Design and Implementation of Single-Layer 4 × 4 and 8 × 8 Butler Matrices for Multibeam Antenna Arrays

<div>(a) Magnitude and (b) phase difference of the <span class="nowrap"><svg height="8.8423pt" id="M63" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 6.25863 8.8423" width="6.25863pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g></svg>-</span>parameters for the 8 × 8 BM when input port 1 is excited.</div>

International Journal of Antennas and Propagation

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Figure 9

Figure 9: Design and Implementation of Single-Layer 4 × 4 and 8 × 8 Butler Matrices for Multibeam Antenna Arrays 