A novel understanding of circular four-coil configuration for uniform magnetic field generation

Abstract

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.