**About the Editors**

**Ben Minnaert** obtained his Ph.D. in Engineering in 2007 at Ghent University, Belgium. He has authored or co-authored more than 50 papers on international journals and conferences. In 2018, he obtained a permanent position as a researcher and lecturer at the University College Odisee, KU Leuven Association. His main research interest is the modelling of energy systems, including energy harvesting, photovoltaic solar cells, and wireless power transfer. Recently, he has developed nearfield wireless power transfer systems for nonstatic applications. His research activities are dedicated to embedded systems, wireless sensor networks, IoT applications, and (inductive and capacitive) wireless power transfer for multiple transmitters and receivers.

**Mauro Mongiardo** (F'11) received the Laurea degree (110/110 cum laude) in Electronic Engineering from the University of Rome "La Sapienza" in 1983. In 1991, he became Associate Professor of Electromagnetic Fields at the University of Perugia; since 2001, he is has been Full Professor of Electromagnetic Fields at the same university. He was elected Fellow of the IEEE "for contributions to the modal analysis of complex electromagnetic structures" in 2011. The scientific interests of Mauro Mongiardo primarily concern the numerical modeling of electromagnetic wave propagation both in closed and in open structures. His research interests involve CAD and optimization of microwave components and antennas. Mauro Mongiardo has served on the Technical Program Committee of the IEEE International Microwave Symposium since 1992. Since 1994, he has is a member of the Editorial Board of the *IEEE Transactions on Microwave Theory and Techniques*. During the years 2008–2010, he was an Associate Editor of the *IEEE Transactions on Microwave Theory and Techniques*. He is an author or co-author of over 200 papers and articles in the fields of microwave components, microwave CAD, and antennas. He is co-author of the books *Open Electromagnetic Waveguides* (IEEE, 1997) and *Electromagnetic Field Computation by Network Methods* (Springer, 2009).

#### **Preface to "Modelling of Wireless Power Transfer"**

Wireless power transfer (WPT) allows the transfer of energy from a transmitter to a receiver across an air gap, without any electrical connections. Technically, any device that needs power can become an application for WPT. The current list of applications in which WPT is applied is therefore very diverse, from low-power portable electronics and household devices to high-power industrial automation and electric vehicles. With the rise of IoT sensor networks and Industry 4.0, the presence of WPT will only increase.

In order to improve the current state of the art, models are being developed and tested experimentally. Such models represent either part of the WPT technology or are focused on a certain application. They allow simulating, quantifying, predicting, or visualizing certain aspects of the power transfer from transmitter(s) to receiver(s). Moreover, they often result in a better understanding of the fundamentals of the wireless link.

This book presents a collection of peer-reviewed papers that focus on the modelling of wireless power transmission. It covers both inductive and capacitive wireless coupling and includes work on multiple transmitters and/or receivers. We hope the readers will be able to apply the research results herein to enhance the technology and allow its further implementation into our society.

Finally, we congratulate and thank the authors, reviewers, *Energies* journal, and the MDPI publishers and press production team. This book is a result of their support and efforts.

> **Ben Minnaert, Mauro Mongiardo** *Editors*

## *Article* **Optimal Terminations for a Single-Input Multiple-Output Resonant Inductive WPT Link**

**Giuseppina Monti 1,\*,†, Mauro Mongiardo 2,†, Ben Minnaert 3, Alessandra Costanzo 4 and Luciano Tarricone 1**


Received: 28 May 2020; Accepted: 22 September 2020; Published: 3 October 2020

**Abstract:** This paper analyzes a resonant inductive wireless power transfer link using a single transmitter and multiple receivers. The link is described as an (*N* + <sup>1</sup>)–por<sup>t</sup> network and the problem of efficiency maximization is formulated as a generalized eigenvalue problem. It is shown that the desired solution can be derived through simple algebraic operations on the impedance matrix of the link. The analytical expressions of the loads and the generator impedances that maximize the efficiency are derived and discussed. It is demonstrated that the maximum realizable efficiency of the link does not depend on the coupling among the receivers that can be always compensated. Circuital simulation results validating the presented theory are reported and discussed.

**Keywords:** resonant; wireless power transfer; inductive coupling; optimal load; single-input multiple-output; power gain
