# A Novel Approach to Reach Impedance Matching in Wireless Power Transfer Systems
## 1 Introduction  
Wireless power transfer (WPT) based on the magnetic resonance was reported by [PERSON] a century ago. In 2007, the strongly coupled magnetic resonances in magnetically-coupled WPT was proposed by researchers from Massachusetts Institute of Technology (MIT) [1]. Due to its convenience, high efficiency and other advantages, WPT technology is widely used in various practical applications, such as industry [2; 3; 4; 5], medicine [6; 7; 8] and commercial portable equipment [9; 10]. In recent years, it has been found that the basic analysis of WPT technology, mainly coupling mode theory (CMT) [1] and circuit theory (CT) [11] need to be optimized further. For an electrical engineer, the analysis method based on CT is simpler and more precise compared to that based on CMT, thus the CT method has been adopted extensively. With in-depth study of the MCR-WPT technology, many problems such as frequency splitting, impedance matching, enhance transfer efficiency and system stability have risen [12; 13; 14; 15], especially with regard to transfer efficiency, which decreases sharply with the increases in transmission distance. This seriously hinders the development of WPT technology. In order to achieve high-efficiency transfer in WPT systems, most previous work has concentrated on two aspects: (1) maintaining high transfer efficiency when transmission distance changes; and (2)maximizing transfer efficiency when transmission distance is fixed. The former is mainly accounted for by increasing the strength of the coil coupling or improving the quality factor of resonant coils, which is actually difficult to achieve in actual application contexts. In addition, due to the limitations of current technology, the quality factor of resonant coils has reached a bottleneck. [PERSON] et al. [16] illustrated that the maximum transfer efficiency could be achieved by adjusting the distance between the resonant coils. The experimental results showed that the transfer efficiency of the system remained unchanged within the critical distance range, but decreased sharply when the critical value was exceeded. [PERSON] et al. [17] elaborated on an ingenious coil structure design that prevented the coupling coefficient between coils from decreasing dramatically with an increase in distance. In [18; 19], metamaterials and intermediate resonators were used to enhance the transfer efficiency by increasing the strength of coil coupling, as a result, the analysis of the system becomes more complicated. On the other hand, the purpose was to maximize the transfer efficiency of the given resonant coils, and impedance matching is the main way to achieve the maximum transfer efficiency. In reference [20; 21], the impedance matching was achieved by changing the distance between the resonant coil and the load coil. However, larger spaces will be occupied due to the introduction of distance regulation, and the change of horizontal distance is difficult to realize in engineering. By using additional circuits containing inductive and capacitive components, impedance matching can be achieved easily [22]. The circuit topology will be more complex and controlling the additional circuit is also difficult. In [23], impedance matching was acquired by controlling the duty ratio of the switching tube of the DC-DC converter circuit. However, additional losses were introduced and switching tubes are also complicated to control. In this paper, a novel method for impedance matching in the four-coil WPT system was proposed. Firstly, the equivalent circuit of the four-coil WPT system was expounded to obtain the optimal relation between electrical parameters. Furthermore, the relationship between the transfer efficiency represented by the scattering parameters and that represented by traditional circuits was also deduced. Then, the theoretical calculation of the coil self-inductance and mutual inductance of the experimental device in this paper was derived.