beams, and equal power division can entirely be retained in the 2-D-BMs. As an integral component of 2-D-BMs, the phase-shifter groups are employed to offer more than two distinct values of phase delay on various paths without reference lines. The design procedure of the 2-D-BM and the analytical solution of the phase-shifter group are discussed and illustrated. As experimental verification, a 2-D-BM with 16 × 16 configurations feeding to a 4 × 4 square array for 2.4-GHz applications are fabricated and tested. Satisfying performances at matching, isolation, equal power division, and progressive phase differences among all ports can be observed covering a 17% relative bandwidth.