Abstract
The computation of self and mutual inductances of coils is a classic problem of electrical engineering. The accurate modeling of coupled coils has received renewed interest with the spread of wireless power transfer systems. This problem has been quite well addressed for coplanar or perfectly coaxial coils but it is known that the misalignment conditions easily lead to a sharp decrease in the efficiency. Hence, it is crucial to take misalignment into account in order to properly design the overall wireless power transfer system. This work presents a study to compute analytically the mutual inductance of non-coaxial pancake coils with parallel axes. The accuracy of the proposed methodology is tested by comparison with the numerical results obtained using the tool Fast-Henry. Then, a wireless power transfer system, comprising a full bridge inverter is considered, showing the impact of the misalignment on the coupling between two pancake coils and, thus, between the source and the load.
Highlights
The computation of mutual inductance between coaxial circular coils has been thoroughly addressed by many authors since the time of Maxwell who gave a formula for two circles whose axes intersect [1]
It should be observed that both the integral expression of Φ(a, b, ρ) and formula (20) are valid subject to the thin-wire assumption, which holds when rw is negligible if compared to the radii of the turns
The mutual inductance is calculated against the radial distance ρ, and the obtained results, illustrated in Figures 2 and 3, are compared with the outcomes from the multipole-accelerated three-dimensional inductance extraction program Fast-Henry
Summary
The computation of mutual inductance between coaxial circular coils has been thoroughly addressed by many authors since the time of Maxwell who gave a formula for two circles whose axes intersect [1]. In [2,3] formulas for circular loops with parallel axes have been derived but, all these results can be applied only within a restricted range of parameters since they converge slowly in general [4] Nowadays, numerical methods such as the finite element method (FEM) and boundary element method (BEM), allow calculation of the mutual inductance of realistic 3-D geometric arrangement of conductors in an accurate and fast way. The calculation of the mutual coupling between two coils with the spread of wireless power transfer (WPT) systems has received new interest This problem has been quite well addressed for coplanar or perfectly coaxial coils [22,23] but it is known that the misalignment conditions lead to a sharp decrease in the efficiency. The case-study of a WPT system comprising two non-coaxial coils and a converter is presented, pointing out the effect of the misalignment on the performance
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