# A Copper Foil Electromagnetic Coupler and Its Wireless Power Transfer System without Compensation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Inductance and Capacitance Integrated Electromagnetic Coupler

_{out}, D

_{in}, w, and s are the outer diameter of the electromagnetic pole, the inner diameter of the electromagnetic pole, the width of the copper foil, and the distance between two turns of copper foil, respectively. The four electromagnetic poles of the coupler are stacked to cause cross coupling with each other. The mutual inductance and mutual capacitance among the four electromagnetic poles must be considered when analyzing the characteristics of the coupler. Therefore, the structure in Figure 2a can be equivalent to the circuit model shown in Figure 2b. L

_{i}is the self-inductance of the electromagnetic pole, M

_{ij}is the mutual inductance of P

_{i}and P

_{j}, C

_{ij}is the cross-coupling capacitance of P

_{i}and P

_{j}, where i, j = 1, 2, 3, 4.

## 3. System Circuit Modelling and Self-Compensating Principle

#### 3.1. System Circuit Model and Its Equivalent Simplification

_{2}of the coupler is connected to the high potential terminal of the inverter output, and the outer electromagnetic pole P

_{1}is connected to the low potential terminal, so as to reduce the leakage electric field. For convenience, the fundamental harmonics approximation (FHA) method is used to analyze the circuit characteristics. The power losses in the coupler are also neglected. For the circuit model of the coupler shown in Figure 2, according to reference [18], the six capacitance cross coupling model can be equivalent to a three capacitance π model, so the system circuit model can be equivalent to the circuit model shown in Figure 4. Combined with the multi inductance coupling theory, the inductance components L

_{1}–L

_{4}can be decoupled, and the circuit shown in Figure 4 can be simplified to the circuit structure shown in Figure 5.

#### 3.2. Circuit Full Resonance and Parameter Self-Compensating Relation

_{1}and I

_{2}, respectively. The current clockwise direction is specified as the positive direction. The loop equation is written based on Kirchhoff’s voltage law (KVL):

_{1}and P

_{3}are identical, and the dimensions of electromagnetic pole P

_{2}and P

_{4}are also identical. If the system is required to work in ZPA state, i.e., the imaginary part of input impedance Im(Z

_{in}) = 0, the following equation must be satisfied:

- (1)
- Equation (10) is satisfied.

- (2)
- Equation (11) is satisfied.

_{in}can be simplified as R

_{eq}. Similarly, the input current, output current, and output voltage of the system can be expressed as follows:

## 4. Analysis and Design of Circuit Parameters and Electromagnetic Coupler Parameters

#### 4.1. Selection for System Working Frequency Considering the Influence of Inner Electromagnetic Poles’ Copper foil Turns

_{A}, C

_{B}, L

_{M}, L

_{1M}and L

_{2M}. The variation of the above capacitances and inductances with N

_{in}can be simulated by Maxwell, as shown in Figure 6a,b. Further combining (10), the variation of the input impedance Z

_{in}with N

_{in}and R

_{eq}is obtained, as shown in Figure 7. It can be seen that N

_{in}has little effect on Z

_{in}which is mainly decided by R

_{eq}. When the value of R

_{eq}is small (10–100 Ω), the input impedance is very high, so the pick-up power of the load will be greatly reduced in this case. When the value of R

_{eq}is large (10

^{3}–10

^{4}Ω), the input impedance varies from 10 Ω to 100 Ω, but the load pick-up current is very small. In addition, we can also analyze the influence of the other parameters in (9) on Z

_{in}through the same way. Z

_{in}is less effected by the other parameters, which can also be verified by Maxwell simulation.

_{in}= R

_{eq}), and the voltage and current of the load are more suitable for most applications. Similarly, the parameters of the coupler shown in Table 1 are taken as invariants, and the changes of the above two frequencies with N

_{in}and R

_{eq}are obtained, as shown in Figure 8. It is concluded that the system resonance frequencies in the second ZPA condition are mainly related to N

_{in}and less affected by R

_{eq}.

_{1}is connected to the negative pole of DC input and P

_{2}is connected to the high potential terminal of inverter output, so the voltage on P

_{1}is zero and the voltage on P

_{2}is U

_{in}. The voltage on P

_{3}and P

_{4}will be mainly considered for comparative analysis. With different values of N

_{in}, the resonance frequency of the coupler is quite different, which will cause the voltages to ground of the four electromagnetic poles distinct. When the system operating frequency is equal to f

_{1}and f

_{2}, the variation of voltage to ground of P

_{3}and P

_{4}with N

_{in}can be obtained, as shown in Figure 9. It is obvious that the U

_{P3}and U

_{P4}obtained by using f

_{2}as the system working frequency are much higher than those obtained by using f

_{1}as the system working frequency. Therefore, choosing f

_{1}as the system working frequency will effectively reduce the fringing electric field of the coupler and improve the safety performance of the system. In the following paper, we will mainly analyze and design the WPT system in the case of f = f

_{1}.

#### 4.2. Influence of Misalignment on Coupling Coefficient

_{IPT}and electric field coupling coefficient k

_{CPT}can be negligible when there is displacement misalignment. Figure 10 shows the variation of k

_{IPT}and k

_{CPT}at X or Y misalignment conditions. It can be seen that the sign of k

_{IPT}and k

_{CPT}will change with the misalignment increasing. k

_{IPT}will equal zero when the misalignment increases to 294.3 mm, while k

_{CPT}will equal zero when the misalignment equals 275.8 mm, which means the power cannot be transferred at this point.

## 5. Parameters Determination and Simulation Verification

_{1}and f

_{2}are selected as the working frequency of the system, which is more in line with the equivalent load resistance in practical application. However, compared with the frequency of f

_{2}, the voltage on electromagnetic pole is greatly reduced under the frequency of f

_{1}, as can be seen from Figure 9. Therefore, f

_{1}will be selected as the working frequency of the system in the following simulation. Figure 12 shows the output voltage and current waveform the inverter. The voltage and current are in the same phase, and the system realizes ZPA operation with a unity power factor in the input. The measurement shows that the input current amplitude of the system is 2.484 A. Because ${U}_{\mathrm{in}}={U}_{\mathrm{dc}}\times 4/\pi $ and ${R}_{\mathrm{eq}}={R}_{\mathrm{L}}\times 8/{\pi}^{2}$, the input current I

_{inv}can be calculated as ${I}_{\mathrm{in}}={U}_{\mathrm{in}}/{R}_{\mathrm{eq}}=2.5\mathrm{A}$, which is consistent with the simulation results. Because the internal resistance loss of the electromagnetic pole is not considered in the simulation, the output power is basically consistent with the input power.

## 6. Conclusions

- (1)
- Low cost, light weight, simple structure, and high power density;
- (2)
- No additional compensation components and little skin effect, so as to improve system efficiency;
- (3)
- High power factor and ZVS condition.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Hu, A.P.; You, Y.W.; Chen, F.Y.; McCormick, D.; Budgett, D.M. Wireless Power Supply for ICP Devices with Hybrid Supercapacitor and Battery Storage. IEEE J. Emerg. Sel. Top. Power Electron.
**2016**, 4, 273–279. [Google Scholar] [CrossRef] - Liu, C.; Hu, A.P.; Covic, G.A.; Nair, N.-K.C. Comparative Study of CCPT Systems with Two Different Inductor Tuning Positions. IEEE Trans. Power Electron.
**2012**, 27, 294–306. [Google Scholar] - Lee, K.; Kim, J.; Cha, C. Microwave-based Wireless Power Transfer using Beam Scanning for Wireless Sensors. In Proceedings of the IEEE EUROCON 2019—18th International Conference on Smart Technologies, Novi Sad, Serbia, 1–4 July 2019; pp. 1–5. [Google Scholar]
- Jin, K.; Zhou, W. Wireless Laser Power Transmission: A Review of Recent Progress. IEEE Trans. Power Electron.
**2019**, 34, 3842–3859. [Google Scholar] [CrossRef] - Li, S.; Mi, C. Wireless Power Transfer for Electric Vehicle Applications. IEEE J. Emerg. Sel. Top. Power Electron.
**2015**, 3, 4–17. [Google Scholar] - Wang, C.-S.; Covic, G.A.; Stielau, O.H. Power Transfer Capability and Bifurcation Phenomena of Loosely Coupled Inductive Power Transfer Systems. IEEE Trans. Ind. Electron.
**2004**, 51, 148–157. [Google Scholar] [CrossRef] - Zhang, W.; Wong, S.C.; Tse, C.; Chen, Q. Design for Efficiency Optimization and Voltage Controllability of Series–Series Compensated Inductive Power Transfer Systems. IEEE Trans. Power Electron.
**2014**, 29, 191–200. [Google Scholar] [CrossRef] - Hou, J.; Chen, Q.; Yan, K.; Ren, X.; Wong, S.C.; Tse, C. Analysis and control of S/SP compensation contactless resonant converter with constant voltage gain. In Proceedings of the 2013 IEEE Energy Conversion Congress and Exposition, Denver, Colorado, 15–19 September 2013; pp. 2552–2558. [Google Scholar]
- Su, Y.-G.; Zhou, W.; Hu, A.P.; Tang, C.-S.; Xie, S.-Y.; Sun, Y. Full-Duplex Communication on the Shared Channel of a Capacitively Coupled Power Transfer System. IEEE Trans. Power Electron.
**2017**, 32, 3229–3239. [Google Scholar] [CrossRef] - Huang, L.; Hu, A. Defining the mutual coupling of capacitive power transfer for wireless power transfer. Electron. Lett.
**2015**, 51, 1806–1807. [Google Scholar] [CrossRef] - Dai, J.; Ludois, D.C. Capacitive Power Transfer through a Conformal Bumper for Electric Vehicle Charging. IEEE J. Emerg. Sel. Top. Power Electron.
**2016**, 4, 1015–1025. [Google Scholar] [CrossRef] - Yao, Y.; Wang, Y.; Liu, X.; Lin, F.; Xu, D.G. A Novel Parameter Tuning Method for a Double-Sided LCL Compensated WPT System with Better Comprehensive Performance. IEEE Trans. Power Electron.
**2017**, 33, 8525–8536. [Google Scholar] [CrossRef] - Lu, F.; Zhang, H.; Hofmann, H.; Mi, C. A Double-Sided LCLC-Compensated Capacitive Power Transfer System for Electric Vehicle Charging. IEEE Trans. Power Electron.
**2015**, 30, 6011–6014. [Google Scholar] [CrossRef] - Lu, F.; Zhang, H.; Hofmann, H.; Mi, C.C. An Inductive and Capacitive Combined Wireless Power Transfer System With LC-Compensated Topology. IEEE Trans. Power Electron.
**2016**, 31, 8471–8482. [Google Scholar] [CrossRef] - Luo, B.; Long, T.; Mai, R.; Dai, R.; He, Z.; Li, W. Analysis and design of hybrid inductive and capacitive wireless power transfer for high-power applications. IET Power Electron.
**2018**, 11, 2263–2270. [Google Scholar] [CrossRef] - Zhou, W.; Su, Y.-G.; Huang, L.; Qing, X.-D.; Hu, A.P. Wireless Power Transfer Across a Metal Barrier by Combined Capacitive and Inductive Coupling. IEEE Trans. Ind. Electron.
**2019**, 66, 4031–4041. [Google Scholar] [CrossRef] - Gao, X.; Liu, C.; Zhou, H.; Hu, W.; Huang, Y.; Xiao, Y.; Lei, Z.; Chen, J. Design and Analysis of a New Hybrid Wireless Power Transfer System with a Space-Saving Coupler Structure. IEEE Trans. Power Electron.
**2021**, 36, 5069–5081. [Google Scholar] [CrossRef] - Wu, X.-Y.; Su, Y.-G.; Hu, A.P.; Zou, L.J.; Liu, Z. A Sleeve-Type Capacitive Power Transfer System with Different Coupling Arrangements for Rotary Application. IEEE Access
**2020**, 8, 69148–69159. [Google Scholar] [CrossRef]

**Figure 1.**Basic structure of integrated electromagnetic coupler. (

**a**) 3D Graph of integrated electromagnetic coupler. (

**b**) Top view of plane rectangular spiral electromagnetic pole.

**Figure 2.**Coupling structure and equivalent model. (

**a**) Front view of integrated electromagnetic coupler. (

**b**) Equivalent model of integrated electromagnetic coupler.

**Figure 6.**Variation of the equivalent cross-coupling capacitances and mutual inductances. (

**a**) Equivalent cross-coupling capacitances. (

**b**) Equivalent mutual inductances.

**Figure 8.**The variation of system operating frequency with N

_{in}and R

_{eq}. (

**a**) The variation of f

_{1}with N

_{in}and R

_{eq}. (

**b**) The variation of f

_{2}with N

_{in}and R

_{eq}.

**Figure 9.**Variation curve of the voltage to ground of P

_{3}and P

_{4}with N

_{in}. (

**a**) f = f

_{1}. (

**b**) f = f

_{2}.

Parameter | N_{out} | s_{out} | w_{out} | s_{in} | w_{in} | d_{s} | d_{t} |
---|---|---|---|---|---|---|---|

Value | 15 | 5 mm | 10 mm | 5 mm | 10 mm | 10 mm | 60 mm |

Parameter | N_{out} | s_{out} | w_{out} | s_{in} | w_{in} | d_{s} | d_{t} |
---|---|---|---|---|---|---|---|

value | 15 | 5 mm | 10 mm | 5 mm | 10 mm | 10 mm | 60 mm |

Parameter | Value | Parameter | Value |
---|---|---|---|

f | 1.056 MHz | L_{2} | 19.517 μH |

U_{dc}(U_{in}) | 78.54 V (100 V) | L_{3} | 64.407 μH |

R_{L}(R_{eq}) | 49.348 Ω (40 Ω) | L_{4} | 19.432 μH |

C_{12} | 324.98 pF | M_{12} | 22.731 μH |

C_{13} | 30.376 pF | M_{13} | 28.369 μH |

C_{14} | 3.0998 pF | M_{14} | 12.367 μH |

C_{23} | 3.1395 pF | M_{23} | 12.366 μH |

C_{24} | 13.198 pF | M_{24} | 7.2848 μH |

C_{34} | 324.14 pF | M_{34} | 22.722 μH |

L_{1} | 64.622 μH |

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**MDPI and ACS Style**

Wu, X.; Mao, M.
A Copper Foil Electromagnetic Coupler and Its Wireless Power Transfer System without Compensation. *World Electr. Veh. J.* **2021**, *12*, 191.
https://doi.org/10.3390/wevj12040191

**AMA Style**

Wu X, Mao M.
A Copper Foil Electromagnetic Coupler and Its Wireless Power Transfer System without Compensation. *World Electric Vehicle Journal*. 2021; 12(4):191.
https://doi.org/10.3390/wevj12040191

**Chicago/Turabian Style**

Wu, Xueying, and Mingxuan Mao.
2021. "A Copper Foil Electromagnetic Coupler and Its Wireless Power Transfer System without Compensation" *World Electric Vehicle Journal* 12, no. 4: 191.
https://doi.org/10.3390/wevj12040191