Simplified Measuring Method of kq Product for Wireless Power Transfer via Magnetic Resonance Coupling

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1 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE. kq, DC k Q kq kq kq 2 kq Simplified Measuring Method of kq Product for Wireless Power Transfer Abstract via Magnetic Resonance Coupling Katsuhiro HATA,, Takehiro IMURA, and Yoichi HORI Graduate School of Engineering, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa-shi, Chiba, , Japan JSPS Research Fellow DC1, 5-3-1, Kojimachi, Chiyoda-ku, Tokyo, , Japan hata@hflab.k.u-tokyo.ac.jp, imura@hori.k.u-toyko.ac.jp, hori@k.u-tokyo.ac.jp An efficiency characteristics of wireless power transfer via magnetic resonance coupling is expressed by kq product, which is given by coupling coefficient and quality factors of a transmitter and receiver. This paper focuses on the input impedance of the wireless power transfer system and proposes a simplified measuring method of kq product based on the shorted load and the opened load without changing the system structure. The effectiveness of the proposed method was verified by experiments with an impedance analyzer and an oscilloscope. Key words Opened load Wireless power transfer, Magnetic resonance coupling, kq product, Input impedance, Shorted load, 1. (Wireless Power Transfer : WPT) [1] [3] [4] WPT cm m [5] [6]kQ [7], [8] WPT kq [2], [7], [8] [9] kq WPT kq 2 WPT S/S S/S Fig. 1

C 1 C 2 V in L 1 L 2 R2 R L Fig. 1 Wireless power transfer via magnetic resonance coupling. Transmitting efficiency η 1 0.8 0.6 0.4 0.2 0 1 10 100 1000 10000 100000 Load resistance R L [Ω] Lm = 77.

2 C 1 C 2 V in L 1 L 2 R2 R L Fig. 1 Wireless power transfer via magnetic resonance coupling. Transmitting efficiency η Load resistance R L [Ω] Lm = 77.9 μh Lm = 37.7 μh Fig. 3 Load resistance R L vs. transmitting efficiency η. Fig. 2 Tab. 1 Transmitter and receiver coils. Specifications of coils. Primary side Secondary side Resistance, R Ω 1.05 Ω Inductance L 1, L µh 619 µh Capacitance C 1, C pf 3990 pf Resonance frequency f 1, f khz khz Quality factor Q 1, Q Mutual inductance Coupling coefficient k Outer diameter Number of turns 77.9 µh (Gap: 200 mm) 37.7 µh (Gap: 300 mm) (Gap: 200 mm) (Gap: 300 mm) 440 mm 50 turns 1 ω 0 ω 0 = 1 1 = (1) L1C 1 L2C 2 L 1, L 2 C 1, C 2 WPT η, R 2 R L η = (ω 0 ) 2 R L (R 2 + R L ){ (R 2 + R L ) + (ω 0 ) 2 } [10] 2. 2 (2) Fig. 2 Tab. 1 R L η Fig. 3 η Fig. 4 Maximum transmitting efficiency η max kq product k 2 Q 1 Q 2 kq product k 2 Q 1 Q 2 vs. maximum transmitting efficiency η max. R Lopt η max (2) R Lopt R Lopt = R (ω0lm)2 R 2 = R k2 Q 1Q 2 (3) η max η max = k 2 Q 1 Q 2 ( k 2 Q 1 Q 2 ) 2 (4) [2]k Q 1, Q 2 Q k = Lm L1 L 2 (5) Q i = ω 0L i R i (i = 1, 2) (6) Q kq k 2 Q 1 Q 2 η max Fig. 4 kq WPT 2. 3 kq kq k Q Q i (i = 1, 2) k Q i 2

3 L o L s L a L b L 1 L 1 L 1 L 2 Open L 1 L 2 Short L 2 L 2 (a) Positive phase. (b) Negative phase. Fig. 5 Measuring method of mutual inductance. (a) Open circuit. (b) Short circuit. Fig. 6 Measuring method of coupling coefficient k. Z in Z 2 Z L Z in C 1 R R C 1 L L V in R L V in Z 2 Fig. 7 (a) T-type equivalent circuit. Equivalent circuit of wireless power transfer via magnetic resonance coupling. (b) Input impedance. k (5) k 2 Fig. 5 L a L b L a = L 1 + L (7) L b = L 1 + L 2 2 (8) = La L b 4 (5) k (9) k Fig. 6 Q L o L s L o = L 1 (10) L s = L 1 2 k k = L 2 (11) 1 L s L o (12) Q i Input impedance Z in [Ω] Load resistance R L [Ω] Lm = 77.8 μh Lm = 37.3 μh Fig. 8 Load resistance R L vs. input impedance Z in. k 3. k Q i WPT kq 3. 1 T S/S WPT Fig. 1 WPT Fig. 7(a) T [11] Z L Z L = R 2 + R L (13) Z 2 3

4 Z in_s Z 2_s Z L_s Z in_s _s C 1 R R2 C 1 L L 2 2 _s V in_s R L = 0 (Short) V in_s (a) T-type equivalent circuit. (b) Input impedance. Fig. 9 Input impedance of wireless power transfer system with short circuit. Z in_o Z 2_o Z L_o Z in_o _o C 1 R R2 C 1 L L 2 2 _o V in_o R L = (Open) V in_o (a) T-type equivalent circuit. (b) Input impedance. Fig. 10 Input impedance of wireless power transfer system with open circuit. Z 2 = (ω0lm)2 Z L = (ω0lm)2 R 2 + R L (14) Z in Z in = V in = + Z 2 = + (ω 0 ) 2 R 2 + R L (15) 3. 2 (15) Z in R L Tab. 1 R L Z in Fig. 8 Z in kq 4. kq 4. 1 Fig. 7(a) Fig. 9(a) R L = 0 Z L s Z L s = R 2 (16) Z 2 s Z 2 s = (ω 0 ) 2 Z L s = (ω 0 ) 2 R 2 (17) Z in s Z in s = V in s s = + Z 2 s = + (ω 0 ) 2 R 2 (18) (5), (6) kq (18) kq k 2 Q 1Q 2 = (ω 0 ) 2 R 2 = Z in s (19) Z in s Z in o R L 4. 2 Fig. 7(a) Fig. 10(a) = Z L o Z L o = (20) Z 2 o Z 2 o = (ω 0 ) 2 Z L o = 0 (21) Z in o Z in o = Vin o o = + Z 2 o = (22) Z in o (19) (22) kq k 2 Q 1Q 2 = (ω 0 ) 2 R 2 = Zin s Zin o Z in o (23) 4

Function generator Impedance analyzer Z in C 1 C 2 L 1 L 2 (a) With impedance analyzer (Prop. 1). High-speed bipolar amp. R2 C 1 C 2 V in L 1 L 2 R2 Short or Open Short or Open Tab.

5 Function generator Impedance analyzer Z in C 1 C 2 L 1 L 2 (a) With impedance analyzer (Prop. 1). High-speed bipolar amp. R2 C 1 C 2 V in L 1 L 2 R2 Short or Open Short or Open Tab. 2 Experimental results of kq product measurement (Gap: 200 mm). Calculation Impedance analyzer Oscilloscope from Tab. 1 (Prop. 1 ) (Prop. 2 ) V in s [V] s [ma] Z in s [Ω] V in o [V] o [ma] Z in o [Ω] k 2 Q 1 Q ( error ) ( - ) ( % ) ( %) R Lopt [Ω] ( error ) ( - ) ( % ) ( % ) η max ( error ) ( - ) ( % ) ( % ) Fig. 11 (b) With oscilloscope (Prop. 2). Experimental setup for kq product measurement. Receiver capacitor Measurement probe Fig. 12 Receiver coil Transmitter coil Experimental overview. Transmitter capacitor Tab. 3 Experimental results of kq product measurement (Gap: 300 mm). Calculation Impedance analyzer Oscilloscope from Tab. 1 (Prop. 1 ) (Prop. 2 ) V in s [V] s [ma] Z in s [Ω] V in o [V] o [ma] Z in o [Ω] k 2 Q 1 Q ( error ) ( - ) ( % ) ( % ) R Lopt [Ω] ( error ) ( - ) ( % ) ( % ) η max ( error ) ( - ) ( % ) ( %) Tab. 1 kq WPT kq Tab. 1 (E4990A, Keysight Technology) 200 mm 300 mm WPT kq Fig. 11 Fig. 12 (E4990A, Keysight Technology) Z in (Prop. 1) (MSO3034, Tektronix) V in Z in (Prop. 2) (AFG3021B, Tektronix) (HSA4014, NF) Z in (Prop. 1) V in (Prop. 2) (23) kq 5. 2 kq kq Tab. 2 Tab. 3 Tab. 1 kq kq kq WPT η max R Lopt kq (3) R Lopt (4) η max WPT Tab. 1 WPT 5

6 Fig. 13 Maximum transmitting efficiency η max g = 200 mm VNA (Exp.) Calculation from Tab.1 Impedance analyzer Oscilloscope g = 300 mm Comparisons of maximum transmitting efficiency η max among measuring methods (Vector Network Analyzer : VNA, E5061B, Keysight Technology) η max Fig. 13 R Lopt R L = R Lopt η opt η max Tab. 4 Tab. 5 Fig. 13 g = 200 mm η max g = 300 mm Tab. 1 WPT kq WPT Tab. 4 Tab. 5 kq R Lopt kq kq 6. kq kq kq Tab. 4 Experimental results of maximum transmitting efficiency η max and optimized transmitting efficiency η opt with optimum load R Lopt (Gap: 200 mm). VNA Calculation Impedance analyzer Oscilloscope (Exp. ) from Tab. 1 (Prop. 1 ) (Prop. 2 ) η max ( - ) ( ) ( ) ( 0.000) η opt Tab. 5 ( - ) ( = η max ) ( = η max ) ( = η max ) Experimental results of maximum transmitting efficiency η max and optimized transmitting efficiency η opt with optimum load R Lopt (Gap: 300 mm). VNA Calculation Impedance analyzer Oscilloscope (Exp. ) from Tab. 1 (Prop. 1 ) (Prop. 2 ) η max ( - ) ( ) ( ) ( ) η opt ( - ) ( = η max ) ( = η max ) ( η max ) JSPS , 15H02232, 16J06942 [1] G. A. Covic and J. T. Boys, Modern trends in inductive power transfer for transportation application, IEEE J. Emerg. Sel. Topics Power Electron., vol. 1, no.1, pp , Mar [2] S. Li and C. C. Mi, Wireless power transfer for electric vehicle applications, IEEE J. of Emerg. Sel. Topics Power Electron., vol. 3, no.1, pp. 4 17, Mar [3] WPT , 2010, pp [4] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljacic, Wireless power transfer via strongly coupled magnetic resonance, Science Express on 7 June 2007, vol. 317, no. 5834, pp , Jun [5] D, vol.135, no.6, pp , Jun [6] BPF, C, vol. 130, no. 12, pp , [7] k Q, D, vol. 132, no. 1, pp , Jan [8] T. Ohira, What in the world is Q?, IEEE Microw. Mag., vol. 17, no.6, pp , May [9] 2, WPT , 2016, pp [10] M. Kato, T. Imura, and Y. Hori, New characteristics analysis considering transmission distance and load variation in wireless power transfer via magnetic resonant coupling, in Proc. IEEE Int. Telecommun. Energy Conf. (INTELEC), 2012, pp [11], D, vol. 130, no. 1, pp ,

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