3-D-Printed Ultracompact Butler Matrix for Wideband Millimeter-Wave Beamforming

An ultracompact 3-D-printed Butler matrix (BM) for wideband millimeter-wave (mm-wave) beamforming is proposed in this article. This is the first time that conductive and dielectric multimaterial 3-D printing technology is applied to realize a 3-D mm-wave <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> BM. By vertically designing and optimizing the BM in 3-D space, we can eliminate a pair of crossovers typically presented in conventional BMs. The hybrid couplers and phase shifters are 3-D printed on different layers for miniaturization. The design flexibility of 3-D-printed multilayer structures is unparalleled. Curved transmission lines and enclosed metal walls are 3-D printed to improve the signal integrity for excellent wideband phase and magnitude imbalance, which are not feasible to achieve via printed circuit board (PCB) manufacturing. Consequently, the spatial footprint of the proposed BM is reduced by over 75% compared to the state-of-the-art mm-wave BMs. The designed 3-D phase shifter shows an excellent phase shift performance in measurement with a phase imbalance of ±2.5° across 16–32 GHz. The measurement results agree well with the simulation results. The measured results show that the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> BM has a wide bandwidth of 53% from 18 to 31 GHz with an ultracompact size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.83\lambda _{0} \times 0.55\lambda _{0} \times 0.05\lambda _{0}$ </tex-math></inline-formula>. For the proof of concept, an antenna array is 3-D printed to demonstrate the endfire beamforming performance.