This letter presents a $4 \times 4$ Butler matrix realized using stereolithography 3-D printing technology and liquid metal filling. The matrix is in coaxial technology and relies on circular branch lines and curved $50~\Omega $ lines. Input and output ports are aligned and placed on the same plane, while branch lines are organized using all three dimensions to minimize the length of the connecting lines. A prototype, designed at an operating frequency of 12 GHz, is manufactured and tested, showing a footprint of only $1.7\times 1.3\,\,\lambda _{0}^{2}$ . A good agreement between simulated and measured transmission coefficients is observed regardless of the selected input port. These encouraging results open the door to the realization of compact low-cost and high-performing RF beam-steering networks in coaxial technology, based on curing-free additive manufacturing processes.

中文翻译：

---

基于低成本和无固化增材制造的紧凑型3D打印4×4 Butler矩阵

这封信提出了一个 $ 4 \时间4 $ 使用立体光刻3-D打印技术和液态金属填充实现的巴特勒矩阵。矩阵采用同轴技术，并依赖于圆形分支线和弯曲的 $ 50〜\ Omega $ 线。输入和输出端口对齐并放置在同一平面上，同时使用所有三个维度来组织分支线，以最大程度地减少连接线的长度。设计并测试了工作频率为12 GHz的原型，其占地面积仅为 $ 1.7 \次1.3 \，\，\ lambda _ {0} ^ {2} $ 。无论选择哪个输入端口，都可以观察到模拟和测量的传输系数之间的良好一致性。这些令人鼓舞的结果为在无固化增材制造工艺的基础上，以同轴技术实现紧凑，低成本，高性能的射频束控制网络打开了大门。