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. clear

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Get Information clear by Bui Huu NguyenBui Huu Nguyen SciProfiles Scilit Preprints.org Google Scholar 1, Pham Thanh SonPham Thanh Son SciProfiles Scilit Preprints.org Google Scholar 2, Le Thi Hong HiepLe Thi Hong Hiep SciProfiles Scilit Preprints.org Google Scholar 3,4,5, Nguyen Hai AnhNguyen Hai Anh SciProfiles Scilit Preprints.org Google Scholar 3,4, Do Khanh TungDo Khanh Tung SciProfiles Scilit Preprints.org Google Scholar 3,4, Bui Xuan KhuyenBui Xuan Khuyen SciProfiles Scilit Preprints.org Google Scholar Dr. Bui Xuan Khuyen is a Researcher at the Vietnam Academy of Science and Technology. He completed a … Dr. Bui Xuan Khuyen is a Researcher at the Vietnam Academy of Science and Technology. He completed his M.Sc. degree from the Institute of Physics, Vietnam Academy of Science and Technology, and received a Ph.D. from Hanyang University. Dr. Khuyen’s research involves metamaterials (negative reflective index, perfect absorber) and their application in radio and telecommunications regions. In addition, he investigates the integrated MMs, whose electromagnetic properties can be modulated by external impacts, such as temperature, magnetic field, electric field, and optical pump. The recent highlighted works focus on developing reconfigurable materials-integrated metamaterials (conductive polymers, graphene, lumped capacitors, and flexible substrates) to achieve switchable absorption and control the absorption bandwidth. Read moreRead less 3,4, Bui Son TungBui Son Tung SciProfiles Scilit Preprints.org Google Scholar 3,4, Vu Dinh LamVu Dinh Lam SciProfiles Scilit Preprints.org Google Scholar Prof. Dr. Vu Dinh Lam received a Ph.D. degree in materials science from the Institute of Materials … Prof. Dr. Vu Dinh Lam received a Ph.D. degree in materials science from the Institute of Materials Sciences, Vietnam Academy of Science and Technology (VAST), Vietnam, in 2006. He was a Postdoctoral Fellow at Hanyang University, Republic of Korea. He is currently a Full Professor at Vietnam Academy of Science and Technology. His research interests include ground plane, incident angle, relative bandwidth, simulation results, surface current, absorption bandwidth, absorption efficiency, absorption performance, etc. Read moreRead less 4,*, Haiyu ZhengHaiyu Zheng SciProfiles Scilit Preprints.org Google Scholar 6,7, Liangyao ChenLiangyao Chen SciProfiles Scilit Preprints.org Google Scholar 8 and YoungPak LeeYoungPak Lee SciProfiles Scilit Preprints.org Google Scholar 6,7,8,*1Department of Physics, Hanoi University of Mining and Geology, Hanoi 100000, Vietnam2Faculty of Electronics Engineering, Hanoi University of Industry, Hanoi 100000, Vietnam3Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi 100000, Vietnam4Faculty of Materials Science and Energy, Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi 100000, Vietnam5Fundamental of Fire Engineering Faculty, University of Fire Prevention and Fighting, 243 Khuat Duy Tien, Thanh Xuan, Hanoi 100000, Vietnam6Department of Physics and Quantum Photonic Science Research Center, Hanyang University, Seoul 04763, Republic of Korea7Alpha ADT, Dongtan Advanced Industrial, No. 1202, 51-9, Hwaseong 18469, Republic of Korea8Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China*Authors to whom correspondence should be addressed. Crystals2024, 14(11), 999; https://doi.org/10.3390/cryst14110999 (registering DOI) Submission received: 18 October 2024 / Revised: 14 November 2024 / Accepted: 17 November 2024 / Published: 19 November 2024 (This article belongs to the Section Hybrid and Composite Crystalline Materials) Download keyboard_arrow_downDownload PDFDownload XMLBrowse FiguresVersions Notes

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:Tx1:28. Rx is the receiver coil, and Tx is the transmitter one.Keywords: digital metamaterial; wireless power transfer; cavity resonance; diffraction limit; flux leakage reduction; selective field localization : 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:Tx1:28. 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 Rout = 19 mm, inter radius Rin = 10 mm, trip width W = 1 mm, and space gap S = 1 mm. The first layer material is copper, which has a thickness of tm = 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 td = 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 fON=12π√L0CON and fOFF=12π√L0COFF, respectively. Here, CON=C0+C1 and COFF=C0+C1+C2.L0=0.96 μH and C0≈0.6 pF are the self- inductance and self-capacitance of the unit cell, respectively. The self-inductance L0 of the unit cell is related to the permeability through Wheeler’s formula 24, defined as L0=31.33 μrμ0n2a28a+11c, where μr=1 is the relative permeability of the air, μ0 is the permeability of the vacuum, n is the number of turns, a=Rout+Rin2 is the average radius in meters, and c=Rout−Rin is the width of the coil in meters. The self-capacitance of the unit cell is related to the permittivity, defined as C0≈0.9εrg+0.1εrsε0tmSlg, where lg=π2a+Wn is the length of the space gap, ε0 is the vacuum dielectric constant, and εrg and εrs 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 (COFF), the unit cell exhibited a minimum reflection coefficient at 11.6 MHz. Conversely, at the other capacitance value of 145.6 pF (CON), 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 CON and COFF, is also shown in Figure 1e. At the frequencies fON and fOFF, 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 dTx-M = 12 cm, while the distance from the metasurface to the Rx coil was dM-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 VS. 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 RTx, LTx, CTx, and RRx, LRx, CRx, respectively. The digital metasurface, with the unit cells operated in different ON/OFF modes, is represented by varying the CON and COFF 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 LON, LOFF, and RON, ROFF. The load coil is smaller than the source coil and represented by LL and VL. 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 kL(S,Tx), kL(Tx,n), and so on (see Figure 3). The unit cells in the metasurface also interacted with each other through coupling coefficients kL(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. 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 (TD/DTx) and the enhanced PTE with respect to the WPT without MM were also compared. In Ref. 27, although a high ratio of TD/DTx (>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 TD/DTx, 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 (TD/DTx < 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.

Author Contributions

Conceptualization, Y.L. and B.H.N.; methodology, P.T.S., L.C. and B.S.T.; validation, B.X.K., H.Z. and Y.L.; investigation, B.H.N., L.T.H.H., D.K.T. and N.H.A.; writing—original draft preparation, B.H.N.; writing—review and editing, V.D.L. and Y.L.; supervision, Y.L. All of the authors discussed and commented on the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Basic Research Foundation of Hanoi University of Mining and Geology, Vietnam (project no. T23-13), and by the Korea Evaluation Institute of Industrial Technology (project no. 20016179).

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns.

Acknowledgments

The authors are also grateful to the support from the Numerical Laboratory to Support Training and Scientific Research, Graduate University of Science and Technology, Vietnam Academy of Science and Technology.

Conflicts of Interest

The authors declare no conflicts of interest.

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182. Lipworth, G.; Ensworth, J.; Seetharam, K.; Huang, D.; Lee, J.S.; Schmalenberg, P.; Nomura, T.; Reynolds, M.S.; Smith, D.R.; Urzhumov, Y. Magnetic metamaterial superlens for increased range wireless power transfer. Sci. Rep.2014, 4, 3642. Google Scholar CrossRef Figure 1. (a) Schematic of MM slab including 37 unit cells. (b) Top and bottom of the 5T-SR hexagonal unit cells. (c) Unit cell circuit model. (d) Reflection coefficient and (e) reflection phase of the unit cell at the ON (CON = 145.6 pF) and OFF states (COFF = 195.6 pF). Figure 1. (a) Schematic of MM slab including 37 unit cells. (b) Top and bottom of the 5T-SR hexagonal unit cells. (c) Unit cell circuit model. (d) Reflection coefficient and (e) reflection phase of the unit cell at the ON (CON = 145.6 pF) and OFF states (COFF = 195.6 pF).Figure 2. Schematic of the WPT-MM system with control panel. Figure 2. Schematic of the WPT-MM system with control panel.Figure 3. The circuit model of the WPT-MM system. Figure 3. The circuit model of the WPT-MM system.Figure 4. H-field intensity distribution (simulations with CST). (a) Free space and (b) metamaterial with a cavity. Figure 4. H-field intensity distribution (simulations with CST). (a) Free space and (b) metamaterial with a cavity.Figure 5. H-field intensity distribution in the x–y plane. (a) One unit cell ON. (b) Three unit cells ON. (c) Five unit cells ON. Figure 5. H-field intensity distribution in the x–y plane. (a) One unit cell ON. (b) Three unit cells ON. (c) Five unit cells ON.Figure 6. Experimental configuration for the proposed WPT-MM system. Figure 6. Experimental configuration for the proposed WPT-MM system.Figure 7. Comparison of the measurement and simulation results. (a) Transmission coefficient (S21) and (b) PTE. Figure 7. Comparison of the measurement and simulation results. (a) Transmission coefficient (S21) and (b) PTE.Figure 8. Measured relative field amplitude via transmission coefficient. (a) One unit cell ON, (b) three unit cells ON, and (c) five unit cells ON. Figure 8. Measured relative field amplitude via transmission coefficient. (a) One unit cell ON, (b) three unit cells ON, and (c) five unit cells ON.Table 1. Comparison of the characteristics of several WPT-MM systems. 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 |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). 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:Tx1:28. In addition, we also investigated multiple hotspots on the metamaterial slab that are useful for charging various devices. 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 Rout = 19 mm, inter radius Rin = 10 mm, trip width W = 1 mm, and space gap S = 1 mm. The first layer material is copper, which has a thickness of tm = 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 td = 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 fON=12π√L0CON and fOFF=12π√L0COFF, respectively. Here, CON=C0+C1 and COFF=C0+C1+C2.L0=0.96 μH and C0≈0.6 pF are the self- inductance and self-capacitance of the unit cell, respectively. The self-inductance L0 of the unit cell is related to the permeability through Wheeler’s formula 24, defined as L0=31.33 μrμ0n2a28a+11c, where μr=1 is the relative permeability of the air, μ0 is the permeability of the vacuum, n is the number of turns, a=Rout+Rin2 is the average radius in meters, and c=Rout−Rin is the width of the coil in meters. The self-capacitance of the unit cell is related to the permittivity, defined as C0≈0.9εrg+0.1εrsε0tmSlg, where lg=π2a+Wn is the length of the space gap, ε0 is the vacuum dielectric constant, and εrg and εrs 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 (COFF), the unit cell exhibited a minimum reflection coefficient at 11.6 MHz. Conversely, at the other capacitance value of 145.6 pF (CON), 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 CON and COFF, is also shown in Figure 1e. At the frequencies fON and fOFF, 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 dTx-M = 12 cm, while the distance from the metasurface to the Rx coil was dM-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 VS. 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 RTx, LTx, CTx, and RRx, LRx, CRx, respectively. The digital metasurface, with the unit cells operated in different ON/OFF modes, is represented by varying the CON and COFF 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 LON, LOFF, and RON, ROFF. The load coil is smaller than the source coil and represented by LL and VL. 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 kL(S,Tx), kL(Tx,n), and so on (see Figure 3). The unit cells in the metasurface also interacted with each other through coupling coefficients kL(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. 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 (TD/DTx) and the enhanced PTE with respect to the WPT without MM were also compared. In Ref. 27, although a high ratio of TD/DTx (>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 TD/DTx, 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 (TD/DTx < 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. 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:Tx1:28, 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. Conceptualization, Y.L. and B.H.N.; methodology, P.T.S., L.C. and B.S.T.; validation, B.X.K., H.Z. and Y.L.; investigation, B.H.N., L.T.H.H., D.K.T. and N.H.A.; writing—original draft preparation, B.H.N.; writing—review and editing, V.D.L. and Y.L.; supervision, Y.L. All of the authors discussed and commented on the manuscript. All authors have read and agreed to the published version of the manuscript. This work was supported by the Basic Research Foundation of Hanoi University of Mining and Geology, Vietnam (project no. T23-13), and by the Korea Evaluation Institute of Industrial Technology (project no. 20016179). The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns. The authors are also grateful to the support from the Numerical Laboratory to Support Training and Scientific Research, Graduate University of Science and Technology, Vietnam Academy of Science and Technology. The authors declare no conflicts of interest. 326. Xiao, C.; Hao, S.; Cheng, D.; Liao, C. Safety enhancement by optimizing frequency of implantable cardiac pacemaker wireless charging system. IEEE Trans. Biomed. Circuits Syst.2022, 16, 372–383. Google Scholar CrossRef PubMed 327. Wang, M.; Liu, H.; Zhang, P.; Zhang, X.; Yang, H.; Zhou, G.; Li, L. Broadband implantable antenna for wireless power transfer in cardiac pacemaker applications. IEEE J. Electromagn. RF Microw. Med. Biol.2020, 5, 2–8. Google Scholar CrossRef 328. 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MDPI and ACS Style Huu Nguyen, B.; Thanh Son, P.; Hiep, L.T.H.; Anh, N.H.; Tung, D.K.; Khuyen, B.X.; Tung, B.S.; Lam, V.D.; Zheng, H.; Chen, L.; et al. Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals2024, 14, 999. https://doi.org/10.3390/cryst14110999

AMA Style Huu Nguyen B, Thanh Son P, Hiep LTH, Anh NH, Tung DK, Khuyen BX, Tung BS, Lam VD, Zheng H, Chen L, et al. Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals. 2024; 14(11):999. https://doi.org/10.3390/cryst14110999

Chicago/Turabian Style Huu Nguyen, Bui, Pham Thanh Son, Le Thi Hong Hiep, Nguyen Hai Anh, Do Khanh Tung, Bui Xuan Khuyen, Bui Son Tung, Vu Dinh Lam, Haiyu Zheng, Liangyao Chen, and et al. 2024. “Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations” Crystals 14, no. 11: 999. https://doi.org/10.3390/cryst14110999

APA Style Huu Nguyen, B., Thanh Son, P., Hiep, L. T. H., Anh, N. H., Tung, D. K., Khuyen, B. X., Tung, B. S., Lam, V. D., Zheng, H., Chen, L., & Lee, Y. (2024). Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals, 14(11), 999. https://doi.org/10.3390/cryst14110999

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NoNo Article metric data becomes available approximately 24 hours after publication online. MDPI and ACS Style Huu Nguyen, B.; Thanh Son, P.; Hiep, L.T.H.; Anh, N.H.; Tung, D.K.; Khuyen, B.X.; Tung, B.S.; Lam, V.D.; Zheng, H.; Chen, L.; et al. Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals2024, 14, 999. https://doi.org/10.3390/cryst14110999

AMA Style Huu Nguyen B, Thanh Son P, Hiep LTH, Anh NH, Tung DK, Khuyen BX, Tung BS, Lam VD, Zheng H, Chen L, et al. Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals. 2024; 14(11):999. https://doi.org/10.3390/cryst14110999

Chicago/Turabian Style Huu Nguyen, Bui, Pham Thanh Son, Le Thi Hong Hiep, Nguyen Hai Anh, Do Khanh Tung, Bui Xuan Khuyen, Bui Son Tung, Vu Dinh Lam, Haiyu Zheng, Liangyao Chen, and et al. 2024. “Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations” Crystals 14, no. 11: 999. https://doi.org/10.3390/cryst14110999

APA Style Huu Nguyen, B., Thanh Son, P., Hiep, L. T. H., Anh, N. H., Tung, D. K., Khuyen, B. X., Tung, B. S., Lam, V. D., Zheng, H., Chen, L., & Lee, Y. (2024). Enhancing Wireless Power Transfer Performance Based on a Digital Honeycomb Metamaterial Structure for Multiple Charging Locations. Crystals, 14(11), 999. https://doi.org/10.3390/cryst14110999

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