The uniform magnetic field is widely used in sensors and other laboratory devices. The four-coil configuration has the advantage of open space and good uniformity. Traditional schemes include Lee-Whiting, Tetracoil, Braunbeck, etc. The first two schemes have rounding errors of coil turns. The Braunbeck configuration avoids rounding errors, but the structure is solidified and cannot meet the requirements of flexible sensors. In this study, we derive a general constraint equation that fits various four-coil configurations and show that the constraint parameter uniquely defines the configuration. Moreover, we develop a simple optimization approach that allows building the optimized configuration that lacks rounding errors of coil turns. We analyzed system performance for different coil cross sections and configurations. The comparison of the original Lee-Whiting and optimized coils revealed that the normalized maximum radius R_max increased by 7.67%. Finally, the increase in cross-section resulted in performance that was principally different from classical models. The proposed approach makes both scientific and educational contributions for future studies.

均匀磁场广泛用于传感器和其他实验室设备。四线圈配置具有开放空间和良好均匀性的优点。传统方案包括Lee-Whiting，Tetracoil，Braunbeck等。前两种方案具有线圈匝数的舍入误差。布劳恩贝克（Braunbeck）配置避免了舍入误差，但是结构坚固并且不能满足柔性传感器的要求。在这项研究中，我们得出了适合各种四线圈构型的一般约束方程，并表明约束参数唯一地定义了构型。此外，我们开发了一种简单的优化方法，该方法允许构建优化的配置，而该配置没有线圈匝数的舍入误差。我们分析了不同线圈截面和配置的系统性能。R _max增加了7.67％。最后，横截面的增加导致性能与经典模型大不相同。所提出的方法为将来的研究做出了科学和教育上的贡献。