Optimal Relay Coil Placement in Magnetic Resonant Coupling-Based Power Transfer

Wireless power transfer system based on magnetic resonant coupling (MRC-WPT) is widely used to prolong the lifetime of energy-limited devices for short-distance transmission. To maximize the harvested power for the three-coil MRC-WPT system, in this letter a novel optimization problem is proposed to determine the location of relay coil. Although this problem is non-convex, we still have been able to obtain the globally optimal solution in the form of roots of five degree polynomial. We also present a tight closed-form approximation for the optimal location of relay coil to gain analytical insights. Numerical results verify the global optimality claim and provide insights on the coil location for different system parameters. Lastly, it's shown that the optimal relay location is closer to the destination coil.