[PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 430000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, 43000 Wuhan, China; [EMAIL_ADDRESS] (Z.H.) [PERSON]  
1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazexchange ratio and transfer loss are determined by the coupling strength and the quality factor of coils. In the mid-range WPT system, the system energy efficiency and transmission distance are important indicators. In mid-range operation, the transfer distance is usually 50-200 cm [6]. The magnetic coupling coefficient between the two coils decreases sharply when the transfer distance increases. In recent years, a number of research methods have been adopted to analyze the mid-range WPT system. [PERSON] et al. [7] presented an effective method using the \"matching condition\" technology, which is based on adaptively varying the coupling coefficient between the drive (load) coil and transmission (receiver) coil for the impedance matching to achieve maximum efficiency. [PERSON] et al. [8] introduced three significant factors in the four-coil structure of resonant WPT and simplified the circuit calculate formula to attain maximum transfer efficiency and output power. [PERSON] et al. [9] manifested that the system de-to-load efficiency based on the two-coil inductive mode can be improved greatly by using a Class-E power amplifier, and the system also employed high Q factor coils operating at about 6 MHz. Reference [10; 11; 12] employed the physics of the magneto-inductive wave method to explain the behavior of the WPT system with several planar printed resonators in which each capacitive loaded resonator was coupled magnetically to a series of other resonators. The studies in [13; 14; 15] reported relay resonators applied between the drive loop and load loop to improve the transmission efficiency and increase the transfer distance operating at a high-frequency situation. The works in [16; 17; 18; 19; 20; 21; 22] showed that the negative permeability MMs enhanced the system efficiency and transmission distance due to its abilities of controlling the magnetic field and evanescent wave amplification. However, most research with the MMs has used the scattering parameter (mainly the S\({}_{21}\) parameter) to describe the transfer efficiency by the network analyzer experimentally, rather than practical system energy efficiency, let alone using the Class-E power amplifier as a high frequency source to drive the whole WPT system with the MMs. In this paper, we adopt the four-coil WPT system based on magnetically coupled resonance with the MMs in the near field.