Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations

Abstract

Enhancing the efficiency is an essential target of the wireless power transfer (WPT) technology. Enabling the WPT systems requires careful control to prevent power from being transferred to unintended areas. This is essential in improving the efficiency and minimizing the flux leakage that might otherwise occur. Selective field localization can effectively reduce the flux leakage from the WPT systems. In this work, we propose a method using a digital honeycomb metamaterial structure that has a property operation as a function of switching between 0 and 1 states. These cavities were created by strongly confining the field by using a hybridization bandgap that arose from wave interaction with a two-dimensional array of local resonators on the metasurface. A WPT efficiency of 64% at 13.56 MHz was achieved by using the metamaterial and improved to 60% compared to the system without the metamaterial with an area ratio of Rx:Tx~1:28. Rx is the receiver coil, and Tx is the transmitter one.

1. Introduction

Wireless power transfer (WPT) is a convenient method to transfer power from the source to the loads without employing any conductor connection. Because of power transmission in a cordless way, WPT is useful in several applications, such as cardiac pacemakers [1,2] and car charging stations [3,4,5]. The first remarkable experiment in WPT, based on high radio-frequency resonance, was performed by Tesla in 1891 [6]. By using a simple system with two resonant coils, which is currently called the Tesla coil, the electric power can be transferred through the air. Based on the comparison between transferring distance and operating wavelength, the WPT is divided into near-field and far-field categories [7,8]. In the context of WPT, the far-field regime is characterized by the utilization of radiated electromagnetic waves as the underlying energy transmission mechanism. In this paradigm, the transmission distance is significantly greater than the wavelength of the electromagnetic radiation employed [9,10]. This is in contrast to the near-field WPT approach, which relies on non-radiative electromagnetic fields and typically operates at transmission distances on the order of the wavelength or shorter. The fundamental distinction between the far-field and near-field regimes lies in the underlying electromagnetic principles governing the energy transfer process. In the far-field scenario, the WPT is facilitated by the propagation of radiated electromagnetic waves through space. These waves carry the energy from the transmitter to the receiver, enabling a longer-range energy transmission. The transmission distance in the far-field regime is, therefore, much larger than the wavelength of the electromagnetic radiation used, particularly in the case of high-power antennas. Conversely, near-field wireless power transfer exploits the localized, non-radiative electromagnetic fields usually generated by the resonating structures, such as coils or loops [11,12]. The energy is transferred by electric or magnetic coupling through these non-radiative near-fields, which decay rapidly with distance, thereby limiting the transmission range to be on the order of the wavelength or less. The choice between far-field and near-field wireless power transfer depends on the specific application requirements, including the desired transmission distance, power level, and system constraints. The far-field systems offer the advantage of longer-range energy transmission but might suffer from the lower energy transfer efficiency, while the near-field ones trade-off the transmission range for potentially higher power transfer efficiency in shorter-range applications.

Near-field WPT transmission has a higher performance compared with far-field WPT transmission, thanks, for example, in the case of inductive WPT, to a good magnetic coupling coefficient between the transmitter (Tx) and receiver (Rx) coils. However, when the transfer distance increases, the WPT efficiency is degraded, owing to the rapid reduction in the magnetic coupling coefficient [13,14,15]. To overcome the distance limitation while maintaining the WPT efficiency, metamaterials were used to improve the efficiency of the near-field WPT system, proposed by Wang in 2011 [16]. Metamaterial is known as an artificial material having tunable electrical and magnetic properties by changing the structural parameters of the unit cell, which is called an “artificial atom”, including a single material or multiple ones. In this way, the metamaterial achieves unique properties that cannot be found in natural materials, such as negative permeability, negative permittivity, or both [17].

Among the types of metamaterials, magnetic metamaterial (MM) possesses a negative permeability and only responds to magnetic fields, which is very suitable for the characteristics and operating frequency of the MR-WPT system, where MR is magnetic resonant. Numerous research studies using MMs to improve the performance of MR-WPT have been conducted [16,18]. Nevertheless, these MM structure configurations are often homogeneous, leading to an overall amplification of the magnetic field within the MR-WPT system. This causes energy dissipation and raises safety concerns. To address these issues, hybrid metamaterial structures have been proposed. However, a systematic approach in using the defect cavity profiles to optimize the WPT performance has yet to be established for the multiple loads [19,20].

By incorporating a defect cavity within the metamaterial architecture, it is possible to induce two distinct resonance modes characterized by localized energy concentration within the defect cavity region and dispersion throughout the remaining regions in the structure. These modes can be discretely represented in binary form as levels 0 and 1. The operational states of the unit cells within the metamaterial structure can be meticulously governed via computational means. This digital metamaterial configuration enables precise control over energy transfer destinations, thereby improving efficiency and mitigating undesired energy leakage. Furthermore, this digital metamaterial framework holds significant promise for optimizing the functionality of metamaterial slabs in planar WPT systems.

In this paper, we present a tunable honeycomb metamaterial structure that can switch the resonant frequency in the bandgap domain at 11.6 MHz to the bandpass domain at 13.56 MHz with the lowest league power by using high circuit isolation. Employing this method, we developed a multiple-cavity region on the metamaterial where the magnetic field can be localized through Fano constructive interference in the cavity [21]. Based on the field localized on the metamaterial for the wireless power transfer, the efficiency of the system could be increased significantly, owing to the power leakage being blocked by the bandgap. The efficiency of the wireless power transfer system increased from 4% without the metamaterial to 64% with the metamaterial at an area ratio of Rx:Tx~1:28. In addition, we also investigated multiple hotspots on the metamaterial slab that are useful for charging various devices.

2. Results and Analysis

Figure 1a illustrates a planar metamaterial configuration, commonly referred to as a metasurface. The metasurface exhibits a hexagonal honeycomb morphology comprising 37 metamaterial unit cells. Each unit cell within the metasurface adopts a hexagonal geometry, facilitating contact with six neighboring unit cells when assembled on the metasurface. This geometrical arrangement enhances the interconnectivity compared with the configurations with square or circular unit cells, which are typically adjacent to only four neighboring unit cells. The increased contact density among the unit cells in the honeycomb metasurface is advantageous in enhancing the coupling coefficient and optimizing the energy transmission pathways within the structure. Figure 1b shows a five-turn split ring (5T-SR) honeycomb metamaterial unit cell (top and bottom) that consists of two layers. The first layer is a five-turn spiral coil having the outer radius R_out = 19 mm, inter radius R_in = 10 mm, trip width W = 1 mm, and space gap S = 1 mm. The first layer material is copper, which has a thickness of t_m = 0.035 mm. The second layer is the FR-4 dielectric substance, which has a hexagonal shape with a circumcircle and interactive of a = 46.19 and b = 40 mm, respectively. The substance thickness is t_d = 1 mm, and the dielectric constant (ɛ) is 4.4. Figure 1c illustrates the equivalent circuit model of the metamaterial unit cell. The schematic circuit model is divided into two parts. The first part of the circuit is an R₀L₀C₀ resonator tank relative to the metamaterial unit cell, and the second one controls the capacitance circuit. The control circuit involves a resistor R₁ to limit the current on the diode D₁, two parallel external capacitors C₁ and C₂, and a mini-relay RL₁ that plays as a high isolation switch compared to the semiconductor switch, such as varactor in previous reports [22,23]. By utilizing the control circuit depicted in Figure 1c, the metamaterial can function in two distinct modes associated with two external capacitances of 145 and 50 pF. The resonance frequency of the metamaterial unit cell in the ON and OFF states are $f_{ON}={\displaystyle \frac{1}{2\pi \surd L_0{C}_{ON}}}$ and $f_{OFF}={\displaystyle \frac{1}{2\pi \surd L_0{C}_{OFF}}}$, respectively. Here, $C_{ON}=C_0+C_1$ and $C_{OFF}=C_0+C_1+C_2.L_0=0.96\mathsf{\mu }\mathrm{H}$ and $C_0\approx 0.6\mathrm{pF}$ are the self- inductance and self-capacitance of the unit cell, respectively. The self-inductance $L_0$ of the unit cell is related to the permeability through Wheeler’s formula [24], defined as $L_0=31.33{\mu }_r{\mu }_0{n}^2{\displaystyle \frac{a^2}{8a+11c}}$, where ${\mu }_r=1$ is the relative permeability of the air, ${\mu }_0$ is the permeability of the vacuum, $n$ is the number of turns, $a={\displaystyle \frac{R_{out}+R_{in}}{2}}$ is the average radius in meters, and $c=R_{out}-R_{in}$ is the width of the coil in meters. The self-capacitance of the unit cell is related to the permittivity, defined as $C_0\approx \left(0.9{\epsilon }_{rg}+0.1{\epsilon }_{rs}\right){\epsilon }_0{\displaystyle \frac{t_m}{S}}{l}_g$, where $l_g=\pi \left(2a+W\right)n$ is the length of the space gap, ${\epsilon }_0$ is the vacuum dielectric constant, and ${\epsilon }_{rg}$ and ${\epsilon }_{rs}$ are the relative dielectric constants of the space gap S and substrate materials, respectively [25].

The reflection coefficient of the metamaterial unit cell in the ON and OFF states is illustrated in Figure 1d. At a capacitor value of 195.6 pF (C_OFF), the unit cell exhibited a minimum reflection coefficient at 11.6 MHz. Conversely, at the other capacitance value of 145.6 pF (C_ON), the resonant frequency of the metamaterial unit cell experienced a blue shift to 13.56 MHz. These operational states can be discretely denoted as 0 and 1 when integrating the unit cells into the metasurface structure shown in Figure 1a. In addition, the reflection phase of the unit cell in the ON and OFF states, corresponding to C_ON and C_OFF, is also shown in Figure 1e. At the frequencies f_ON and f_OFF, the phases of the two states differed by 180 degrees.

We have designed a WPT system based on magnetic resonance, which showed an enhanced performance through the utilization of the ON/OFF capable metasurface. Figure 2 illustrates the schematic diagram of the WPT system incorporating a computer-controlled metasurface. The distance from the Tx coil to the metasurface was denoted as d_Tx-M = 12 cm, while the distance from the metasurface to the Rx coil was d_M-Rx = 3 cm. The two ends of the system, that is, the source coil and load one, were connected to the vector network analyzer (VNA) to measure the transmission performance. Notably, the metasurface was connected to a digital control panel to be computer-controlled. We could manipulate the operating mode of any unit cell on the metasurface, thereby affecting the performance of the WPT system. Due to its digital control, the metasurface exhibited a rapid and accurate response. Depending on the position of the Rx coil, the corresponding unit cells on the metasurface could be activated selectively in the ON mode. Then, the remaining unit cells on the metasurface are in the OFF mode, preventing the transmission of energy. Furthermore, the resonance frequency design in the ON mode has fallen into the hybridization bandgap region of the OFF mode, which also inhibited energy transmission [22]. This configuration resulted in the strong concentration of the magnetic field energy only in the ON-mode locations within the metasurface.

The WPT-MM system configuration shown in Figure 2 can be modeled by using the RLC circuit depicted in Figure 3. The source coil was supplied with an input voltage V_S. Since the source coil consisted of only one wire loop, the resistance and capacitance values were very small. The Tx and Rx coils are represented by R_Tx, L_Tx, C_Tx, and R_Rx, L_Rx, C_Rx, respectively. The digital metasurface, with the unit cells operated in different ON/OFF modes, is represented by varying the C_ON and C_OFF values. The inductance and resistance values of the unit cells do not change but are denoted according to the operating mode of the unit cells and, therefore, set as L_ON, L_OFF, and R_ON, R_OFF. The load coil is smaller than the source coil and represented by L_L and V_L. Since the coils and the metasurface were operated in magnetic resonance mode, they interacted with each other through the mutual inductances with coupling coefficients. The coupling coefficients between the source coil, Tx, Rx, load coil, and metasurface were denoted by k_L(S,Tx), k_L(Tx,n), and so on (see Figure 3). The unit cells in the metasurface also interacted with each other through coupling coefficients k_L(n,m). However, it is important to note that, for the metasurface, only the unit cells operated in the ON mode had the same resonant frequency as Tx and Rx and, therefore, were able to interact strongly with these two resonators.

To demonstrate the capability of localizing and amplifying the magnetic field in the ON unit cell region, the magnetic field distribution of a four-coil WPT system with and without integrated MMs was extracted by using the CST Studio Suite simulator. Figure 4a shows the magnetic field distribution for the WPT system without MMs. The system consisted of a source coil, a Tx one, an Rx one, and a load one, with a 15 cm separation between the Tx and Rx coils. The results indicate that the magnetic field strength at the Rx coil and load coil positions is less than 10 A/m. In contrast, in the WPT system integrated with MMs, where the central unit cell was in the ON state and positioned 12 cm from the Tx coil, the magnetic field distribution at the Rx coil and load one reached 18 A/m, as shown in Figure 4b. These results demonstrate that the WPT system with MMs can localize and amplify significantly the magnetic field transmitted from the Tx coil to the Rx and load ones. This effect is due to the much smaller size of the Rx coil compared to the Tx one (with a size ratio of 1:28), allowing for only a small portion of the magnetic flux from the Tx coil to be captured by the Rx one, while most of the magnetic flux was lost to the surrounding environment. By utilizing the MMs, the magnetic flux transmitted from the Tx coil was received by the MMs and localized at the ON unit cell position through the cavity resonance effect. As a result, the magnetic field density was enhanced and transmitted efficiently to the Rx and load coils.

Moreover, the magnetic field distribution on the metamaterial slab for various configurations of ON and OFF unit cell states was analyzed. In Figure 5a, the distribution is shown with a single unit cell in the ON state, located at the center of the slab. Figure 5b depicts the magnetic field distribution with three unit cells in the ON state, positioned at the vertices of an equilateral triangle. Figure 5c presents the distribution with five unit cells in the ON state. The H-field amplitude at the ON unit cells reached 20 A/m, which is significantly higher than the approximately 10 A/m observed at the OFF-state ones. These results demonstrate that varying the unit cell configurations significantly influenced the localization and amplification of the magnetic field. This underscores the potential of metamaterial slabs with tunable unit cell states for wireless energy transfer to multiple devices simultaneously, enabling more efficient and versatile power delivery systems.

Figure 6 details the setup used to measure the performance of the WPT-MM system, as configured in Figure 2. The system consisted of a source coil, Tx one, a metamaterial slab, Rx one, load one, a VNA, and a control circuit that toggles the ON/OFF states of the MM unit cells. The control circuit utilized an Arduino R3 board paired with seven 74HC-595 IC expanders, allowing for the independent control of 37 unit cells. This was connected to a computer via an RS232 communication protocol, and the control interface was programmed in Python. When the unit cell states were toggled in the program, the corresponding unit cells on the MM slab were adjusted in real-time, mirroring the Python 3.11 software commands.

Figure 7a illustrates the measurement and simulation comparison of transmission spectra (S₂₁) for the WPT system in different configurations. The first configuration is the WPT four-coil system without the MM slab. The second one indicates the WPT system with the MM slab where all unit cells were in the OFF state. The third one features the WPT MM system with one central unit cell in the ON state, while the remaining unit cells were in the OFF state. The measured results showed that the third configuration achieved the highest transmission coefficient at 13.56 MHz, with a value of 0.81. The simulated highest transmission coefficient at 13.56 MHz was 0.83. The difference between the simulated and measured highest transmission coefficient was caused by the ohmic loss in the electric components. In comparison, the transmission coefficients of the four-coil WPT system and the WPT-MM system with all cells in the OFF state were 0.16 and 0.07, respectively. Corresponding to the transmission coefficient, the comparison of power transfer efficiency (PTE) is also shown in Figure 7b. The measured result revealed that the third configuration yielded an efficiency of 64% at 13.56 MHz. In comparison, the efficiency of the four-coil WPT system and the WPT-MM system with all cells in the OFF state was 2.6% and 0.5%, respectively, at 13.56 MHz.

To investigate the effectiveness of the WPT systems based on MM, the characteristics of several previously studied WPT-MM systems, including this work, are presented in

Table 1. Comparison of the characteristics of several WPT-MM systems.

Ref. (MM Categorization)	Operating Frequency (MHz)	Diameter of Tx Coil (DTx) (cm)	Rx/Tx Ratio	Tx-MM Distance (cm)	Transfer Distance (TD)/DTx	PTE (with MM)/PTE (w/o MM)
[26] (1D)	2600	6.65	1:1	1.25	0.37	70.64/60.15
[27] (2D)	2.65	4.25	1:1	6.1	2.86	50/33
[28] (2D)	15	11	1:1	10.5	0.91	72/50
[29] (3D)	13–16	2	1:1	4	4	1/0.01
This work (2D)	13.56	20	1:28	12	0.75	64/4

. The comparison of these systems is interesting, owing to their different configurations and frequency ranges [26,27,28,29]. The ratio of transmission distance to the size of the Tx coil (T_D/D_Tx) and the enhanced PTE with respect to the WPT without MM were also compared. In Ref. [27], although a high ratio of T_D/D_Tx (>2) was achieved due to the small size of the Tx coil, the efficiency improvement of the WPT system combined with the MM slab was modest at only 51.52%. In addition, with a high ratio of T_D/D_Tx, Ref. [29] shows the significance of improving the PTE of the WPT system based on a 3D metamaterial structure (9900%). However, the PTE achieved by this system is only 1% higher than 0.99% compared to the system without metamaterials. For the systems with (T_D/D_Tx < 1), the overall efficiency is high (>49%) due to the large size of the Tx coil and an Rx/Tx ratio of 1, as reported in Refs. [26,28]. Nevertheless, the efficiency improvement with the integration of the MM slab reached 17.44% and 44%, respectively. In contrast, the WPT-MM system proposed in this study demonstrates a significant improvement in the transmission efficiency of up to 1500%, with an Rx/Tx ratio of 1:28 and a PTE of 64%. In addition, the electrical capacitor components used in this study are similar to those used in previous work [22]; therefore, the transmission power range of this system extends from μW to approximately 4 W.

Figure 8a–c illustrate the relative field distribution for various configurations of unit cells in the ON state. By adjusting the positions of the load and Rx coils along the x and y axes, the transmission coefficients were measured across all unit cells on the metamaterial slab. The experimental results matched closely with the simulated field distributions shown in Figure 5. In the ON state, the relative field distribution exceeds 0.7, significantly higher than the values for the OFF-state unit cells, which remain below 0.3. These surface scan results highlight the potential for magnetic field-controlled imaging, where the field distribution across the ON-state unit cells accurately reflects the shape of the target object. This advantageous feature has potential applications in WPT systems for devices with various receiver coil sizes and shapes.

3. Conclusions

In this paper, we present a digital honeycomb metamaterial structure that can switch the resonant frequency at the bandgap domain at 11.6 MHz (state 0) to the bandpass domain at 13.56 MHz (state 1) with the lowest leakage power by using a high circuit isolation. Using this method, we developed a multiple-cavity region on the metamaterial where the magnetic field was localized through the cavity resonance. Based on the field localized on the metamaterial for the WPT, the efficiency of the system was increased significantly, owing to the power leakage being blocked by the bandgap. At an area ratio of Rx:Tx~1:28, the efficiency of the WPT system increased from 4% without metamaterial to 64% with metamaterial. In addition, we also investigated multiple hotspots on the metamaterial slab that are useful in charging various devices.