Asymptotic Decay of the Quasi-static Near-field Electromagnetic Field Components of the DD Wireless Power Transfer Coupler

Abstract

The extraneous electromagnetic field of the double-D (DD) coupler is analyzed in detail to determine the asymptotic decay rate with distance of the near field components; that is, the magnetic and electric field components in the quasi-static far field. In this region the source-observation distance is many times the maximum source dimension, but still well within the reactive near field. It is shown that, because of the operating frequency of 85 kHz, when current electromagnetic compatibility standards are considered, it is this quasi-static far field that is of most interest. In spite of the appearance of the DD coupler, the near magnetic field is shown to decay asymptotically with radial distance as does that of a horizontal magnetic dipole, −60 dB/decade. This result is somewhat counter-intuitive as the DD coupler clearly physically resembles a higher-order multipole source. The results here contradict other published work which predict a greater decay rate with distance. A full multipole model of the DD coupler is presented and discussion of the relationship between this multipole model and a spherical wavefunction expansion is given. For the DD design given in the current SAE J2954 TIR, it is shown that, primarily due to the presence of the inhomogeneous ferrite core, a pronounced net horizontal dipole moment exists. However, the inhomogeneous ferrite core is a central part of the DD coupler design and without it the electrical performance, e.g., efficiency and tolerance to offset and alignment, are diminished. It can be deduced that in order for the extraneous fields to behave as a $\text{TE}_{12}-z$ multipole with the attendant quasi-static far field decay rate, careful attention would have to be devoted to maintaining the symmetry and this would likely degrade performance parameters such as efficiency. Without such a modification, the DD coupler produces a near extraneous magnetic field that decays at −60 dB/decade.