CubeSats are miniature satellites used to carry experimental payloads into orbit, where it is often critical to precisely control their spatial orientation. One way to do this is through the use of magnetorquers, which can be integrated into PCBs. This technique saves considerable space and capital when compared with more common torque-rod magnetorquer systems. Here we derive a method of analyzing different PCB-integrated magnetorquer geometries, parametrizing them such that the moment and efficiency are maximized. Furthermore, by modulating the trace width, the trace number, and other electrical characteristics of the magnetorquer coil, this paper optimizes the generated magnetic moment. Both constant voltage and constant current sources are analyzed as inputs. These optimizations are then simulated in COMSOL for multiple geometries, and it is found that there exists an optimal geometry, given a specified power dissipation. Simulations verify the general trend and maxima of these derivations, barring small, consistent re-scaling in the magnitude of the coil resistance. It is also found that these PCB-magnetorquers provide a sufficient alternative to commercial coil magnetorquers - particularly in volume-restricted configurations. Optimizations for common PCB-implementable geometries on small satellites are tabulated in the Appendix.

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用于立方体卫星的 PCB 集成磁矩器的效率优化设计

立方体卫星是用于将实验有效载荷送入轨道的微型卫星，在轨道上精确控制其空间方向通常至关重要。一种方法是使用可以集成到 PCB 中的磁矩器。与更常见的扭矩杆磁力系统相比，该技术可节省大量空间和资金。在这里，我们推导出了一种分析不同 PCB 集成磁矩几何形状的方法，对它们进行参数化以使力矩和效率最大化。此外，本文通过调制磁矩线圈的走线宽度、走线数量和其他电气特性，优化了产生的磁矩。恒压源和恒流源都作为输入进行分析。然后在 COMSOL 中针对多种几何形状对这些优化进行仿真，并且发现给定指定的功率耗散，存在最佳几何形状。模拟验证了这些推导的总体趋势和最大值，除非线圈电阻大小的小而一致的重新缩放。还发现这些 PCB 磁力器为商业线圈磁力器提供了足够的替代品 - 特别是在体积受限的配置中。附录中列出了小型卫星上常见的 PCB 可实施几何结构的优化。还发现这些 PCB 磁力器为商业线圈磁力器提供了足够的替代品 - 特别是在体积受限的配置中。附录中列出了小型卫星上常见的 PCB 可实施几何结构的优化。还发现这些 PCB 磁力器为商业线圈磁力器提供了足够的替代品 - 特别是在体积受限的配置中。附录中列出了小型卫星上常见的 PCB 可实施几何结构的优化。