Magnetic Beamforming for Wireless Power Transfer

Magnetic resonant coupling (MRC) is an efficient method for realizing the near-field wireless power transfer (WPT). The use of multiple transmitters (TXs) each with one coil can be applied to enhance the WPT performance by focusing the magnetic fields from all TX coils in a beam toward the receiver (RX) coil, termed as "magnetic beamforming". In this paper, we study the optimal magnetic beamforming for an MRC-WPT system with multiple TXs and a single RX. We formulate an optimization problem to jointly design the currents flowing through different TXs so as to minimize the total power drawn from their voltage sources, subject to the minimum power required by the RX load as well as the TXs' constraints on the peak voltage and current. For the special case of identical TX resistances and neglecting all TXs' constraints on the peak voltage and current, we show that the optimal current magnitude of each TX is proportional to the mutual inductance between its TX coil and the RX coil. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP) problem, which is reformulated as a semidefinite programming (SDP) problem. We show that its semidefinite relaxation (SDR) is tight. Numerical results show that magnetic beamforming significantly enhances the deliverable power as well as the WPT efficiency over the uncoordinated benchmark scheme of equal current allocation.