Coil Array Structures Compared for Contactless Battery ... - IEEE Xplore

IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 5, MAY 2008

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Coil Array Structures Compared for Contactless Battery Charging Platform Jaron Achterberg, Elena A. Lomonova, and Jeroen de Boeij Electromechanics and Power Electronics Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands We propose two new coil topologies for a contactless battery charging platform. The new topologies consist of square printed circuit board (PCB) coils, grouped in two layers on a PCB. We compare the new topologies to each other and to a previously published topology that consists of three layers of hexagonal coils. For each topology, the magnetic flux density is calculated above the coil layers. In addition, the position dependence of the flux linkage between the primary coil array and a secondary coil is simulated and compared for all three topologies. For one of the new topologies, we compare the simulations with measurements. Index Terms—Battery, charging, contactless, energy transfer, inductive coupling, PCB coil.

I. INTRODUCTION

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IRELESS communication is available for an increasing number of devices, such as cellular phones, PDAs, headsets, and laptops. However, due to the limited battery power, these devices must be connected to the utility grid to recharge the batteries. In order to remove all cables to the device, contactless energy transfer using an inductive coupling is studied to transfer the energy to recharge the battery. The device can then be recharged simply by putting it on top of a charging platform or a desk. Contactless energy transfer has been studied by various researchers [1]–[9]. The majority of the studies focuses on inductive coupling. To achieve a considerable area of operation, coreless planar transformers are useful. In literature, multiple solutions for inductive planar energy transfer are known [1]–[9]. Coreless printed circuit board (PCB) coils, being flat, lightweight, and easy to manufacture, are most promising for this application. In [1] and [7], a battery charging platform using inductive coupling with PCB coil arrays is demonstrated. Although these coreless PCB coils in general have a low coupling factor between the primary and secondary coil, high efficiency can be attained by using a high-frequency resonant circuit [4]. Operating the circuit at high frequency makes the impedance of the coils large [4]. Therefore, power will be transmitted using low currents and high voltage. Because of these low currents, heat generation by the fine conductors of the PCB-coil stays within acceptable bounds. The charging platform topology of [1] and [7] consists of three layers of hexagonal coil arrays. Those layers are spatially shifted relative to each other to generate a magnetic field of uniform amplitude over the charging surface. This configuration shows good results, but this study has not included other types of configurations. Possibly, configurations of square coil arrays can achieve equal results using only two layers. This paper focuses on the comparison of two square coil arrays and the three-layer hexagonal coil array. The effect of coil diameter, number of turns, and track width on coupling has already been

Fig. 1. Inductance measurement of a single hexagonal coil.

studied by Tang [3]. To make a good comparison of the different coil arrays, those parameters are kept equal for all three topologies. II. SIMULATION OF THE MAGNETIC FLUX DENSITY Simulating an entire array of coils in a finite-element tool is computationally intensive. Accurate simulation of multiple coils demands large computing time and memory. To overcome this problem, only a single coil is simulated in Maxwell 3D 10 [10] using FEM magnetostatic analysis. The coil does not contain any iron or other magnetic nonlinear materials. Measurements of the inductance of a single hexagonal coil, which are shown in Fig. 1, show that the behavior of the coil is linear up to high operating frequencies of 10 MHz. Therefore, the superposition of magnetic fields of multiple coils is allowed. The field of a layer of coils is composed by superposing the spatially shifted magnetic field of a single coil. The magnetic field of multiple layers can also be composed by superposing the spatially shifted magnetic field of a single layer. A. FEM Simulation of a Single Coil

Digital Object Identifier 10.1109/TMAG.2008.917022 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

To compare the different topologies, first the magnetic flux density distribution of a single square coil and a single

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Fig. 2. Section of two layers of square coils.

Fig. 4. Flux density B [T] of square coil at 1 mm above the surface. (a) Top view. (b) Side view.

TABLE I PRIMARY COIL PROPERTIES

Fig. 3. Flux density B [T] of hexagonal coil at 1 mm above the surface. (a) Top view. (b) Side view.

hexagonal coil is calculated using Maxwell 3D 10. The dimensions of the coils are shown in Fig. 2 and listed in Table I. The magnetic flux density is calculated in a grid of points spaced 0.5 mm apart in the plane parallel to the surface of the coil at several heights above the coil, in order to account for the 1.6 mm epoxy glass board between the conducting layers and air gap of the measurement setup, as shown in Fig. 2. Only the magnetic flux density perpendicular to the surface of contributes to the flux linkage with the secondary the coil coil. In Figs. 3 and 4 the magnetic flux density is shown at 1 mm above the coil surface for a hexagonal coil and a square coil, respectively. The noise visible in the side views of both simulations is related to the limited accuracy of the FEM simulations and the high density of grid points that have been extracted from this solution. B. Simulation of an Array of Coils First, the magnetic flux density of a single coil is used to assemble the magnetic flux density of one layer by spatially

Fig. 5. Steps in simulation of B [T] above the hexagonal coil array. (a) B of the one layer at 1 mm above the layer. (b) B of the two layers combined at 1 mm above the two layers. (c) B of the two layers combined at 1 mm above the three layers.

shifting the values calculated in the single-coil FEM simulation. The magnetic flux density of the three-layer hexagonal coil array is calculated by shifting each new layer by one third of the coil diameter to the right with respect to the position of the previous layer. The resulting magnetic flux density of these steps are shown in Fig. 5. Two different topologies for the square coils are simulated. The first set is a double-layer structure with layers shifted by half of the coil width along the - and -axes (shifted square coil array), as shown in Fig. 6(a). In the next double-layer structure, the second-layer coils are rotated about 45 and are scaled to fit the coils of first layer (rotated square coil array), which is shown in Fig. 6(b). In Figs. 7 and 8, the magnetic flux density is shown for the shifted square coil array and the rotated square coil array, respectively. In both cases, the second layer is put underneath the first layer. Since the PCB used to manufacture the coils is

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Fig. 6. Two topologies of double-layer square coil arrays. (a) Shifted coils array. (b) Rotated coils array.

Fig. 8. B [T] above the rotated squares array. (a) B of the first layer at 1 mm above the layer. (b) B of the second layer rotated at 2.6 mm above the layer diameter. (c) B at 1 mm above the double-layer structure.

Fig. 7. B [T] above the shifted squares array. (a) B of the first layer at 1 mm above the layer. (b) B of the second layer at 2.6 mm above the layer and shifted half a coil diameter. (c) B at 1 mm above the double-layer structure.

1.6 mm thick, 1 mm above the first layer equals 2.6 mm above the second layer. III. SIMULATION OF THE FLUX LINKAGE BETWEEN THE PRIMARY AND THE SECONDARY COIL To determine the position dependence of the coupling, the flux linkage with a secondary coil is simulated. The flux linkage in the secondary coil with concentrated windings is calculated by the flux generated by the primary coil array passing through the secondary coil times the number of turns (1) In the case of distributed windings, the flux linkage is (2)

Fig. 9. Multiplication template for secondary coil induced MMF. (a) A simple square coil. (b) The 14-turn hexagonal coil.

denotes the number of times the field at the position where is enclosed by the coil. is shown graphically with being the position from the center of the coil in Fig. 9 for a square spiral coil of four turns and for the secondary coil, a hexagonal coil with 14 turns, used in the simulations. and The flux linkage is given by the correlation of with the position of the center of the secondary coil relative to the primary coil array (3)

In order to simulate the whole system, a numerical correlation of the simulated flux density generated by the primary coil array and the multiplication template of the secondary coil is done. The position dependence of the mutual inductance between the array and the secondary coil is sensitive to relative coils sizes. Therefore, the flux linkage of each topology is calculated with the same secondary coil.

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TABLE II SECONDARY COIL DIMENSIONS

TABLE III STATISTICAL PROPERTIES OF THE SIMULATED FLUX LINKAGE [Wb]

array, with a hexagonal secondary coil, whose dimensions are listed in Table II. The value at each position in Fig. 10 corresponds to the flux linkage with the center of the secondary coil at that position. IV. ANALYSIS OF THE SIMULATED RESULTS To compare the coupling properties of the different topologies, the position dependence is quantified by the mean and variance of the flux linkage of the simulated positions. These properties are numerically determined from the simulated flux linkage by (4) (5) where is the number of simulated positions. End effects are discarded from the statistical analysis in order to make a good comparison. The results from these calculations are shown in Table III. The position dependence is highest for the rotated squares array and lowest for the hexagonal array. The mean coupling is the best for the shifted squares array the worst for the hexagonal array. V. EXPERIMENTAL VERIFICATION

Fig. 10. Flux linkage [Wb] at every position of a hexagonal secondary coil with a primary coil array. (a) The shifted layers square coil array. (b) The rotated square coil array. (c) The three-layer hexagonal coil array.

To verify the simulation methods and results, several experiments are done. Since the three-layer hexagonal array is already built and measured in [1], one of square coils arrays is chosen for experimental verification. From the analysis of the simulations followed, the shifted squares array is less position dependent than the rotated squares array and has higher mean coupling than both the rotated square array and the hexagonal array. Therefore, the shifted squares array is selected for experimental verification. A. Flux Density Distribution

Fig. 10 shows the result of the correlation of the magnetic flux distribution of the shifted squares array, the rotated squares array (both with two layers), and the three-layer hexagonal

In order to measure the flux density distribution in the direc, each coil is tion perpendicular to the surface of the coil excited with a 1 A direct current. A gaussmeter (type 912-039

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Fig. 13. Induced voltage to primary current ratio plotted against frequency.

Fig. 11. Measured values (bottom).

B

[T] of a coil in a single layer (top) and the simulated

Fig. 14. Measured induced peak-to-peak voltage [mV] in the secondary coil (top) and simulated fluxed linkage [Wb] (bottom).

Fig. 12. Measured B [T] of the two-layer shifted squares array (top) and the simulated values (bottom).

of Magnetic Instrumentation Inc.) is used to measure manually in a two-dimensional grid at every 5 and 1 mm above the is shown for a single coil in a array. In Fig. 11, the measured single layer. The magnetic flux density is also measured on a 100 100 mm grid for a two-layer shifted squares array. The results are shown in Fig. 12. B. Induced Voltage in a Secondary Coil To determine the position dependence of the flux linkage, the induced voltage in the secondary coil is measured. The secondary coil has the same dimensions as the secondary coil used in the simulations (see Table II). The coils in the two-layer shifted squares coil array are all connected in series to a voltage

controlled current source, which forces the same sinusoidal current through each primary coil. The ratio of induced voltage to primary current at a fixed position is measured in a range of frequencies up to 30 kHz to verify that the coils have a linear behavior. Fig. 13 shows that the coils are linear up to 30 kHz. The induced voltage in the secondary coil is measured while the center of the secondary coil is moved in a grid of 180 120 mm with grid points spaced at 10 mm. The reference signal for the current source was a 10 kHz sine wave voltage that was amplified to a 10 kHz sinusoidal current of 2 A peak-to-peak. The results are shown in Fig. 14. VI. COMPARING SIMULATIONS AND MEASUREMENTS As the coils have linear behavior up to high frequencies, the magnetic flux density distribution is assumed linear with the primary coil current. The magnetic flux density generated by the primary coil array in the area overlapped by the secondary coil when excited by a sinusoidal current with angular frequency and an amplitude of 1 A can be expressed by (6) where is the magnetic flux density as a result of a 1 A direct current at a certain position with being the relative

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position of the center of the secondary coil to the primary coil array and being the position from the center of the secondary coil. The induced voltage in the secondary coil can be expressed as the time derivative of the flux linkage

already results in a 40% difference in field strength, according to FEM simulations.

(7)

Two new topologies are presented for contactless battery charging platforms, which consist of an array of square PCB coils and only two PCB layers. The mean flux linkage with a secondary coil above the array and the position dependence of the flux linkage of both topologies are compared to each other and to a three-layer hexagonal coil array in simulation. In simulation, both two-layer square coil arrays show comparable performance with respect to the three-layer hexagonal coil array, which has one more layer and thus more coils resulting in more heat dissipation. One topology with two layers of square coils of which the coils in the lower layer are shifted with respect to the coils in the upper layer is built, and measurements of the flux density distribution and flux linkage with a secondary coil show reasonable agreement with the simulations. Further improvements can be reached by using a gaussmeter probe with a smaller active area and a scanner robot instead of manual measurements.

The position-dependent flux linkage between the secondary coil and the primary coil array is stated to be (8)

(9) (10) Substituting (10) into (7) results in (11) The peak value of

, denoted as

, can be expressed as

VII. CONCLUSION

(12) REFERENCES By (12), the simulated flux linkage can be linked to the measured induced voltage. The peak value of the simulated flux linkage is 4.5 10 , which corresponds with an induced voltage of an amplitude of 282 mV, when excited with a sinusoidal current of 10 kHz. The maximum measured peak-to-peak induced voltage is 350 mV, which corresponds with an amplitude of 175 mV. The predicted value is about 60% larger than the measured value. The large peaks at the edges of the array and the smaller peaks in the center part of the array, which are clearly visible in the simulation [Fig. 10(a)], are only partially visible in the induced voltage measurements (Fig. 14). The field simulations and measurements show a comparable value is 0.9 mT, while the match. The maximum simulated measured top maximum value is 0.6 mT. In this case the predicted value is 50% higher than the measured one, which is in the same order as the error made when calculating the induced voltage. The distribution, i.e., the peaks and the cross-like valleys, of the measured flux density and the simulated flux density also show good agreement. The error between simulation and measurements is most likely to be caused by measuring on a too coarse grid. For the flux density measurement a grid spacing of 5 mm is used, while the flux linkage is measured on a grid with 10 mm spacing. All simulations have been performed with a grid spacing of 0.5 mm. In addition, the gaussmeter does not measure flux density in a point, but an average value over an area of 4 7 mm. This will also result in lower flux density values. Finally, all simulations are done with an air gap of exactly 1 mm. Since all measurements are done manually, the actual air gap is likely to be not exact. A difference in air gap of 1 mm

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Manuscript received January 19, 2007; revised January 16, 2008. Corresponding author: E. Lomonova (e-mail: [email protected]).