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    Asymmetrical 4×4 butler matrix and its application for single layer 8×8 butler matrix

    , Article IEEE Transactions on Antennas and Propagation ; Volume 67, Issue 8 , 2019 , Pages 5372-5379 ; 0018926X (ISSN) Tajik, A ; Shafiei Alavijeh, A ; Fakharzadeh, M ; Sharif University of Technology
    Institute of Electrical and Electronics Engineers Inc  2019
    Abstract
    The design procedure and measured results of a novel 4 × 4 Butler matrix are presented in this paper. This asymmetrical structure provides fairly flexible phase outputs; therefore, the array radiation pattern can be rotated around the array normal axis. The structure of this modified Butler matrix is discussed in detail, and the explicit design formulas are derived to achieve the arbitrary main beams direction. Using the proposed design procedure, the Butler matrix can provide even broadside and endfire beams. In addition, this structure is employed to design two Butler matrices, which generate similar patterns as a conventional 8 × 8 Butler matrix, using only single layer circuits with...