Quantum mechanics

Phase (matter)

Bandwidth (computing)

Materials science

Radiation pattern

Return loss

Eigenvalues and eigenvectors

Telecommunications

Computer science

Antenna (radio)

Electronic circuit

Matrix (chemical analysis)

Insertion loss

Physics

Mathematics

Optics

Composite material

Combinatorics

Topology (electrical circuits)

Matrix algebra

IEEE Transactions on Antennas and Propagation

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 significantly lower sizes. Both structures are implemented for Wi-Fi frequency (2.45 GHz), and the measured results are presented. The first structure employs two asymmetrical 4 × 4 Butler matrices, while the second one uses only one 4 × 4 Butler matrix with single-pole double-throw (SPDT) switches added to select the proper constant phase shifts. The measured return loss, the average insertion loss, and the fractional bandwidth for the first structure are ≥ 23 dB, 6.6 dB, and 24%, respectively. These parameters for the second structure are ≥17 dB, 7.8 dB, and 20%, respectively. Moreover, the size reduction for the first and second structures compared to a conventional 8 × 8 Butler matrix is about 50% and 80%, respectively.

Asymmetrical $4\times4$ Butler Matrix and its Application for Single Layer $8\times8$ Butler Matrix