Network Methods for Analysis and Design of Resonant Wireless Power Transfer Systems

In this chapter we illustrate networks methods for the analysis an design of Wireless Power Transfer (WPT) systems. We begin with an introduction which compares the alternatives available for transfering electromagnetic power. In particular, we illustrate the advantages and disadvantages of the various possibilities: transmission lines, antennas, and mid-range reactive field couplings. Then, in the introduction, we also illustrate practical applications for WPT and discuss relevant papers published so far. In the second section, after introducing a basic structure for realizing WPT (see Fig.1), we discuss the relevant theory for WPT by considering a very simple network which, nevertheless, contains all the relevant phenomenology. We derive formulas for maximizing the efficiency of power transfer and we show the necessity of introducing matching networks. Several possible realizations of matching networks are then illustrated. In the next section we introduce appropriate methods, based on the ABCD matrix, for the narrow-band analysis of WPT systems including matching networks. An example of such a network is reported in Fig. 2. A section will be devoted to the input and output coupling design where we will provide new formulas for the design of the matching networks. In particular we show that, for a given type of resonators with a given quality factor Q and a given value of the coupling between the two resonators, we can find the optimal coupling coefficients which maximize the efficiency. An example of the results achievable when optimizing the input/output coupling is reported in Fig. 3. Having derived a procedure for attaining maximum efficiency, it is also possible to establish the theoretical limits that can be achieved for a given value of coupling and for specified values of the resonators Q. A section will be also devoted to the case of multiple transmitting and multiple receiving resonators. For this arrangement, which has practical relevance and is illustrated in Fig 5, we also introduce a rigorous general network model for its analysis. Several different types of resonators will be investigated and compared. Closed form formulas relevant to the resonators' design will be introduced and also fullwave analysis of resonators well be exploited. Theoretical results will be compared with measured ones and measurement methods will be discussed. One of the problems of WPT, i.e. the frequency shift occurring when resonators are placed at different distances, will be discussed and the solution will be outlined. This is very important in practice because allows to realize systems without the need of complex sources or difficult tracking mechanisms. Finally, we will also illustrate how to analyze, both in frequency and time domain, the network representations used for WPT.