# Reduction in Human Interaction with Magnetic Resonant Coupling WPT Systems with Grounded Loop

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometric Structure of the Proposed MRC-WPT System

_{TR}represents the coupling coefficient between the transmitter (denoted as T) and receiver (denoted as R). Resistance is connected to the receiving coil, imitating the load. All coils used in this study were made of 1-mm-diameter copper wire. Copper wire is widely used in laboratory and industrial applications for WPT systems in different thicknesses/diameters. [42] showed that 1 mm-diameter copper wire has more transmission efficiency than other diameters. Therefore, this study adopted the 1-mm-diameter copper wire. The working frequency was set to 13.56 MHz since this is a promising frequency for WPT applications in industrial, scientific, and medical fields [16,34,43].

#### 2.2. Transmission Efficiency of the Proposed MRC-WPT System

_{TR}is the coupling coefficient, Γ

_{T/R}denotes the attenuation rates of the transmitter and receiver due to ohmic and radiation losses, and Γ

_{W}refers to the attenuation rates of the load [1]. Thus, efficient transmission occurs when the MRC-WPT system operates in a strongly coupled system, i.e., κ

_{TR}

^{2}/Γ

_{T}Γ

_{R}> 1. The variables Γ

_{T}and Γ

_{R}can be calculated using Equation (2).

_{0}is the resonant angular frequency of the resonator and Q = ω

_{0}L/R is the quality factor of the transmitter or receiver.

_{S}is transferred to the receiver part at resonant frequency f

_{0}and is then delivered to load R

_{L}. The transmitter and receiver can be represented by series inductors (L

_{1}and L

_{2}) and resistances (R

_{1}and R

_{2}). The parameter R

_{1}and R

_{2}represent the resistances due to the ohmic and radiation losses of the transmitter and receiver [42]. The function M = κ

_{TR}(L

_{1}× L

_{2})

^{1/2}represents the mutual inductance. Capacitors C

_{1}and C

_{2}are used to tweak the transmitter and receiver resonance to the desired frequency [45].

_{in}, and actual output power P

_{RL}, which is expressed as follows:

#### 2.3. Human-Body Model

#### 2.4. Exposure Scenarios

#### 2.5. Simulation of Mutual Interaction

_{0}, and R were calculated using the frequency domain solver of the full-wave electromagnetic simulation package COMSOL Multiphysics 5.3. Compensation capacitors C

_{1}and C

_{2}were used to make the transmitter and receiver resonant at the desired frequency [45], in which the lumped inductances were numerically extracted using COMSOL Multiphysics 5.3. The theoretical maximum transmission efficiency was obtained by adjusting the load impedance R

_{L}[1]. The dependence of transmission efficiency on the transmission distance d for the matched state of the MRC-WPT system with grounded and non-grounded resonators was evaluated using Equation (3) based on the processes mentioned above. The stray magnetic field was also evaluated at the same time.

#### 2.6. Simulation of Exposure Dose in the TARO Model

## 3. Results and Discussion

#### 3.1. Validation of the MRC-WPT System Computation

#### 3.2. Interactions between the Human Body and MRC-WPT System

_{11}), corresponding to a grounded resonator with and without a human-body model, was lower than that of the WPT with a non-grounded resonator. The bandwidth characteristics of the two resonator types were also different. The narrower peak for the grounded resonator is a clear indicator that the Q value is higher than that of the non-grounded resonator, indicating an increase in transmission efficiency. The simulation results in Figure 6 suggest that the grounded loop could mitigate the reflection coefficient changes and suppress the electric field strength.

_{11}values of the two WPTs with and without a human model at their resonant frequencies are listed in Table 1. The resonant frequency was set to 13.56 ± 0.01 MHz. The S

_{11}values of the WPT with a non-grounded resonator varied from −8.16 to −6.06 dB when the human model was considered. Meanwhile, the S

_{11}values of the WPT with a grounded resonator varied from −14.97 to −14.1 dB. This result implied that the grounded resonator suppressed the interaction of the human model with the WPT performance. As a result, the bandwidths of the curves in Figure 6 became wider, indicating reduced quality factors with human models.

_{11}[14].

#### 3.3. Exposure Doses in the TARO Model

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geometrical structure of the proposed MRC-WPT system. (

**a**) Four-coil MRC-WPT system. (

**b**) Non-grounded resonator. (

**c**) Proposed resonator with a grounded loop.

**Figure 3.**Human-body model. (

**a**) Homogeneous axial-symmetric human model. (

**b**) Japanese adult male model TARO.

**Figure 4.**The MRC-WPT with respect to the (

**a**) homogeneous body and (

**b**) TARO models. (

**c**) Top view of the MRC-WPT and homogenous human model.

**Figure 5.**Experimental validation of transmission efficiency of MRC-WPTs’ two resonator types (10 MHz).

**Figure 7.**Dependence of transmission efficiency on d in Case A (l = 0), Case B (l = d/2), and Case C (l = d), and without a human model for a (

**a**) non-grounded and (

**b**) grounded resonator.

**Figure 8.**Electromagnetic-field distribution of two 13.56-MHz MRC-WPT systems without a human model when the input power is 1 W and the transmission distance d = 9 cm. (

**a**) Electric and magnetic field distributions around the WPT systems. (

**b**) Electric field on a horizontal line. The gray circle illustrates the location of the grounded loop.

**Figure 9.**Induced electric field distribution on TARO. (

**a**) Body surface. (

**b**) Cross-sectional plane of input power 1 W, and transmission distance d = 9 cm.

**Figure 10.**Local SAR distributions on TARO. (

**a**) Body surface. (

**b**) Cross-sectional plane of input power 1 W, and transmission distance d = 9 cm.

**Table 1.**S

_{11}(dB) of the two WPT systems with and without a human-body model at resonant frequency.

Resonator Type | Frequency (MHz) | Without Human Body | With Human Body |
---|---|---|---|

Non-grounded | 13.55 | −8.16 | −6.06 |

Grounded | 13.57 | −14.97 | −14.10 |

**Table 2.**Quality factor and coupling coefficient of the MRC-WPT systems for two types of resonators, d = 9 cm.

Resonator | Quality Factor | Coupling Coefficient | ||
---|---|---|---|---|

Without Human Body | With Human Body | Without Human Body | With Human Body | |

Non-grounded | 215.4 | 222.7 | 0.128 | 0.144 |

Grounded | 234.2 | 235.3 | 0.146 | 0.198 |

Model Displacement | Non-Grounded | Grounded | RD |
---|---|---|---|

Case A | 3.44 | 1.94 | 43.6% |

Case B | 3.22 | 2.02 | 37.3% |

Case C | 2.98 | 1.85 | 37.9% |

Model Displacement | Non-Grounded | Grounded | RD |
---|---|---|---|

Case A | 1.88 × 10^{−4} | 0.57 × 10^{−4} | 69.7% |

Case B | 2.04 × 10^{−4} | 0.67 × 10^{−4} | 67.1% |

Case C | 1.35 × 10^{−4} | 0.50 × 10^{−4} | 63.0% |

Model Displacement | Non-Grounded | Grounded | RD |
---|---|---|---|

Case A | 8.34 × 10^{−6} | 2.87 × 10^{−6} | 65.6% |

Case B | 7.94 × 10^{−6} | 3.48 × 10^{−6} | 56.1% |

Case C | 6.12 × 10^{−6} | 2.39 × 10^{−6} | 61.0% |

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**MDPI and ACS Style**

Duan, X.; Lan, J.; Diao, Y.; Gomez-Tames, J.; Hirayama, H.; Hotta, M.; Fischer, G.; Hirata, A.
Reduction in Human Interaction with Magnetic Resonant Coupling WPT Systems with Grounded Loop. *Energies* **2021**, *14*, 7253.
https://doi.org/10.3390/en14217253

**AMA Style**

Duan X, Lan J, Diao Y, Gomez-Tames J, Hirayama H, Hotta M, Fischer G, Hirata A.
Reduction in Human Interaction with Magnetic Resonant Coupling WPT Systems with Grounded Loop. *Energies*. 2021; 14(21):7253.
https://doi.org/10.3390/en14217253

**Chicago/Turabian Style**

Duan, Xianyi, Junqing Lan, Yinliang Diao, Jose Gomez-Tames, Hiroshi Hirayama, Masashi Hotta, George Fischer, and Akimasa Hirata.
2021. "Reduction in Human Interaction with Magnetic Resonant Coupling WPT Systems with Grounded Loop" *Energies* 14, no. 21: 7253.
https://doi.org/10.3390/en14217253