Two-Dimensional Tunable Butler Matrix

A two-dimensional tunable Butler matrix is presented in this paper, where two 4×4 tunable Butler matrices are stacked in a vertical configuration to achieve a progressive phase difference in the horizontal direction. Four tunable couplers are applied to the 8 output ports of the stacked tunable Butler matrices and achieve progressive phase tuning in the vertical direction. By combining two dimensions of progressive phase, a two-dimensional radiation beam is formed and thus permits the beam to be continuously steered by controlling the bias voltage of varactors embedded in the tunable transmission line within the Butler matrix.