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Abstract: Wireless power transfer (WPT) system based on magnetic resonance is presented here. The aim is to transfer energy wirelessly from transmitter coil to receiver coil based on magnetic resonance. A novel system with a two-coil transmitter connected to a single power source is proposed here in a triplet configuration with a single receiving coil. The two-coil transmitter is introduced as an extension to the converge area. The equivalent lumped element circuit model is presented and mathematical equations for scattering parameters have been derived. The proposed configuration is simulated using both circuit (ADS) and electromagnetic (EMPRO) simulators. The effect of the coupling between coils is investigated using simulation. The proposed configuration is practically implemented using solenoid coils and tested to verify the simulation results. The effect of receiver displacement on efficiency is also investigated.

Keywords: Magnetic resonance, Triplet configuration, Two-coil transmitter, Wireless Power Transfer.

1. Introduction

In the recent years, an extensive research has been done on wireless power transfer, particularly between two coils across an air gap via magnetic coupling. Wireless power transfer can be used in many applications such as battery charging for portable electronic devices [1], electric vehicles [2,3], robots [4,5] and implantable medical devices [6,7]. In [8], researchers in Massachusetts Institute of Technology presented wireless energy transmission via strong magnetic resonant coupling with experimental demonstration. The transfer efficiency rapidly decreases as the transmission distance increases. Hence, several researches reported in literature are focused on increasing transfer distance as well as efficiency. To increase the transmission distance, extra coils called repeaters may be added between the transmitter and receiver as reported in [9]-[11]. Furthermore, the transfer efficiency is affected by the orientation and displacement of the receiving coil. In [12], the study demonstrates the efficiency dependence on receiver orientation and deviation.

Some applications need powering various devices at the same time and studies on multi-receiver wireless power transfer systems have been reported [13,14]. Other applications require multiple transmitters to cover larger area available for wireless power transfer, but most of the research reported in literature considered only a single transmitting coil. In [15], a parallel line feeder is proposed as the transmitter in wireless power transfer system to extend the coverage area. However, the efficiency of such system still needs further study for enhancement. In [16], a multiple-input multiple-output wireless power transfer systems is proposed whereby multiple separated transmission sources are used. However, this system still needs multiple voltage sources. Here we propose a wireless power transfer system using two-transmitting coils connected to a single voltage source so that the power of the single source is divided and delivered to both transmitting coils as depicted in Figure 1 (b). In such configuration, the coverage area is extended in comparison to conventional configuration in Figure 1 (a). Mathematical equations have been derived for the proposed system and circuit simulation has been performed based on the equivalent lumped element model. Moreover, Electromagnetic professional program EMPRO [17] has been utilized to model the proposed configurations. The proposed system is practically implemented and tested to verify the simulation results.

2. Equivalent Lumped Element Model

The lumped element equivalent circuits for the single-coil transmitter and two-coil transmitter systems are shown in Figure 2 (a) and Figure 2 (b), respectively. The AC voltage source has internal resistance [R.sub.s] and the driving loop is represented by internal resistance [R.sub.1] and self inductance [L.sub.1]. Similarly, the load loop is represented by internal resistance and self inductance connected to a load [Z.sub.L]=[R.sub.L].

The equivalent model of a transmitting or receiving coil is a series RLC resonating circuit with an internal resistance R, self inductance L and capacitance C. The mutual coupling between coils is represented in the model by inductive coupling coefficient [K.sub.i,j] between coil i and coil j and it is calculated by:

[K.sub.i,j] =[M.sub.i,j]/[square root of [L.sub.i] [L.sub.j]] (1)

where [M.sub.ij] is the mutual inductance between coils i and j and [L.sub.i] and [L.sub.j] are self-inductances of coils i and j respectively. The self-inductance of coil i is calculated by [9],

[mathematical expression not reproducible] (2)

where [n.sub.i] and [r.sub.i] are the number of turns and radius of coil i respectively, and [a.sub.i] is the radius of copper wire for coil i. The mutual inductance [M.sub.i,j] between coils i and j is calculated by [12],

[mathematical expression not reproducible] (3)

where [n.sub.i] and [n.sub.j] are number of turns of coils i and j, [r.sub.i] and [r.sub.j] are the radii of coils i and j and D is the distance between the two coils.

The operating angular frequency for the single-coil transmitter in Figure 2 (a) is [[omega].sub.0]=1/[([L.sub.2][C.sub.2]).sup.0.5]=1/[([L.sub.3][C.sub.3]).sup.0.5] and for the two-coil transmitter in Figure 2 (b) is [[omega].sub.0]=1/[([L.sub.2][C.sub.2]).sup.0.5] =1/[([L.sub.3][C.sub.3]).sup.0.5]=1/[([L.sub.4][C.sub.4]).sup.0.5]. The mathematical equations for the conventional model in Figure 2 (a) are reported in literature and the mathematical description of the proposed model in Figure 2 (b) can be written in matrix form as [Z][i]=[e] where

[mathematical expression not reproducible] (4)

[mathematical expression not reproducible] (5)

where [Z] is the impedance matrix and

[mathematical expression not reproducible] (6)

The [Z] matrix can be written in term of coupling coefficients [K.sub.ij] using (1) by replacing j[omega][M.sub.ij] by [omega][K.sub.i,j][square root of [L.sub.i][L.sub.j]]. The scattering parameters of the circuit are found as,

[mathematical expression not reproducible] (7)

where [b.sub.1], [b.sub.2] represent waves reflected from ports 1 and 2, respectively, and a1, a2 represent waves incident on ports 1 and 2 respectively, and they can be found by:

[mathematical expression not reproducible] (8)

where [V.sub.N] and [I.sub.N] represent the voltage and current at port N and they are found from the equivalent circuit in Figure 2 (b) as [V.sub.1]=[e.sub.s] - [I.sub.1][R.sub.S] and [V.sub.2]=-[I.sub.2][R.sub.L]= [I.sub.5][R.sub.L]. By substitution of [V.sub.1], [V.sub.2], [I.sub.1] and [I.sub.2] into (8) the wave equations are now found in terms of circuit parameters as follows:

[mathematical expression not reproducible] (9)

The scattering parameters of the circuit are now found in terms of circuit parameters by substitution of (9) into (7) as follows:

[mathematical expression not reproducible] (10)

Solving [Z][i]=[e] for currents [I.sub.1] and [I.sub.5] we obtain,

[mathematical expression not reproducible] (11)

and by substitution of (11) into (10), the scattering parameters are now found in terms of impedance matrix as follows,

[mathematical expression not reproducible] (12)

3. Two-coil transmitter system simulation

The configuration of single transmitting coil is extensively studied and presented in literature. To extend the coverage area, the two-coil transmitter configuration in Figure 1 (b) is investigated here. Here we use a single driving loop connected to a single AC voltage source. The power is delivered from the driving loop and is divided to both the transmitting coils. The two-coil transmitter configuration is simulated firstly using ADS circuit simulator and then using EMPRO electromagnetic simulator.

3.1. Circuit Simulation

The system equivalent lumped-element circuit simulated using ADS is depicted in Figure 3 whereby coupling is represented by coupling coefficient K. The internal resistance of any coil is assumed 0.5 [OMEGA] and the transmitting and receiving coils have capacitance C=5 pF and inductance L=75 [micro]H which give resonant frequency of 8.21873 MHz. The single-turn driving and receiving loops have an inductance of 1.7387 [micro]H and [R.sub.s]=[R.sub.L]=50 [OMEGA]. The effect of the couplings between coils on power transfer efficiency is investigated by observing the scattering parameters [S.sub.21] and [S.sub.11]. The efficiency ([eta]) is calculated directly by [eta]= [|[S.sub.21]|.sup.2] x 100%.

The coupling between the transmitting coils [K.sub.23] is firstly investigated to study the effect on efficiency. Other coupling coefficients are kept constant with [K.sub.12]=[K.sub.13]=[K.sub.45]=0.2, and [K.sub.24]=[K.sub.34]=0.04. The coupling [K.sub.23] is changed from 0.07 to 0.28 and the [S.sub.21] magnitude response is observed as depicted in Figure 4. It can be noticed that the transmission efficiency degrades as coupling between the transmitting coils is increased.

Furthermore, the coupling between the transmitting coils and the receiving coil ([K.sub.24] and [K.sub.34]) is also investigated by varying the coupling [K.sub.24] and [K.sub.34] from 0.01 to 0.05 while keeping other coupling coefficients fixed as [K.sub.12]=[K.sub.13]=[K.sub.45]=0.2 and [K.sub.23]=0.14. The [S.sub.21] magnitude response is shown in Figure 5 and it can be noticed that as the coupling decreases the efficiency decreases.

3.2. Electromagnetic Simulation

The two-coil transmitter configuration is simulated using electromagnetic simulator EMPRO to model the physical structure of the proposed configuration in Figure 1 (b). The transmitting and receiving coils are identical solenoid coils with height (H), radius (R), and number of turns (N). The transmission coils and the receiving coil are separated by a distance of 1 meter. The system parameters of the coils are set with fixed values: H=16 Cm, N= 5.5 and R=35 Cm. Other parameters such as the distance between two transmitters (ds), the distance between the transmitters and the driving loop (dl), and the radius of the driving loop (r) are set as variables. A parametric study has been carried out on these parameters and best efficiency of 66.49% is obtained at r=290 mm, dl=65 mm and ds= 30 mm. The simulated scattering parameters are shown in Figure 6 and the best transfer efficiency is obtained at frequency 8.4072 MHz. The structure of the two-coil transmitter system along with the magnetic field distribution is shown in Figure 7. The axis of the receiving coil lies in the middle of separation distance between the two transmitting coils.

4. Simulation of receiver displacement

The angle [theta] representing the displacement between the transmitter and receiver coils is also investigated to see its effect on the efficiency by using EMPRO. Table 1 shows the efficiency versus [theta] for the proposed configuration. It is noticed that the highest efficiency is obtained when ([theta]=0) that is when the axis of the receiving coil lies in the middle of separation distance between the two transmitting coils. Moreover, it is clear that when the angle [theta] is increased by displacing the receiving coil away from concentric axis the efficiency decreases. As we increase the angle [theta] from 0 (o) to 35 (o), the efficiency for two-coil transmitter system drops from 66.49% to 40.37%.

5. Experimental results

To verify the simulation results, the proposed two-coil transmitter configuration has been implemented practically. The coils are made of copper wires of the same length and wire diameter of 2.75 mm and they are wounded around wooden cylinders to from solenoid coils. The parameters of the coils are those obtained from simulation results and they are N=5.5, H=160 mm and R=350 mm. A signal generator with frequency up to 10 MHz is used as the source for the transmitter and a digital oscilloscope has been utilized to show the received signal.

The two-coil transmitter experimental model is shown in Figure 8. The distance between the transmitting and receiving coils is 1 meter and the parameters of the system are ds= 30 mm, dl= 65 mm, and r= 290 mm. A sinewave of voltage amplitude 10 V is set at the generator and its frequency is tuned until maxim power transfer is obtained at resonant frequency of 9.3 MHz. The voltage at the receiving coil terminals was measured and the efficiency was then calculated and found about 61.01%. The efficiency ([eta]) has been experimentally found for different receiver displacement angles ([theta]) and the results are shown in Table 2. It can be noticed that the simulation results in Table 1 are slightly different from the experimental results due to imperfection in fabrication of coils that resulted in some changes in the dimensions in the structure. Moreover, the ohmic losses of the conducting coils contributed in efficiency degradation.

It is noticed that the highest simulated efficiency is 66.49% while the experimental efficiency is 61.01% that is about 5% lower than the simulated. The experimental results show a drop of efficiency of 30% when the angle [theta] is increased from 0 (o) to 35 (o).

6. Conclusions

In this paper, a two-coil transmitter single-coil receiver wireless power transfer system is presented. The system is proposed as an extension for the coverage area in comparison to conventional single-transmitter configurations. Mathematical model has been derived and both circuit and electromagnetic simulations have been done to show the scattering parameters and transfer efficiency. Receiver displacement has also been investigated and experimental solenoid coil models have been implemented.

6. References

[1] S.Y. Hui, "Planar wireless charging technology for portable electronic products and Qi," in Proceedings of the IEEE , vol.101, no.6, pp.1290-1301, June 2013.

[2] C-S. Wang, O.H. Stielau, and G.A.Covic, "Design considerations for a contactless electric vehicle battery charger," in IEEE Transactions on Industrial Electronics, vol.52, no.5, pp.1308-1314, Oct. 2005.

[3] T. Imura, H. Okabe, and Y. Hori, "Basic experimental study on helical antennas of wireless power transfer for Electric Vehicles by using magnetic resonant couplings," in proceedings of Vehicle Power and Propulsion Conference, pp.936-940, 7-10 Sept. 2009.

[4] I-K. Cho, S-M Kim, J-I. Moon, J-H. Yoon; S-I. Jeon, and J-I. Choi, "Wireless power transfer system for docent robot by using magnetic resonant coils," in proceedings of IEEE 5th International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications (MAPE), pp.251-254, 29-31 Oct. 2013.

[5] T. Deyle and M. Reynolds, "Surface based wireless power transmission and bidirectional communication for autonomous robot swarms," in proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp.1036-1041, 19-23 May 2008.

[6] X. Li; C-Y. Tsui, and W-H. Ki, "A 13.56 MHz wireless power transfer system with reconfigurable resonant regulating rectifier and wireless power control for implantable medical devices," in IEEE Journal of Solid-State Circuits, vol.50, no.4, pp.978-989, April 2015.

[7] J. Walk, J. Weber, C. Soell, R. Weigel, G. Fischer, and T. Ussmueller, "Remote powered medical implants for telemonitoring," in Proceedings of the IEEE , vol.102, no.11, pp.1811-1832, Nov. 2014.

[8] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljacic, "Wireless power transfer via strongly coupled magnetic resonances," Science, vol. 317, no. 6, pp. 83-86, 2007.

[9] B. Luo, S. Wu, and N. Zhou, "Flexible design method for multi-repeater wireless power transfer system based on coupled resonator bandpass filter model," in IEEE Transactions on Circuits and Systems, vol.61, no.11, pp.3288-3297, Nov. 2014.

[10] T. Imura, "Equivalent circuit for repeater antenna for wireless power transfer via magnetic resonant coupling considering signed coupling," in proceeding of 6th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp.1501-1506, 21-23 June 2011.

[11] D. Ahn and S. Hong, "A study on magnetic field repeater in wireless power transfer," in IEEE Transactions on Industrial Electronics, vol.60, no.1, pp.360-371, Jan. 2013.

[12] Z. Yan, Y. Li, C. Zhang, and Q. Yang, "Influence factors analysis and improvement method on efficiency of wireless power transfer via coupled magnetic resonance," in IEEE Transactions on Magnetics, vol.50, no.4, pp.1-4, April 2014.

[13] V. Jiwariyavej, T. Imura, and Y. Hori, "Coupling coefficients estimation of wireless power transfer system via magnetic resonance coupling using information from either side of the system," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol.3, no.1, pp.191-200, March 2015.

[14] K.E. Koh, T.C. Beh, T. Imura, and Y. Hori, "Multi-receiver and repeater wireless power transfer via magnetic resonance coupling - Impedance matching and power division utilizing impedance inverter," in proceeding of 15th International Conference on Electrical Machines and Systems (ICEMS), pp.1-6, 21-24 Oct. 2012.

[15] T. Higashino, M. Ziji, M. Okada, Y. Tatsuta, Y. Goto, Y. Tsuruda, and R. Tanaka, "A new configuration of magnetic coupled power transfer using parallel line feeder," in proceedings of Wireless Power Transfer (WPT) conference, pp.171-174, 15-16 May 2013.

[16] M.Q. Nguyen, Y. Chou, D. Plesa, S. Rao, and J-C. Chiao, "Multiple-inputs and multiple-outputs wireless power combining and delivering systems," in IEEE Transactions on Power Electronics, vol.30, no.11, pp.6254-6263, Nov. 2015.


Talal Skaik received the B.Sc. degree in 2004 from the Islamic University of Gaza, where he worked as a teaching assistant until 2006. He was awarded Hani Qaddumi scholarship and received M.Sc. degree in Communications Engineering with distinction in 2007 from the University of Birmingham, UK. He was awarded the ORSAS scholarship for doctoral study at the University of Birmingham, UK and received PhD degree in Microwave Engineering in 2011. Throughout his PhD study, he worked as a teaching assistant, and also as a research associate on micromachined microwave circuits. He was the Head of Electrical Engineering Department at the Islamic University of Gaza from Sept. 2014 until August 2016. He is currently an assistant professor at the Islamic University of Gaza. His research interests include design of microwave filters, diplexers, multiplexers, energy harvesting systems, reconfigurable antennas and microwave passive components.

Basel AlWadiya received BSc degree from Misr University for science and technology and MSc degree in communications engineering from the Islamic University of Gaza in 2012. He is currently working at AlAzhar University in Gaza.

Talal F. Skaik (1), Basel O. AlWadiya (2),

Electrical Engineering Department, Islamic University of Gaza, P.O. Box 108, Palestine Engineering Department, Al-Azhar University - Gaza, P.O. Box 1277, Palestine,

Received on: 24.11.2016

Accepted on: 08.02.2017
Table 1. Efficiency versus receiver displacement

Angle         Efficiency ([eta]) for two
(9[degrees])      coil transmitter

 0                    66.49%
 5                    63.99%
10                    61.45%
15                    58.03%
20                    57.65%
25                    53.75%
30                    44.35%
35                    40.37%

Table 2. Experimental results of efficiency versus receiver dispalcement

Angle               Two-Coil Transmitter
([theta][degrees])  Experimental ([eta])

 0                         61.01%
 5                         57.32%
10                         48.10%
15                         44.23%
20                         40.61%
25                         38.25%
30                         32.56%
35                         30.90%
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Article Details
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Author:Skaik, Talal F.; AlWadiya, Basel O.
Publication:Istanbul University - Journal of Electrical & Electronics Engineering
Article Type:Report
Date:Jan 1, 2017

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