Since wireless power transfer (WPT) was proposed by Nikola Tesla, WPT applications have increasingly attracted interest. Types of WPT are categorized as radiative and non-radiative forms, such as microwaves, lasers, electromagnetic induction, and magnetic resonance coupling (MRC). Earlier research shows that WPT via MRC has the considerably higher transmission efficiency than microwave transmission at the same distance as the transmission coil diameter. In 2007, an MIT group demonstrated WiTricity, the first MRC system, which conducted 1 m distance transmission with 90% efficiency [1] [2] . That year, the Nevada Lightning Laboratory achieved 800 W power transfers over 5 m distance ‎[3] . In 2009, Sony group achieved long-distance transmission with a relay coil between the resonators [4] . The benefits of MRC include the considerable practical applications of WPT to electric vehicles. Recently, interest has also arisen in MRC applications for mobile devices. In 2009, Qualcomm demonstrated a wireless charging technology for eZONE mobile devices ‎[5] . A WPT demonstration for stationary devices was conducted. However, many difficulties persist in transmission for moving objects.

To develop WPT technology that is applicable to mobile devices, it is first necessary to manufacture a small, light, and highly efficient receiver for use with the transmission system. Furthermore, automatic impedance- matching and load-power control systems are needed because the relative positions of the transmitter and receiver coils can change. For an impedance matching technique, some researchers have used a circuit with a tuning capacitor and inductor, controlling several condensers in the circuit ‎[6] .

For our previous study, a small helicopter with a light-receiving resonator (3.8 g) was developed using a resonance frequency ω of 40.68 MHz [7] . A four-coil system comprising an excitation coil, transmitter resonator coil, receiver resonator coil, and pickup coil was adopted. Its transmission efficiency of 50% was achieved by one-side impedance matching and 100 mm altitude flight. Impedance was controlled on the transmitter side by adjusting the distance between the excitation coil and the transmitter resonator, avoiding the changes in its resonant frequency. However, to minimize the receiver weight on the helicopter, impedance on the receiver side was not matched.

For this study, a flight attitude of 590 mm was achieved by optimizing the transmitter designing. In addition, a method for estimating the transmission efficiency was proposed to maintain the transmission power as constant against the change in the coupling coefficient.

To achieve a higher flight altitude than that reported from an earlier study, the transmission system was redesigned. An open-source software package of moment method, 4NEC2, was used to estimate the coupling coefficient between the coils [8] . According to this software, the relation between the total length of coil l_c and wavelength λ is expected to satisfy λ/l_c < 0.15. However, it is difficult to satisfy this relation at ω = 40.68 MHz. Therefore, ω was changed to 13.56 MHz. The transmitter resonator was enlarged to 600 mm diameter while the receiver size remained the same. The method of one-side impedance matching on the transmitter side was the same as that used in our previous study [7] . A vector network analyzer (MS2035B; Anritsu Corp.) with a calibration material (3750R; Anritsu Corp.) was used to measure the reflected power. Table 1 presents resonator specifications. The skin depth at this frequency is about 0.02 mm in copper. Thereby, a copper tube with a 5-mm cross-sectional radius was used for a transmitter resonator. A copper-foil tube was use for a receiver resonator to minimize weight. The receiver resonator was a square of 110 mm × 110 mm weighing 3.11 g. The equivalent diameter D_R of a circular resonator is the same as that of 124 mm rectangular resonator. Because the voltage in the excitation coil and the resonator increases rapidly with the transmission distance, open-type coils were used as the excitation coil and the transmitter resonators. D_T is the transmitter resonator diameter, which is an open spiral coil like that shown in Figure 1. Transmission power P_T was set to about 5 W, which is 25% of the nor-

mal rated power of the helicopter’s motor. The nominal transmission distance l was set at 550 mm, which is twice as large as the average resonator diameter of 1930 mm. Here the non-dimensional distance l' is introduced as

The optimum impedance ratio r_T is a function of Q_T, Q_R, r_R, and the coupling-coefficient k as

where Q is a quality factor defined as Q = ωL/R. Subscripts T and R respectively denote the transmitter side and receiver side. Impedance ratios r_T and r_R are defined respectively as r_T = Z_src/R_T and r_T = Z_load/R_R. Subscripts src and the load respectively denote the power source and external load. At l = 0, k approaches unity and r_T,opt increases to 37. In preliminary testing, the impedance ratio of transmission side r_T was measured to confirm that the excitation coil can satisfy Equation (2). r_T is tunable by adjusting the coupling coefficient between the excitation coil and the transmitter resonator k_ET, as [9]

Subscript E denotes the excitation coil. To design the excitation coil, the voltage and the current between the excitation coil and the transmitter resonator were analyzed using LTspice [10] . Table 2 presents excitation coil specifications. A pick-up coil was made of a copper-foil tube that was the same as the receiver resonator. The helicopter load resistance was assumed as 5 Ω at P_T = 5 W. In this study, the receiver impedance was matched at l = 500 mm and fixed. Here, k_ET was measured in the same manner as k. Figure 2 portrays the measured impedance ratio on the transmitter side as a function of distance between the centers of respective coil. Results show that r_T satisfied the relation of Equation (2) within the movable range of the coil. Finally, Figure 3 presents the

measured and computed power transmission efficiency η with and without impedance matching as a function of l'. Measured values showed good agreement with the computed values. In addition, the present transmission system achieved high transmission efficiency in the low-altitude region up to 45% by appropriate impedance matching.

Automatic impedance matching with WPT to a small electric powered helicopter was proposed and demonstrated. Results show that the power transmission efficiency was improved up to 45% in the high k region. The flight altitude of 590 mm was achieved with the average resonator diameter = 1930 mm.

Furthermore, the transmission efficiency estimation method was proposed using only the properties on the transmitter side. By sliding a light bulb from 0 mm to 600 mm distant from the transmitter resonator, a constant power supply of the power of 10 W was demonstrated.