I. Introduction
Wireless power transfer (WPT) systems for the wireless transmission of energy has been steadily researched for several years. Recently, with the commercialization of wireless charging for various devices, research on related technologies has been actively conducted [1–5]. The wireless charging method that is currently commercially available is the magnetic induction method, which implements short-distance power transmission in range of hundreds of kHz, characterized by a power transfer efficiency (PTE) of around 90%. However, in this method, charging is possible only when the wireless charging coils inside the transceiver are perfectly aligned. Charging becomes impossible if the receiving coil (RX) moves horizontally or vertically, or if a change in angle is registered. This issue can be addressed by employing the magnetic resonance method, which involves resonating the transmitting coil (TX) and RX at a specific frequency. Since the magnetic resonance method operates at high frequencies in the MHz band, power transfer is possible while maintaining a high efficiency of 70% or more over a transmission distance of several meters. Moreover, despite changes in the position and angle of the RX, the current flow is sustained in this method due to magnetic field coupling. In other words, magnetic resonance WPT can transmit power in a three-dimensional space, regardless of the location or angle of the RX. As a result, research and commercialization are underway in a variety of areas, such as wireless charging of transportation, including electric bicycles and electric vehicles, and flexible charging of smart devices [6–10]. Moreover, magnetic resonance WPT offers the advantage of charging many devices simultaneously [11].
To implement a WPT system that offers spatial freedom within a specific area, it is critical to maintain constant efficiency, regardless of RX alignment. In a typical WPT system comprising a single TX (SISO or single-input single-output), the PTE declines when the RX is located outside the effective magnetic field region, as shown in Fig. 1(a) [12, 13]. In such a case, as shown in Fig. 1(b), using a multiple-coil system (MISO or multiple-input single-output) capable of achieving a certain efficiency for various RX alignment states may be a solution. Since a multiple-coil system forms magnetic fields in various directions, it can transmit constant power to an RX that moves or rotates in a space. Furthermore, using a multiple-coil system enables the simultaneous wireless charging of RXs in various states. However, since PTE degradation due to magnetic field interference between coils is a concern, the influence of the coils must also be accounted for in this context.
Research on multiple-coil structures to improve PTE during RX misalignment is being actively pursued. For instance, in [14], the PTE of an RX rotating inside a cylinder was improved by arranging the coils at regular intervals along the side of the cylinder. In [15], a charging method for several RXs placed obliquely inside the charging area was proposed by optimally positioning a TX on a bowl-shaped substrate. There have also been cases in which the angular freedom of the RX was improved using the phase control of the TX or by overlapping and arranging planar coils [16, 17]. Furthermore, the spatial TX proposed in [18] successfully enhanced the spatial freedom of the RX by adopting an 8-shape coil. However, these studies involved a narrow transmitting area compared to the size of the TX and necessitated the use of additional devices, such as phase control, for the transmission system. Moreover, a theoretical analysis of the relationship between TX interference and PTE has become increasingly essential.
Several TX structures that reduce TX interference have been developed over the years. In [19–21], coil structures that can be freely charged both within and outside the coils and that orthogonalize the circular coils to prevent magnetic field interference between each coil were proposed. Meanwhile, the authors of [22] intended to create a magnetic field in the x, y, and z directions using a single coil to produce the same effect as multiple coils. Recently, in [23], isolation of coils was achieved by purposefully misaligning them using an overlapping technique for planar coils.
Drawing on the literature, this paper seeks to contribute to the rapid commercialization of the field of magnetic resonance WPT by presenting a 3D overlapping multiple coil that satisfies the need for spatial freedom of the RX based on a theoretical analysis of the interference between coils and its influence on PTE in a multiple WPT environment.
II Power Transfer Efficiency of WPT System
1. SISO-WPT System
A SISO-WPT system is composed of three components: a transmission unit with a power source, TX/RX, and a reception unit with a rectifier circuit and a voltage regulator, as shown in Fig. 2. The overall system efficiency (ηtotal) of a SISO-WPT system can be calculated using the following equation:
Notably, the product of the transmission/reception unit efficiency, efficiency between the transmitting and receiving coils, and link efficiency (ηlink) is defined as coil-to-coil efficiency. Considering that ηtotal is heavily reliant on ηlink, ηlink in the single WPT system depicted in Fig. 2 can be represented as follows [22]:
According to Eq. (2), link efficiency depends on the load impedance and impedance matching state of the coil.
Optimal link efficiency ηlinkopt can be computed using the following equation:
Furthermore, when the resonance frequencies of the TX and RX coincide [24], k is the coupling coefficient formed between the TX and RX, and Q denotes their quality coefficient (Q). Notably, Q and k can be determined as follows:
k is dependent on the mutual inductance M generated between TX and RX. Consequently, Eqs. (3) and (4) clarify that both the mutual inductance between TX and RX and the Q of the coil affect the link efficiency. Therefore, to achieve consistent link efficiency, regardless of the condition of the RX in a WPT system, the mutual inductance between the TX and RX must be constant.
2. MISO-WPT System
The findings of [25, 26] theoretically proved that when the coupling coefficient between two coils—i.e., mutual inductance— increases, the resonance frequency is distorted by fluctuations in self-inductance, leading to a decline in PTE, as shown in Fig. 3(a).
Based on the findings of these analyses, it is established that the mutual inductance M21, M32, and M31 between coils should be kept as low as possible when designing a multiple-coil system, as shown in Fig. 3(b). The following section proposes an isolation method for an overlapping multiple coil system by conducting mathematical analysis to minimize the mutual inductance between coils.
III. Mutual Inductance Analysis of Multiple Coil System
The mutual inductance between two coils can be calculated using the Franz Ernst Neumann formula, as follows:
where μ0 denotes the free-space permeability, l1 and l2 refer to the current paths of each coil, dl1 and dl2 indicate the infinitesimal lengths of each coil, and R12 is the distance between coils [24]. In the case of a rectangular coil, each side of the coil is defined as a straight segment to obtain the mutual inductance between each segment, while the total mutual inductance between the coils can be obtained through summation.
The mutual inductance generated between two straight segments on the same plane that form an angle of θ, as shown in Fig. 4, can be calculated as follows [27]:
Moreover, when analyzing the mutual inductance between coil segments in parallel or orthogonal spaces, this equation can be applied by considering only those segments that are parallel to each other.
1. Two-Dimensional Multiple Coils
An analysis model for the two-dimensional (2D) multiple coil was constructed, as shown in Fig. 5, to examine the variation in mutual inductance with regard to the structure of the coils.
In Fig. 5(a), square coils A and B, both having a single turn, are parallel to the xy plane and spaced h = 2 mm apart, sharing a portion of the coil at d. As shown in Fig. 5(b), each side of the coil is divided into segments, an and bn. The mutual inductance Mab between these two parallel segments can be calculated using the following formula:
In Fig 5(b), the current flowing through coils A and B are denoted as la and Ib, respectively. Considering the direction of the current flowing in the two coil segments, the mutual inductance in the same direction was calculated as positive (+), while that in the opposite direction was estimated to be negative (−). Therefore, since segments a1 and b1 have the same current direction, Ma1b1 became a positive (+) value. Meanwhile, since segments a1 and b3 have opposite current directions, Ma1b3 became a negative (−) value. Following this theory, the total mutual inductance between coils A and B (M2D) was determined as follows:
where Maibj is the mutual inductance between segments ai and bj of the 2D multiple coil.
When two planar coils are chosen as TX and RX, the efficiency declines when the RX moves horizontally to the TX, as determined in [11]. The low efficiency between coils suggests that they can be isolated. Therefore, the length d that satisfies the isolation of two planar coils can be determined by analyzing the mutual inductance according to the change in d in Fig. 5 using Eqs. (7) and (8).
Fig. 6 presents the results of analyzing the mutual inductance between two planar coils with respect to coil size l and the degree to which the two coils overlap d. It is evident that regardless of the existence of the part of the coil, dopt, which is the value of d with minimized mutual inductance, as the length l increases, so does dopt. Therefore, the mutual inductance analysis of the 2D multiple coil suggests that the coils can be isolated using an overlapping method that purposefully misaligns the two coils.
2. Proposed Overlapping Multiple Coil
Since the isolation of coils was achieved by overlapping multiple planar coils, the same approach was adopted to isolate the 3D overlapping multiple coil. However, when applying the same overlapping structure as the 2D structure to a 3D structure, three adjacent overlapping areas situated too close to each other emerged, making it difficult to achieve isolation. Therefore, in the proposed 3D coil, the overlapping areas were placed as far away as possible, and the t variable was set to distinguish it from the d variable of the 2D multiple coil. The structure of the proposed 3D coil is illustrated in Fig. 7(a), while Fig. 7(b) describes the segmentation of each coil.
The proposed coil comprises three overlapping coils, with each coil equipped with seven conductors, as shown in Fig. 7(b). Notably, when analyzing the mutual inductance between coils A and B of the proposed multiple coil, some formulas pertaining to a5, a6, and a7 had to be modified to account for the addition of the a7 segment, as follows:
where Maibj is the mutual inductance between segments ai and bj of the 3D multiple coil.
Based on this, the mutual inductance between coils A and B of the proposed coil system can be calculated as follows:
(12)
Consequently, each mutual inductance between the proposed multiple coil can be expressed as:
(13)
Furthermore, the three coils can be defined using Eq. (14) due to their counterclockwise pairing, as follows:
Fig. 8(a) presents the results of the calculated mutual inductance with respect to the overlapping thickness t of the proposed coil and the coil size l. It is evident that the proposed coil is competitive in terms of coil manufacturing and performance because it achieves isolation by taking advantage of the small overlapping areas. Furthermore, as shown in Fig. 8(b), the calculated and simulated topt values are nearly the same.
Fig. 9 illustrates the optimal overlap length (dopt) and thickness (topt) necessary for isolation, which may vary based on the dimensions of the 2D and 3D coils—as the dimensions of the coil expand, the overlapping area must also be enlarged to dampen the magnetic field. Hence, the optimal overlapping area must be proportional to the size of the coil. To achieve isolation for the 2D coils, two coils were required to directly overlap in a specific region, thus requiring a substantial overlapping area. However, for the proposed 3D coils, the area covered by the three-square loops situated on each plane was fixed, while an additional overlapping area was generated with the neighboring coil to modulate the magnetic field. Owing to these structural features, the increment in the additional overlapping area necessary for isolation was comparatively minor, even as the dimensions of the coil increased. As outlined in Fig. 9, the 3D coils require a relatively stable optimal overlap thickness for isolation, even with increased dimensions, thereby allowing for the minimization of the overlapping area and simplification of the design.
IV. Performance Analysis of the 3d Multiple Coil
The theoretical analysis in the previous section emphasizes that isolation can be accomplished in a 3D multiple coil using overlapping methods. In this section, the dopt and topt values from the previous section are employed as parameters in CST Microwave Studio 2022. Furthermore, a 3D multiple coil with p = 150 mm composed of 1-mm thick copper wire is designed to conduct isolation and PTE simulations.
The analytical models employed to examine the 3D multiple coil are depicted in Fig. 10(a)–10(c). Fig. 10(a) presents a conventional coil, and Fig. 10(b) illustrates the proposed multiple coil using overlapping methods. Fig. 10(a) depicts an RX constructed in five turns on a 1.2 mm thick FR-4 substrate (ɛr = 4.4, tanδ = 0.02) of 100 mm × 100 mm, positioned horizontal to the xy coil at positions P1 to P5, with P representing the point where the center of the receiving coil is located on the xy plane. A schematic circuit of the coils and the RX for electromagnetic analysis is shown in Fig. 10(c). Ports 1 to 3 refer to the xy, yz, and zx coils, respectively, while port 4 is the RX. Signals are delivered to the xy coil and the RX through the capacitor matching circuit, with the yz and zx coils functioning as shorted circuits on adding a 50Ω series resistance. These settings were implemented to test the influence of deactivated coils on the activated coil by activating only the xy coil, as shown by the dotted lines in Fig. 10(a) and 10(b), to examine the PTE achieved based on the isolation of the coils.
Fig. 11 demonstrates the results of the simulation analysis of the 3D multiple coil. As shown in Fig. 11(a), three types of coils were designed to resonate at 6.78 MHz. Meanwhile, Fig. 11(b) indicates that the isolation between individual coils in the conventional and proposed coils are −6 dB and −28 dB, respectively, with the proposed coil exhibiting better isolation performance. Fig. 11(c)–11(d) show the simulated mutual inductance and PTE between the xy coil and RX, considering the setting presented in Fig. 10.
Notably, the PTE (%) between TX and RX can be derived from the following formula:
where τ is the transmission coefficient of the S-parameters between the TX and RX. Notably, the capacitor values of the matching circuit were fixed for each height and were optimally matched when the RX was in the P1 position.
Fig. 11 also highlights that the mutual inductance of the conventional and proposed multiple coils remains constant as the RX moves parallelly from P1 to P5. The PTE also remains constant since the matching state is maintained independent of the location of the RX. Furthermore, the simulated minimum PTE with respect to the height of the RX in the conventional and proposed multiple coils is 60% and 70% or higher, respectively, thus verifying that PTE can be improved by isolating the coils in a multiple-coil system.
Fig. 12 presents the results obtained from simulating the near magnetic field distribution of the conventional and proposed multiple coils. To confirm magnetic field interference between the coils, all coils except the RX were activated and then matched at 6.78 MHz during the magnetic field analysis. The conventional multiple coil exhibited very modest overall magnetic field strengths since the magnetic fields formed by the adjacent coils canceled each other out, as illustrated in Fig. 12(a)–12(c). In comparison, in the xy, yz, and zx planes, the magnetic fields formed by each coil in the proposed multiple coil did not cancel each other out, instead exhibiting a uniform magnetic field distribution. Therefore, it is concluded that the proposed multiple-coil system can be employed in a multiple-charging environment, allowing three coils to be simultaneously operational.
V. Experimental Results and Discussion
While the transmission distance in a magnetic resonance WPT system is usually longer than that required for the magnetic induction method, the coupling coefficient k is low. As a result, the TX of a magnetic resonance WPT system must be designed using material with high Q. Fig. 13 presents the coils and the measurement method used to determine Q with respect to the material of the coil. Fig. 13(a)–13(c) show square single-turn coils with 200 mm side lengths fabricated using Litz wire, non-insulated copper wire, and enameled insulated copper wire, respectively. The Q of each coil was determined by calculating the 3-dB bandwidth for the resonant frequency, as illustrated in Fig. 13(d) [28]. Thus, a few capacitors were parallelly inserted into the coil to set 6.78 MHz as the resonance frequency, as illustrated in Fig. 13(e).
Table 1 summarizes the Qs measured for the various coil materials. Drawing on the measurement results, an enameled insulated copper wire with a diameter of 3 mm diameter, which achieved the highest Q of 437, was chosen as the TX material for the performance test. Fig. 14 depicts the TX and RX manufactured for performance testing. In Fig. 14(a)–14(c), W = 150 mm, t = 25 mm, WR = 100 mm, LW = 2 mm, and g = 2 mm. Notably, the RX was fabricated in five turns on a 1.2 mm thick FR-4 substrate (ɛr = 4.4, tanδ = 0.02), as shown in Fig. 14(c).
Fig. 15 presents the setup environment for measuring the isolation performance of the proposed multiple coil. The xy, yz, and zx coils of the multiple coil are connected to ports 1–3 of a 4-port vector network analyzer (VNA), together with impedance matching circuits (IMCs), as shown in Fig. 15(a). In addition, as shown in Fig. 15(b) and 15(c), IMCs with variable capacitors were employed to resonate the three coils at 6.78 MHz.
Table 2 provides the details of the coil sizes of the TX and RX, the capacitors used in the IMC, and the measured unloaded Q of the manufactured TX and RX. The S-parameter measurement results of the conventional and proposed multiple coils are shown in Fig. 16, with Fig. 16(a) clarifying that all coils used in the experiment operated at 6.78 MHz. Furthermore, the simulated and measured isolations between the coils are presented in Fig. 16(b). In the case of the conventional multiple coil, the measured isolation between each coil is S21 = −5.93 dB and S31 = S32 = −5.92 dB. In contrast, in the case of the proposed multiple coil, the measured isolations are S21 = −20.10 dB, S31 = −24.45 dB, and S32 = −20.31 dB, indicating higher isolation levels than conventional multiple coils.
The measurement environment shown in Fig. 17(a) was established to calculate the PTE of the proposed multiple coil. Fig. 17(b) illustrates the related factors, such as transmitting area, position, and angle of RX. The transmitting area is 150 mm × 150 mm × 150 mm—same as the overall size of the multiple coil. Five measurement points, from P1 to P5, were set while also accounting for the size of the RX. The measurement angles were rotated at 45° intervals with respect to the x, y, and z axes, with the origin being the center of the RX and the rotation angles for each axis defined as roll, pitch, and yaw. In the case of yaw rotation, the RX was rotated in the φ direction based on the state parallel to the zx coil. Furthermore, the xy coil of the multiple coil was set to z = 0 mm, and the measurement height was set to 50 mm, 100 mm, and 150 mm.
However, since the RX departed from the transmitting area when rotated at a height of 150 mm, the PTE was measured only when the RX was parallel to the xy plane. Drawing on these measurement parameters, the strongest coupling coil with regard to the position and angle of the RX was activated, and two unused coils were deactivated by connecting a 50Ω series resistor.
An active coil and RX were then matched at 6.78 MHz at the location where the mutual inductance varied the least in response to the RX state. The S-parameters between the active coil and RX were measured, with the capacitors’ values kept constant. Notably, variable capacitors of 30 pF were utilized to improve the impedance matching accuracy. Moreover, they were not adjusted randomly based on the measurement position or angle.
Using Eq. (15), the PTE was derived by converting the transmission coefficient (τ) between the TX and RX, measured using the VNA, into a percentage (%). Fig. 18 displays the measured PTE with respect to the position (P1–P5) and angle (roll, pitch, and yaw) of the RX when the height is 50 mm. It is observed that the PTE of the proposed multiple coil (solid line) is 50% or higher—significantly higher than that of the conventional multiple coil (dotted line). Furthermore, Figs. 19(a)–(c) show the PTE estimates when the RX has a height of 100 mm, while Fig. 19(d) presents the PTE when RX is parallel to the xy coil. With respect to the RX point, the PTE of the proposed multiple coil exhibits a similar tendency as that of the conventional multiple coil, but with an increased overall PTE. This demonstrates that a high PTE can be achieved by decreasing the power loss delivered to the RX and by ensuring isolation between coils.
The PTE measurement results pertaining to the position, height, and angle of the RX are listed in Table 2. When compared to conventional non-isolated coils, the proposed high-isolation multiple coil enhanced both the minimum and maximum PTE, increasing the average PTE by around 41.7%—from 43.4% to 61.5%. Furthermore, as shown in Table 2, the proposed multiple coil has a lower standard deviation than the conventional multiple coil. Therefore, it is confirmed that spatial freedom is achieved by the proposed multiple coil, since it has a consistent PTE of 50% or higher, regardless of the spatial state of the RX.
Table 3 compares the performance of the proposed overlapping multiple coil to those of the multiple coils employed in previous studies to improve the PTE depending on the spatial state of the RX. The proposed multiple coil offers sufficient isolation between coils and offers a uniform PTE, regardless of the distance between the TX and RX or the location or angle of the RX. In the cases of [15, 16, 20, 23, 29–31], PTE losses due to impedance mismatch were eliminated by utilizing an impedance auto-matching circuit (IAMC), which automatically compensates for impedance changes based on RX state changes. Additionally, previous studies have utilized additional auxiliary features to achieve high PTE and spatial freedom. Furthermore, although the IAMC yields optimal PTE, it is an inefficient choice in terms of utilization and economic feasibility because it requires the use of additional systems and circuits. Conversely, the proposed multiple coil achieved a maximum efficiency of approximately 69%, while ensuring the spatial freedom of the RX without having to employ an impedance auto-matching circuit.
VI. Conclusion
In this paper, a 3D overlapping multiple coil with high isolation characteristics is proposed to improve the spatial freedom of RX in a spatial WPT system. The proposed multiple coil was applied using the overlapping method to reduce the coupling between coils. By conducting mutual inductance calculation and EM simulations using the Neumann formula, sufficient isolation between the coils was established, and spatial flexibility was ensured for the RX. The isolations of the conventional and proposed multiple coils were measured to be −5.92 dB and −20.1 dB or less, respectively, confirming that isolation can be achieved in multiple-coil systems using the overlapping method. Furthermore, the PTE measurements with respect to the position and angular fluctuation of the RX exhibited a 41.7% improvement in PTE when using the proposed multiple coil over a conventional multiple coil. Finally, because of its high practicability and affordability, coupled with a structure that can be easily placed in a box or at the corner, the proposed multiple coil is predicted to be widely adopted in spatial WPT systems.
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