# Wireless Power Charger Based on Class E Amplifier with the Maximum Power Point Load Consideration

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Impedance Analysis and Parameter Design

#### 2.1. Mutual Inductance Model of the Coupler

#### 2.2. Power Transfer Capability Analysis

#### 2.3. Parameter Design

## 3. Magnetic Circuit of the Coupler

#### 3.1. Magnetic Circuit Model Analysis

#### 3.2. Impact of Gap Length and Magnet Core Size

#### 3.3. Impact of Coils’ Position

## 4. Simulation and Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Sakamoto, H.; Harada, K.; Washimiya, S.; Takehara, K. Large air-gap coupler for inductive charger [for electric vehicles]. IEEE Trans. Magn.
**1999**, 35, 3526–3528. [Google Scholar] [CrossRef] - Sugimori, K.; Sakamoto, H.; Harada, K. A one-converter contactless charger for electric vehicles. Electr. Eng. Jpn.
**2000**, 132, 73–81. [Google Scholar] [CrossRef] - Wang, C.S.; Stielau, O.H.; Covic, G.A. Design Considerations for a Contactless Electric Vehicle Battery Charger. IEEE Trans. Ind. Electron.
**2005**, 52, 1308–1314. [Google Scholar] [CrossRef] - Watada, M.; Iwawaki, K.; Tamada, T.; Ouchi, K.; Takatani, S.; Um, Y.S. The development of core-type Transcutaneous Energy Transmission System for artificial heart. IEEE Eng. Med. Biol. Soc.
**2005**, 4, 3849–3852. [Google Scholar] - Lim, H.G.; Yoon, Y.H.; Lee, C.W.; Park, I.Y.; Song, B.S.; Cho, J.H. Implementation of a Transcutaneous Charger for Fully Implantable Middle Ear Hearing Device. IEEE Eng. Med. Biol. Soc.
**2005**, 7, 6813–6816. [Google Scholar] - Casanova, J.J.; Low, Z.N.; Lin, J.S. Design and Optimization of a Class-E Amplifier for a Loosely Coupled Planar Wireless Power System. IEEE Trans. Circuits Syst. Express Briefs
**2009**, 56, 830–834. [Google Scholar] [CrossRef] - Low, Z.N.; Chinga, R.A.; Tseng, R.; Lin, J. Design and test of a high-power high-efficiency loosely coupled planar wireless power transfer system. IEEE Trans. Ind. Electron.
**2009**, 56, 1801–1812. [Google Scholar] - Chaimanonart, N.; Olszens, K.R.; Zimmerman, M.D.; Ko, W.H.; Young, D.J. Implantable RF Power Converter for Small Animal In Vivo Biological Monitoring. IEEE Eng. Med. Biol. Soc.
**2005**, 5, 5194–5197. [Google Scholar] - Bradley, A.M.; Feezor, M.D.; Singh, H.; Sorrell, F.Y. Power systems for autonomous underwater vehicles. IEEE J. Ocean. Eng.
**2001**, 26, 526–538. [Google Scholar] [CrossRef] - Li, Z.S.; Li, D.J.; Lin, L.; Chen, Y. Design Considerations for electromagnetic couplers in contactless power transmission systems for deep-sea applications. J. Zhejiang Univ. Sci. C
**2010**, 11, 824–834. [Google Scholar] [CrossRef] - Manikandan, J.; Akash, S.; Vishwananth, A.; Nandakumar, R.; Agrawal, V.K.; Manu, K. Design and development of contactless battery charger for underwater vehicles. In Proceedings of the Michael Faraday IET International Summit, Kolkata, India, 12–13 September 2015; pp. 362–367. [Google Scholar]
- Zoran, H.V.; Nikola, Z.; Trung, Q.D.; Schober, R. Rate Maximization of Decode-and-Forward Relaying Systems With RF Energy Harvesting. IEEE Commun. Lett.
**2015**, 19, 2290–2293. [Google Scholar][Green Version] - Tsiropoulou, E.E.; Mitsis, G.; Papavassiliou, S. Interest-aware Energy Collection & Resource Management in Machine to Machine Communications. Ad Hoc Netw.
**2018**, 68, 48–57. [Google Scholar] - Vamvakas, P.; Tsiropoulou, E.E.; Vomvas, M.; Papavassiliou, S. Adaptive Power Management in Wireless Powered Communication Networks: A User-Centric Approach. In Proceedings of the 38th IEEE Sarnoff Symposium, Newark, NJ, USA, 18–20 September 2017; pp. 1–6. [Google Scholar]
- Le, T.A.; Vien, Q.T.; Nguyen, H.X.; Ng, D.W.K.; Schober, R. Robust Chance-Constrained Optimization for Power-Efficient and Secure SWIPT Systems. IEEE Trans. Green Comm. Netw.
**2017**, 1, 333–346. [Google Scholar] [CrossRef][Green Version] - Wu, Q.Q.; Chen, W.; Ng, D.W.K.; Schober, R. Spectral and Energy-Efficient Wireless Powered IoT Networks: NOMA or TDMA? IEEE Trans. Veh. Technol.
**2018**, 67, 6663–6667. [Google Scholar] [CrossRef][Green Version] - Kurs, A.; Karalis, A.; Moffatt, R.; Joannopoulos, J.D.; Fisher, P.; Soljacic, M. Wireless Power Transfer via Strongly Coupled Magnetic Resonances. Science
**2007**, 317, 83–85. [Google Scholar] [CrossRef] [PubMed] - Baker, M.W.; Sarpeshkar, R. Feedback analysis and design of RF power links for low-power bionic system. IEEE Trans. Biomed. Circuits Syst.
**2007**, 1, 28–38. [Google Scholar] [CrossRef] [PubMed] - Sokal, N.O.; Sokal, A.D. Class E-A new class of high-efficiency tuned single-ended switching power amplifiers. IEEE J. Solid-State Circuits
**1975**, 10, 168–176. [Google Scholar] [CrossRef] - Raab, F.H. Idealized operation of the class E tuned power amplifier Class. IEEE Trans. Circuits Syst.
**1977**, 24, 725–735. [Google Scholar] [CrossRef] - Raab, F.H. Effects of Circuit Variations on the Class E Tuned Power Amplifier. IEEE J. Solid-State Circuits
**1978**, 13, 239–247. [Google Scholar] [CrossRef]

**Figure 2.**Equivalent circuit model of the electromagnetic coupling power transfer charger (ECPTC). (

**a**) Simplified schematic circuit of the charger; (

**b**) Schematic circuit reflected to the transmitter side.

**Figure 4.**Structure and magnetic circuit of the coupler. (

**a**) Structure; (

**b**) 2D finite element model; (

**c**) Magnetic flux distribution; (

**d**) Magnetic circuit model.

**Figure 5.**Relation to coupler parameters and coupling coefficient. (

**a**) The relation between coupling coefficient and gap length; (

**b**) Coupling coefficient versus effective radius of the magnet core.

**Figure 8.**Simulation waveforms under different loads: (

**a**) ${R}_{L}=100\phantom{\rule{0.166667em}{0ex}}\Omega $; (

**b**) ${R}_{L}=600\phantom{\rule{0.166667em}{0ex}}\Omega $.

**Figure 9.**Prototype of the coupler and ECPTC: (

**a**) Electromagnetic coupler; (

**b**) Coils of the coupler; (

**c**) Prototype.

**Figure 10.**Experimental waveforms under different loads: (

**a**) ${R}_{L}=100\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\Omega $; (

**b**) ${R}_{L}=600\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\Omega $.

**Figure 11.**Power transfer and efficiency curves of ECPTC: (

**a**) Output power versus the load; (

**b**) System efficiency versus the load.

**Table 1.**Electromagnetic parameters of the coupler. (${l}_{g}=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}$).

Coils Position | H (mm) | ${\mathit{L}}_{\mathit{p}}$ ($\mathsf{\mu}$H) | ${\mathit{L}}_{\mathit{s}}$ ($\mathsf{\mu}$H) | M ($\mathsf{\mu}$H) | k |
---|---|---|---|---|---|

2 | 160.4 | 52.4 | 54.9 | 0.598 | |

3 | 164.4 | 53.6 | 51.6 | 0.549 | |

Top | 4 | 171.1 | 55.9 | 49.8 | 0.509 |

5 | 178.5 | 58.3 | 48.9 | 0.479 | |

6 | 186.0 | 60.7 | 48.5 | 0.456 | |

2 | 258.0 | 84.3 | 53.7 | 0.364 | |

3 | 256.1 | 83.7 | 52.3 | 0.357 | |

Bottom | 4 | 256.7 | 83.8 | 52.3 | 0.356 |

5 | 253.0 | 82.6 | 50.8 | 0.351 | |

6 | 246.2 | 80.4 | 50.4 | 0.358 |

Parameters | Measured | Parasitic Resistance |
---|---|---|

${R}_{load}$ | 100 $\Omega $ | |

${L}_{p}$ | 168 $\mathsf{\mu}$H | 0.38 $\Omega $ |

${L}_{s}$ | 55.8 $\mathsf{\mu}$H | 0.19 $\Omega $ |

M | 53.66 $\mathsf{\mu}$H |

Components | Calculated | Simulation Value | Experimental Value |
---|---|---|---|

${L}_{dc}$ | 1.6 mH | 1.6 mH | 1.6 mH |

${C}_{out}$ | 3.6 nF | 4.7 nF | 4.7 nF |

${C}_{s}$ | 0.9 nF | 1 nF | 1 nF |

${C}_{sh}$ | 2.5 nF | 2.6 nF | 2 nF |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dai, W.; Tang, W.; Cai, C.; Deng, L.; Zhang, X. Wireless Power Charger Based on Class E Amplifier with the Maximum Power Point Load Consideration. *Energies* **2018**, *11*, 2378.
https://doi.org/10.3390/en11092378

**AMA Style**

Dai W, Tang W, Cai C, Deng L, Zhang X. Wireless Power Charger Based on Class E Amplifier with the Maximum Power Point Load Consideration. *Energies*. 2018; 11(9):2378.
https://doi.org/10.3390/en11092378

**Chicago/Turabian Style**

Dai, Weili, Wei Tang, Changchun Cai, Lihua Deng, and Xiaofeng Zhang. 2018. "Wireless Power Charger Based on Class E Amplifier with the Maximum Power Point Load Consideration" *Energies* 11, no. 9: 2378.
https://doi.org/10.3390/en11092378