Pure-Analytical Field Distribution and DC-Inductance Prediction of Air-Cored Planar Circular Coils Considering Wire Width

Abstract

An analytical self-inductance calculation method for air-cored planar spiral coils is investigated. To this end, (1) the spiral coil is approximated by a number of concentric circular loops, (2) Poisson equation is solved for the azimuthal magnetic vector potential in the axisymmetric plane via Bessel-Fourier expansion and (3) the inductance is obtained using magnetostatic energy analysis. Since potential distribution is accurately predicted inside the conductors as well as outside, the challenges of many previous works, e.g. Neumann’s formula are overcome. Although the solution is in the series form rather than an integral or closed form; it is fully analytical, requiring no numerical assistance and has a good accuracy. The only drawback is that the accuracy drops as the gap between loops increases. Some case-studies are investigated to prove the efficacy of the proposed approach. Three dimensional finite element analysis results confirm both validity and computational efficiency of the proposed analytical method.