Reactive Shield for Reducing the Magnetic Field of a Wireless Power Transfer System with Dipole Coil Structure

Abstract

This paper proposes a reactive shield structure to reduce the leakage magnetic field of a wireless power transfer (WPT) system with a dipole coil structure. The reactive shield resonates at a frequency lower than that of the WPT system and operates in an inductive region where the reactance is positive. Therefore, the magnetic field generated by the shield coil is 180° different in phase from that generated by the transmitting coil, resulting in an effective reduction in the leakage magnetic field. The methodology for designing the reactive shield for the dipole coil structure is mathematically analyzed, and the current and magnetic field phases are compared. Its effectiveness has been validated through simulations and experiments. Specifically, the proposed method is validated through a 50 W class WPT experiment, which showed that the proposed shielding structure achieves efficiency reductions ranging from 0.3% to 1.5% and has a leakage magnetic field reduction effect of up to 67% compared to the comparison groups.

1. Introduction

Wireless power transfer (WPT) technology has garnered significant attention as a viable replacement for wired power transfer [1,2,3]. WPT systems transfer energy through a magnetic field without connecting a conductor between the transmitting side (TX) and the receiving side (RX). Therefore, the WPT system is safe, eliminating the risk of electric shock, and convenient as it does not require a separate physical connection [4,5]. In particular, as various applications operate using electrical energy and batteries are essential, the WPT system is receiving significant attention as a battery charging technology [6]. Representative examples of WPT system applications are being studied in various areas, including electric vehicles, mobile applications, industrial electronics, and biomedical devices [7,8,9].

The most commonly used coil structure in WPT systems is the planar-type coil, as shown in Figure 1 [10,11]. As shown in Figure 1a, WPT systems with planar-type coils face each other. This is because the magnetic field is transmitted from the TX side to the RX side in a direction perpendicular to the coil, as shown in Figure 1b. Consequently, the wider the cross-sectional area of the coil, the better the various characteristics of the WPT system, including power transfer efficiency and power transfer capacity [12,13,14].

However, securing a large coil cross-sectional area is not feasible in certain applications. For example, in biomedical device applications where WPT systems are widely used, securing a large coil cross-sectional area is challenging [9,15,16]. Additionally, in-home appliance applications, such as wireless charging between monitors or televisions, the cross-sectional area where TX and RX face each other is often very narrow [17].

In applications with such a narrow coil cross-sectional area, a dipole-type coil is used instead of a planar-type coil [18,19,20,21]. The dipole coil shape is shown in Figure 2. The dipole-type coil has a structure in which the coil is wound around a magnetic material (ferrite) with high magnetic permeability, such as a solenoid. Figure 2b shows how the magnetic field is transmitted from TX to RX in the dipole-type coil. It can be observed that most of the magnetic field in the dipole-type coil is transmitted through the magnetic core, and the magnetic field is transmitted from the TX to RX coils at both ends of the magnetic core. The amount of magnetic field transmitted is significantly less dependent on the area facing the WPT coil system than on the planar type. Therefore, the dipole coil structure is used in various applications where the area facing each other is very narrow.

However, the dipole coil structure has a major disadvantage compared to the planar-type coil structure, which is the problem of leakage magnetic fields [18]. In a planar-type coil, the magnetic field is mainly transmitted between the magnetic cores, whereas in the dipole coil structure, it radiates outward from the ends of the magnetic core, as shown in Figure 2b. Due to the nature of the dipole structure in which the magnetic field radiates in the longitudinal direction, it is very difficult to reduce leakage magnetic fields. This drawback of the dipole coil structure poses a significant obstacle to its application in devices that are inevitably sensitive to leakage magnetic fields. For example, devices used near the human body must meet the ICNIRP 1998 standard for magnetic field strength [18], and biomedical devices used very closely to the human body must meet the Specific Absorption Rate (SAR) standard [19].

Research on WPT systems with dipole structures has been extensive [20,21,22,23,24]. First, Choi et al. [20] and Park et al. [21] proposed a method for transmitting power over a relatively long distance using a dipole structure. Specifically, they found that the effectiveness of the dipole coil structure was maximized when the cross-sectional area between the TX and RX sections was small compared to the power transfer distance. In addition, Rong et al. [22] proposed a WPT system capable of transferring power omnidirectionally in low-power applications using multiple dipole coils, and Rong et al. [23] studied an angle-free WPT system with a similar structure. Moreover, in Khan et al.’s study [24], the WPT system was applied using a dipole coil structure in a missile application with a small cross-sectional area where the TX and RX sections faced each other. However, in the above-mentioned WPT systems using the dipole structure, no mention was made of reducing the leakage magnetic field of the corresponding structure. In fact, there has been no research to date on reducing the leakage magnetic field of the dipole structure.

Among the methods for reducing magnetic leakage from planar coils, the most actively researched is the reactive shield (SH) method [25,26,27]. Park et al. [25] proposed a method to reduce magnetic leakage in a WPT system using a planar coil for mobile applications. In Kim et al.’s study [27], power transfer efficiency was increased, and the leakage magnetic field was reduced using a dual-loop reactive shield. Furthermore, Wei and Wu [28] studied similar content using the frequency split phenomenon. However, these reactive shield methods all have the limitation that they apply only to planar coils. The reason why so much research has only been conducted on magnetic field reduction methods in planar-type WPT coils is because, as can be seen in Figure 1b, the magnetic field radiating outward from this type of coil is relatively smaller than that of the dipole type.

This paper proposes a reactive shield coil structure to minimize leakage magnetic fields from a WPT system with a dipole-type coil. The proposed reactive shield generates an induced voltage by Faraday’s law. The induced voltage generates a current with an opposite phase to the magnetic field generated from the WPT coil, thereby producing a magnetic field with an opposite phase. Therefore, the magnetic fields are canceled at both ends of the magnetic material, reducing the leakage magnetic field. Section 2 provides a mathematical analysis of the reactive shield for the dipole structure. Section 3 confirms the shield performance through simulation, while Section 4 validates the performance of the proposed shield structure through experimentation. Finally, Section 5 presents the conclusion of this paper.

2. Principle of Reactive Shield for Dipole Coil Type

The dipole-type WPT coil with the proposed reactive shield applied is shown in Figure 3. The proposed reactive shield has a structure in which reactive shield coils are added to both sides of the TX coil in a typical dipole-type coil, as shown in Figure 2. The RX side lacks a separate reactive shield structure because WPT systems with a dipole coil structure are generally designed in very narrow spaces, especially considering the severe spatial constraints of the RX. Therefore, only the TX side, with fewer spatial constraints, has a re-active shield structure. As will be validated in Section 3 and Section 4, the leakage magnetic field from the coil of the dipole structure can be reduced, even with a shield structure only on the TX side.

The equivalent circuit of the dipole-type WPT system with the proposed shield structure in Figure 3 is shown in Figure 4. Figure 4a shows the entire circuit from direct current (DC) input to DC output. The input DC voltage (Vin) is converted into an alternating current (AC) component through an inverter and transferred as a DC voltage (V_load) to the load (R_load) through resonant circuits, coils, and a rectifier. The resonant circuit for impedance compensation adopted the LCC-series topology, known for its constant voltage out-put characteristics, and its effectiveness has been proven in various studies [12,28,29,30,31]. In addition, as the resonant circuit on the RX side only has a capacitor, it provides spatial advantages on the RX side and is suitable for a dipole-structured coil. As shown in Figure 3, there are four coils (TX, RX, SH1, and SH2), resulting in six types of mutual inductance between coils, as shown in Figure 4a (four combinations of two).

Figure 4b is a simplified and approximated circuit of Figure 4a. In Figure 4b, V_inv represents the root mean square (RMS) value of the fundamental component of the inverter output voltage. This has a relationship (1) with the V_in:

$${\mathbf{V}}_{\mathbf{i}\mathbf{n}\mathbf{v}}=\frac{4}{\pi \surd 2}{V}_{in}\angle 0°$$

(1)

As V_inv is an RMS value, all voltages and currents in Figure 4a,b are RMS values. Additionally, the load resistance (R_rect) seen from the rectifier is as shown in (2):

$$R_{rect}=\frac{8}{{\pi }^2}{R}_{load}$$

(2)

Furthermore, the six magnetic couplings (mutual inductances) approximate only two meaningful mutual inductances. First, the mutual inductance between the TX and RX coils (M_TX-RX) is significant in the WPT system. Second, because RX and shield coils (SH1 and SH2) are sufficiently far apart magnetically, the corresponding mutual inductances (M_RX-SH1, M_RX-SH2) are ignored:

$$M_{RX\text{-}SH1}=M_{RX\text{-}SH2}\simeq 0$$

(3)

Third, the resonant capacitor of the shield coils is selected simultaneously by winding the two shield coils in series. Specifically, the two shield coils are viewed as one. Therefore, the relationships between L_SH1 and L_SH2 in Figure 4a and L_SH in Figure 4b are as follows (4):

$$L_{SH}=L_{SH1}+L_{SH2}+2M_{SH1\text{-}SH2}\simeq L_{SH1}+L_{SH2}$$

(4)

As shown in Figure 3, the SH coils are sufficiently far apart, making the mutual inductance (M_SH1-SH2) between them negligible. Finally, because L_SH1 and L_SH2 are connected in series, the relationships between M_TX-SH1 and M_TX-SH2 in Figure 4a and M_TX-SH in Figure 4b can be expressed as follows (5):

$$M_{TX\text{-}SH}=M_{TX\text{-}SH1}+M_{TX\text{-}SH2}$$

(5)

All approximations will be validated through simulation in Appendix A.

Next, the resonant condition on the TX side follows that of the LCC topology [12]. This is equivalent to (6), and the resulting TX coil current (I₁) is equivalent to (7):

$$\frac{1}{\sqrt{L_{S1}{C}_{P1}}}=\frac{1}{\sqrt{\left(L_{TX}-L_{S1}\right)C_{S1}}}={\omega }_{n1}={\omega }_o$$

(6)

$${\mathbf{I}}_1=-j{\omega }_o{C}_{P1}{\mathbf{V}}_{\mathbf{i}\mathbf{n}\mathbf{v}}=-j\frac{4}{\pi \surd 2}{\omega }_o{C}_{P1}{V}_{in}\angle 0°$$

(7)

In (6), ${\omega }_{n1}$ is the resonant frequency of the TX side, and ${\omega }_o$ is the operating frequency of the inverter. Additionally, the resonant condition of the RX side is a series topology, so it is equal to (8), and the voltage delivered to the load (R_rect) due to mutual inductance is equal to (9):

$$\frac{1}{\sqrt{L_{RX}{C}_{S2}}}={\omega }_{n2}={\omega }_o$$

(8)

$${\mathbf{V}}_{\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{t}}=j{\omega }_o{M}_{TX\text{-}RX}{\mathbf{I}}_1={\omega }_o^2{M}_{TX\text{-}RX}{C}_{P1}{\mathbf{V}}_{\mathbf{i}\mathbf{n}\mathbf{v}}$$

(9)

In (8), ${\omega }_{n2}$ is the resonant frequency of the RX side.

Meanwhile, the resonant circuit on the SH side is adjusted with a capacitor (C_SH), as shown in Figure 4. Studies have found that for the magnetic field generated in the SH coil to have an opposite phase of the magnetic field generated in the TX coil, the resonant frequency of the SH coil (${\omega }_{SH}$) must be set lower than that of the system operating frequency (${\omega }_o$) [25,26,27]. In essence, the resonant of the SH coil must be in the inductive region, as shown in Figure 5a,b.

To have the above relationship, the impedance of the SH coil must be equal to (10) and (11):

$$Z_{SH}=j\left({\omega }_o{L}_{SH}-\frac{1}{{\omega }_o{C}_{SH}}\right)=j{\omega }_o{L}_{eq}$$

(10)

$$\frac{1}{\sqrt{L_{SH}{C}_{SH}}}={\omega }_{SH}<{\omega }_o$$

(11)

In (10), the resonant condition on the SH coil side is in the inductive region, so L_eq is the equivalent inductance. According to Faraday’s law, voltage is induced in the SH coil by the TX coil current, as shown in (12), if the resonant condition on the SH side is equal to (10) and (11), and the current (I_SH) flowing through the SH coil is equal to (13):

$${\mathbf{V}}_{\mathbf{S}\mathbf{H}}=j{\omega }_o{M}_{TX\text{-}SH}{\mathbf{I}}_1$$

(12)

$${\mathbf{I}}_{\mathbf{S}\mathbf{H}}=\frac{-j{\omega }_o{M}_{TX\text{-}SH}{\mathbf{I}}_1}{Z_{SH}}=-\frac{M_{TX\text{-}SH}}{L_{eq}}{\mathbf{I}}_1$$

(13)

As seen in (13), the current phase of the SH coil (I_SH) is 180$°$ different from that of the TX coil (I₁).

In Figure 3, the dipole shares the same structure as the solenoid; hence, the magnetic field at its end equals (14):

$$B_{coil}\simeq \mu n{I}_{coil}$$

(14)

Therefore, the phase of the magnetic field generated in the coils aligns with the coil current. Specifically, as the currents in the TX and SH coils have a 180$°$ phase difference, as shown in (13), the magnetic field generated in the TX coil will be reduced by that generated in the SH coil. Figure 6 shows a phasor diagram of the magnetic field of the WPT system with and without the SH coil. As shown in Figure 6a, without an SH coil, only the sum of the magnetic fields generated from the TX and RX coils exists. However, with an SH coil, the magnetic field (B_SH) caused by the SH coil reduces the magnetic field of the TX coil (B_TX), thereby reducing the vector sum (B_total) of the magnetic field. Moreover, as can be seen in Figure 3, since the SH coil is wound in high permeability ferrite, the magnetic field generated by the SH (B_SH) coil will become stronger and cancel out the magnetic field of the TX coil (B_TX).

The magnetic fields of the TX and SH coils have opposite phases, causing them to cancel each other, as depicted in Figure 7. This figure shows only the TX, RX, and SH coils; the magnetic core (ferrite) is omitted to emphasize the magnetic field. For the standard of current and magnetic field phase, a dot convention is indicated for each coil. The TX and SH coil currents have a phase difference of 180°. Therefore, in the direction where the magnetic field of the TX coil goes out, the counterpart SH coil (L_SH2) is also generated in the outgoing direction. Similarly, in the direction where the magnetic field of the TX coil enters the coil, a magnetic field is generated in the direction where the counterpart SH coil (L_SH1) also enters. However, the TX magnetic field, essential for power transfer, passes through without cancellation and reaches the RX coil. In essence, the reactive SH coil cancels unnecessary leakage magnetic fields, allowing only the magnetic fields essential for the WPT to reach the RX coil. The reactive shield for the dipole-type coil limits the magnetic field of the WPT coils and reduces the leakage magnetic field.

3. Validation of the Effectiveness of the Proposed Reactive Shield through Simulation

Figure 8a is WPT coils with the proposed reactive shield, as shown in Figure 3, and Figure 8b,c are comparison groups to validate the reactive shield performance. Figure 8c, unlike Figure 8a, has a structure in which only ferrite is added without SH coils. In other words, both Figure 8b,c are structures in which the reactive shield structure is not applied. The geometric information of each coil model is shown in Figure 8. In addition,

Table 1. Additional information on magnetic field simulation.

Parameters	Value
Operating frequency	85 kHz
Relative permeability of magnetic core (TX, RX, SH)	150
Air gap (d)	15 mm
Air gap (dshield)	3 mm
Diameter of coil wire	2.8 mm
Number of turns of TX and RX coils	12 turns
Number of turns of SH coil	4 turns

lists the remaining information on the simulation (operating frequencies, air gaps, and wire information). In Figure 8a–c, note that the color of the magnetic material on the SH side is shown in gray, and the color of the magnetic material on the WTP coil side is shown in blue. This is simply to distinguish the magnetic material structure and the permeability of all magnetic materials is the same.

Table 2. Inductance extraction results through magnetic field simulation.

Model	Parameters	$\mathbf{Value}[\mathsf{\mu }\mathbf{H}$]
Proposed model	Inductance of TX coil (LTX)	29.52
	Inductance of RX coil (LRX)	25.41
	Mutual inductance between TX and RX (MTX-RX)	6.2
	Inductance of SH coils (LSH1, LSH2)	5.82
	Mutual inductance between SH and TX (MTX-SH)	3.91
Comparison Case 1	Inductance of TX coil (LTX)	35.76
	Inductance of RX coil (LRX)	25.62
	Mutual inductance between TX and RX (MTX-RX)	7.15
Comparison Case 2	Inductance of TX coil (LTX)	29.57
	Inductance of RX coil (LRX)	25.44
	Mutual inductance between TX and RX (MTX-RX)	6.21

summarizes the information on the coils extracted by performing magnetic field simulation with the setup in Figure 8 and Table 1. The notation for each inductance matches the circuit in Figure 4.

Table 3. Resonant circuit parameters for circuit simulation.

Model	Parameters	Value
Proposed model	TX series inductance (LS1)	16.8 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	208 nF
	TX series capacitance (CS1)	302 nF
	RX series capacitance (CS2)	140 nF
	SH capacitance (CSH)	1740 nF
Comparison Case 1	TX series inductance (LS1)	16.8 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	208 nF
	TX series capacitance (CS1)	217 nF
	RX series capacitance (CS2)	138 nF
Comparison Case 2	TX series inductance (LS1)	16.8 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	208 nF
	TX series capacitance (CS1)	217 nF
	RX series capacitance (CS2)	139 nF

shows the resonant circuit values for each case. Please refer to Figure 4 for the notation of resonant circuit values. In the circuit simulation, the V_in of Figure 4 is 60 V, and the target TX current (I₁) is selected as 6 A_RMS. Based on the selected values, each resonant circuit value is calculated through (6) to (8). All resonant frequencies except for the SH coil are set to 85 kHz, matching the system operating frequency. Additionally, the SH frequency of the proposed model is selected as 50 kHz (f_SH = 50 kHz). The power delivered to the final load resistance (R_load) is 50 W in all three cases. The current magnitude of each part for 50 W of power to be delivered to the loads is summarized in

Table 4. Current in each coil when transmitting 50 W of power.

Model	Parameters	Value
Proposed model	Current of TX coil (I1)	6 ARMS
	Current of RX coil (I2)	2.35 ARMS
	Current of SH coil (ISH)	5.6 ARMS
	Phase difference between TX current and SH current	177$°$
Comparison Case 1	Current of TX coil (I1)	6 ARMS
	Current of RX coil (I2)	1.98 ARMS
Comparison Case 2	Current of TX coil (I1)	6 ARMS
	Current of RX coil (I2)	2.21 ARMS

. Due to the characteristics of the LCC topology, the TX coil currents are all identical, while the RX coil currents vary. Notably, the output current required to deliver 50 W to the load is the largest for the proposed model.

Figure 9 shows the simulation setup for leakage magnetic field measurements. To simulate the leakage magnetic field measurement, the currents in Table 4 are applied to the dipole coil structures in Figure 8. The magnitude of the current and the phase difference between the currents are considered. In the x-axis direction, measurements are made starting from the center of the TX and RX coil air gap, while in the y-axis direction, measurements are made in the longitudinal direction from the end of the magnetic material. Additionally, in the z direction, the magnetic field is simulated upward from the end of the RX coil. Simulations are performed to measure the magnetic field from 0 to 300 mm in all axial directions. Moreover, the magnetic field simulation method shown in Figure 9 is performed identically for all coils in Figure 8.

Figure 10 shows the magnetic field simulation results. In Figure 10a–c, the proposed case shown in the blue line is the case to which the shield structure is applied, and comparison Case 1 on the orange line and comparison Case 2 on the yellow line are both cases where the shield is not applied. As shown in Figure 10a–c, the magnetic field is the lowest in the dipole coil structure with the proposed reactive shield in all directions. The case with the next lowest magnetic field level is comparison Case 2 in Figure 8c, attributed to the addition of ferrites on both sides of the TX coil, which partially inhibits the magnetic field from leaking outside. Finally, in comparison Case 1 in Figure 8b, the TX magnetic core has a long ferrite bar, and in this case, the leakage magnetic field is the highest. Moreover, a common belief suggests that in a planar coil, large or thick magnetic material (ferrite) minimizes the leakage magnetic field. However, it can be confirmed that this does not apply to the dipole coil structure. Figure 11 shows a graphical representation of the magnetic field strength simulation results, specifically for the yz-plane shown in Figure 9. As expected, in Figure 10, the dipole coil structure with the proposed reactive shield showed the lowest magnetic field intensity. In addition, it can be confirmed graphically that the magnetic field of comparison Case 2 is slightly lower than that of comparison Case 1, aligning with the results depicted in Figure 10.

4. Validation of the Effectiveness of the Proposed Reactive Shield through Experiments

Figure 12 shows coil structures fabricated to experimentally validate the effectiveness of the proposed reactive shield for dipole coil structures. The geometric dimensions of the coil structures in Figure 12 align with the simulation setup shown in Figure 8 and Table 1. Dipole coils are fabricated using Litz wire with a diameter of 2.8 mm (0.05 mm/1300 strands) to reduce the AC resistance of the coils. In Figure 12, polycarbonate with a relative permeability of 1 is used as the gap between the TX, RX, and SH coils. In addition, the shape of the magnetic core is created by stacking several magnetic plates with a thickness of 5 mm and a relative magnetic permeability of 150.

Table 5. Measured electrical parameters of fabricated coils.

Model	Parameters	Value
Proposed model	Inductance of TX coil (LTX)	30.0 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of TX coil (RTX)	30 $\mathrm{m}\mathsf{\Omega }$
	Inductance of RX coil (LRX)	25.7 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of RX coil (RRX)	27 $\mathrm{m}\mathsf{\Omega }$
	Mutual inductance between TX and RX (MTX-RX)	6.01 $\mathsf{\mu }\mathrm{H}$
	Inductance of SH coils (LSH)	6.11 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of SH coils (RSH)	16 $\mathrm{m}\mathsf{\Omega }$
	Mutual inductance between SH and TX (MTX-SH)	3.78 $\mathsf{\mu }\mathrm{H}$
	Mutual inductance between SH and RX (MRX-SH)	0.1 $\mathsf{\mu }\mathrm{H}$
Comparison Case 1	Inductance of TX coil (LTX)	34.2 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of TX coil (RTX)	37 $\mathrm{m}\mathsf{\Omega }$
	Inductance of RX coil (LRX)	26.7 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of RX coil (RRX)	27 $\mathrm{m}\mathsf{\Omega }$
	Mutual inductance between TX and RX (MTX-RX)	6.15 $\mathsf{\mu }\mathrm{H}$
Comparison Case 2	Inductance of TX coil (LTX)	30.7 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of TX coil (RTX)	30 $\mathrm{m}\mathsf{\Omega }$
	Inductance of RX coil (LRX)	26.7 $\mathsf{\mu }\mathrm{H}$
	Equivalent series resistance of RX coil (RRX)	27 $\mathrm{m}\mathsf{\Omega }$
	Mutual inductance between TX and RX (MTX-RX)	6.03 $\mathsf{\mu }\mathrm{H}$

shows the results of measuring the electrical parameters (inductance, equivalent series resistance) of the coils fabricated in Figure 12.

Table 6. Resonant circuit parameter values for the experiment.

Model	Parameters	Value
Proposed model	TX series inductance (LS1)	16.9 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	203 nF
	TX series capacitance (CS1)	260 nF
	RX series capacitance (CS2)	136 nF
	SH capacitance (CSH)	1410 nF
Comparison Case 1	TX series inductance (LS1)	16.9 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	203 nF
	TX series capacitance (CS1)	203 nF
	RX series capacitance (CS2)	136 nF
Comparison Case 2	TX series inductance (LS1)	17.0 $\mathsf{\mu }\mathrm{H}$
	TX parallel capacitance (CP1)	203 nF
	TX series capacitance (CS1)	256 nF
	RX series capacitance (CS2)	136 nF

shows the resonant parameters of each circuit under 85 kHz resonant conditions. As can be seen from Table 5, the inductance of the TX and RX coils is different in each case. Therefore, to compensate circuit values for the changed coil inductances, the values of the compensation circuits must be different, which can be confirmed in Table 6. As explained previously, the LCC topology is applied to all TX sides, and the resonant conditions are as in (6). In all cases, the resonant value is calculated to ensure that the current of the TX coil is 6 A_RMS. As with the simulation, the V_in is selected as 60 V, and resonant parameters are calculated. Furthermore, a series topology is applied to the RX side with the same resonant conditions as (8). The resonant capacitance (C_SH) of the shield coil is 1410 nF, and the resonant frequency of the SH side is 54.2 kHz. Given that the system operating frequency (${\mathsf{\omega }}_{\mathrm{o}}$) is 85 kHz and the resonant frequency of the SH side (${\mathsf{\omega }}_{\mathrm{S}\mathrm{H}}$) is 54.2 kHz, the SH side operates in the inductive region, as shown in Figure 5. As with the simulation, the notation of each circuit element aligns with Figure 4.

Figure 13 shows the overall configuration for a WPT experiment. As shown in Figure 4, DC power is supplied from the DC power supply to the input and is subsequently delivered to the DC electronic load. The resonant elements on the TX, RX, and SH sides are configured, as shown in Figure 13. In addition, a full bridge inverter and rectifier are configured. All waveform measurements are performed using an oscilloscope, and DC input and output are referenced to the values displayed on the DC power supply and electronic load, respectively.

Table 7. Power transfer experiment results.

Model	Parameters	Value
Common condition	Operating frequency (${\mathsf{\omega }}_{\mathrm{o}}$)	85 kHz
	Target TX coil current (I1)	6 ARMS
	Target load power (Pload)	50 W
Proposed model	Input voltage (Vin)	60 VDC
	Input current (Iin)	1.15 ADC
	Input power (Pin)	69 W
	Output voltage (Vload)	19.09 VDC
	Output current (Iload)	2.63 ADC
	Output power (Pout)	50.2
	Power transfer efficiency (Pout/Pin $\times$ 100)	72.8%
Comparison Case 1	Input voltage (Vin)	60 VDC
	Input current (Iin)	1.12 ADC
	Input power (Pin)	67 W
	Output voltage (Vload)	20.6 VDC
	Output current (Iload)	2.43 ADC
	Output power (Pout)	50.1
	Power transfer efficiency (Pout/Pin $\times$ 100)	74.2%
Comparison Case 2	Input voltage (Vin)	60 VDC
	Input current (Iin)	1.15 ADC
	Input power (Pin)	69 W
	Output voltage (Vload)	19.3 VDC
	Output current (Iload)	2.62 ADC
	Output power (Pout)	50.5
	Power transfer efficiency (Pout/Pin $\times$ 100)	73.1%

shows the measurement results of the WPT experiment. As in the previous simulation, the current of the TX coil (${\mathbf{I}}_{\mathbf{T}\mathbf{X}}$) is fixed at 6 A_RMS, and the power delivered to the load is fixed at 50 W. Similar to the simulation results, the output current in the proposed model is the highest when delivering 50 W to the load. Therefore, the power transfer efficiency in the proposed model is reduced by about 1.5% compared to comparison Case 1 and by about 0.3% compared to comparison Case 2. This is because, as shown from the measurement results in Table 5, the mutual inductance is the lowest in the WPT coils to which the proposed reactive shield is applied. Figure 14 shows the current waveforms of the TX and SH coils measured through an oscilloscope. As previously analyzed in Figure 6 and Figure 7, the TX and SH coil currents are about 180$°$ out of phase.

Figure 15 shows how to measure the leakage magnetic field from each WPT coil. Magnetic field measurements are performed using NARDA’s ELT-400 EMF antenna (measurement uncertainty of ELT-400: $\pm 6$%). Similar to the simulation, the measurement method involves varying the distance from the WPT coil in each axis direction, as shown in Figure 9. That is, the x-axis direction is measured in the horizontal direction of the coil, the y-axis direction is measured in the longitudinal direction of the coil, and the z-axis direction is measured in the height direction of the coil. The measured magnetic field is converted to Tesla (T) and recorded.

Figure 16 shows the measurement results of the magnetic field from each WPT coil. Similar to the previous simulation, the leakage magnetic field is the lowest in the dipole coil structure with the proposed reactive shield applied in all x-, y-, and z-axis directions. Specifically, the proposed model showed a magnetic field reduction rate ranging from 50.4% to 67.7% compared to comparison Case 1. Additionally, compared to comparison Case 1, the magnetic field reduction rate is shown to be from a minimum of 17.4% to a maximum of 41.8%. The decrease is particularly high in the longitudinal direction (y-axis) of the magnetic core.

Finally, Figure 17 shows the measured magnetic field (measured at 300 mm in the y-axis direction) and power transfer efficiency of the dipole coil with the proposed reactive shield and the comparison case. Compared to the comparison groups, the proposed reactive shield reduces power transfer efficiency by about 1.5% and 0.3%, respectively. This can be attributed to the cancellation of some of the magnetic fields generated from the TX coil with the SH coil, as shown in Figure 7, resulting in a decrease in mutual inductance and, thus, a decrease in efficiency. However, the leakage magnetic field, a significant problem in the dipole structure, is reduced by up to 63% compared to the comparison groups. This illustrates a trade-off relationship between efficiency and the magnetic field. However, in applications in which leakage magnetic fields are a crucial design indicator, the dipole structure for the reactive shield is deemed sufficiently useful.

5. Conclusions

This paper proposes a reactive shield for a WPT system using dipole coils. The dipole coil structure has a magnetic field that radiates in the length direction of the magnetic core, making leakage magnetic fields a significant design concern. The reactive shield for the dipole structure proposed in this paper is designed to resonate at a frequency lower than that of the operating frequency and operates in an inductive region where the reactance is positive. Therefore, the magnetic field induced by the current in the reactive shield is generated in the direction opposite to the magnetic field of the TX coil, thereby reducing the leakage magnetic field. The method for designing the shield coil was mathematically analyzed, and the current and magnetic field phases of each coil were compared. In addition, through simulation and experiment, the effectiveness of the reactive shield was validated in a 50 W class WPT system. Specifically, it was experimentally validated that in a WPT system with a reactive shield, the power transfer efficiency is reduced by at least 0.3% to up to 1.5%, whereas the leakage magnetic field is reduced by up to 68%. Although the shielding system increases the weight, size, and cost of the TX side, the 68% reduction in leakage magnetic fields is well worth it. Since there is no need to include a separate SH system on the RX side, the proposed system is judged to be sufficiently valuable. Therefore, the reactive shield proposed in this paper is sufficiently effective in a WPT system adopting dipole-type coils, where the leakage magnetic field is a crucial design factor. In particular, it is expected that the magnetic field shielding method proposed in this paper can be actively used in human body implantable applications where reducing leakage magnetic fields is very important.