Design of a Planar, Concentric Coil for the Generation of a Homogeneous Vertical Magnetic Field Distribution

This paper describes an algorithm to design a planar, concentric coil that generates a homogeneous vertical magnetic field distribution, with a target self inductance. The algorithm consists of several steps. The first step is the random generation of a large set of concentric coils, taken into consideration a number of boundary conditions such as the outer dimensions and the radius of the conducting wire. The optimal coil is found from this set after a twofold selection, namely on the self inductance value and on the uniformity of the vertical magnetic field, which was evaluated using a cost function. The algorithm is straightforward and based on closed expressions, which leads to a rapid execution of the procedure. We evaluated the algorithm on a representative reference configuration. The best coil of the large set was selected and the quasi-uniform field distribution of this coil was confirmed by experimental verification.