**7. Conclusions**

A general CPT system with any number of transmitters and a single receiver was optimized towards power-transfer efficiency. It was shown that in order to maximize the efficiency of a system with given wireless links and couplings, three conditions must be fulfilled simultaneously. First, the ratio of the input current sources is dependent on the coupling between each transmitter and the receiver, given by Equation (47). Secondly, the undesired cross-coupling between the transmitters themselves can be eliminated by adding appropriate shunt susceptances, given by Equation (41), at the input terminals. Finally, the optimal load is purely resistive, equal to Equation (55), if the receiver has no self-susceptance. If a self-susceptance is present at the receiver's side, a compensating load susceptance is required.

Additionally, by conjugate-matching the internal shunt admittance of the generators, the maximum-efficiency solution coincides with the configuration that maximizes the output power.

It was shown that the maximum achievable efficiency *ηmax*, the optimal loads, and the optimal input currents are independent on the cross-coupling between the transmitters, since this unwanted cross-coupling can be entirely annihilated with the transmitter shunt susceptances *B<sup>S</sup> n*. As a result, it is possible to increase the system efficiency by adding more transmitters, and compensating every time for transmitter cross-coupling.

The expression for the extended kQ-factor for each transmitter–receiver link was determined, allowing an estimate of the maximum efficiency of the CPT system via the system kQ-product.

Finally, the analytical derivation was verified by simulation of an example CPT system with three transmitters and a single receiver. Measurements on a CPT setup with multiple transmitters are required to confirm the accuracy of the analytical results and are part of future research.

**Author Contributions:** Conceptualization, methodology, B.M., M.M.; validation, B.M., G.M., M.M.; writing–original draft preparation, B.M.; writing–review and editing, A.C., G.M., M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to remember the colleague Franco Mastri who suddenly passed away on April 3rd, 2020. He was a grea<sup>t</sup> colleague and a profound scientist. Fundamental discussions and studies on the theoretical modelling of near-field WPT systems were of grea<sup>t</sup> inspiration also for the results presented in this work.

**Conflicts of Interest:** The authors declare no conflict of interest.
