Abstract
A planar $4\times 4$ Butler matrix with a compact size is proposed. With the dual transmission lines, the proposed Butler matrix has arbitrary phase difference and phase delay for the used couplers and crossovers, respectively. In terms of experimental verification, the circuit size of the fabricated Butler matrix is $0.86\lambda_{g}\times 0.66\lambda_{g}$. In addition, the matched results between measurement and theoretical calculation can validate the proposed Butler matrix.
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