It seems a good idea to place the relay coil in the middle to maximise the load voltage in a 3-coil wireless power transfer system; however, no literature points out clearly the reason and the necessary conditions that it holds. In this study, the complex relationship between coupling coefficients and distances is approximated by a simple polynomial, and then a rigorous analysis is carried out to show clearly that the optimal relay coil position of a 3-coil wireless power transfer system is just the middle of the drive loop and the load loop under the symmetrical condition that coil quality factors of the drive loop and the load loop are equal, and furthermore the middle is not the optimal position if the symmetrical condition is destroyed. Finally, the theoretical results are confirmed by the physical experiments.
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