Suppression of Leakage Magnetic Fields in Wireless Power Transfer Using a Sandwich Structure

This study proposes a wireless power transfer (WPT) system using a sandwich structure comprising two transmitter coils and two receiver coils with distinct magnetic field configuration modes. The primary objective of this research is to suppress leakage magnetic fields while maintaining high power transfer efficiency. The results of the electromagnetic field analysis and experimental tests demonstrated that the magnetic field leakage of the differential-differential (DD) mode of the sandwich structure was significantly lower than that of the conventional structure, which employs a single coil pair and the cumulative-cumulative (CC) mode of the sandwich structure. Compared to the conventional and CC modes, the leakage magnetic field of the DD mode decreased by 10.1-12.3 dB at 1 m from the coils. This corresponds to suppressing the magnetic field leakage by approximately 76.0% compared to the conventional mode and 68.7% compared to the CC mode. These reductions were attributed to antiphase magnetic fields canceling each other in the DD mode. Moreover, the power transfer efficiency in the DD mode exceeds 95%. The proposed system was shown to effectively suppress electromagnetic interference without compromising transmission efficiency.

SECTION I. Introduction

Wireless power transfer (WPT) technology has attracted considerable attention as a power-supply method for battery-equipped electric vehicles and personal mobility devices. This technology can be used in various fields and environments because WPT can realize power transmission without physically connecting the power source and receiver. Studies have revealed that magnetic resonance can be used to achieve high-efficiency WPT over a medium distance (several meters) [1]. However, this technology exhibits certain technical limitations. When the position of the receiver changes, the optimal resonant frequency used for the power transfer changes, decreasing power transfer efficiency. Therefore, establishing a fixed receiver position or controlling the circuit constants according to the transfer distance becomes necessary. Tian et al. proposed the use of a movable intermediate coil [2], while Li et al. addressed efficiency loss due to receiver misalignment in WPT systems using magnetic flux controlled inductors and magnetic couplers with hybrid coils [3]. Fixing the position of the power-receiving section limits its applicability, whereas incorporating control circuitry increases system complexity. Alternatively, a magnetic flux generated by the current flowing through the transmitter and receiver coils forms leaked magnetic fields around the WPT system. Magnetic field leakage exceeding a prescribed level is hazardous to the human body and interferes with the operation of other electronic devices. Therefore, international committees have established certain regulations [4], [5]. Compliance with these regulations is crucial for ensuring the safety and promotion of WPT.

A multitude of techniques have been proposed to reduce magnetic field leakage, employing conductors or magnetic materials, or the application of cancellation loops. For example, Campi et al. and other researchers have discussed magnetic shielding techniques that can be used to mitigate magnetic interference in WPT systems [6], [7], [8]. In particular, Duan et al. employ composite cores to reduce the magnetic field strength [8]. Nevertheless, magnetic shielding can effectively reduce magnetic flux only in the vicinity of the coil, and the reduction is less effective at distances greater than 1.2 m from the coil (Human Body Position).

Numerous studies have been conducted with the objective of reducing the magnetic field using active cancellation coils. These coils are used to cancel the magnetic field of the main coil used for transmission [7], [9], [10], [11], [12]. Kim and Ahn designed a resonant reactive shield for electric vehicles and demonstrated its efficacy in reducing leakage magnetic fields by an average of 55.5% [11]. However, these methods induce various problems, such as decreasing power transmission efficiency and increasing system weight. Coupling the canceling coils with the main coils should be considered. The change in the WPT system’s resonance frequency and decrease in power transfer efficiency depends on the coupling conditions. Further, most studies on shielding techniques mainly reference magnetic field suppression near the coil, and few mention the suppression of far leakage magnetic fields.

To overcome these challenges, we proposed “WPT with the sandwich structure” [13]. Compared with conventional systems, the sandwich structure improves robustness against positional changes in the direction of the coil’s central axis [14]. In previous studies, multiple coils used in both the transmitter and receiver have been considered to be a single coil. In a sandwich structure, the magnetic fields of multiple coils have independently of each other. Therefore, the direction of the coil connections changes the characteristics of the magnetic field leaking from the coil [15]. This study evaluated the reduction of the magnetic field leakage in WPT with a sandwich structure. In the cumulative–cumulative (CC) mode, the transmitter and receiver coils are connected in phase, whereas in the differential–differential (DD) mode, the coils are connected in antiphase. Chapter II details mode definition. In the DD mode, antiphase magnetic fields are generated for each pair of transmitter and receiver coils. Greater the distance from the coils, the more the antiphase magnetic fields canceled each other. These results indicate that WPT with a sandwich structure can establish a stable power transmitter efficiency and safety for the human body and surrounding electronic devices.

SECTION II. WPT With the Sandwich Structure

Figure 1 displays a schematic of a WPT with a sandwich structure consisting of two receiver coils and two transmitter coils. The transmitter coils were connected in series with the same power source. Similarly, the receiver coils were connected in series with the same load. As one example of a WPT system using the sandwich structure, an image adapted to an electrically power assisted bicycle is shown in Fig. 2. ChatGPT was used to create the bicycle image. The transmitter coils are embedded in the bicycle parking stand, and the receiver coils are fixed to both sides of the bicycle front wheel. In this arrangement, the distance between the transmitter and receiver coils is fixed. In this configuration, the position of the receiver has a degree of freedom within the range between transmitter coils. However, this study did not assume a shift in the receiver position.

FIGURE 1.

Schematic of wireless power transfer (WPT) with the sandwich structure.

FIGURE 2.

Application of WPT systems to an electrically assisted bicycle.

Because four coils are used to feed power in this structure, the current flow direction changes depending on the orientation of the coil connections, resulting in multiple magnetic field configuration modes. The modes are defined based on the phases of the magnetic fields in the transmitter and receiver coils. The mode name is derived from the initial letters of “Cumulative” and “Differential”. The configuration is described in the order of the transmitter and receiver. Figure 3 illustrates the current flow in the coils and directions of the magnetic moments in each mode. In the CC mode, an in-phase magnetic field is generated in both the transmitter and the receiver, as displayed in Fig. 3(a). In the DD mode, an antiphase magnetic field is generated in both the transmitter and receiver, as depicted in Fig. 3(b). In addition, CD and DC modes with different phases exist on the transmitter and receiver sides. In these modes, the mutually induced electromotive forces cancel each other. Therefore, if the transmitter–receiver coil pairs are symmetrically positioned, power transmission does not occur. Because receiver misalignment was not considered in this study, the analysis focused on the CC and DD modes. Two receivers were used to efficiently transmit power. A single receiver can be used. However, the configuration is closer to the DC mode than the DD mode because the receiver cannot be antiphase. In addition, if the transmitter is the antiphase and there is only one receiver, power transmission is impossible under conditions where the receiver is placed in the center of the transmitter. For leakage field suppression, having two transmitters is crucial, whereas the number of receivers is less significant.

FIGURE 3.

Current flowing in the coils and the direction of the magnetic fields: (a) CC mode and (b) DD mode.

As displayed in Fig. 4, the shapes of the magnetic lines of force generated by coils in the CC and DD modes differ considerably. Using electromagnetic field analysis software (CST Studio Suite 2023, Dassault Systèmes), a three-dimensional model of the coils was created, and the magnetic field was calculated using the finite integration technique [16]. When the magnetic field was calculated, the calculation area was surrounded by an open-boundary condition. ParaView 5.10.1 (Kitware Inc.) was used to visualize the distribution of magnetic field lines. The stream tracer provide by ParaView was used to calculate the trajectory of the magnetic field vector, which was subsequently visualized as a magnetic field line. In the CC mode, the magnetic lines of the force spread uniformly around the transmitter and receiver coils. In the DD mode, the magnetic lines formed by each transmitter and receiver coil pair repel each other. The structure is similar to a cusp magnetic field, which has a magnetic field strength is of zero at the center [17]. This effect causes the magnetic fields to interfere with and cancel each other in the DD mode as the distance from the coils increases. Therefore, the reduction of the magnetic field leakage is greater in the DD mode than that with a conventional WPT structure in which only one pair of transmitter and receiver coils or the CC mode of the sandwich structure.

FIGURE 4.

Magnetic field lines of WPT with the sandwich structure: (a) CC mode, and (b) DD mode.

SECTION III. Theoretical Model of Sandwiched Structure and Verified by Actual Measurement

A. Theoretical Model

Figure 5 displays the equivalent circuit diagram of WPT with a sandwich structure. C is the capacitor used to resonate each coil, $R_{t}$ and $R_{r}$ comprise the internal resistance of each coil, and $R_{L}$ is the load resistance. Connecting capacitors and coils in series is considered more suitable for battery charging. Series resonant circuits are stable to load variations and are effective for loads such as batteries that require a stable current supply. In addition, battery charging often requires high current, and series resonant circuits can efficiently supply power to the battery because of their characteristic of maximizing current at resonance. In contrast, a parallel resonant circuit produces a theoretically infinite impedance and minimizes current, making it unsuitable for battery charging, which requires high current. Because the proposed structure has multiple coils and the coupling between the coils is complex (see table 1), the circuit equations are described by a Z-matrix.

$$\begin{align*} \left [{{ \begin{array}{cc} V_{t} \\ 0 \\ \end{array} }}\right ]= \left [{{ \begin{array}{cc} Z_{11} & \quad Z_{12} \\ Z_{21} & \quad Z_{22} \\ \end{array} }}\right ] \left [{{ \begin{array}{cc} I_{t} \\ I_{r} \\ \end{array} }}\right ] \tag {1}\end{align*}$$ Because the receiving and transmitting circuits are connected in series, the elements of the Z matrix are respectively expressed in Eqs. (2)–(4). $$\begin{align*} Z_{11} & = R_{t_{1}} + R_{t_{2}} + j \omega (L_{t_{1}} + L_{t_{2}} + 2 M_{t_{1}t_{2}}) + \frac {1}{j \omega C_{t}} \tag {2}\\ Z_{12} & = Z_{21} =j \omega M_{t_{1}r_{1}} + M_{t_{2}r_{2}} M_{t_{1}r_{2}} + M_{t_{2}r_{1}} \tag {3}\\ Z_{22} & = R_{r_{1}} + R_{r_{2}} + j \omega (L_{r_{1}} + L_{r_{2}} + 2 M_{r_{1}r_{2}}) + \frac {1}{j \omega C_{r}} + R_{L} \tag {4}\end{align*}$$ Considering cross-coupling and selecting capacitors so that the imaginary parts of Equations (2) and (4) is zero (matching the resonant frequency of the transmitter and receiver coils), the Z matrix can be expressed as follows. For further simplification, the mutual inductance and internal resistance of the circuit are defined as follows: $$\begin{align*} M_{trans}& = M_{t_{1}r_{1}} + M_{t_{2}r_{2}} + M_{t_{1}r_{2}} + M_{t_{2}r_{1}} \tag {5}\\ R_{t} & = R_{t_{1}} + R_{t_{2}} \tag {6}\\ R_{r} & = R_{r_{1}} + R_{r_{2}} \tag {7}\\ \left [{{ \begin{array}{cc} V_{t} \\ 0 \\ \end{array} }}\right ]& = \left [{{ \begin{array}{cc} R_{t} & \quad j \omega M_{trans} \\ j \omega M_{trans} & \quad R_{r} + R_{L} \\ \end{array} }}\right ] \left [{{ \begin{array}{cc} I_{t} \\ I_{r} \\ \end{array} }}\right ] \tag {8}\end{align*}$$ Based on the Z matrix, the voltage-current values and power transmission efficiency of each part can be calculated. For example, the formula for calculating power transfer efficiency is as follows: $$\begin{equation*} \eta = \frac {P_{r}}{P_{t}} = \frac {(\omega M_{trans})^{2} R_{L}}{\{(R_{t}+R_{L}) R_{t} + (\omega M_{trans})^{2})\}(R_{r} + R_{L})} \tag {9}\end{equation*}$$ The equation demonstrates that in the sandwiched structure, the properties can be discussed by the sum of the couplings in the circuit. As shown in the second paragraph of Section II, the characteristics of the sandwiched structure vary depending on the direction of coil connection. Note that the mutual inductance is negative for anti-phase connections.

TABLE 1 Coupling Coefficients Considered in the Sandwiched Structure

FIGURE 5.

Equivalent circuit of the sandwiched structure.

B. Coil Properties and System Configuration

The prototype coil is a spiral coil using Litz wire with a wire diameter of 4 mm, inner diameter of 80 mm, and outer diameter of 180 mm. The width between the wires was set to 1 mm, and the number of turns was 10, as displayed in Fig. 6(a). The average value of the inductance of each coil was $\mathrm {15.8~\mu \text {h} }$ , and the capacitors were connected in series to the transmitter and receiver coils, such that each part resonated at 85 kHz. The distance between the transmitter and receiver coils in the conventional structure was fixed at 50 mm, as displayed in Fig. 6(b). In the sandwich structure, the distances between the transmitter and receiver coils were 180 mm and 80 mm, respectively, with each pair of transmitter and receiver coils fixed at a distance of 50 mm, as displayed in Fig. 6(c). In this coil arrangement, all coils were centered on the same line, and the misalignment of the power receiver was not considered.

FIGURE 6.

Coil appearance and placement conditions: (a) Coil appearance, (b) Placement condition of the conventional, and (c) Placement condition of the CC and DD modes.

The power source on the transmitter was amplified by a bipolar power-supply (HSA4052, NF Corporation) by using a sine wave output from a signal generator (AFG3252, Textronix). The equivalent circuit diagram in Fig. 5 presents each element name and the locations of voltage and current measurements. The resistance $R_{L}$ of $\mathrm {5.5~\Omega }$ was connected as a load on the receiver. The $\mathrm {5.5~\Omega }$ load resistance was selected to evaluate the fundamental system performance with a purely resistive load (Small reactance component). Given the rated power of the resistors, a series connection of multiple resistors was implemented, resulting in a total resistance of $\mathrm {5.5~\Omega }$ . The change in the efficiency characteristics with the value of the load are evaluated using Equation (9), and the results are shown in Fig. 7. The value of the load at which maximum efficiency is obtained for the conventional and the CC mode is slightly less than $\mathrm {5.5~\Omega }$ . However, this is a reasonable value to compare each mode considering the power rating of the resistor. The system configurations discussed in this paper do not include circuit configurations that are typically used in practice, such as the DC-AC inverter and the AC-DC rectifier. Focusing on the simple transmitter and receiver coils section, the theoretical model of the most basic sandwiched structure was verified. Table 2 lists the values of the other elements. Values such as power transfer efficiency can be calculated from the values listed in Table 2 based on (9). Power was calculated by observing both ends of the load terminals using a differential voltage probe (THDP0200, Tektronix), current with a current probe (TCP150, Tektronix), and using an oscilloscope (MSO4104, Tektronix) to acquire voltage and current waveforms and calculate RMS and phase difference, as presented in Table 3. The voltage and current measurement points are the same as in Fig. 5. The output of the signal generator was adjusted such that the load power for the receiver, $P_{r}$ was 2.5 W, as calculated using Equation (10). The value of 2.5 W was selected to ensure stable operation of the bipolar power supply utilized in the experiments.

$$\begin{equation*} P_{r} = V_{r} I_{r} \cos \theta _{r} \tag {10}\end{equation*}$$ The proposed WPT system achieved an efficiency of more than 95% in both modes, which is better than the common WPT system with one transmitter or one receiver.

TABLE 2 Circuit Constants

TABLE 3 Voltage and Current in Each Mode

FIGURE 7.

The efficiency characteristics depending on the value of the load.

SECTION IV. Leakage Magnetic Field Strength

A. Analysis and Measurement

The dependence of the leakage magnetic field strength on the distance was evaluated in the conventional, CC, and DD modes when power was transmitted. The coils were positioned on a Styrofoam platform (800 mm in height) inside a 10-m semi-anechoic chamber, as displayed in Fig. 8. To measure the strength of the magnetic field leakage, a magnetic field meter (FT3470, HIOKI) compliant with IEC/EN62233 was used (Fig. 9). Using a 100 cm² magnetic field probe, the composite effective value of the magnetic field strength obtained from the x-, y-, and z-axes sensors was recorded. Figure 10 displays the analysis and measurement results. Figure 10 shows the results obtained for 2.5 W transmission, normalized to 1 W. The evaluation of the dependence on the distance is based on the axial definition displayed in Fig. 6(b) and Fig. 6(c). The horizontal axis in Fig. 10 represents the distance away from each axis direction from the center of transmitter and receiver coils, and the vertical axis represents the magnetic field strength. Figure 10(a) shows the dependence of the leakage magnetic field strength on the distance in the x-axis direction. The solid lines represent the magnetic field strength obtained from electromagnetic field analysis. Peaks appear around 40 mm and 90 mm, corresponding to the positions of the coils, where the magnetic field strength increases. However, in the DD mode, the antiphase magnetic fields cancel each other out, significantly reducing the field strength at 0 mm. Figure 10(b) shows the dependence of the leakage magnetic field strength on the distance in the y-axis direction. In the CC mode, the points where the magnetic fields generated by each coil pair cancel each other are around 100 mm, resulting in a dip in the field strength. In the DD mode, this cancellation occurs at 0 mm, creating a dip at the center. As displayed in Fig. 10, the results of the magnetic field strength analysis were consistent with the measurements. The leakage magnetic field strength of the DD mode was lower than those of in conventional and CC modes. For example, at 1 m from the center in the x-axis direction, the strengths of the conventional and CC modes were 89.1 dB$\mu$ A/m and 86.9 dB$\mu$ A/m, respectively, whereas that of the DD mode was 76.8 dB$\mu$ A/m. This represents a reduction of approximately 22.6% in the leakage magnetic field in the CC mode and approximately 76.0% in the DD mode in comparison to the conventional mode. The attenuation rate, which depends on the distance, is greater in the DD mode than in conventional and CC modes. Table 4 summarizes the attenuation rates for each mode calculated based on the actual measurements. However, the leakage magnetic field strength in the DD mode was approximately 3 dB greater than those in the other modes at a distance of less than 200 mm from the coils because the DD mode requires a larger current to flow through the transmitter coils than those of other modes when the same power is received at the receiver. Similar characteristics are observed along the y-axis.

TABLE 4 Attenuation Rate of Leakage Magnetic Fields Depending on the Distance

FIGURE 8.

Schematic inside an anechoic chamber.

FIGURE 9.

Magnetic leakage field measurement.

FIGURE 10.

Dependence of the leakage magnetic field strength on the distance: (a) in X-axis direction, and (b) in Y-axis direction.

B. Discussion

To compare the effect of leakage magnetic field reduction, the results of some references with coil sizes relatively close to the proposed design were compared. In a case study using a resonant reactive shield [10], the leakage magnetic fields decreased by up to 64% at approximately 1 m from the coil. The proposed structure reduces the equivalent to about 80% at similar measurement positions. By contrast, in the example study with the composite core [8], the leakage field intensity near the coils (within 1 m from the center of the coils) is approximately 10 dB lower than the presented results. However, the reduction in magnetic field leakage by the core acts in the vicinity of the coil, and the reduction is less effective at about 1.2 m, which is defined as the “Human Body Position” in the reference paper. When the power is normalized to 1 W, the leakage magnetic field strength of the reference study at 1.2 m is 75 dB$\mu$ A/m, while the proposed structure achieves 65 dB$\mu$ A/m. Therefore, the proposed structure can be said to have a leakage magnetic field suppression effect equivalent to that of existing shielding technologies in areas where the human body is close. This effect is achieved without using cores and only with the coil configuration used for transmitter and receiver. However, the suppression effect of the leakage magnetic field near the coil requires consideration of combining with cores.

SECTION V. Conclusion

This study investigated the simplest theoretical model consisting only of transmitter and receiver coils and the effectiveness of having a sandwich structure in mitigating the magnetic field leakage of WPT.

Equivalent circuit equations for the proposed structure were derived using the equivalent circuit model and Z-matrix. The proposed structure has complex mutual inductance owing to multiple coils, and cross-coupling occurs between the transmitter and receiver coils. By setting the resonance capacity considering these cross-couplings, the power transfer efficiency can be obtained with the defined $M_{trans}$ . In this study, the voltage–current values and power transfer efficiencies obtained from the theoretical model and the measured results were in good agreement.

Next, Electromagnetic field analysis and experimental results using the prototype coil revealed that the magnetic field in the DD mode was lower than that in conventional and CC modes. In the DD mode, the leakage magnetic field strength 1 m from the center of the coils was mitigated by approximately 10.1-12.3 dB compared with the conventional and CC modes. This corresponds to a suppression of the leakage magnetic field of approximately 76.0% compared to the conventional mode and 68.7% compared to the CC mode. The magnetic fields generated in the DD mode cancel each other out and mitigate the leakage fields in an area several meters away from the coils. We achieved a positive effect by mitigating the leakage of the magnetic fields at a distance by changing the direction of the coil connections. This phenomenon can reduce the exposure to the human body and other electronic devices. The use of the sandwich structure may increase complexity or cost. However, owing to the magnetic leakage field suppression, the system can be configured without the use of magnetic materials or other known shielding techniques. The trade-off between the effectiveness of leakage suppression and the cost increase, as well as the possibility of using this technology in combination with known shielding techniques, should be the subject of future research.

The consistency between analytical and measurement results confirmed the reliability of the evaluation method used in this study. The presented results are only examples of a coil arrangement. Various factors should be considered when designing the actual systems. In the future, studies should perform extensive evaluation and verification using actual measurements. For example, the magnetic field leakage mitigation effect under different coil arrangement conditions, particularly with the misalignment and rotation of the power-receiving part, should be performed.

ACKNOWLEDGMENT

The authors would like to thank Editage (https://www.editage.jp) for English language editing. They also like to thank OpenAI for providing access to the ChatGPT model, which was instrumental in generating images of this study.