Progress In Electromagnetics Research Letters, Vol. 72, 127 134, 2018 A Quantitative Analysis of Coupling for a WPT System Incluing Dielectric/Magnetic Materials Yangjun Zhang *, Tatsuya Yoshiawa, an Taahiro Kitahara Abstract Dielectric or magnetic materials introuce in a wireless power transfer (WPT) system affect the properties of WPT. This paper quantitatively stuies the coupling between the transmitting an receiving elements for a WPT system incluing either ielectric or magnetic materials. The transmitting an receiving elements are open spirals an solenoi coils which are usually use in WPT systems. The analysis metho is the perturbation metho which can calculate the total coupling coefficient, the electric coupling component e an the magnetic coupling component m simultaneously. This paper gives quantitatively analyze ata on m an e to inicate how much m an e are affecte by a ielectric or magnetic material introuce in a WPT system. 1. INTRODUCTION Electromagnetic inuction, coupling an raiation are 3 methos for Wireless Power Transfer (WPT) [1 4]. Electromagnetic coupling WPT is wiely stuie aroun the worl since a MIT group reporte their WPT system [2]. In an electromagnetic coupling WPT, energy transfer is realize by the magnetic an electric coupling between the transmitting an receiving elements [1 5]. It is very important to unerstan the physical nature an the strength of electromagnetic coupling for a WPT system [4, 5]. The coupling epens on many properties of WPT systems, such as the type of transmitting an receiving elements, the structure of elements an the istance between the elements. Our previous stuies have presente some results on the coupling of WPT systems [6, 7]. The electromagnetic coupling is also affecte by a ielectric or a magnetic material introuce in the WPT system, which is usual for many potential WPT applications. Generally, the intrue matter is a ielectric matter. For example, human boy or furniture may appear in the transfer path in a home wireless power istribution. Human tissues must be penetrate when an electromagnetic power is transferre to a small evice lie artificial cariac pacemaer implante in the human boy. It is essential to unerstan what is the effect from such introuce ielectric material on the WPT coupling. On the other han, magnetic materials are introuce in some WPT systems. It is well nown that a magnetic core inserte into a solenoial coil is able to strengthen magnetic coupling. We nee to evaluate how much of coupling is improve by the magnetic material. Not only the total coupling coefficient, but also the nature of coupling, i.e., the electric an magnetic components of coupling nee to be investigate. The information on the electric an magnetic coupling components will greatly help an engineer to esign a goo WPT system. For example, a WPT system can be esigne as a main magnetic coupling to avoi interruption from the introuce ielectric material. It is obvious that a ielectric or a magnetic material affects the electromagnetic coupling. Some physical phenomena are well nown an have been accepte in the EM community. Unfortunately, there are very few reports on the quantitative stuy of coupling for the WPT systems incluing ielectric Receive 20 October 2017, Accepte 10 January 2018, Scheule 17 January 2018 * Corresponing author: Yangjun Zhang (zhang@rins.ryuou.ac.jp). The authors are with the Department of Electronics & Informatics, Ryuou University, Seta, Ohtsu 520-2194, Japan.
128 Zhang, Yoshiawa, an Kitahara an/or magnetic materials. The quantitative ata is important for a WPT system, especially after the formulas between the efficiency of energy transfer an Q prouct is reveale [2, 5, 8, 9]. This paper focuses on the analysis of the coupling. It gives a quantitative analysis of coupling for a WPT system incluing ielectric or magnetic materials. The transmitting an receiving elements uner stuy are spiral resonators an solenoial resonators which are most often use as the transmitting an receiving elements in WPT system, for example, as reporte in [1, 2, 6, 7, 10, 11] etc.. We analyze the coupling coefficient using the perturbation metho [12]. The perturbation metho can calculate the total coupling coefficient, as well as gives the electric coupling component an magnetic coupling component. 2. METHOD TO OBTAIN THE COUPLING COEFFICIENT AND THE ELECTRIC AND MAGNETIC COUPLING COMPONENTS Coupling coefficient is a ey parameter for many electric evices, such as microwave filters, electron paramagnetic resonance probes, stereometamaterials an WPT systems [13 15]. The coupling coefficient mainly escribes the strength of energy exchange between the resonators. The conventional metho to calculate coupling coefficient between the resonators is the frequency metho [13]. The frequency metho uses the following equation to obtain the coupling coefficient, = 2(f h f 1 ), f h + f 1 (1) where f h an f l are the higher an lower split frequencies of the couple resonators, respectively. The frequency metho is simple an wiely use in eterminations of coupling coefficient. However, it only gives the total coupling coefficient. There is no other physical information on the coupling between the resonators. In this stuy, the total coupling coefficient an the electric an magnetic coupling components are calculate by the perturbation metho. Using the perturbation metho [12], electric coupling component e an magnetic coupling component m can be separate using the next equation, μ H 1 2 v ε E 1 2 v = ev ev = m e, (2) ε E 2 v v where E is the electric fiel of resonator 1, an E 1, H 1 are the evanescent fiels of resonator 1 extening outsie of the symmetry plane between the two resonators. As inicate by Eq. (2), not only the total coupling coefficient is given, but also the magnetic coupling component m an the electric coupling component e are obtaine by the perturbation metho. It shoul be note that the perturbation metho is only suitable for the resonators in a symmetric alignment [12]. Our previous stuy also shows that the electric coupling will cancel the magnetic coupling if m an e are in the same sign an otherwise they will be ae up [6, 7]. The valiity of the perturbation metho has been prove in the previous stuy [12]. Here, we give an analyze example for a WPT system shown in Figure 1, which is the result of coupling coefficient for the open spiral resonators. The values of coupling coefficient in Figure 1(c) were obtaine by 3 methos, which are the frequency metho (Eq. (1)), the perturbation metho (Eq. (2)) an the measurement metho. The measurement metho uses the experimental setup shown in Figure 1 to obtain the split resonant frequencies f l an f h, an then etermine accoring to Eq. (1). The two loop coils are use for electromagnetic wave exciting an receiving respectively. In the measurement, a 0.5m 0.5m 1.0m metal box is use to contain the loop coils an the spiral resonators, to correspon with the bounary conition in the simulation. We can see that the results by 3 ifferent methos fit well. 3. COUPLING ANALYSIS FOR A WPT SYSTEM WITH A DIELECTRIC MATERIAL In this section, a WPT system with a ielectric material is stuie. At first, the effect from the ielectric material on the resonant frequency is investigate. Figure 2 shows the simulate result of resonant
Progress In Electromagnetics Research Letters, Vol. 72, 2018 129 Loop coil Networ Analyzer Coupling coefficient 1 0.1 Frequency metho Perturbation metho Measurement 0.01 0 50 100 150 200 Distance between the spiral resonators [mm] (c) Figure 1. Comparisons of coupling coefficients obtaine by 3 methos. Open spiral resonators in a symmetric alignment. Structure of open spiral: Wire iameter w = 1 mm, out iameter D = 120 mm, turn T = 18 an pitch p = 6 mm. Measurement setup for the couple spiral resonators. (c) Simulate an measure coupling coefficients for the open spiral resonators as a function of the istance between the resonators. 50 mm t 2 =80 f 0 16 15 14 13 12 11 10 0 5 10 15 20 25 30 35 40 45 t 2 [mm] ( =80) Figure 2. Simulation moel. Open spiral is the same as that of Figure 1. Size of ielectric slab: 300 mm 300 mm, of ielectric slab: 80. Resonant frequency f with respect to the thicness of ielectric slab. frequency affecte by a ielectric slab. It inicates that the resonant frequency oes not remain at a constant value. The resonant frequency ecreases when a ielectric slab comes close. Next, the coupling is investigate when a ielectric slab is inserte between the open spiral resonators. Figure 3 shows, m an e as a function of the thicness of ielectric slab when the istance between the open spirals is 100 mm. The open spiral is the same as that of Figure 1. The calculate results show that m is constant because it is not affecte by the ielectric slab. e is very small even when the thicness of slab is large as much as 80 mm. The ielectric slab has little effect on the total coupling coefficient at = 100 mm. The ielectric slab affects the coupling when the istance between the resonators is small. Figure 4 shows the coupling coefficient, m an e as a function of at =30mman = 100 mm. The open spirals are still the same as that of Figure 1. The results show that all of, m an e at =30mm have larger values. At = 30 mm, m eepsas0.50espitethat increases from 1 to 10, an e ecreases from 0.33 to 0.21 when increases from 1 to 10. increase with the slab increasing because of = m e. at = 10 is almost twice as strong as at = 1 (without ielectric slab). At = 100 mm, the epenences of, m an e on are similar to those at = 30 mm, but the
130 Zhang, Yoshiawa, an Kitahara 10 0 10-1 t 10-2 m 10-3 e 10-4 0 10 20 30 40 50 60 70 80 90 100 t [mm] ( =80, =100 mm) Figure 3. Simulation moel of the couple spirals with a ielectric slab. = 100 mm. Dielectric slab size: 300 mm 300 mm, = 80., m an e with respect to the thicness of ielectric slab. 1 1 t 0.1 0.1 m e 0.01 1 2 3 4 5 6 7 8 9 10 11 12 (t=10mm, =30mm) m e 0.01 1 2 3 4 5 6 7 8 9 10 11 12 (t=10mm, =100mm) (c) Figure 4., m an e with respect to the ielectric constant of ielectric slab. Simulation Moel. Dielectric slab size: 300 mm 300 mm 10 mm., m an e at = 30 mm. (c), m an e at = 100 mm. values are small because of the wea coupling. Accoring to Figures 2, 3 an 4, the analysis results can be summarize as follows 1. Dielectric slab has no effect on the m. 2. Dielectric slab affects e. e ecreases as of slab increases. 3. Dielectric slab has little effect on if e is very wea. However, when the spiral resonators become close, electric coupling becomes strong an the total is marely affecte by the inserte ielectric slab. 4. For open spiral resonators, m is larger than e. 5. e is fairly strong, especially when the resonators are close. It is aroun half of m. Usually it is not expecte that the total coupling coefficient varies ue to an introuce ielectric material. Our previous stuy has shown that an open spiral ae with a capacitor maes the coupling less affecte by an introuce ielectric material [7, 16]. The resonator is mae of a ouble-spiral coil connecte with a lumpe capacitor, as shown in Figure 5. Such a resonator can enclose the electric fiel in the resonator, hence a WPT system with such resonators is almost immune to the ielectric material [7, 16]. Figure 5 shows the results of, m an e for the propose resonator loae with a capacitor. It is shown that e is very small because the electric fiel is almost enclose in the resonator, thus an m are both constant with changing.
Progress In Electromagnetics Research Letters, Vol. 72, 2018 131 10 1 t 0.1 m e 0.01 0 1 2 3 4 5 6 7 8 9 10 11 12 (t=10mm, =30mm) Figure 5. Coupling analysis for the spiral resonator loae a capacitor. Simulation moel. Open spiral: Out iameter D = 120 mm, Turn T =5,Pitchp = 21 mm. Capacitor C =2.4 pf. Dielectric slab size: 300 mm 300 mm 10 mm. = 30 mm., m an e with respect to the ielectric constant of ielectric slab. 4. COUPLING ANALYSIS FOR A WPT SYSTEM WITH A MAGNETIC MATERIAL In this section, a WPT system with a magnetic material is stuie. The transmitting an receiving elements are the solenoial coils. Solenoial coil is another basic resonator use for wireless power transfer. It is well nown that a magnetic core inserte into the coil is able to increase the magnetic coupling. This section presents a quantitative analysis on the total coupling as well as its electric an magnetic coupling components on such solenoial resonators. The basic Solenoial Resonator (SR) structure in this stuy has a coil connecte by a lumpe capacitor. The loae capacitor is use in orer to obtain the expecte resonator frequency easily. Figure 6 shows the simulate result of resonant frequency as a function of the permeability of the magnetic core. Similar to the ielectric material, a magnetic matter inserte in a solenoial coil changes the resonant frequency. The frequency ecreases with the permeability increasing because the effective inuctance increases in the solenoial resonator. The coupling coefficient changes when a magnetic core is inserte in the solenoial coil. In the next analysis, we investigate 3 types of solenoial resonators (SR), as shown in the Figure 7. SR1 is a solenoial coil without magnetic material. SR2 is a resonator by inserting a magnetic material in SR1, 16.0 15.8 C f O [ MHz] 15.6 15.4 15.2 15.0 0 100 200 300 400 500 Figure 6. Resonant frequency of a solenoial coil as a function of the permeability of magnetic core inserte in the coil. Coil raius R =15.5 mm, Turn number T =5,Pitchp = 2 mm, C is ept at 56.1 pf.
132 Zhang, Yoshiawa, an Kitahara C 1 C 1 C 2 f o =15.23MHz μ r : 1 C 1 : 103pF f o =8.25MHz μ r : 500 C 1 : 103pF f o =15.23MHz μ r : 500 C 2 : 29.5pF (c) Figure 7. The structure of 3 ins of solenoial resonators (SR). Coils in 3 ins of resonators have the same structure. Raius of coil R = 25 mm. Pitch of coil p = 10 mm. Turn T = 5. SR1, SR2, (c) SR3. 10 0 Total 10-1 10-2 SR1-SR1 SR2-SR2 SR3-SR3 10-3 10 0 10-4 0 50 100 150 200 [mm] 10 0 m 10-1 10-2 SR1-SR1 SR2-SR2 SR3-SR3 e 10-1 10-2 10-3 SR1-SR1 SR2-SR2 SR3-SR3 10-3 10-4 10-4 0 50 100 150 200 [mm] 10-5 0 50 100 150 200 [mm] (c) Figure 8., m an e with respect to the istance between the resonators for 3 ins solenoial resonators. thus the resonator frequency changes from 15.23 M to 8.25 MHz. SR3 is a resonator of 15.23 MHz by ajusting the capacitor value in SR2 being 29.5 pf. The calculate results of, m, e forsr1,sr2ansr3aresummarizeinfigure8.ingeneral, e is very small for the solenoial resonators. e is smaller than two percent of m. of SR2 an of SR3 are both larger than that of SR1, because they have the inserte magnetic materials. m increases from 0.03 to 0.12 at = 30 mm when a magnetic core is inserte. It is interesting that of SR2 is almost same with that of SR3. The reason can be foun from the separate m an e by the perturbation metho. m of SR2 an SR3 are almost the same because they have the same coil an the same inserte magnetic core. The lumpe capacitor in SR2 is ifferent to that in SR3, however the capacitors have little effect on the total because the electric coupling is very wea.
Progress In Electromagnetics Research Letters, Vol. 72, 2018 133 5. CONCLUSIONS In this paper, we give a quantitative analysis on coupling coefficient for WPT systems incluing ielectric or magnetic materials. The analyze ata is useful to unerstan the coupling in a WPT system quantitatively, although some physical phenomena are well nown. The coupling investigation inclues not only the total coupling coefficient, but also the electric an magnetic coupling components. The transmitting an receiving elements uner stuy are spiral an solenoial resonators. Firstly, this paper gives an analysis on the spiral resonators with a ielectric material. The results show that a ielectric material oes not affect the magnetic coupling component m. It is also shown that a ielectric material has little effect on the electric coupling components when the resonators are in a far istance. However, electric coupling becomes fairly strong when the resonators are arrange close. For the spiral resonators in this stuy, e can be as large as half of m. Hence the total coupling will be influence by a ielectric material inserte in the WPT system. A loae capacitor can enclose the electric fiel within the resonator. The coupling between the resonators loae with capacitors is therefore immune to the ielectric material. Seconly the paper gives an analysis on the solenoial resonators with a magnetic material. The results show that electric coupling is fairly wea, an the effect of e on the total coupling can be ignore. Magnetic coupling components m is marely affecte by a magnetic material For the solenoial resonators in this stuy, an inserte core can improve the total coupling coefficient 4 times as large as that of the resonators without an iron core. REFERENCES 1. Tesla, N., Transmission of electrical energy without wire, Elect. Worl Eng., Mar. 5, 1904, Online Available: www.tfcboos.com/tesla/. 2. Kurs, A., A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, an M. Soljacic, Wireless power transfer via strongly couple magnetic resonances, Science, Vol. 317, 83 86, Jul. 2007. 3. Shonohara, N., Wireless Power Transfer via Raiowaves, ISTE Lt an John Wiley & Sons, Inc, 2014. 4. Awai, I., Magnetic resonant wireless power transfer, Niei Electronics, 2011 (in Japanese). 5. Ohira, T., Maximum available efficiency formulation base on a blac-box moel of linear twoport power transfer systems, IEICE Electronics Express, ELEX, Vol. 11, No. 13, 1 6, #20140448, Jun. 2014. 6. Awai, I., Y. Zhang, T. Komori, an T. Ishizai, Coupling coefficient of spiral resonators use for wireless power transfer, 2010 Asia-Pacific Microwave Conference, 773 776, Dec. 2010. 7. Zhang, Y., T. Yoshiawa, an I. Awai, Analysis of electric an magnetic coupling components for spiral resonators use in wireless power transfer, 2014 Asia-Pacific Microwave Conference, 1366 1368, Nov. 2014. 8. Awai, I. an T. Ishizai, Design of magnetic resonance type WPT systems base on filter Theory, Electronics an Communications in Japan, Vol. 96, No. 10, 1 11, 2013. 9. Hui, S. Y. R., Magnetic resonance for wireless power transfer [A loo bac], IEEE Power Electronics Magazine, Vol. 3, No. 1, 14 31, 2016. 10. Zhang, J., X. Yuan, C. Wang, an Y. He, Comparative analysis of two-coil an three-coil structures for wireless power transfer, IEEE Transactions on Power Electronics, Vol. 32, No. 1, 341 352, 2017. 11. Tierney, B. B. an A. Grbic, Design of self-matche planar loop resonators for wireless nonraiative power transfer, IEEE Transactions on Microwave Theory an Techniques, Vol. 62, No. 4, 909 919, 2014. 12. Awai, I., S. Iwamujra, H. Kubo, an A. Sanaa, Separation of coupling coefficient between resonators into electric an magnetic contributions, IEICE Trans. Electron, Vol. J88-C, No. 12, 1033 1039, 2005 (in Japanese). 13. Hong, J.-S. an M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, Inc., 2001.
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