Design of E-Band 3D-Printed WR12 Air-filled Waveguide-Based 4x4 Butler Matrix for Beam Steering in 77 GHz Automotive Radar Systems

This paper presents the design and simulation of a 3D-printed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4 \times 4$</tex> Butler Matrix (BM) using WR12 air-filled waveguides for a linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1\times A$</tex> array antenna operating in the 77 GHz band. The air-filled waveguides significantly reduce insertion losses compared to dielectric and printed technologies while maintaining benefits such as compactness, ease of fabrication, and low weight. The Butler Matrix enables beam steering across four fixed elevation angles, complemented by digital beamforming (DBF) for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$360^{\mathrm{o}}$</tex> azimuth coverage, making it highly suitable for automotive radar. A miniaturized WR12 3-dB hybrid coupler with five branch lines ensures amplitude balance within 1 dB and a phase difference of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 90^{\mathrm{o}}\pm 0.5^{\mathrm{c}}$</tex> over the 65–90 GHz range. Key components, including the 3-dB coupler, 0-dB crossover, and phase shifters, were optimized in HFSS and integrated into a compact design. The BM achieves a 32.26% relative bandwidth, with dimensions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3.6\lambda_{0}\times 9.2\lambda_{0}\times 0.8\lambda_{0}$</tex>.