Two-Dimensional Butler Matrix Concept for Planar Array

A new concept of the two-dimensional (2-D) Butler Matrix (BM) is proposed for 2-D beam steering of a 2-D planar array. An example of a 16 x 16 BM for a 4 x 4 planar array is presented. All phase-delay values of the phase shifters in the proposed BM can be calculated merely from traditional 4 x 4 BM by summation according to their positions. All the crossovers can be avoided by using a double-layer microstrip structure in a backto- back configuration. Furthermore, all ports can be arranged in the required locations that can straightforwardly connect to the corresponding array elements. An example of 2.4 GHz applications is fabricated and measured, which exhibited satisfying performances of matching, isolation, equal power division, and progressive phase differences in a more than 10% relative bandwidth.