Inductance-geometry Relation in the Flat Concentric Coils

Flat concentric coils are widely used in inductive powering devices. Thus, interest arises in the investigation of their magnetic properties in relation to the geometry. This paper is devoted to the calculation of the flat concentric coils self-inductance as a function of inner and outer radii for a given turns number. The self-inductance comprises a sum of the self-inductance of each turn and the mutual inductance between each turns pair. The first term increases linearly with the outer radius increasing. The second term depends on the outer radius non-monotonically. It decreases relatively fast until the certain value of the outer radius and then rose relatively slowly. Thus, there is the ratio of the outer radius to the inner radius which corresponds to the minimum coil self-inductance. It was found that this ratio lies between 1.2 and 1.9 and is higher for the coils with the higher turns number. For certain values of the number of turns and the wire's cross-section radius of the coil, there is no cavity with a local minimum point.