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. These 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. The goal is to maximize the average magnetic field strength and uniform magnetic field section of the receiving plane. Hence, figures of merit (FoM_{1} and FoM_{2}) are introduced and defined as product of average magnetic field strength and length or surface along which uniform magnetic field is generated, respectively. The 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.

Numerous wireless power transfer (WPT) systems operate through nonuniform magnetic field strength distribution at receiving plane. Magnetic field nonuniformity in magnetically coupled resonant (MCR) WPT system causes resonant frequency splitting phenomena and impedance mismatching when receiving coil (RX-coil) is not properly aligned with transmitting coil (TX-coil) [

In this paper, a novel 3D structure of TX-coil is proposed to achieve uniform magnetic field distribution at the given receiving plane (114 × 28 cm). Presence of uniform magnetic field strength distribution at the receiving plane will provide stable resonant frequency regardless of RX-coil position due to steady value of magnetic coupling factor

The proposed TX-coil structure consists of two layers and is based on optimization method which is validated by simulation and measurement results. Since the proposed TX-coil structure is characterized by folded sides, it is more suitable for large sized WPT systems, for instance, installation under office desk. Computer simulations of TX-coils with different winding arrangement (coil layers relative spacing), but with the same outer dimensions (114 × 28 cm), were run, and magnetic field distribution at the given receiving plane which is above the TX-coil was observed. According to the simulation results, experimental TX-coils are made out of Litz wire instead of PCB realization which is not appropriate for large receiving plane. Both computer simulation and measurement results verified that uniform magnetic field distribution at considerable surface of the 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 enables simultaneous wireless charging of monitors, smartphones, laptops, etc.

To maintain stable transfer efficiency and power delivery to freely moving RX-coil(s), TX-coil in WPT system should generate uniform magnetic field [

If the 3D TX-coil structure can be represented as a number of linear sections, the magnetic field simulations can be significantly simplified. Uniformity of magnetic field of the TX-coil is evaluated with respect to the plane of interest. In MCR-WPT, where multiple loads can be wirelessly powered, a flat surface (e.g., office desk) should have uniform magnetic field distribution. Therefore, magnetic field evaluations are done with respect to this plane of interest, i.e., referent plane. Under these conditions (coil represented by linear sections and a defined referent plane), a fast magnetic field simulation model can be developed. Since a coil is defined as a piecewise linear structure, a magnetic field in any given point can be calculated as a vector sum of magnetic fields generated by each linear segment of 3D coil structure. Each linear segment is defined by two points in 3D space,

Magnetic field in the point

The shortest distance between

The angles

For coil current I in linear segment flowing from P1 to P2, the direction of the magnetic field strength

With respect to the referent plane, only the part of the magnetic field directed in the

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

Simulated magnetic field distribution generated by single-layer rectangular coil (114 × 28 cm).

The magnetic field has a bowl-like shape with pronounced spikes at the coil corners. For application in position tolerant (in terms of RX-coil) WPT system, such magnetic field shape is not suitable. The rectangular shape of the coil is one of the least favorable candidates for uniform magnetic field (with triangular coil shape being the worst), but it is the shape widely used in WPT systems. This is the main motivation for the development of the rectangular 3D coil structures which can generate uniform magnetic field.

In this paper, we focused on a two-layer 3D coil structure, due to simpler fabrication compared to a multilayer coil with respect to required precision of manufacture.

Figure _{2} relative to the first coil layer, and it has narrower width _{2} compared to width of the first coil layer

Two-layer 3D coil structure.

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 _{1} in Figure _{2} in Figure

Figure _{2}, _{2}), and end fold depth

Optimization framework.

Extensive analysis is conducted, resulting in mathematical model for rectangular coil optimization. Conducted analysis and mathematical model are explained in the next two sections.

To ensure a uniform magnetic field distribution over cross-section _{1} (width of the coil), a position of the second coil layer must be optimized. Perfectly uniform magnetic field distribution cannot be achieved, so one parameter that must be taken into account is the maximal ripple of the magnetic field. The second parameter is the distance _{2} and _{2}) obtain “most” uniform field distribution. Similarly, for different allowed ripple values of a magnetic field, different values of the second coil layer variables (_{2} and _{2}) result in different shortest distance of the referent plane

Optimization deals with the following problem: finding values of the second coil layer variables to generate the most 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 generally results in high magnetic field strength. Certain values of the second coil layer variables that ensure uniform field at short distances do that at the cost of a lower magnetic field strength. This would decrease the overall performance of WPT system. The second important aspect is the percentage of the cross-section over which the uniform field is achieved. It is quite easy to get uniform field at short distance with high field strength, but only over a small fraction of total coil width.

Accordingly, the first part of the optimization process is finding values of the second coil layer variables to get uniform field on most of the cross-section, but also with a highest magnetic field strength value. Therefore, as a figure of merit (FoM_{1}), we propose the product of average magnetic flux density (calculated only for part of the cross-section where magnetic field strength is uniform with respect to defined ripple value) and percentage of cross-section on which the uniform field is achieved.

The first step in second coil variables’ optimization is the FoM_{1} analysis. This is a 4-dimensional problem. FoM_{1} is affected by the referent plane distance _{2}, _{2}) of second coil layer (third and fourth dimension, respectively). Since the referent plane distance _{1} analysis. We assume the same current magnitude and direction in both coil layers.

The four parameters are varied in the following ranges: _{2} ranges from 0 to the coil width _{2} ranges from 0 to half of the coil width

The following methodology was used: for fixed values of _{2} and _{2} was calculated over the _{1} cross-section of the coil, and magnetic field shape is analyzed. In this step of the coil optimization, the coil length _{2} and _{2}.

Examples of magnetic field shape analysis: (a) ripple = 1%, _{2}/_{2}/_{2}/_{2}/_{2}/_{2}/_{2}/_{2}/

Ripple of the magnetic field is used as input parameter in the optimization process. It is used to determine the size of the uniform section of magnetic field. Uniform section is defined as a section of the coil where the magnetic field deviation does not exceed the defined ripple value. The analysis of the magnetic field begins at the center of the cross-section and moves to the sides. The magnetic field strength at the center is used as an initial average field strength value. The two adjacent magnetic field strengths are compared to the initial value, and if they do not deviate from initial value by more than the defined ripple, they are considered to be in the uniform section of the magnetic field. New average field strength of uniform section is then calculated. The next two adjacent field values are then evaluated using the same methodology. At one point, the field values that deviate by more than the defined ripple value will be reached. These field values and all the remaining ones are not a part of the uniform magnetic field section. This can be seen in Figures

In Figures

To summarize, there are two possible outcomes of magnetic field shape analysis. The uniform section of the magnetic field is identified, or the magnetic field is considered nonuniform. For magnetic field shapes that have a uniform section, the FoM_{1} is calculated:_{avg} is an average value of magnetic flux density calculated only for the uniform section of magnetic field.

The same methodology is used to evaluate the magnetic field shapes for each possible position of the second coil layer. As a result, we get FoM_{1} values for each position of the second coil layer. Figure _{1} values for five different

FoM_{1} values for different combinations of

For low _{1} value. This maximal FoM_{1} value is represented as one dot in Figure _{1} values for all evaluated combinations of

FoM_{1} analysis results.

It can be seen that, for a higher ripple value, a higher FoM_{1} can be achieved. For each ripple value, the maximal FoM_{1} value is achieved at different _{1} is achieved at optimal distance from the coil (optimal

Optimal

For a given ripple value and known coil width

Once the distance of the referent plane is selected, the position of second coil layer can be determined. Figure _{1}, for different ripple values with referent plane at optimal distance.

Positions of second coil layer that achieve maximal FoM_{1}, for different ripple values with referent plane placed at optimal distance.

For the lowest evaluated ripple values (0.5%–2%), the optimal width of the second coil layer, _{2}, is 70% of the first coil layer width, _{2}, shows direct correlation with the ripple value (Figure

Optimal depth of second coil layer (_{2} for different ripple values: simulated results are denoted by blue markers, and fitted mathematical model is represented by solid line.

For a given ripple value and known coil width

Figure _{1} cross-section, for 0.5% ripple.

Simulated magnetic field distribution generated by two-layer coil with optimized _{1}.

To achieve uniform magnetic field across _{2} (Figure _{1} across the length of the coil

The second part of the optimization process is determining the depth, _{2} cross-section. If the same ripple value as in _{1} optimization would be allowed during _{2} optimization, the result would have unwanted field increase at the coil ends, as shown in Figure

Magnetic field shape (top view) for different ripple values: (a) _{1} 5%, _{2} 5% (_{1} 5%, _{2} 0.5% (_{1} 0.5%, _{2} 5% (_{1} 2.5%, _{2} 2.5% (

Uniform field section (top view) for different combinations of _{1} and _{2} ripple values: (a) uniform magnetic field section (49.81%) for magnetic field shape from Figure _{2} = 0.0015 T; (b) uniform magnetic field section (75.78%) for magnetic field shape from Figure _{2} = 0.0021 T; (c) uniform magnetic field section (75.92%) for magnetic field shape from Figure _{2} = 0.0019 T; (d) uniform magnetic field section (79.85%) for magnetic field shape from Figure _{2} = 0.0021 T.

It is not practical to try to optimize _{2} cross-section for 0% ripple, but using a ripple value 10 times lower than that used during _{1} optimization gives good enough result (Figure

Due to high _{1} for 5% ripple and _{2} for 0.5% ripple.

Alternative approach is to first optimize _{1} for 0.5% ripple and then optimize _{2} for 5% ripple. The resulting magnetic field is given in Figure _{2} value is 10% lower, but the shape of the surface with uniform magnetic field follows the rectangular shape significantly better, as shown in Figure

There is a trade-off between FoM_{2} value and the shape of the surface with uniform magnetic field. The best results are obtained when both the _{1} and the _{2} optimizations are done for ripple value equal to one-half of the desired ripple. Figure _{1} and _{2} are optimized for 2.5% ripple. The uniform surface (Figure _{2} value and largest uniform surface. This approach is chosen as optimal.

The depth of the end fold

Required end fold depth (D) for different ripple values and

Results of _{2} optimization are given as markers, and solid lines represent mathematical model, (

The proposed optimization method is developed for rectangular coil where the percentage of uniform surface increases with higher

Percentage of uniform field surface for different

To evaluate the developed optimization method, magnetic field measurements are performed on fabricated coils (proposed and conventional). The first coil layer size is set as _{1} and _{2} are done for 0.5% ripple (one-half of the desired ripple). Optimal height of the referent plane equals (_{2} = 19.6 cm, _{2} = 5.6 cm. Calculated end fold depth is _{2} = 20 cm, _{2} = 6 cm,

Fabricated proposed TX-coil, bottom view.

Conventional, single-layer rectangular coil (114 × 28 cm) is also fabricated using Litz wire placed in the white wire casings installed at one side of the flat plywood board (Figure

Fabricated conventional TX-coil, bottom view.

The magnetic field strength of these coils was measured at a temperature of 26°C and humidity of 50%. Field strength measurements are performed in the near field zone with measuring equipment consisting of a Spectran NF-5035 spectral analyzer, PBS-H3 probe (25 mm magnetic field test with 50 Ohms SMB m socket), and SMA cable. In performed experiments, fabricated TX-coils were energized by Agilent 33250A signal generator at operating frequency of 150 kHz.

Magnetic field strength of both fabricated TX-coils is measured at 900 points in a receiving plane 30 mm above the coil. Because it is measured by a PBS-H3 probe connected to the SMA input of a Spectran NF-5035 instrument, the analyzer provides highly sensitive measurement of an external alternating field up to 0.2 V max. Thus, the spectrum analyzer returns voltage values that are proportional to the magnetic field strength values. Hold mode is selected to measure the field strength values. Measuring setup is shown in Figure

Measuring setup.

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).

Simulation results of the proposed folded 3D coil structure are shown in Figures

Measured characteristics of different TX-coil designs which generate uniform magnetic field strength distribution at receiving plane are listed in Table

Comparison of various optimized TX-coils’ characteristics.

Ref. | Structure | TX-coil (cm) | Uniform section (%) | ||
---|---|---|---|---|---|

[ | 3D rectangular | 22 × 18 × 2 | 20 | 0.5 | ∼32 |

[ | Planar square | 20 × 20 | 20 | 150 | ∼48 |

[ | Planar square | 20 × 20 | 20 | 1 | ∼36 |

[ | Planar square | 20 × 20 | 20 | 50 | ∼51.8 |

[ | Planar square | 80 × 80 | 9.6 | 10 | ∼42.3 |

This paper | 3D rectangular | 114 × 28 × 12 | 10 | 30 | ∼55.3 |

A novel 3D TX-coil structure with improved uniform magnetic field distribution is proposed. Optimization methodology is presented and optimizing method is developed for rectangular 3D coil structure. Optimization results in coil structure that has maximized average magnetic field strength and uniform surface section. Computer simulations and experimental verification of the optimization method are successfully carried out. Both TX-coils, conventional and proposed, are fabricated to carry out magnetic field measurements which confirmed that proposed coil, unlike conventional coil, generates uniform magnetic field strength distribution at receiving plane. Furthermore, measured results show larger uniform section in comparison to other optimized TX-coil structures. Depending on the maximal ripple and proportions of the coil, optimization method results in 3D coil structure that generates improved uniform magnetic field strength distribution across 50% to 90% of the receiving plane.

The data used to support the findings of this study can be available upon request.

The authors declare that they have no conflicts of interest.

This work has been supported in part by Croatian Science Foundation under the project “Efficient Wireless Power Supply” (UIP-2017-05-5373).