Millimeter-Wave Three-Layer Substrate-Integrated 9 × 9 Butler Matrix and Its Application to Wide-Angle Endfire Multibeam Metasurface Antenna

A novel three-layer substrate-integrated waveguide (SIW) <tex-math notation="LaTeX">9×9 </tex-math> Butler matrix (BM) that can produce a broadside beam and wide-angle coverage is presented in this article. Unlike the traditional <tex-math notation="LaTeX">8×8 </tex-math> BM, the proposed BM is realized by cascading three-way couplers. Connecting to the radiation structure and feeding the center input port, a phase difference of 0° is observed and a broadside beam can be produced. When exciting the side input ports, a maximum phase difference of ±160° is obtained and wide-angle side beams are generated. The operation principle and design development of the <tex-math notation="LaTeX">9×9 </tex-math> BM are illustrated in detail to determine the topology and the phase shifters. With the desired phase differences and amplitude distributions, a three-layer topology of the <tex-math notation="LaTeX">9×9 </tex-math> BM is developed to reduce the footprint and improve the compactness, which is subsequently realized in SIW technology. To realize wide-angle coverage, a new endfire metasurface antenna derived from the traditional Vivaldi antenna is proposed, which achieves a fractional 10-dB impedance bandwidth of 72% and a half-power beamwidth (HPBW) of 128° at 28 GHz. By integrating the three-layer SIW <tex-math notation="LaTeX">9×9 </tex-math> BM with an endfire metasurface antenna array, a wide-angle endfire multibeam metasurface antenna is obtained, which achieves a wide HPBW coverage of ±113° and a maximum gain of 12.1 dBi. The topology of an extended single-layer <tex-math notation="LaTeX">18×18 </tex-math> BM based on the designed <tex-math notation="LaTeX">9×9 </tex-math> BM is presented, and multilayer solutions are adopted to demonstrate the possibility of realizing higher order BMs.