*Article* **Capacitive Wireless Power Transfer with Multiple Transmitters: Efficiency Optimization**

#### **Ben Minnaert 1,***∗***, Alessandra Costanzo 2, Giuseppina Monti 3 and and Mauro Mongiardo 4**


Received: 28 May 2020; Accepted: 28 June 2020; Published: 6 July 2020

**Abstract:** Wireless power transfer with multiple transmitters can have several advantages, including more robustness against misalignment and extending the mobility and range of the receiver(s). In this work, the efficiency maximization problem is analytically solved for a capacitive wireless power transfer system with multiple coupled transmitters and a single receiver. It is found that the system efficiency can be increased by adding more transmitters. Moreover, it is proven that the cross-coupling between the transmitters can be eliminated by adding shunt susceptances at the input ports. Optimal values for the input currents and receiver load are determined to achieve maximum efficiency. As well the optimal load, the optimal input currents and the maximum efficiency are independent on the cross-coupling. By impedance-matching the internal conductances of the generators, the maximum-efficiency solution also becomes the one that provides the maximum output power. Finally, by expressing each transmitter–receiver link with its kQ-product, the maximum system efficiency can be calculated. The analytical results are verified by circuital simulation.

**Keywords:** capacitive wireless power transfer; resonance; wireless power transfer; power-transfer efficiency; multiports; multiple-input single-output
