Optimal design of a wireless power transfer link using parallel and series resonators

The optimal design problem for a wireless power transfer link based on a resonant inductive coupling is addressed in this paper. It is assumed that the magnetic coupling coefficient and the inductor quality factors are known. By employing the conjugate image impedances, the values of the inductances realizing the optimal design with respect to given values of the network input and load impedances are derived. It is demonstrated that there is just one optimal design maximizing both the power delivered to the load and the power transfer efficiency of the link. The four possible schemes corresponding to the use of a parallel or a series arrangement for the two coupled resonators (Parallel-Parallel, Series-Series, Parallel-Series, and Series-Parallel) are considered and discussed. Closed form analytical formulas are derived and validated by circuital simulations.