Magnetic resonance power feeding, a unique wireless power transmission technology, is now in demand in various fields. In 2007 and 2008, an MIT group reported wireless power transmission theory based on optics and photonic crystal theories, explaining it as a phenomenon caused by near-field evanescent waves [1,2]. One feature of this technology is its high transmission efficiency at meter-order distance [3], which will enable feeding of power in applications such as electric cars, micro-robots, and battery-less sensors.

A formula for the transmission efficiency can be derived from electric circuit theory [4]. Efficiency is expressed as a function of a Figure-of-Merit (fom) fom = kQ under an impedance-matched condition. Here, k and Q respectively denote the induction coupling coefficient and coil quality factor. The formula is valid for magnetic resonance power transmission and for inductive power transmission.

A remarkable feature of wireless power transmission with strongly coupled magnetic resonance is its effectiveness at mid-ranges, which is several times greater than the resonator diameter. This feature enables wireless power feeding to a mobile object moving freely in a three-dimensional space. This report describes a powerfeeding demonstration to an electrically powered helicopter. The objective is development of an efficient, compact, and lightweight resonator, with validation of the impedance-matching theory through the demonstration.

Impedance matching, adjustment of the impedance ratio, is conducted in antenna tuners using variable capacitor units and inductive transformers to maintain high transmission efficiency. In the helicopter application, the coupling coefficient k varies dynamically because of the helicopter’s altitude change; both very low Ohm loss and a wide range of impedance transformation are necessary for strongly coupled magnetic resonance.

Considering the power transmission from a resonator with quality factor Q_S, impedance Z₀, and resonance frequency ω₀ to another resonator with Q_D, Z₀, and ω₀ at the AC frequency of ω, then the transmission efficiency can be derived using Kirchhoff’s second law as shown below [4].

Therein, r_S and r_D respectively represent ratios of the source’s and device’s impedance Z_0S and Z_0D to the resonator resistance R_S and R_D, defined as

and

In the ω-r_S-r_D domain, η reaches its maximum value under conditions of

and

Then, maximum efficiency is expressed as

A typical resonant coupling system with input and output inductive transformers is presented in Figure 1. The excitation coil is inductively coupled to the transmitter resonator, and the pickup coil is connected to the receiver resonator. r_S and r_D are adjustable by changing their respective coupling coefficients k_S and k_D.

Figure 2 portrays an equivalent circuit of the system. The source impedance ratio is transformed to k_SZ_0S/R_S. The device impedance ratio is transformed to k_DZ_0D/R_D.

One-side impedance matching is one means to simplify the receiver device. The transmitter takes the optimum impedance ratio, although the receiver impedance ratio is not controlled. The theoretical efficiency of oneside control η₁ is expressed as [5]

The theoretical transmission efficiencies indicated in Equations (1), (5), and (6) are depicted in Figure 3 for

Q_S = Q_D = 200. When the impedance ratio is matched, then the transmission efficiency is improved, especially at a short transmission distance.

A high Q, compact, and lightweight receiver resonator is necessary to make a helicopter fly without a battery. For this study, a resonator was fabricated consisting of a rectangular loop and a mica condenser. It was composed of a copper pipe with 4 mm outer diameter to reduce its weight. The loop side length and the mica condenser capacitance were selected for the resonator to have a resonance frequency exactly equal to 40.68 MHz, which is the power source AC frequency.

Table 1 presents specifications of the receiver resonator along with those of the transmitter resonator whose structure was the same as that of the receiver. As the table shows, the dielectric loss and ohmic loss in the mica capacitor was the predominant energy loss mechanism limiting Q for both resonators.