Microfluidics-Based 3D-Printed 4×4 Butler Matrix in Coaxial Technology for Applications up to K Band

This work presents a 4×4 Butler matrix in coaxial technology, realized by combining 3D printing and liquid metal filling. The dielectric part of the coaxial cables is 3D printed using stereolithography. According to such a technology, a liquid photo-reactive resin (i.e., the clear resin V4 from FormLab) is UV cured with a laser beam layer by layer, leading to a solid object. The inner conductor of the coaxial line is implemented with an eutectic Gallium-Indium (GaIn) alloy which is liquid at room temperature and features a conductivity σ = 3.4×10⁶ S/m. The outer conductor, instead, is realized by applying silver nanoparticle ink (σ = 1×10⁶) to the exterior of the 3D-printed circuit and curing the structure at 100°C. Firstly, a branch-line hybrid junction working at 20 GHz has been implemented and measured in order to validate the technology. The magnitudes of the transmission coefficients of direct and coupled ports are equal to about -6 dB, whereas their relative phases are about 90°. Eventually, a complete Butler matrix working at 12 GHz has been optimized with CST and a prototype has been fabricated in order to demonstrate the feasibility of this approach. Transmission coefficients with a magnitude of -12 dB and a phase error of ±6° have been obtained at the design frequency, in good agreement with simulations. Although preliminary, these results open the way to a new class of coaxial millimeter-wave circuits and sensors obtained by 3D printing and liquid metal filling methodologies.