Optimization Design of Biplane Coil With Ultrasmall Coil Constant Based on Co-Directional Ferromagnetic Boundary Coupling Effect

There are two problems in the low-noise magnetic field compensation of desktop small magnetic shielding boxes (SMSBs). First, the uniformity of the magnetic field generated by the coil is reduced due to the strong coupling effect of the ferromagnetic boundary. Second, the larger coil constant requires a highly accurate current source. To improve uniformity and reduce the coil constant, an optimization design method with an ultrasmall coil constant biplane coil (BC) based on the same trend coupling effect of the ferromagnetic boundary is proposed. In this article, for the first time, the relationship between coil constant and shielding distance is analyzed by constructing the magnetic field and distance (M-D) function. The parameters of the primary coils and the secondary coils are optimized by particle swarm optimization (PSO). The combined BCs (CBCs) with an ultrasmall coil constant are designed based on the double image method and M-D function. Compared with traditional BCs, the ${B}_{x}$ and ${B}_{y}$ coil constants of CBCs are reduced by two orders of magnitude to 41.8 and 35.4 nT/A, respectively, and the $ {B}_{z} $ coil constant is reduced by three orders of magnitude to 49.9 nT/A. The uniformity of the magnetic field in the target area is improved by 4.4 times in the X-direction and 7.4 times in the Z-direction. The peak-to-peak value of the magnetic field is reduced by 24.7%, and magnetic field noise is reduced by 49% at 1 Hz in the closed loop.