Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

Davor Vinko; Domagoj Bilandžija; Vanja Mandrić Radivojević

doi:10.1155/2021/6303628

Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

Vinko, Davor;Bilandžija, Domagoj;Mandrić Radivojević, Vanja 2021-10-14 00:00:00 Hindawi Wireless Power Transfer Volume 2021, Article ID 6303628, 11 pages https://doi.org/10.1155/2021/6303628 Research Article Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field Davor Vinko , Domagoj Bilandzˇija , and Vanja Mandric´ Radivojevic´ Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, Josip Juraj Strossmayer University of Osijek, Osijek 31000, Croatia Correspondence should be addressed to Domagoj Bilandzija; domagoj.bilandzija@ferit.hr Received 11 April 2021; Revised 25 June 2021; Accepted 28 September 2021; Published 14 October 2021 Academic Editor: Hao Gao Copyright © 2021 Davor Vinko et al. .is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conventional magnetically coupled resonant wireless power transfer systems are faced with resonant frequency splitting phenomena and impedance mismatch when a receiving coil is placed at misaligned position. .ese problems can be avoided by using uniform magnetic ﬁeld distribution at receiving plane. In this paper, a novel 3D transmitting coil structure with improved uniform magnetic ﬁeld distribution is proposed based on a developed optimization method. .e goal is to maximize the average magnetic ﬁeld strength and uniform magnetic ﬁeld section of the receiving plane. Hence, ﬁgures of merit (FoM and FoM ) are 1 2 introduced and deﬁned as product of average magnetic ﬁeld strength and length or surface along which uniform magnetic ﬁeld is generated, respectively. .e validity of the optimization method is veriﬁed through laboratory measurements performed on the fabricated coils driven by signal generator at operating frequency of 150 kHz. Depending on the allowed ripple value and predeﬁned coil proportions, the proposed transmitting coil structure gives the uniform magnetic ﬁeld distribution across 50% to 90% of the receiving plane. ﬁeld strength distribution at the receiving plane will provide 1. Introduction stable resonant frequency regardless of RX-coil position due Numerous wireless power transfer (WPT) systems operate to steady value of magnetic coupling factor k between TX- through nonuniform magnetic ﬁeld strength distribution at and RX-coil. Hence, uniform magnetic ﬁeld strength dis- receiving plane. Magnetic ﬁeld nonuniformity in magneti- tribution at a receiving plane results in a WPT system that cally coupled resonant (MCR) WPT system causes resonant does not require frequency tracking and automatic im- frequency splitting phenomena and impedance mismatch- pedance matching [8]. Uniform magnetic ﬁeld strength ing when receiving coil (RX-coil) is not properly aligned distribution also provides uniform and simultaneous power with transmitting coil (TX-coil) [1, 2]. Namely, the eﬃciency delivery to multiple RX-coils, i.e., loads. Furthermore, of WPT system is signiﬁcantly impaired due to frequency uniform magnetic ﬁeld strength distribution at a receiving splitting phenomena or impedance mismatching [1, 3]. plane ensures nondegraded wireless power transfer eﬃ- Consequently, to achieve eﬃcient energy transfer along with ciency regardless of RX-coil position within receiving plane greater degree of freedom, in terms of RX-coil position, such [1]. WPT systems require frequency tracking [3] and automatic .e proposed TX-coil structure consists of two layers impedance matching [3, 4]. In order to create uniform and is based on optimization method which is validated by magnetic ﬁeld strength distribution at a receiving plane, simulation and measurement results. Since the proposed various TX-coil designs are developed [1, 5–21]. TX-coil structure is characterized by folded sides, it is more In this paper, a novel 3D structure of TX-coil is proposed suitable for large sized WPT systems, for instance, instal- to achieve uniform magnetic ﬁeld distribution at the given lation under oﬃce desk. Computer simulations of TX-coils receiving plane (114 × 28 cm). Presence of uniform magnetic with diﬀerent winding arrangement (coil layers relative 2 Wireless Power Transfer spacing), but with the same outer dimensions (114 × 28 cm), z were run, and magnetic ﬁeld distribution at the given re- z ceiving plane which is above the TX-coil was observed. P 0 According to the simulation results, experimental TX-coils α 2 are made out of Litz wire instead of PCB realization which is x not appropriate for large receiving plane. Both computer simulation and measurement results veriﬁed that uniform magnetic ﬁeld distribution at considerable surface of the P2 P1 receiving plane is produced by the novel 3D TX-coil structure. With the approximately 100 W of output power at receiving side of a WPT system, application of such TX-coil Figure 1: Magnetic ﬁeld in the point P0 generated by the linear segment P1-P2. enables simultaneous wireless charging of monitors, smartphones, laptops, etc. 2. Model Explanation |H| � sin α − sin α , (1) 1 2 4πd To maintain stable transfer eﬃciency and power delivery to .e shortest distance between P0 and the line which freely moving RX-coil(s), TX-coil in WPT system should passes through P1 and P2 equals generate uniform magnetic ﬁeld [18, 21]. Such ﬁeld distri- |P1P2 × P0P1| bution is diﬃcult to achieve with “standard” ﬂat wound coils. (2) d � . When designing a 3D coil structure, a fast method for |P1P2| magnetic ﬁeld evaluation is a signiﬁcant advantage. A .e angles α1 and α2 are calculated as follows: common approach for magnetic ﬁeld evaluation is using dedicated software (e.g., Ansys Maxwell, FEMM, MATLAB, P1P2 · P0P1 α � 90 − arccos􏼠 􏼡, etc.) which executes a numerical analysis. Such approach is 1 |P1P2| · |P0P1| very time consuming, both in preparation (model pre- (3) processing) and in simulation itself. P1P2 · P0P2 If the 3D TX-coil structure can be represented as a α � 90 − arccos􏼠 􏼡. |P1P2| · |P0P2| number of linear sections, the magnetic ﬁeld simulations can be signiﬁcantly simpliﬁed. Uniformity of magnetic ﬁeld of For coil current I in linear segment ﬂowing from P1 to the TX-coil is evaluated with respect to the plane of interest. P2, the direction of the magnetic ﬁeld strength H at point P0 In MCR-WPT, where multiple loads can be wirelessly is perpendicular to the plane deﬁned by points P0, P1, and P2 powered, a ﬂat surface (e.g., oﬃce desk) should have uniform (Figure 1). Equation (1) gives only the magnitude of the magnetic ﬁeld distribution. .erefore, magnetic ﬁeld eval- magnetic ﬁeld strength, but the direction of magnetic ﬁeld uations are done with respect to this plane of interest, i.e., strength can be calculated by referent plane. Under these conditions (coil represented by P1P2 × P0P1 linear sections and a deﬁned referent plane), a fast magnetic (4) H � . ﬁeld simulation model can be developed. Since a coil is |P1P2 × P0P1| deﬁned as a piecewise linear structure, a magnetic ﬁeld in With respect to the referent plane, only the part of the any given point can be calculated as a vector sum of magnetic ﬁeld directed in the z-axis (Hz in Figure 1) is of magnetic ﬁelds generated by each linear segment of 3D coil interest. .e proposed magnetic ﬁeld modelling method is structure. Each linear segment is deﬁned by two points in 3D implemented in MATLAB. Coil is deﬁned as piecewise space, P1 and P2, as shown in Figure 1. When a current ﬂows linear structure using the array, where each row in array from P1 to P2, the linear segment P1-P2 generates a mag- deﬁnes one segment of the coil. .e ﬁrst three values deﬁne netic ﬁeld. Figure 1 shows magnetic ﬁeld generated by one the position of point P1, the next three values deﬁne the linear segment (P1-P2) in a single point (P0) on referent position of point P2, and the last value deﬁnes the current plane. Magnitude of the magnetic ﬁeld strength at point P0 from P1 to P2. can be calculated using (1). [P1x P1y P1z P2x P2y P2z I12 P2x P2y P2z P3x P3y P3z I23 coil � . (5) P(n − 1)x P(n − 1)y P(n − 1)z Pnx Pny Pnz I(n − 1)n] Length [cm] Wireless Power Transfer 3 For a coil structure deﬁned as an array of linear current segments, a magnetic ﬁeld in each point of a referent plane can be calculated. Figure 2 shows the simulated magnetic ﬁeld for a single-layer rectangular coil (114 × 28 cm) at referent plane placed 30 mm above the coil. 0.5 .e magnetic ﬁeld has a bowl-like shape with pro- nounced spikes at the coil corners. For application in po- -0.5 sition tolerant (in terms of RX-coil) WPT system, such -100 magnetic ﬁeld shape is not suitable. .e rectangular shape of the coil is one of the least favorable candidates for uniform -50 magnetic ﬁeld (with triangular coil shape being the worst), but it is the shape widely used in WPT systems. .is is the main motivation for the development of the rectangular 3D coil structures which can generate uniform magnetic ﬁeld. -50 In this paper, we focused on a two-layer 3D coil structure, due to simpler fabrication compared to a multi- Figure 2: Simulated magnetic ﬁeld distribution generated by layer coil with respect to required precision of manufacture. single-layer rectangular coil (114 × 28 cm). 2.1. Optimization of Coil Structure. Figure 3 shows the generalized structure of two-layer 3D coil. Coil layers can be distinguished by their color; the ﬁrst layer is shown in black cs and the second layer in red. Second coil layer is placed at a 1 depth D relative to the ﬁrst coil layer, and it has narrower width W compared to width of the ﬁrst coil layer W. 3D coil cs structure has a length L with both coil layers folded to a depth D at the coil ends. Grey surface represents the referent plane placed at the distance h from the coil. Coil structure optimization is a two-step procedure. In step one, the goal is to ensure a uniform ﬁeld distribution across a width of the coil, i.e., over cross-section of the referent plane named cs in Figure 3. In step two, the goal is to ensure a uniform ﬁeld distribution across a length of the coil, i.e., over cross-section of the referent plane named cs in Figure 3. Figure 4 shows the proposed optimization framework. W .e maximal allowed ripple value of magnetic ﬁeld (r) and ﬁrst coil layer dimensions (width W and length L) are considered as inputs. .e optimization outputs are optimal Figure 3: Two-layer 3D coil structure. transfer distance (h), second coil layer variables (D , W ), 2 2 and end fold depth D, for which the magnetic ﬁeld strength and uniform surface size are maximized. second coil layer variables (W and D ) result in diﬀerent 2 2 Extensive analysis is conducted, resulting in mathe- shortest distance of the referent plane h. matical model for rectangular coil optimization. Conducted Optimization deals with the following problem: ﬁnding analysis and mathematical model are explained in the next values of the second coil layer variables to generate the most two sections. uniform ﬁeld possible at a shortest distance between TX-coil and a referent plane. However, such optimization problem misses some important aspects. Namely, the short distance 2.2.OptimizationofSecondCoilLayerVariables. To ensure a generally results in high magnetic ﬁeld strength. Certain uniform magnetic ﬁeld distribution over cross-section cs values of the second coil layer variables that ensure uniform (width of the coil), a position of the second coil layer must be ﬁeld at short distances do that at the cost of a lower magnetic optimized. Perfectly uniform magnetic ﬁeld distribution ﬁeld strength. .is would decrease the overall performance cannot be achieved, so one parameter that must be taken of WPT system. .e second important aspect is the per- into account is the maximal ripple of the magnetic ﬁeld. .e centage of the cross-section over which the uniform ﬁeld is second parameter is the distance h of the referent plane from achieved. It is quite easy to get uniform ﬁeld at short distance the coil. For diﬀerent distances h, diﬀerent values of the with high ﬁeld strength, but only over a small fraction of second coil layer variables (W and D ) obtain “most” total coil width. 2 2 uniform ﬁeld distribution. Similarly, for diﬀerent allowed Accordingly, the ﬁrst part of the optimization process is ripple values of a magnetic ﬁeld, diﬀerent values of the ﬁnding values of the second coil layer variables to get Width [cm] Magnetic ﬁeld - normalized 4 Wireless Power Transfer Optimization of second coil layer Optimization of coil depth D variables W , and D Predeﬁned L,W and r 2 2 Predeﬁned L,W and r START START Initial values of Initial value W , D and h of D 2 2 Update values of Update value W , D and h 2 2 of D FoM calculation Save FoM value Save FoM value FoM calculation 1 1 2 2 Choose max. Choose max. All iterations No All iterations No FoM value FoM value 1 2 completed? completed? Yes Yes Optimal values Optimal value of D , W and h of D 2 2 END END Optimal 3D coil structure Figure 4: Optimization framework. uniform ﬁeld on most of the cross-section, but also with a larger than the coil width W, and the ends of the coil are not highest magnetic ﬁeld strength value. .erefore, as a ﬁgure folded down to the depth D. Figure 5 shows results of the of merit (FoM ), we propose the product of average analysis of a magnetic ﬁeld shape for four diﬀerent positions magnetic ﬂux density (calculated only for part of the cross- of second coil layer. Position of the second coil layer is section where magnetic ﬁeld strength is uniform with completely determined by the values of the second coil layer respect to deﬁned ripple value) and percentage of cross- variables, D and W . 2 2 section on which the uniform ﬁeld is achieved. Ripple of the magnetic ﬁeld is used as input parameter in .e ﬁrst step in second coil variables’ optimization is the the optimization process. It is used to determine the size of the FoM analysis. .is is a 4-dimensional problem. FoM is uniform section of magnetic ﬁeld. Uniform section is deﬁned 1 1 aﬀected by the referent plane distance h (ﬁrst dimension), as a section of the coil where the magnetic ﬁeld deviation does maximal allowed ripple of the uniform ﬁeld (second di- not exceed the deﬁned ripple value. .e analysis of the mension), and variables (W , D ) of second coil layer (third magnetic ﬁeld begins at the center of the cross-section and 2 2 and fourth dimension, respectively). Since the referent plane moves to the sides. .e magnetic ﬁeld strength at the center is distance h must be observed with respect to coil width W, used as an initial average ﬁeld strength value. .e two adjacent their ratio (h/W) will be used in FoM analysis. We assume magnetic ﬁeld strengths are compared to the initial value, and the same current magnitude and direction in both coil layers. if they do not deviate from initial value by more than the .e four parameters are varied in the following ranges: deﬁned ripple, they are considered to be in the uniform h/W ratio ranges from 1% to 20% (20 steps), ripple value section of the magnetic ﬁeld. New average ﬁeld strength of ranges from 1% to 20% (6 steps), width of the second coil uniform section is then calculated. .e next two adjacent ﬁeld layer W ranges from 0 to the coil width W (50 steps), and values are then evaluated using the same methodology. At one point, the ﬁeld values that deviate by more than the deﬁned depth of the second coil layer D ranges from 0 to half of the coil width W/2 (50 steps). ripple value will be reached. .ese ﬁeld values and all the .e following methodology was used: for ﬁxed values of remaining ones are not a part of the uniform magnetic ﬁeld h/W ratio and ripple, magnetic ﬁeld strength was calculated section. .is can be seen in Figures 5(a) and 5(b). .e section for each possible value of the second coil layer variables. of the magnetic ﬁeld shape that is considered uniform (with Namely, magnetic ﬁeld strength for each value of D and W deﬁned ripple) corresponds to the top section of the square 2 2 was calculated over the cs cross-section of the coil, and waveform (Figures 5(a) and 5(b)). magnetic ﬁeld shape is analyzed. In this step of the coil In Figures 5(c) and 5(d), diﬀerent shapes of the magnetic optimization, the coil length L is set to be at least 10 times ﬁeld that correspond to diﬀerent positions of the second coil Wireless Power Transfer 5 -6 -6 ×10 ×10 8 8 6 6 4 4 2 2 0 0 W/2 0 W/2 W/2 0 W/2 Cross-section cs width relative to W Cross-section cs width relative to W 1 1 (a) (b) -6 -6 ×10 ×10 8 8 6 6 4 4 2 2 0 0 W/2 W/2 W/2 0 W/2 Cross-section cs width relative to W Cross-section cs width relative to W 1 1 (c) (d) Figure 5: Examples of magnetic ﬁeld shape analysis: (a) ripple � 1%, h/W � 0.08, D /W � 0.18, W /W � 0.7; (b) ripple � 1%, h/W � 0.08, D / 2 2 2 W � 0.12, W /W � 0.6; (c) ripple � 1%, h/W � 0.08, D /W � 0.24, W /W � 0.7; (d) ripple � 1%, h/W � 0.08, D /W � 0.1, W /W � 0.7. 2 2 2 2 2 layer are shown. Such magnetic ﬁeld shapes are not con- Figure 7. Figure 7 shows maximal FoM values for all sidered uniform because of the two peaks at the sides. While evaluated combinations of h/W ratio and ripple. the center part of the magnetic ﬁeld has uniform ﬁeld It can be seen that, for a higher ripple value, a higher distribution (Figure 5(c)), the overall magnetic ﬁeld shape is FoM can be achieved. For each ripple value, the maximal considered nonuniform. .e parts of the coil cross-section FoM value is achieved at diﬀerent h/W ratio (diﬀerent where the magnetic ﬁeld strength exceeds the maximal distance between the referent plane and the coil). For higher allowed ﬁeld strength (average strength + ripple value) can values of h/W ratio, large uniform section can be easily potentially be harmful for receiver circuits in WPT system, achieved, but the average magnetic ﬁeld strength is lower. which are designed for uniform magnetic ﬁeld. For that For lower h/W ratio values, we have higher average magnetic reason, Figures 5(c) and 5(d) have no square waveform ﬁeld values, but narrower uniform sections. .e maximal representing the uniform section of the magnetic ﬁeld. FoM is achieved at optimal distance from the coil (optimal To summarize, there are two possible outcomes of h/W ratio) with large uniform section and high average magnetic ﬁeld shape analysis. .e uniform section of the magnetic ﬁeld strength. .ese optimal h/W ratios are shown magnetic ﬁeld is identiﬁed, or the magnetic ﬁeld is con- with blue markers in Figure 8. sidered nonuniform. For magnetic ﬁeld shapes that have a For a given ripple value and known coil width W, op- uniform section, the FoM is calculated: timal distance h of the referent plane can be calculated as uniform section width h � W[0.0191 − 0.013 · ln(r)]. (7) (6) FoM � B · , 1 avg coil width Once the distance of the referent plane is selected, the where B is an average value of magnetic ﬂux density avg position of second coil layer can be determined. Figure 9 calculated only for the uniform section of magnetic ﬁeld. shows the positions of second coil layer that achieve max- .e same methodology is used to evaluate the magnetic imal FoM , for diﬀerent ripple values with referent plane at ﬁeld shapes for each possible position of the second coil optimal distance. layer. As a result, we get FoM values for each position of the For the lowest evaluated ripple values (0.5%–2%), the second coil layer. Figure 6 shows the FoM values for ﬁve optimal width of the second coil layer, W , is 70% of the ﬁrst diﬀerent h/W ratios with ﬁxed ripple value. coil layer width, W. For larger ripple values, the second coil For low h/W ratio value, majority of positions of second layer width increases. .e depth of second coil layer, D , coil layer result in nonuniform ﬁeld (dark blue areas). With shows direct correlation with the ripple value (Figure 10). higher h/W ratio values, more positions of second coil layer For a given ripple value and known coil width W, with generate uniform magnetic ﬁeld. For each ﬁxed combination referent plane placed at optimal distance, the depth of of h/W ratio and ripple value, there is an optimal position of second coil layer can be calculated as the second coil layer which results in maximal FoM value. D � W[0.041 − 0.03 · ln(r)]. (8) .is maximal FoM value is represented as one dot in Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] 6 Wireless Power Transfer -6 -6 ×10 ×10 0 6 0 6 4 4 2 2 W/2 0 W/2 0 W/2 0 W/2 W/2 0 W/2 W relative to W W relative to W 2 2 (a) (b) -6 -6 ×10 ×10 0 6 0 6 4 4 2 2 W/2 0 W/2 0 W/2 0 W/2 W/2 0 W/2 W relative to W W relative to W 2 2 (c) (d) -6 ×10 W/2 W/2 0 W/2 W relative to W (e) Figure 6: FoM values for diﬀerent combinations of h/W ratio and ripple value of 2%: (a) ripple � 2%, h/W � 0.05; (b) ripple � 2%, h/ W � 0.07; (c) ripple � 2%, h/W � 0.10; (d) ripple � 2%, h/W � 0.14; (e) ripple � 2%, h/W � 0.20. Figure 11 shows resulting magnetic ﬁeld with optimized ﬁeld increase at the coil ends, as shown in Figure 12(a). .us, cs cross-section, for 0.5% ripple. surface enclosed by W and L of the coil has a minor part of uniform magnetic ﬁeld, as shown in Figure 13(a). In this stage of optimization, modiﬁed ﬁgure of merit is adopted: 2.3. Optimization of Coil Depth D. To achieve uniform magnetic ﬁeld across cs (Figure 3), the narrower sides of the uniform section surface (9) FoM � B · . coil structure are folded downwards to the depth D. .e goal 2 avg coil surface is to get magnetic ﬁeld shape from cross-section cs across It is not practical to try to optimize cs cross-section for the length of the coil L. If the coil ends are not folded down, 0% ripple, but using a ripple value 10 times lower than that at the ends of the coil there is a signiﬁcant increase in the used during cs optimization gives good enough result magnetic ﬁeld strength (Figure 11). (Figure 12(b)). .e second part of the optimization process is deter- Due to high D/W ratio (0.43), the uniform section of the mining the depth, D, to which the sides have to be folded magnetic ﬁeld at the coil end is quite irregular (Figure 13(b)). down. .e methodology to achieve this is the same as in the Such shape of the uniform ﬁeld was obtained by optimizing ﬁrst part of the optimization process, but with one signif- cs for 5% ripple and cs for 0.5% ripple. icant diﬀerence. .e magnetic ﬁeld shape throughout the 1 2 Alternative approach is to ﬁrst optimize cs for 0.5% coil length should be consistent, meaning that the magnetic 1 ripple and then optimize cs for 5% ripple. .e resulting ﬁeld strength should not deviate across cs cross-section. If magnetic ﬁeld is given in Figure 12(c). Uniform surface is the same ripple value as in cs optimization would be allowed 0.14% larger, and FoM value is 10% lower, but the shape of during cs optimization, the result would have unwanted D relative to W D relative to W 2 2 D relative to W D relative to W D relative to W 2 2 Length [cm] Wireless Power Transfer 7 8 0.25 0.2 0.15 y = -0.03ln (x) + 0.041 0.1 0.05 0 0.05 0.1 0.15 0.2 Ripple Figure 10: Optimal depth of second coil layer (D) for diﬀerent ripple values: simulated results are denoted by blue markers, and ﬁtted mathematical model is represented by solid line. 0 0.05 0.1 0.15 0.2 h/W ratio 20 % 2 % 10 % 1 % 5 % 0.5 % Figure 7: FoM analysis results. 0.5 0.1 -0.5 0.08 -100 0.06 y = -0.013ln (x) + 0.0191 -50 0.04 0.02 -50 0 0.05 0.1 0.15 0.2 Figure 11: Simulated magnetic ﬁeld distribution generated by two- Ripple layer coil with optimized cs . Figure 8: Optimal h/W ratios for diﬀerent ripple values: simulated results are denoted by blue markers, and ﬁtted mathematical model optimized for 2.5% ripple. .e uniform surface is represented by solid line. (Figure 13(d)) is drawn for ripple value of 5%. It results in the highest FoM value and largest uniform surface. .is approach is chosen as optimal. .e depth of the end fold D is a function of the ripple 20% 20% 10% 10% 5% value (r) and the length to width ratio (L/W) of the coil. 5% 2% 2% 1% 1% Figure 14 shows the end fold depths for diﬀerent ripple 20 0.5% 0.5% values and L/W ratios. .e fold depth increases for coils with 30 larger L/W ratio and with lower allowed ripple value. 50 40 30 20 10 0 10 20 30 40 50 Results of cs optimization are given as markers, and W relative to W [%] solid lines represent mathematical model, (9), which can be used to calculate required folding depth. Figure 9: Positions of second coil layer that achieve maximal FoM , for diﬀerent ripple values with referent plane placed at √� − 3.25 r (L/W) √� D � W · 􏼐1 − e 􏼑. (10) optimal distance. 20.4 · r .e proposed optimization method is developed for rectangular coil where the percentage of uniform surface the surface with uniform magnetic ﬁeld follows the rect- increases with higher L/W ratio of the coil (Figure 15). angular shape signiﬁcantly better, as shown in Figure 13(c). .ere is a trade-oﬀ between FoM value and the shape of the surface with uniform magnetic ﬁeld. .e best results are 3. Measurements obtained when both the cs and the cs optimizations are 1 2 To evaluate the developed optimization method, magnetic done for ripple value equal to one-half of the desired ripple. Figure 12(d) shows the magnetic ﬁeld when cs and cs are ﬁeld measurements are performed on fabricated coils 1 2 Width [cm] D relative to W [%] h/W ratio FoM [μT] D /W ratio Magnetic ﬁeld - normalized 8 Wireless Power Transfer -6[T] -6[T] ×10 ×10 10 10 5 5 0 0 Coil length L Coil length L (a) (b) -6[T] -6[T] ×10 ×10 10 10 5 5 0 0 Coil length L Coil length L (c) (d) Figure 12: Magnetic ﬁeld shape (top view) for diﬀerent ripple values: (a) cs 5%, cs 5% (D/W � 0.19); (b) cs 5%, cs 0.5% (D/W � 0.43); (c) 1 2 1 2 cs 0.5%, cs 5% (D/W � 0.19); (d) cs 2.5%, cs 2.5% (D/W � 0.26). 1 2 1 2 Coil length L Coil length L (a) (b) Coil length L Coil length L (c) (d) Figure 13: Uniform ﬁeld section (top view) for diﬀerent combinations of cs and cs ripple values: (a) uniform magnetic ﬁeld section 1 2 (49.81%) for magnetic ﬁeld shape from Figure 12(a), FoM � 0.0015 T; (b) uniform magnetic ﬁeld section (75.78%) for magnetic ﬁeld shape from Figure 12(b), FoM � 0.0021 T; (c) uniform magnetic ﬁeld section (75.92%) for magnetic ﬁeld shape from Figure 12(c), FoM � 0.0019 T; (d) uniform magnetic ﬁeld section (79.85%) for magnetic ﬁeld shape from Figure 12(d), FoM � 0.0021 T. 2 2 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0421 68 102 021 4 68 102 L (W) L/W ratio 0.5% ripple 2% ripple 1% ripple 4% ripple 1% ripple 5% ripple 2% ripple 10% ripple Figure 14: Required end fold depth (D) for diﬀerent ripple values Figure 15: Percentage of uniform ﬁeld surface for diﬀerent L/W and L/W ratios. ratios. D (W) Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Percentage of uniform ﬁeld surface [%] Wireless Power Transfer 9 Figure 16: Fabricated proposed TX-coil, bottom view. Figure 17: Fabricated conventional TX-coil, bottom view. Figure 18: Measuring setup. (proposed and conventional). .e ﬁrst coil layer size is set as spectral analyzer, PBS-H3 probe (25 mm magnetic ﬁeld test L � 114 cm, W � 28 cm. .e position of second coil layer is with 50 Ohms SMB m socket), and SMA cable. In performed calculated using proposed optimization method for ripple experiments, fabricated TX-coils were energized by Agilent value of 1%. Optimizations for cross-sections cs and cs are 33250A signal generator at operating frequency of 150 kHz. 1 2 done for 0.5% ripple (one-half of the desired ripple). Op- Magnetic ﬁeld strength of both fabricated TX-coils is timal height of the referent plane equals (7): h � 2.46 cm. measured at 900 points in a receiving plane 30 mm above the Calculated variables of the second coil layer position are coil. Because it is measured by a PBS-H3 probe connected to W �19.6 cm, D � 5.6 cm. Calculated end fold depth is the SMA input of a Spectran NF-5035 instrument, the 2 2 D � 11.8 cm. .e fabricated proposed TX-coil prototype is analyzer provides highly sensitive measurement of an ex- shown in Figure 16. Actual placement of the coil layers ternal alternating ﬁeld up to 0.2 V max. .us, the spectrum diﬀers a bit from the calculated values, mainly due to the analyzer returns voltage values that are proportional to the limited precision of fabrication (W magnetic ﬁeld strength values. Hold mode is selected to � 20 cm, D � 6 cm, 2 2 D � 12 cm). .e wire that forms coil layers is placed in the measure the ﬁeld strength values. Measuring setup is shown white wire casing. Moreover, proposed TX-coil prototype is in Figure 18, and measurement results are given in Figure 19, constructed using plywood framework to hold wire casings along with the simulation results. and ensure ﬂat surface above in order to carry out magnetic Simulation results of the proposed folded 3D coil ﬁeld measurements in the same plane. Each coil layer structure are shown in Figures 19(a) and 19(b). Measure- consists of 4 windings of Litz wire, resulting in inductance of ments of magnetic ﬁeld strength distribution at receiving 103μH. plane for both fabricated TX-coils (Figures 19(c) and 19(d)) Conventional, single-layer rectangular coil (114 × 28 cm) conﬁrmed that optimal and proposed folded 3D TX-coil structure provides signiﬁcantly larger uniform magnetic is also fabricated using Litz wire placed in the white wire casings installed at one side of the ﬂat plywood board ﬁeld strength section in comparison to conventional TX-coil (Figure 17). Coil is made up of 6 windings, which results in structure. From measured magnetic ﬁeld shape inductance of 116μH. (Figures 19(c) and 19(d)), it can be seen that one side of the .e magnetic ﬁeld strength of these coils was measured coil has slightly higher ﬁeld values than the opposite side. at a temperature of 26 C and humidity of 50%. Field strength .is is due to limited precision of wire windings placement measurements are performed in the near ﬁeld zone with in the wire casing. Aside from that, measurement and measuring equipment consisting of a Spectran NF-5035 simulation results match to a high degree. Length [cm] 10 Wireless Power Transfer 0.75 0.5 0.25 0.5 0 Coil length L -0.5 -100 -50 0 50 100 -50 (a) (b) 1 1 0.75 0.75 0.5 0.5 0.25 0.25 0 0 Coil length L Coil length L (c) (d) Figure 19: Simulation and measurement results: (a) simulated magnetic ﬁeld distribution of optimized folded 3D coil structure; (b) normalized simulation results, top view; (c) normalized measurement results, top view (optimized folded 3D coil structure); (d) normalized measurement results, top view (conventional coil structure). Table 1: Comparison of various optimized TX-coils’ characteristics. Ref. Structure TX-coil (cm) r (%) h (mm) Uniform section (%) [1] 3D rectangular 22 ×18 × 2 20 0.5 ∼32 [6] Planar square 20 × 20 20 150 ∼48 [10] Planar square 20 × 20 20 1 ∼36 [18] Planar square 20 × 20 20 50 ∼51.8 [20] Planar square 80 × 80 9.6 10 ∼42.3 .is paper 3D rectangular 114 × 28 ×12 10 30 ∼55.3 Measured characteristics of diﬀerent TX-coil designs optimization method are successfully carried out. Both TX- coils, conventional and proposed, are fabricated to carry out which generate uniform magnetic ﬁeld strength distribution at receiving plane are listed in Table 1. In comparison with magnetic ﬁeld measurements which conﬁrmed that pro- other TX-coil characteristics from Table 1, the proposed coil posed coil, unlike conventional coil, generates uniform generates improved magnetic ﬁeld strength distribution magnetic ﬁeld strength distribution at receiving plane. with respect to uniform section of receiving plane. Further Furthermore, measured results show larger uniform section development of the proposed TX-coil will be aimed at re- in comparison to other optimized TX-coil structures. ducing coil depth, D, which will result in lower proﬁle of TX- Depending on the maximal ripple and proportions of the coil. coil, optimization method results in 3D coil structure that generates improved uniform magnetic ﬁeld strength dis- tribution across 50% to 90% of the receiving plane. 4. Conclusion Data Availability A novel 3D TX-coil structure with improved uniform magnetic ﬁeld distribution is proposed. Optimization .e data used to support the ﬁndings of this study can be methodology is presented and optimizing method is de- available upon request. veloped for rectangular 3D coil structure. Optimization results in coil structure that has maximized average magnetic Conflicts of Interest ﬁeld strength and uniform surface section. Computer simulations and experimental veriﬁcation of the .e authors declare that they have no conﬂicts of interest. Width [cm] Coil width W Magnetic field - normalized Coil width W Coil width W Wireless Power Transfer 11 Electrical Machines and Systems (ICEMS), pp. 1030–1034, Acknowledgments Pattaya, .ailand, October 2015. [14] T.-D. Yeo, D.-H. Kim, S. C. Chae, S.-T. Khang, and J.-W. Yu, .is work has been supported in part by Croatian Science “Design of free-positioning wireless power charging system Foundation under the project “Eﬃcient Wireless Power for aaa rechargeable battery,” in Proceedings of the 2016 46th Supply” (UIP-2017-05-5373). European Microwave Conference (EuMC), pp. 759–762, London, UK, October 2016. References [15] E. Elkhouly and S. Yang, “Transmitter coil design for resonant wireless power transfer,” in Proceedings of the 2016 IEEE PELS [1] W.-S. Lee, H. L. Lee, K.-S. Oh, and J.-W. 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J. Casanova, Z. N. Low, J. Lin, and R. Tseng, “Transmitting coil achieving uniform magnetic ﬁeld distribution for planar wireless power transfer system,” in Proceedings of the 2009 IEEE Radio and Wireless Symposium, pp. 530–533, San Diego, CA, USA, January 2009. [11] D. Yinliang, S. Yuanmao, and G. Yougang, “Design of coil structure achieving uniform magnetic ﬁeld distribution for wireless charging platform,” in Proceedings of the 2011 4th International Conference on Power Electronics Systems and Applications, pp. 1–5, Hong Kong, China, June 2011. [12] L. Shen, W. Tang, H. Xiang, and W. Zhuang, “Uniform magnetic ﬁeld by changing the current distribution on the planar coil for displacement-insensitive wireless power transfer/near ﬁeld communication,” Microwave and Optical Technology Letters, vol. 57, no. 2, pp. 424–427, 2014. [13] Y. Zhang, T. Lu, Z. Zhao, F. He, K. Chen, and L. Yuan, “Quasi- uniform magnetic ﬁeld generated by multiple transmitters of magnetically-coupled resonant wireless power transfer,” in Proceedings of the 2015 18th International Conference on http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Wireless Power Transfer Hindawi Publishing Corporation http://www.deepdyve.com/lp/hindawi-publishing-corporation/optimization-of-a-two-layer-3d-coil-structure-with-uniform-magnetic-Hb3fT0sdSy

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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2021 Davor Vinko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
eISSN: 2052-8418
DOI: 10.1155/2021/6303628
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Abstract

Hindawi Wireless Power Transfer Volume 2021, Article ID 6303628, 11 pages https://doi.org/10.1155/2021/6303628 Research Article Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field Davor Vinko , Domagoj Bilandzˇija , and Vanja Mandric´ Radivojevic´ Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, Josip Juraj Strossmayer University of Osijek, Osijek 31000, Croatia Correspondence should be addressed to Domagoj Bilandzija; domagoj.bilandzija@ferit.hr Received 11 April 2021; Revised 25 June 2021; Accepted 28 September 2021; Published 14 October 2021 Academic Editor: Hao Gao Copyright © 2021 Davor Vinko et al. .is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conventional magnetically coupled resonant wireless power transfer systems are faced with resonant frequency splitting phenomena and impedance mismatch when a receiving coil is placed at misaligned position. .ese problems can be avoided by using uniform magnetic ﬁeld distribution at receiving plane. In this paper, a novel 3D transmitting coil structure with improved uniform magnetic ﬁeld distribution is proposed based on a developed optimization method. .e goal is to maximize the average magnetic ﬁeld strength and uniform magnetic ﬁeld section of the receiving plane. Hence, ﬁgures of merit (FoM and FoM ) are 1 2 introduced and deﬁned as product of average magnetic ﬁeld strength and length or surface along which uniform magnetic ﬁeld is generated, respectively. .e validity of the optimization method is veriﬁed through laboratory measurements performed on the fabricated coils driven by signal generator at operating frequency of 150 kHz. Depending on the allowed ripple value and predeﬁned coil proportions, the proposed transmitting coil structure gives the uniform magnetic ﬁeld distribution across 50% to 90% of the receiving plane. ﬁeld strength distribution at the receiving plane will provide 1. Introduction stable resonant frequency regardless of RX-coil position due Numerous wireless power transfer (WPT) systems operate to steady value of magnetic coupling factor k between TX- through nonuniform magnetic ﬁeld strength distribution at and RX-coil. Hence, uniform magnetic ﬁeld strength dis- receiving plane. Magnetic ﬁeld nonuniformity in magneti- tribution at a receiving plane results in a WPT system that cally coupled resonant (MCR) WPT system causes resonant does not require frequency tracking and automatic im- frequency splitting phenomena and impedance mismatch- pedance matching [8]. Uniform magnetic ﬁeld strength ing when receiving coil (RX-coil) is not properly aligned distribution also provides uniform and simultaneous power with transmitting coil (TX-coil) [1, 2]. Namely, the eﬃciency delivery to multiple RX-coils, i.e., loads. Furthermore, of WPT system is signiﬁcantly impaired due to frequency uniform magnetic ﬁeld strength distribution at a receiving splitting phenomena or impedance mismatching [1, 3]. plane ensures nondegraded wireless power transfer eﬃ- Consequently, to achieve eﬃcient energy transfer along with ciency regardless of RX-coil position within receiving plane greater degree of freedom, in terms of RX-coil position, such [1]. WPT systems require frequency tracking [3] and automatic .e proposed TX-coil structure consists of two layers impedance matching [3, 4]. In order to create uniform and is based on optimization method which is validated by magnetic ﬁeld strength distribution at a receiving plane, simulation and measurement results. Since the proposed various TX-coil designs are developed [1, 5–21]. TX-coil structure is characterized by folded sides, it is more In this paper, a novel 3D structure of TX-coil is proposed suitable for large sized WPT systems, for instance, instal- to achieve uniform magnetic ﬁeld distribution at the given lation under oﬃce desk. Computer simulations of TX-coils receiving plane (114 × 28 cm). Presence of uniform magnetic with diﬀerent winding arrangement (coil layers relative 2 Wireless Power Transfer spacing), but with the same outer dimensions (114 × 28 cm), z were run, and magnetic ﬁeld distribution at the given re- z ceiving plane which is above the TX-coil was observed. P 0 According to the simulation results, experimental TX-coils α 2 are made out of Litz wire instead of PCB realization which is x not appropriate for large receiving plane. Both computer simulation and measurement results veriﬁed that uniform magnetic ﬁeld distribution at considerable surface of the P2 P1 receiving plane is produced by the novel 3D TX-coil structure. With the approximately 100 W of output power at receiving side of a WPT system, application of such TX-coil Figure 1: Magnetic ﬁeld in the point P0 generated by the linear segment P1-P2. enables simultaneous wireless charging of monitors, smartphones, laptops, etc. 2. Model Explanation |H| � sin α − sin α , (1) 1 2 4πd To maintain stable transfer eﬃciency and power delivery to .e shortest distance between P0 and the line which freely moving RX-coil(s), TX-coil in WPT system should passes through P1 and P2 equals generate uniform magnetic ﬁeld [18, 21]. Such ﬁeld distri- |P1P2 × P0P1| bution is diﬃcult to achieve with “standard” ﬂat wound coils. (2) d � . When designing a 3D coil structure, a fast method for |P1P2| magnetic ﬁeld evaluation is a signiﬁcant advantage. A .e angles α1 and α2 are calculated as follows: common approach for magnetic ﬁeld evaluation is using dedicated software (e.g., Ansys Maxwell, FEMM, MATLAB, P1P2 · P0P1 α � 90 − arccos􏼠 􏼡, etc.) which executes a numerical analysis. Such approach is 1 |P1P2| · |P0P1| very time consuming, both in preparation (model pre- (3) processing) and in simulation itself. P1P2 · P0P2 If the 3D TX-coil structure can be represented as a α � 90 − arccos􏼠 􏼡. |P1P2| · |P0P2| number of linear sections, the magnetic ﬁeld simulations can be signiﬁcantly simpliﬁed. Uniformity of magnetic ﬁeld of For coil current I in linear segment ﬂowing from P1 to the TX-coil is evaluated with respect to the plane of interest. P2, the direction of the magnetic ﬁeld strength H at point P0 In MCR-WPT, where multiple loads can be wirelessly is perpendicular to the plane deﬁned by points P0, P1, and P2 powered, a ﬂat surface (e.g., oﬃce desk) should have uniform (Figure 1). Equation (1) gives only the magnitude of the magnetic ﬁeld distribution. .erefore, magnetic ﬁeld eval- magnetic ﬁeld strength, but the direction of magnetic ﬁeld uations are done with respect to this plane of interest, i.e., strength can be calculated by referent plane. Under these conditions (coil represented by P1P2 × P0P1 linear sections and a deﬁned referent plane), a fast magnetic (4) H � . ﬁeld simulation model can be developed. Since a coil is |P1P2 × P0P1| deﬁned as a piecewise linear structure, a magnetic ﬁeld in With respect to the referent plane, only the part of the any given point can be calculated as a vector sum of magnetic ﬁeld directed in the z-axis (Hz in Figure 1) is of magnetic ﬁelds generated by each linear segment of 3D coil interest. .e proposed magnetic ﬁeld modelling method is structure. Each linear segment is deﬁned by two points in 3D implemented in MATLAB. Coil is deﬁned as piecewise space, P1 and P2, as shown in Figure 1. When a current ﬂows linear structure using the array, where each row in array from P1 to P2, the linear segment P1-P2 generates a mag- deﬁnes one segment of the coil. .e ﬁrst three values deﬁne netic ﬁeld. Figure 1 shows magnetic ﬁeld generated by one the position of point P1, the next three values deﬁne the linear segment (P1-P2) in a single point (P0) on referent position of point P2, and the last value deﬁnes the current plane. Magnitude of the magnetic ﬁeld strength at point P0 from P1 to P2. can be calculated using (1). [P1x P1y P1z P2x P2y P2z I12 P2x P2y P2z P3x P3y P3z I23 coil � . (5) P(n − 1)x P(n − 1)y P(n − 1)z Pnx Pny Pnz I(n − 1)n] Length [cm] Wireless Power Transfer 3 For a coil structure deﬁned as an array of linear current segments, a magnetic ﬁeld in each point of a referent plane can be calculated. Figure 2 shows the simulated magnetic ﬁeld for a single-layer rectangular coil (114 × 28 cm) at referent plane placed 30 mm above the coil. 0.5 .e magnetic ﬁeld has a bowl-like shape with pro- nounced spikes at the coil corners. For application in po- -0.5 sition tolerant (in terms of RX-coil) WPT system, such -100 magnetic ﬁeld shape is not suitable. .e rectangular shape of the coil is one of the least favorable candidates for uniform -50 magnetic ﬁeld (with triangular coil shape being the worst), but it is the shape widely used in WPT systems. .is is the main motivation for the development of the rectangular 3D coil structures which can generate uniform magnetic ﬁeld. -50 In this paper, we focused on a two-layer 3D coil structure, due to simpler fabrication compared to a multi- Figure 2: Simulated magnetic ﬁeld distribution generated by layer coil with respect to required precision of manufacture. single-layer rectangular coil (114 × 28 cm). 2.1. Optimization of Coil Structure. Figure 3 shows the generalized structure of two-layer 3D coil. Coil layers can be distinguished by their color; the ﬁrst layer is shown in black cs and the second layer in red. Second coil layer is placed at a 1 depth D relative to the ﬁrst coil layer, and it has narrower width W compared to width of the ﬁrst coil layer W. 3D coil cs structure has a length L with both coil layers folded to a depth D at the coil ends. Grey surface represents the referent plane placed at the distance h from the coil. Coil structure optimization is a two-step procedure. In step one, the goal is to ensure a uniform ﬁeld distribution across a width of the coil, i.e., over cross-section of the referent plane named cs in Figure 3. In step two, the goal is to ensure a uniform ﬁeld distribution across a length of the coil, i.e., over cross-section of the referent plane named cs in Figure 3. Figure 4 shows the proposed optimization framework. W .e maximal allowed ripple value of magnetic ﬁeld (r) and ﬁrst coil layer dimensions (width W and length L) are considered as inputs. .e optimization outputs are optimal Figure 3: Two-layer 3D coil structure. transfer distance (h), second coil layer variables (D , W ), 2 2 and end fold depth D, for which the magnetic ﬁeld strength and uniform surface size are maximized. second coil layer variables (W and D ) result in diﬀerent 2 2 Extensive analysis is conducted, resulting in mathe- shortest distance of the referent plane h. matical model for rectangular coil optimization. Conducted Optimization deals with the following problem: ﬁnding analysis and mathematical model are explained in the next values of the second coil layer variables to generate the most two sections. uniform ﬁeld possible at a shortest distance between TX-coil and a referent plane. However, such optimization problem misses some important aspects. Namely, the short distance 2.2.OptimizationofSecondCoilLayerVariables. To ensure a generally results in high magnetic ﬁeld strength. Certain uniform magnetic ﬁeld distribution over cross-section cs values of the second coil layer variables that ensure uniform (width of the coil), a position of the second coil layer must be ﬁeld at short distances do that at the cost of a lower magnetic optimized. Perfectly uniform magnetic ﬁeld distribution ﬁeld strength. .is would decrease the overall performance cannot be achieved, so one parameter that must be taken of WPT system. .e second important aspect is the per- into account is the maximal ripple of the magnetic ﬁeld. .e centage of the cross-section over which the uniform ﬁeld is second parameter is the distance h of the referent plane from achieved. It is quite easy to get uniform ﬁeld at short distance the coil. For diﬀerent distances h, diﬀerent values of the with high ﬁeld strength, but only over a small fraction of second coil layer variables (W and D ) obtain “most” total coil width. 2 2 uniform ﬁeld distribution. Similarly, for diﬀerent allowed Accordingly, the ﬁrst part of the optimization process is ripple values of a magnetic ﬁeld, diﬀerent values of the ﬁnding values of the second coil layer variables to get Width [cm] Magnetic ﬁeld - normalized 4 Wireless Power Transfer Optimization of second coil layer Optimization of coil depth D variables W , and D Predeﬁned L,W and r 2 2 Predeﬁned L,W and r START START Initial values of Initial value W , D and h of D 2 2 Update values of Update value W , D and h 2 2 of D FoM calculation Save FoM value Save FoM value FoM calculation 1 1 2 2 Choose max. Choose max. All iterations No All iterations No FoM value FoM value 1 2 completed? completed? Yes Yes Optimal values Optimal value of D , W and h of D 2 2 END END Optimal 3D coil structure Figure 4: Optimization framework. uniform ﬁeld on most of the cross-section, but also with a larger than the coil width W, and the ends of the coil are not highest magnetic ﬁeld strength value. .erefore, as a ﬁgure folded down to the depth D. Figure 5 shows results of the of merit (FoM ), we propose the product of average analysis of a magnetic ﬁeld shape for four diﬀerent positions magnetic ﬂux density (calculated only for part of the cross- of second coil layer. Position of the second coil layer is section where magnetic ﬁeld strength is uniform with completely determined by the values of the second coil layer respect to deﬁned ripple value) and percentage of cross- variables, D and W . 2 2 section on which the uniform ﬁeld is achieved. Ripple of the magnetic ﬁeld is used as input parameter in .e ﬁrst step in second coil variables’ optimization is the the optimization process. It is used to determine the size of the FoM analysis. .is is a 4-dimensional problem. FoM is uniform section of magnetic ﬁeld. Uniform section is deﬁned 1 1 aﬀected by the referent plane distance h (ﬁrst dimension), as a section of the coil where the magnetic ﬁeld deviation does maximal allowed ripple of the uniform ﬁeld (second di- not exceed the deﬁned ripple value. .e analysis of the mension), and variables (W , D ) of second coil layer (third magnetic ﬁeld begins at the center of the cross-section and 2 2 and fourth dimension, respectively). Since the referent plane moves to the sides. .e magnetic ﬁeld strength at the center is distance h must be observed with respect to coil width W, used as an initial average ﬁeld strength value. .e two adjacent their ratio (h/W) will be used in FoM analysis. We assume magnetic ﬁeld strengths are compared to the initial value, and the same current magnitude and direction in both coil layers. if they do not deviate from initial value by more than the .e four parameters are varied in the following ranges: deﬁned ripple, they are considered to be in the uniform h/W ratio ranges from 1% to 20% (20 steps), ripple value section of the magnetic ﬁeld. New average ﬁeld strength of ranges from 1% to 20% (6 steps), width of the second coil uniform section is then calculated. .e next two adjacent ﬁeld layer W ranges from 0 to the coil width W (50 steps), and values are then evaluated using the same methodology. At one point, the ﬁeld values that deviate by more than the deﬁned depth of the second coil layer D ranges from 0 to half of the coil width W/2 (50 steps). ripple value will be reached. .ese ﬁeld values and all the .e following methodology was used: for ﬁxed values of remaining ones are not a part of the uniform magnetic ﬁeld h/W ratio and ripple, magnetic ﬁeld strength was calculated section. .is can be seen in Figures 5(a) and 5(b). .e section for each possible value of the second coil layer variables. of the magnetic ﬁeld shape that is considered uniform (with Namely, magnetic ﬁeld strength for each value of D and W deﬁned ripple) corresponds to the top section of the square 2 2 was calculated over the cs cross-section of the coil, and waveform (Figures 5(a) and 5(b)). magnetic ﬁeld shape is analyzed. In this step of the coil In Figures 5(c) and 5(d), diﬀerent shapes of the magnetic optimization, the coil length L is set to be at least 10 times ﬁeld that correspond to diﬀerent positions of the second coil Wireless Power Transfer 5 -6 -6 ×10 ×10 8 8 6 6 4 4 2 2 0 0 W/2 0 W/2 W/2 0 W/2 Cross-section cs width relative to W Cross-section cs width relative to W 1 1 (a) (b) -6 -6 ×10 ×10 8 8 6 6 4 4 2 2 0 0 W/2 W/2 W/2 0 W/2 Cross-section cs width relative to W Cross-section cs width relative to W 1 1 (c) (d) Figure 5: Examples of magnetic ﬁeld shape analysis: (a) ripple � 1%, h/W � 0.08, D /W � 0.18, W /W � 0.7; (b) ripple � 1%, h/W � 0.08, D / 2 2 2 W � 0.12, W /W � 0.6; (c) ripple � 1%, h/W � 0.08, D /W � 0.24, W /W � 0.7; (d) ripple � 1%, h/W � 0.08, D /W � 0.1, W /W � 0.7. 2 2 2 2 2 layer are shown. Such magnetic ﬁeld shapes are not con- Figure 7. Figure 7 shows maximal FoM values for all sidered uniform because of the two peaks at the sides. While evaluated combinations of h/W ratio and ripple. the center part of the magnetic ﬁeld has uniform ﬁeld It can be seen that, for a higher ripple value, a higher distribution (Figure 5(c)), the overall magnetic ﬁeld shape is FoM can be achieved. For each ripple value, the maximal considered nonuniform. .e parts of the coil cross-section FoM value is achieved at diﬀerent h/W ratio (diﬀerent where the magnetic ﬁeld strength exceeds the maximal distance between the referent plane and the coil). For higher allowed ﬁeld strength (average strength + ripple value) can values of h/W ratio, large uniform section can be easily potentially be harmful for receiver circuits in WPT system, achieved, but the average magnetic ﬁeld strength is lower. which are designed for uniform magnetic ﬁeld. For that For lower h/W ratio values, we have higher average magnetic reason, Figures 5(c) and 5(d) have no square waveform ﬁeld values, but narrower uniform sections. .e maximal representing the uniform section of the magnetic ﬁeld. FoM is achieved at optimal distance from the coil (optimal To summarize, there are two possible outcomes of h/W ratio) with large uniform section and high average magnetic ﬁeld shape analysis. .e uniform section of the magnetic ﬁeld strength. .ese optimal h/W ratios are shown magnetic ﬁeld is identiﬁed, or the magnetic ﬁeld is con- with blue markers in Figure 8. sidered nonuniform. For magnetic ﬁeld shapes that have a For a given ripple value and known coil width W, op- uniform section, the FoM is calculated: timal distance h of the referent plane can be calculated as uniform section width h � W[0.0191 − 0.013 · ln(r)]. (7) (6) FoM � B · , 1 avg coil width Once the distance of the referent plane is selected, the where B is an average value of magnetic ﬂux density avg position of second coil layer can be determined. Figure 9 calculated only for the uniform section of magnetic ﬁeld. shows the positions of second coil layer that achieve max- .e same methodology is used to evaluate the magnetic imal FoM , for diﬀerent ripple values with referent plane at ﬁeld shapes for each possible position of the second coil optimal distance. layer. As a result, we get FoM values for each position of the For the lowest evaluated ripple values (0.5%–2%), the second coil layer. Figure 6 shows the FoM values for ﬁve optimal width of the second coil layer, W , is 70% of the ﬁrst diﬀerent h/W ratios with ﬁxed ripple value. coil layer width, W. For larger ripple values, the second coil For low h/W ratio value, majority of positions of second layer width increases. .e depth of second coil layer, D , coil layer result in nonuniform ﬁeld (dark blue areas). With shows direct correlation with the ripple value (Figure 10). higher h/W ratio values, more positions of second coil layer For a given ripple value and known coil width W, with generate uniform magnetic ﬁeld. For each ﬁxed combination referent plane placed at optimal distance, the depth of of h/W ratio and ripple value, there is an optimal position of second coil layer can be calculated as the second coil layer which results in maximal FoM value. D � W[0.041 − 0.03 · ln(r)]. (8) .is maximal FoM value is represented as one dot in Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] Magnetic ﬂux density B [T] 6 Wireless Power Transfer -6 -6 ×10 ×10 0 6 0 6 4 4 2 2 W/2 0 W/2 0 W/2 0 W/2 W/2 0 W/2 W relative to W W relative to W 2 2 (a) (b) -6 -6 ×10 ×10 0 6 0 6 4 4 2 2 W/2 0 W/2 0 W/2 0 W/2 W/2 0 W/2 W relative to W W relative to W 2 2 (c) (d) -6 ×10 W/2 W/2 0 W/2 W relative to W (e) Figure 6: FoM values for diﬀerent combinations of h/W ratio and ripple value of 2%: (a) ripple � 2%, h/W � 0.05; (b) ripple � 2%, h/ W � 0.07; (c) ripple � 2%, h/W � 0.10; (d) ripple � 2%, h/W � 0.14; (e) ripple � 2%, h/W � 0.20. Figure 11 shows resulting magnetic ﬁeld with optimized ﬁeld increase at the coil ends, as shown in Figure 12(a). .us, cs cross-section, for 0.5% ripple. surface enclosed by W and L of the coil has a minor part of uniform magnetic ﬁeld, as shown in Figure 13(a). In this stage of optimization, modiﬁed ﬁgure of merit is adopted: 2.3. Optimization of Coil Depth D. To achieve uniform magnetic ﬁeld across cs (Figure 3), the narrower sides of the uniform section surface (9) FoM � B · . coil structure are folded downwards to the depth D. .e goal 2 avg coil surface is to get magnetic ﬁeld shape from cross-section cs across It is not practical to try to optimize cs cross-section for the length of the coil L. If the coil ends are not folded down, 0% ripple, but using a ripple value 10 times lower than that at the ends of the coil there is a signiﬁcant increase in the used during cs optimization gives good enough result magnetic ﬁeld strength (Figure 11). (Figure 12(b)). .e second part of the optimization process is deter- Due to high D/W ratio (0.43), the uniform section of the mining the depth, D, to which the sides have to be folded magnetic ﬁeld at the coil end is quite irregular (Figure 13(b)). down. .e methodology to achieve this is the same as in the Such shape of the uniform ﬁeld was obtained by optimizing ﬁrst part of the optimization process, but with one signif- cs for 5% ripple and cs for 0.5% ripple. icant diﬀerence. .e magnetic ﬁeld shape throughout the 1 2 Alternative approach is to ﬁrst optimize cs for 0.5% coil length should be consistent, meaning that the magnetic 1 ripple and then optimize cs for 5% ripple. .e resulting ﬁeld strength should not deviate across cs cross-section. If magnetic ﬁeld is given in Figure 12(c). Uniform surface is the same ripple value as in cs optimization would be allowed 0.14% larger, and FoM value is 10% lower, but the shape of during cs optimization, the result would have unwanted D relative to W D relative to W 2 2 D relative to W D relative to W D relative to W 2 2 Length [cm] Wireless Power Transfer 7 8 0.25 0.2 0.15 y = -0.03ln (x) + 0.041 0.1 0.05 0 0.05 0.1 0.15 0.2 Ripple Figure 10: Optimal depth of second coil layer (D) for diﬀerent ripple values: simulated results are denoted by blue markers, and ﬁtted mathematical model is represented by solid line. 0 0.05 0.1 0.15 0.2 h/W ratio 20 % 2 % 10 % 1 % 5 % 0.5 % Figure 7: FoM analysis results. 0.5 0.1 -0.5 0.08 -100 0.06 y = -0.013ln (x) + 0.0191 -50 0.04 0.02 -50 0 0.05 0.1 0.15 0.2 Figure 11: Simulated magnetic ﬁeld distribution generated by two- Ripple layer coil with optimized cs . Figure 8: Optimal h/W ratios for diﬀerent ripple values: simulated results are denoted by blue markers, and ﬁtted mathematical model optimized for 2.5% ripple. .e uniform surface is represented by solid line. (Figure 13(d)) is drawn for ripple value of 5%. It results in the highest FoM value and largest uniform surface. .is approach is chosen as optimal. .e depth of the end fold D is a function of the ripple 20% 20% 10% 10% 5% value (r) and the length to width ratio (L/W) of the coil. 5% 2% 2% 1% 1% Figure 14 shows the end fold depths for diﬀerent ripple 20 0.5% 0.5% values and L/W ratios. .e fold depth increases for coils with 30 larger L/W ratio and with lower allowed ripple value. 50 40 30 20 10 0 10 20 30 40 50 Results of cs optimization are given as markers, and W relative to W [%] solid lines represent mathematical model, (9), which can be used to calculate required folding depth. Figure 9: Positions of second coil layer that achieve maximal FoM , for diﬀerent ripple values with referent plane placed at √� − 3.25 r (L/W) √� D � W · 􏼐1 − e 􏼑. (10) optimal distance. 20.4 · r .e proposed optimization method is developed for rectangular coil where the percentage of uniform surface the surface with uniform magnetic ﬁeld follows the rect- increases with higher L/W ratio of the coil (Figure 15). angular shape signiﬁcantly better, as shown in Figure 13(c). .ere is a trade-oﬀ between FoM value and the shape of the surface with uniform magnetic ﬁeld. .e best results are 3. Measurements obtained when both the cs and the cs optimizations are 1 2 To evaluate the developed optimization method, magnetic done for ripple value equal to one-half of the desired ripple. Figure 12(d) shows the magnetic ﬁeld when cs and cs are ﬁeld measurements are performed on fabricated coils 1 2 Width [cm] D relative to W [%] h/W ratio FoM [μT] D /W ratio Magnetic ﬁeld - normalized 8 Wireless Power Transfer -6[T] -6[T] ×10 ×10 10 10 5 5 0 0 Coil length L Coil length L (a) (b) -6[T] -6[T] ×10 ×10 10 10 5 5 0 0 Coil length L Coil length L (c) (d) Figure 12: Magnetic ﬁeld shape (top view) for diﬀerent ripple values: (a) cs 5%, cs 5% (D/W � 0.19); (b) cs 5%, cs 0.5% (D/W � 0.43); (c) 1 2 1 2 cs 0.5%, cs 5% (D/W � 0.19); (d) cs 2.5%, cs 2.5% (D/W � 0.26). 1 2 1 2 Coil length L Coil length L (a) (b) Coil length L Coil length L (c) (d) Figure 13: Uniform ﬁeld section (top view) for diﬀerent combinations of cs and cs ripple values: (a) uniform magnetic ﬁeld section 1 2 (49.81%) for magnetic ﬁeld shape from Figure 12(a), FoM � 0.0015 T; (b) uniform magnetic ﬁeld section (75.78%) for magnetic ﬁeld shape from Figure 12(b), FoM � 0.0021 T; (c) uniform magnetic ﬁeld section (75.92%) for magnetic ﬁeld shape from Figure 12(c), FoM � 0.0019 T; (d) uniform magnetic ﬁeld section (79.85%) for magnetic ﬁeld shape from Figure 12(d), FoM � 0.0021 T. 2 2 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0421 68 102 021 4 68 102 L (W) L/W ratio 0.5% ripple 2% ripple 1% ripple 4% ripple 1% ripple 5% ripple 2% ripple 10% ripple Figure 14: Required end fold depth (D) for diﬀerent ripple values Figure 15: Percentage of uniform ﬁeld surface for diﬀerent L/W and L/W ratios. ratios. D (W) Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Coil width W Percentage of uniform ﬁeld surface [%] Wireless Power Transfer 9 Figure 16: Fabricated proposed TX-coil, bottom view. Figure 17: Fabricated conventional TX-coil, bottom view. Figure 18: Measuring setup. (proposed and conventional). .e ﬁrst coil layer size is set as spectral analyzer, PBS-H3 probe (25 mm magnetic ﬁeld test L � 114 cm, W � 28 cm. .e position of second coil layer is with 50 Ohms SMB m socket), and SMA cable. In performed calculated using proposed optimization method for ripple experiments, fabricated TX-coils were energized by Agilent value of 1%. Optimizations for cross-sections cs and cs are 33250A signal generator at operating frequency of 150 kHz. 1 2 done for 0.5% ripple (one-half of the desired ripple). Op- Magnetic ﬁeld strength of both fabricated TX-coils is timal height of the referent plane equals (7): h � 2.46 cm. measured at 900 points in a receiving plane 30 mm above the Calculated variables of the second coil layer position are coil. Because it is measured by a PBS-H3 probe connected to W �19.6 cm, D � 5.6 cm. Calculated end fold depth is the SMA input of a Spectran NF-5035 instrument, the 2 2 D � 11.8 cm. .e fabricated proposed TX-coil prototype is analyzer provides highly sensitive measurement of an ex- shown in Figure 16. Actual placement of the coil layers ternal alternating ﬁeld up to 0.2 V max. .us, the spectrum diﬀers a bit from the calculated values, mainly due to the analyzer returns voltage values that are proportional to the limited precision of fabrication (W magnetic ﬁeld strength values. Hold mode is selected to � 20 cm, D � 6 cm, 2 2 D � 12 cm). .e wire that forms coil layers is placed in the measure the ﬁeld strength values. Measuring setup is shown white wire casing. Moreover, proposed TX-coil prototype is in Figure 18, and measurement results are given in Figure 19, constructed using plywood framework to hold wire casings along with the simulation results. and ensure ﬂat surface above in order to carry out magnetic Simulation results of the proposed folded 3D coil ﬁeld measurements in the same plane. Each coil layer structure are shown in Figures 19(a) and 19(b). Measure- consists of 4 windings of Litz wire, resulting in inductance of ments of magnetic ﬁeld strength distribution at receiving 103μH. plane for both fabricated TX-coils (Figures 19(c) and 19(d)) Conventional, single-layer rectangular coil (114 × 28 cm) conﬁrmed that optimal and proposed folded 3D TX-coil structure provides signiﬁcantly larger uniform magnetic is also fabricated using Litz wire placed in the white wire casings installed at one side of the ﬂat plywood board ﬁeld strength section in comparison to conventional TX-coil (Figure 17). Coil is made up of 6 windings, which results in structure. From measured magnetic ﬁeld shape inductance of 116μH. (Figures 19(c) and 19(d)), it can be seen that one side of the .e magnetic ﬁeld strength of these coils was measured coil has slightly higher ﬁeld values than the opposite side. at a temperature of 26 C and humidity of 50%. Field strength .is is due to limited precision of wire windings placement measurements are performed in the near ﬁeld zone with in the wire casing. Aside from that, measurement and measuring equipment consisting of a Spectran NF-5035 simulation results match to a high degree. Length [cm] 10 Wireless Power Transfer 0.75 0.5 0.25 0.5 0 Coil length L -0.5 -100 -50 0 50 100 -50 (a) (b) 1 1 0.75 0.75 0.5 0.5 0.25 0.25 0 0 Coil length L Coil length L (c) (d) Figure 19: Simulation and measurement results: (a) simulated magnetic ﬁeld distribution of optimized folded 3D coil structure; (b) normalized simulation results, top view; (c) normalized measurement results, top view (optimized folded 3D coil structure); (d) normalized measurement results, top view (conventional coil structure). Table 1: Comparison of various optimized TX-coils’ characteristics. Ref. Structure TX-coil (cm) r (%) h (mm) Uniform section (%) [1] 3D rectangular 22 ×18 × 2 20 0.5 ∼32 [6] Planar square 20 × 20 20 150 ∼48 [10] Planar square 20 × 20 20 1 ∼36 [18] Planar square 20 × 20 20 50 ∼51.8 [20] Planar square 80 × 80 9.6 10 ∼42.3 .is paper 3D rectangular 114 × 28 ×12 10 30 ∼55.3 Measured characteristics of diﬀerent TX-coil designs optimization method are successfully carried out. Both TX- coils, conventional and proposed, are fabricated to carry out which generate uniform magnetic ﬁeld strength distribution at receiving plane are listed in Table 1. In comparison with magnetic ﬁeld measurements which conﬁrmed that pro- other TX-coil characteristics from Table 1, the proposed coil posed coil, unlike conventional coil, generates uniform generates improved magnetic ﬁeld strength distribution magnetic ﬁeld strength distribution at receiving plane. with respect to uniform section of receiving plane. Further Furthermore, measured results show larger uniform section development of the proposed TX-coil will be aimed at re- in comparison to other optimized TX-coil structures. ducing coil depth, D, which will result in lower proﬁle of TX- Depending on the maximal ripple and proportions of the coil. coil, optimization method results in 3D coil structure that generates improved uniform magnetic ﬁeld strength dis- tribution across 50% to 90% of the receiving plane. 4. Conclusion Data Availability A novel 3D TX-coil structure with improved uniform magnetic ﬁeld distribution is proposed. Optimization .e data used to support the ﬁndings of this study can be methodology is presented and optimizing method is de- available upon request. veloped for rectangular 3D coil structure. Optimization results in coil structure that has maximized average magnetic Conflicts of Interest ﬁeld strength and uniform surface section. Computer simulations and experimental veriﬁcation of the .e authors declare that they have no conﬂicts of interest. Width [cm] Coil width W Magnetic field - normalized Coil width W Coil width W Wireless Power Transfer 11 Electrical Machines and Systems (ICEMS), pp. 1030–1034, Acknowledgments Pattaya, .ailand, October 2015. [14] T.-D. Yeo, D.-H. Kim, S. C. Chae, S.-T. Khang, and J.-W. Yu, .is work has been supported in part by Croatian Science “Design of free-positioning wireless power charging system Foundation under the project “Eﬃcient Wireless Power for aaa rechargeable battery,” in Proceedings of the 2016 46th Supply” (UIP-2017-05-5373). European Microwave Conference (EuMC), pp. 759–762, London, UK, October 2016. References [15] E. Elkhouly and S. Yang, “Transmitter coil design for resonant wireless power transfer,” in Proceedings of the 2016 IEEE PELS [1] W.-S. Lee, H. L. Lee, K.-S. Oh, and J.-W. 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J. Casanova, Z. N. Low, J. Lin, and R. Tseng, “Transmitting coil achieving uniform magnetic ﬁeld distribution for planar wireless power transfer system,” in Proceedings of the 2009 IEEE Radio and Wireless Symposium, pp. 530–533, San Diego, CA, USA, January 2009. [11] D. Yinliang, S. Yuanmao, and G. Yougang, “Design of coil structure achieving uniform magnetic ﬁeld distribution for wireless charging platform,” in Proceedings of the 2011 4th International Conference on Power Electronics Systems and Applications, pp. 1–5, Hong Kong, China, June 2011. [12] L. Shen, W. Tang, H. Xiang, and W. Zhuang, “Uniform magnetic ﬁeld by changing the current distribution on the planar coil for displacement-insensitive wireless power transfer/near ﬁeld communication,” Microwave and Optical Technology Letters, vol. 57, no. 2, pp. 424–427, 2014. [13] Y. Zhang, T. Lu, Z. Zhao, F. He, K. Chen, and L. 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Wireless Power Transfer – Hindawi Publishing Corporation

Published: Oct 14, 2021

References

Uniform magnetic field distribution of a spatially structured resonant coil for wireless power transfer,

W.-S. Lee, H. L. Lee, K.-S. Oh, and J.-W. Yu
Impact of receiver power and coupling coefficient on resonant frequency in wireless power transfer system,

D. Vinko, I. Biondić, and D. Bilandžija
Investigation of adaptive matching methods for near-field wireless power transfer,

J. Park, Y. Tak, Y. Kim, Y. Kim, and S. Nam
Gains maximization via impedance matching networks for wireless power transfer,

Q. Wang, W. Che, M. Dionigi, F. Mastri, M. Mongiardo, and G. Monti
Wireless power transfer system with high misalignment tolerance for bio-medical implants,

Q. Wang, W. Che, M. Mongiardo, and G. Monti
Planar multiple-antiparallel square transmitter for position-insensitive wireless power transfer,

S. Wang, Z. Hu, C. Rong, C. Lu, J. Chen, and M. Liu
Modular inductive power transmission system for high misalignment electric vehicle application,

C. Qiu, K. T. Chau, C. Liu, T. W. Ching, and Z. Zhang
A planar positioning-free magnetically-coupled resonant wireless power transfer,

F. Jolani, Y. Yu, and Z. Chen
Optimal design of a hybrid winding structure for planar contactless battery charging platform,

X. Liu and S. Y. Hui
Transmitting coil achieving uniform magnetic field distribution for planar wireless power transfer system,

J. J. Casanova, Z. N. Low, J. Lin, and R. Tseng
Design of coil structure achieving uniform magnetic field distribution for wireless charging platform,

D. Yinliang, S. Yuanmao, and G. Yougang
Uniform magnetic field by changing the current distribution on the planar coil for displacement-insensitive wireless power transfer/near field communication,

L. Shen, W. Tang, H. Xiang, and W. Zhuang
Quasi-uniform magnetic field generated by multiple transmitters of magnetically-coupled resonant wireless power transfer,

Y. Zhang, T. Lu, Z. Zhao, F. He, K. Chen, and L. Yuan
Design of free-positioning wireless power charging system for aaa rechargeable battery,

T.-D. Yeo, D.-H. Kim, S. C. Chae, S.-T. Khang, and J.-W. Yu
Transmitter coil design for resonant wireless power transfer,

E. Elkhouly and S. Yang
A wireless batteryless implantable radiofrequency lesioning device powered by intermediate-range segmented coil transmitter,

S. C. Tang, N. J. McDannold, and M. Vaninetti
Resonant inductive power transfer system for freely moving capsule endoscope with highly uniform magnetic field,

M. R. Basar, M. Y. Ahmad, F. Ibrahim, and J. Cho
Asymmetric coil structures for highly efficient wireless power transfer systems,

T.-H. Kim, G.-H. Yun, W. Y. Lee, and J.-G. Yook
Omnidirectional wireless power transfer system with multiple receivers and a single wire wound spiral transmitter,

H. Wang, L. Deng, H. Luo, S. Huang, and C. Liao
Optimisation of planar rectangular coil achieving uniform magnetic field distribution for EV wireless charging based on genetic algorithm,

Y. Zhang, L. Wang, Y. Guo, and Y. Zhang
Optimal design of planar spiral coil for uniform magnetic field to wirelessly power position-free targets,

Q. Xu, Q. Hu, H. Wang, Z.-H. Mao, and M. Sun

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Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

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Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

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