IEEJ Journal of Industry Applications Vol.3 No.1 pp.35–40 DOI: 10.1541/ieejjia.3.35

Paper

Dependence of Efficiency on Type and Number of Strands of Litz Wire for Wireless Power Transfer of Magnetic Resonant Coupling

∗a) ∗ Tsutomu Mizuno Senior Member, Takuto Ueda Student Member ∗ ∗ Shintaro Yachi Student Member, Ryuhei Ohtomo Student Member ∗ Yoshihito Goto Student Member

(Manuscript received Jan. 15, 2013, revised Sep. 26, 2013)

Wireless power transfer is expected to be applied to portable devices and electric automobiles in the future. To achieve this, it is necessary to improve the transmission efficiency of the coils used in wireless power transfer, that is, to improve the quality factor and coupling coefficient of the coils. To improve the quality factor of the coils, the authors propose the use of a litz wire with a magnetoplated wire (MPW), which is a copper wire plated with a thin iron film. The MPW increases the quality factor of the coils by reducing the AC resistance owing to the proximity effect. In this study, the effect of the number of strands of a litz wire on the quality factor of the coils and efficiency characteristics is considered. Moreover, the quality factor of the coils and efficiency characteristics using three types of coil — a solid copper wire (COW), a litz wire with a copper wire (LCW), and a litz wire with an MPW (LMW) — are considered. At the transmission frequency f = 13.56 MHz, it is experimentally demonstrated that many strands, whose number becomes the highest in terms of the quality factor of the coils, exist. The transmission efficiencies of the COW, LCW and LMW coils at an output power of 5 W and a transmission distance of 9 mm are 89%, 84%, and 91%, respectively, and the efficiency of the LMW coil is the highest. Also, in this case, the temperature increases of the COW, LCW, and LMW coils are 12◦,16◦, and 10◦, respectively, and the LMW coil reduces the temperature increase.

Keywords: wireless power transfer of magnetic resonant coupling, magnetoplated wire, number of strands, quality factor, transmis- sion efficiency, temperature increase

permeability and a higher resistivity than a copper wire. As 1. Introduction a result, the Rp of the MPW is smaller than that of the cop- The technology of wireless power transfer has already been per wire because the in the MPW also is smaller utilized, for example, in IC cards. The international standard than that in the copper wire (7). It is known that the MPW (9) output power of 5 W at a short distance (Qi standard) has increases the transmission efficiency . Rp depends on the been considered and its practical application to portable de- number of strands of the litz wire, and to further improve the vices and electric automobiles is expected (1)–(4). transmission efficiency, it is necessary to consider the effect An improvement in transmission efficiency is required in of the number of strands of the litz wire on the quality factor wireless power transfer. To achieve this, it is necessary to of the coils and efficiency characteristics (10). improve the quality factor of the coils and coupling coeffi- In this study, the effect of the number of strands of each of cient (5) (6). The quality factor of the coils is proportional to the the three types of wire, which are a solid copper wire (COW), angular frequency and of the coils and inversely an LCW and a litz wire with an MPW (LMW), on the qual- proportional to the resistance of the coils. Therefore, it is ity factor of the coils and efficiency characteristics is consid- necessary to reduce the resistance in order to improve the ered. In addition, an output power of 5 W for portable devices quality factor. The resistance is represented by the sum of and a transmission frequency of 13.56 MHz in the industry- DC resistance Rdc, AC resistance due to the skin effect, Rs, science-medical band (ISM band) are used. Moreover, the (7) and that due to the proximity effect, Rp . A litz wire, which following are discussed. is a twisted plural copper wire with small diameter (LCW), 1) Equivalent circuit of wireless power transfer and struc- (8) is generally used to reduce Rs . ture of coils The authors proposed the use of a magnetoplated wire 2) Quality factor of coil characteristics dependent on num- (MPW), which is a copper wire plated with a magnetic thin ber of strands (7) film, to reduce Rp . This is because an alternating mag- 3) Transmission characteristics netic flux flows in a magnetic thin film, which has a higher 2. Equivalent Circuit of Wireless Power Transfer a) Correspondence to: Tsutomu Mizuno. E-mail: mizunot@ and Structure of Coils shinshu-u.ac.jp ∗ Shinshu Uiversity 2.1 Equivalent Circuit of Wireless Power Transfer 4-17-41, Wakasato, Nagano, Nagano 380-8553, Japan Figure 1 shows a model of the wireless power transfer of

c 2014 The Institute of Electrical Engineers of Japan. 35 Efficiency Dependence on Wire Type for Wireless Power（Tsutomu Mizuno et al.）

 magnetic resonant coupling. The structures of the transmit- 1 Lmj = ZA(ZB − ZA)(H)(Zi < Z0, Zo < ZL) ting and receiving coils are the same. Cr1 and Cr2 are ca- ω ···················· pacitors used to induce resonance with the transmitting and  (4) receiving coils, respectively. The output impedance of the 1 ZB − ZA power source, Z , and the load Z are always 50 Ω. Z is the Cmj = (F) (Zi < Z0, Zo < ZL) 0 L i ωZ Z impedance of the circuit from the power source side and Z B A o ···················· (5) is the impedance of the circuit from the load side. ffi η The transmission e ciency 21 is shown by the following Where ω is the angular frequency (= 2π f rad/s), ZA is equation with the input power Pi and output power Po. Zi(Ω)forj= 1orZo(Ω)forj= 2andZB is Z0 (= 50 Ω) for j = 1orZ (= 50 Ω)forj= 2. η = Po × ··························· L 21 100 (%) (1) 2.2 Structures of Coils and Figure 3 shows Pi the structure of the coils. The diameter of the coils, d,is η In a high-frequency circuit, 21 decreases because of the 36 mm and the bobbin is made of expanded polystyrene. The ff reflection that occurs if Z0 and Zi or ZL and Zo are di erent coils are tightly wound and, as described later, their number ffi η η (11) (reflection e ciencies 11 and 22) . Therefore, a matching of turns, n, is 8. As shown in Table 1, the length of the coils circuit is necessary for high transmission efficiency. in the axial direction, la, depends on the number of strands, Figure 2 shows an equivalent circuit of wireless power N, of the litz wire. transfer. Figure 2(a) shows the inserted matching circuit in Figure 4 shows the structures of the COW, LCW and > > the cases of Zi Z0 and Zo ZL and Fig. 2(b) shows the LMW. The COW has a diameter of 450 μm and is plated with < < inserted matching circuit in the cases of Zi Z0 and Zo ZL. an insulating film of 16 μm thickness. The resistivity of the To insert the matching and capacitors, Lm1 and ρ . × −8 Ω   copper wire used, 1,is172 10 m and its permeability Lm2 and Cm1 and Cm2, Zi and Zo should be the same as Z0 μ is 0.999991 (12). An LCW strand has a diameter of 100 μm η η r1 and ZL, respectively; therefore, both 11 and 22 are expected and is plated with an insulating film of 12 μm thickness. An to be zero. In addition, the value of each of the matching in- LMW strand is a copper wire with a diameter of 100 μmthat (11) ductors and capacitors is given by the following equations . is plated with magnetic thin films (Fe and Ni) followed by a  13-μm-thick insulating film. The Ni film is prepared in or- = 1 − > , > Lmj ω ZB(ZA ZB)(H)(Zi Z0 Zo ZL) der to soft-solder easily. The thicknesses of the Fe and Ni ···················· (2) films are 0.9 μm and 0.05 μm, respectively, where the resis-  ρ . × −8 Ω μ − tivity of iron, 2,is98 10 m and its permeability r2 is 1 ZA ZB (12) Cmj = (F) (Zi > Z0, Zo > ZL) 100 . The conductor cross-sectional area A of the COW is ωZA ZB ···················· (3)

Fig. 1. Model of wireless power transfer (unit: mm) Fig. 3. Structure of coils (unit: mm)

(a) Zi > Z0, Zo > ZL

(b) Zi < Z0, Zo < ZL Fig. 2. Equivalent circuit of wireless power transfer

36 IEEJ Journal IA, Vol.3, No.1, 2014 Efficiency Dependence on Wire Type for Wireless Power（Tsutomu Mizuno et al.）

Table 1. Axial direction lengths of coils changed experimentally and the effect of the dependence of Rp on N is considered to determine Rp. Ri depends on the current that is output power Po. Also there is no Ri of the COW and LCW because the wires do not have magnetic thin films. For the above reason, the quality factor of the coils depends on N, and the highest N in terms of the quality factor of the coils is expected for f = 13.56 MHz. Therefore, the quality factor of the coils characteristic de- pendence on N is considered in the 3rd chapter and the highest transmission characteristic of the coils in terms of the quality factor of in the 3rd chapter is considered in the 4th chapter. 3. Quality Factor of Coil Characteristic Depen- dence on N When f = 13.56 MHz, d = 36 mm and N = 20, the quality factor of the LMW coil was the highest for n = 8 (13).There- fore, the highest N in terms of the quality factor is considered for n = 8. Table 1 shows the relationship between N and la = (a) Solid wire (COW) for n 8. la was measured with a micrometer (Mitutoyo, IP65). Figure 5 shows the impedance vs. number of strands char- acteristics of coils with n = 8and f = 13.56 MHz. The impedance was measured with a network analyzer (Agilent, 5061B) and the power level was P = 1 mW. Figure 5(a) shows the resistance R, (b) the inductance L and (c) the qual- ity factor. According to Fig. 5(a), the R value of the LCW coil de- creased in the range of N = 1to5asN increased. However, the R value of the LCW coil increased in the range of more nd than N = 5asN increased. As above in the 2 chapter, Rdc and Rs decreased as N increased. Therefore, the increase in (b) Litz wires R R R μ was due to p. On the other hand, the of the LMW coil Fig. 4. Structure of wires (unit: m) decreased in the range of N = 1 to 15 and became almost constant in the range of more than N = 15 as N increased. 2 = 0.159 mm and those of the LCW and LMW for N 20 are The reason for this is that the LMW coil reduced Rp.Also, 0.158 mm2; therefore, the A values of such wires are similar the minimum R values of the COW and LCW and LMW coils (refer to Table 1). The N considered is less than or equal to were 2.2 Ω,3.8Ω (N = 15) and 1.6 Ω (N = 15), respectively; 20 for the A values of the LCW and LMW not to exceed that thus, the R of the LMW coil was the lowest. of the COW. According to Fig. 5(b), the L values of the LCW and LMW The quality factor of the coils is shown by the following coils decreased as N increased (14).TheL of the LMW coil equation. was higher than that of the LCW coil because the magnetic ωL thin film of MPW stocks with magnetic energy. Q = ········································ (6) According to Fig. 5(c), the quality factor of the LCW coil R increased in the range of N = 1 to 5 and decreased in the Where L is the inductance of the coils (H) and R is the range of more than N = 5asN increased. This is because, as Ω resistance of the coils ( ). above, the quality factor of the coils is inversely proportional In addition, the R of the coils is given by the following to R and proportional to L,andtheR of the LCW coil in- (7) equation . creased and the L of the LCW coil decreased in the range of more than N = 5asN increased. On the other hand, the qual- R = Rdc + Rs + Rp + Ri (Ω)·····················(7) ity factor of the LMW coil increased in the range of N = 1 Where Rdc is the DC resistance (Ω), Rs is the AC resis- to 15 and decreased at N = 20 as N increased. This is due to tance due to the skin effect (Ω), Rp is the AC resistance due the decrease in the L of the LMW coil at N = 20. to the proximity effect (Ω)andRi is the hysteresis loss of the From the above mentioned results, it was experimentally magnetic thin films (Ω). argued that the highest N in terms of the quality factor of the Rdc is inversely proportional to A; therefore, Rdc decreases coils exists for f = 13.56 MHz. as N increases. The AC resistance due to the skin effect per Also, the maximums quality factor values of the COW, strand is constant and does not depend on N.However,Rs LCW and LMW coils were 166, 120 (N = 5) and 251 decreases as N increases, namely, the strands are connected (N = 15), respectively; thus, the quality factor of the LMW in parallel. On the other hand, since Rp depends on N, N is coil was 51% or 109% greater than those of the COW and

37 IEEJ Journal IA, Vol.3, No.1, 2014 Efficiency Dependence on Wire Type for Wireless Power（Tsutomu Mizuno et al.）

(a) Resistance Fig. 6. Coupling coefficient vs. distance characteristic ( f = 100 kHz)

(b) Inductance Fig. 7. Transmission efficiency vs. output power char- acteristic at l = 9mm(l/d = 0.25, f = 13.56 MHz)

transmission efficiency at l = 9mm(l/d = 0.25) was mea- sured with an oscillator (Agilent 33522A), an amplifier (AR 75A250A), a directional coupler (Werlatone C5091-10) and a wattmeter (Agilent U2004A). In this case, Zi and Zo were larger than Z0 and ZL in all the coils, respectively; thus, the matching circuit shown in Fig. 2(a) was inserted. The matching inductors and capaci- (c) Quality factor tors were determined to be less than 1% for η11 and η22 at Fig. 5. Impedance vs. number of strands characteristics Pi = 1 mW using the network analyzer. In addition, η11 and of coils ( f = 13.56 MHz, n = 8) η22 were always less than 1% regardless of Pi. Figure 7 shows the transmission efficiency η21 vs. output power Po characteristics for the matching circuit at l = 9 mm. LCW coils, respectively. Also, the quality factor of the LCW The η21 values of the COW, LCW and LMW coils were 89%, = coil with N 15 was 104 and that of the LMW coil was 84% and 91% at Po = 5 W, respectively; thus, the transmis- 141% greater than that of the LCW coil. The reason for this sion efficiency of the LMW coil was 2% or 7% greater than is that the LMW coil reduced Rp. those of the COW and LCW coils, respectively. This is due ffi Therefore, the e ciency characteristics of the COW, LCW to the highest quality factor of the LMW coil. Also, η21 of the (N = 15) and LMW (N = 15) are compared in the 4th chap- LMW coil was the highest among the coils, and the change in ter. A target output power of 5 W, a transmission distance l of η21 of the LMW coil depend on Po is the same as that of the 9 mm, which is industrially practical (transmission distance COW coil. Thus, there is no increase in the hysteresis loss / = . l coil diameter d 0 25) and l of 36 mm, which is expected depends on Po in the range of less than 5 W of the Po. for long-distance transmission (l/d = 1), are considered. Figure 8 shows the heat generation characteristic of each coil for P = 5 W and room temperature T = 25◦C, which 4. Transmission Characteristics o was measured with thermoshot (NEC Avio Infrared Tech- 4.1 Coupling Coefficient vs. Distance Characteristic nologies Co., Ltd., TYPE F30). According to Fig. 8, the tem- Figure 6 shows coupling coefficient k vs. distance char- perature increases of the COW, LCW and LMW coils, ΔT, acteristic. k was measured at f = 100 kHz. The k of the were 12 deg, 16 deg and 10 deg, respectively; thus, the ΔT of COW coil was always the highest and that of the LMW coil the LMW coil was lower than those of the COW and LCW was always the lowest among the coils considered. However, coils. The reason for the reduced heating of the LMW coil the difference in k between the COW and LMW coils was is that the LMW coils should be the highest quality factor 5%; thus, the dependence of the difference in k on the type of among the coils considered. wire is negligible. 4.3 Transmission Characteristics at l = 36 mm 4.2 Transmission Characteristics at l = 9mm The Transmission efficiency at l = 36 mm (l/d = 1) was

38 IEEJ Journal IA, Vol.3, No.1, 2014 Efficiency Dependence on Wire Type for Wireless Power（Tsutomu Mizuno et al.）

(a) COW (a) COW

(b) LCW (b) LCW

(c) LMW (c) LMW Fig. 10. Heat generation characteristic for Po = 5Wat Fig. 8. Heat generation characteristic for Po = 5W at = / = . = . l = 36 mm (l/d = 1, f = 13.56 MHz, room temperature l 9mm(l d 0 25, f 13 56 MHz, room temperature = ◦ T = 25◦C) T 25 C)

efficiency of the LMW coil was 6% or 17% greater than those of the COW and LCW coils, respectively. Also, η21 of the LMW coil was the highest among the coils, and the change in η21 of the LMW coil depend on Po is the same as that of the COW coil. Thus, there is no increase in the hysteresis loss depends on Po in the range of less than 5 W of the Po. The difference in η21 between the COW and LMW coils at l = 36 mm (l/d = 1) was larger than that at l = 9mm (l/d = 0.25). The reason for this is that the effect of the qual- ity factor of the coils considered on η21 is large since k is Fig. 9. Transmission efficiency vs. output power char- small. = / = = . acteristic at l 36 mm (l d 1, f 13 56 MHz) Figure 10 shows the heat generation characteristic of each ◦ coil for Po = 2 W and room temperature T = 25 C. Accord- Δ measured. In this case, Zi and Zo were smaller than Z0 and ZL ing to Fig. 10, the T of the COW, LCW and LMW coils in all the coils, respectively; thus, the matching circuit shown were 25 deg, 44 deg and 18 deg, respectively. Thus, the LMW in Fig. 2(b) was inserted. coil reduced the temperature increase. Figure 9 shows transmission efficiency η21 vs. output The reason for this is that the LMW coil reduced Rp;as ffi power Po characteristics for the matching circuit at l = a result, the quality factor of the coil and transmission e - 36 mm. In addition, η11 and η22 were always less than 1% ciency increased, and the loss was minimized. regardless of P and transmission efficiency did not decrease. i 5. Conclusion Since the temperature of the LCW coil in Po = 2W was ◦ 69 C, the experiment was conducted at Po less than 2 W. The In this paper, the following are discussed. η21 values of the COW, LCW and LMW coils were 63%, 52% ( 1 ) Quality factor of coil characteristic dependence and 69% at Po = 2 W, respectively; thus, the transmission on number of strands It was experimentally argued that

39 IEEJ Journal IA, Vol.3, No.1, 2014 Efficiency Dependence on Wire Type for Wireless Power（Tsutomu Mizuno et al.） the highest number of strands, N, in terms of the quality fac- (12) T. Mizuno, S. Enoki, T. Suzuki, M. Noda, H. Shinagawa, S. Uehara, and H. tor of the coils exists for f = 13.56 MHz. The quality factor Kitazawa: “Linearity Range of an Eddy Current Displacement Sensor in Re- N = lation to the Fe Film Thickness of Magnetoplated Wire”, J. Magn. Soc. Jpn., values of the COW, LCW and LMW coils with 15 were Vol.31, No.2, pp.103–108 (2007) 166, 104 and 251, respectively; thus, the quality factor of the (13) T. Mizuno, T. Ueda, S. Yachi, R. Ohotomo, and Y. Goto: “Quality factor LMW coil was 51% or 141% greater than those of the COW of coil dependent on number of strands of litz wire”, SEAD24, pp.211–216 and LCW coils, respectively. The reason for this is that the (2012) (14) D. Sinha, A. Bandyopadhyay, P.K. Sadhu, and N. Pal, “Computation of In- LMW coil reduced Rp. ductance and AC Resistance of a Twisted Lizt-Wire for high Frequency In- ( 2 ) Transmission characteristics The k of the COW duction Cooker”, IECR 2010 International Conference, pp.85–90 (2010) coil was always the highest and that of the LMW coil was al- ways the lowest. However, the difference in k between the COW and LMW coils was 5%; thus, the dependence of the Tsutomu Mizuno (Senior Member) was born in 1958. He received difference in k on the type of wire is negligible. his M.E. degree in electrical engineering from Shin- shu University in 1983. He joined AMADA Co., Ltd., The η21 values of the COW, LCW and LMW coils were = = / = . in April of the same year. He became on assistant 89%, 84% and 91% for Po 5Watl 9mm(l d 0 25); and assistant professor at the Department of Electrical thus, the efficiency of the LMW coil was 2% or 7% greater Engineering, Shinshu University, in 1996 and 1999, than those of the COW and LCW coils, respectively. In this respectively. He has been the same Professor since case, the temperature increases of the COW, LCW and LMW 2011. He has focused on linear motors, linear ac- coils were 12 deg, 16 deg and 10 deg, respectively. tuators, electromagnetic sensors and wireless power transfer. He is a member of IEEE, MSJ and JSAEM. In addition, the η21 values of the COW, LCW and LMW coils were 63%, 52% and 69% for Po = 2W at l = 36 mm (l/d = 1); thus, the efficiency of the LMW coil was 6% or Takuto Ueda (Student Member) received his B.E. degree in electrical 17% greater than those of the COW and LCW coils, respec- and electronic engineering from Shinshu University in 2012. He is currently pursuing his M.E. degree in tively. In this case, the temperature increases of the COW, electrical and electronic engineering at Shinshu Uni- LCW and LMW coils were 25 deg, 44 deg and 18 deg, re- versity. He has focused on wireless power transfer. spectively. Thus, the LMW coil reduced the temperature increase. Namely the LMW coil proves useful for long- distance transmission. The reason for this is that the LMW coil reduced Rp; as a result, the quality factor of the coil and transmission efficiency increased, and the loss was mini- mized. Shintaro Yachi (Student Member) received his B.E. degree in electri- cal and electronic engineering from Shinshu Univer- References sity in 2011. He is currently pursuing his M.E. de- gree in electrical and electronic engineering at Shin- ( 1 ) Y. Matsuda and H. Sakamoto: “Non-contact magnetic coupled power and shu University. He has focused on wireless power data transferring system for an electric vehicle”, J. Magn. Mater., Vol.310, transfer. No.2, Part 3, pp.2853–2855 (2007) ( 2 ) L. Xiaoyu, F. Zhang, A. S. Hackworth, J. R. Sclabassi, and M. Sun: “Wireless power transfer system design for implanted and worn devices”, Proc. IEEE Annu. Northeast Bioeng. Conf., Vol.35, pp.52–53 (2009) ( 3 ) B.G. Jong and B.H. Cho: “An energy transmission system for an artficial heart using leakage inductance compensation of transcutaneous ”, IEEE Trans. Power Electron., Vol.13, No.6, pp.1013–1022 (1998) Ryuhei Ohtomo (Student Member) received his B.E. degree in elec- ( 4 ) Wireless Power Consortium, http://www.wirelesspowerconsortium.com/ trical and electronic engineering from Shinshu Uni- ( 5 ) T. Mizuno, A. Kamiya, D. Yamamoto, S. Yachi, and H. Kanazawa: “The- oretical expression of efficiency of wireless power transfer using magnetic versity in 2012. He is currently pursuing his M.E. de- resonant coupling”, JSAEM, Vol.19, No.2, pp.153–158 (2011) gree in electrical and electronic engineering at Shin- ( 6 ) T. Takura, Y. Ota, K. Kato, F. Sato, H. Matsuki, T. Sato, and T. Nonaka: shu University. He has focused on LLC converters. “Relationship between efficiency and figure-of-merit in wireless power trans- fer through electromagnetic induction”, J. Magn. Soc. Jpn., Vol.35, No.2, pp.132–135 (2011) ( 7 ) H. Shinagawa, T. Suzuki, M. Noda, Y. Shimura, and T. Mizuno: “Theoreti- cal analysis of AC resistance in coil using magnetoplated wire”, IEEE Trans. Magn., Vol.45, No.9, pp.3251–3259 (2009) ( 8 ) J. Acero, R. Alonso, M.J. Burdio, A.L. Barragan, and D. Puyal: “Frequency- dependent resistance in litz-wire planar windings for domestic induction Yoshihito Goto (Student Member) received his B.E. degree in electri- heating appliances”, IEEE Trans. Power Electron., Vol.21, No.4, pp.856–866 (2006) cal and electronic engineering from Shinshu Univer- ( 9 ) T. Mizuno, S. Yachi, A. Kamiya, and D. Yamamoto: “Improvement in effi- sity in 2012. He is currently pursuing his M.E. de- ciency of wireless power transfer of magnetic resonant coupling using mag- gree in electrical and electronic engineering at Shin- netoplated wire”, IEEE Trans. Magn., Vol.47, No. 0, pp.4445–4448 (2011) shu University. He has focused on wireless power (10) T. Mizuno, A. Kamiya, Y. Shimura, K. Iida, D. Yamamoto, N. Miyao, and H. transfer for robots inside the body Sasadaira: “Consideration on influences of number of strands on AC resis- tance of litz wire”, JSAEM, Vol.18, No.3, pp.300–305 (2010) (11) T. Yoshimoto: “Antenna introduction to learn from basic”, CQ publisher, pp.94–125 (2007)

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