# A Wireless Power Transfer System Using a Double DD Quadrature Coil Structure

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Upgraded Coil Structure

_{T}

_{1}and L

_{R}

_{1}are the self-inductances of the transmitter and receiver DD1 coil, L

_{t}

_{1}, L

_{t}

_{2}, L

_{r}

_{1}, and L

_{r}

_{2}are the self-inductances of each D shaped planar coil that forms the DD1 transmitter and receiver coil, and M

_{t}

_{12}and M

_{r}

_{12}are mutual inductances between the DD1 transmitter and the receiver coil.

_{T}

_{2}and L

_{R}

_{2}are the self-inductances of the transmitter and receiver DD2 coil, L

_{t}

_{3}, L

_{t}

_{4}, L

_{r}

_{3}, and L

_{r}

_{4}are the self-inductances of each D shaped planar coil that forms the DD2 transmitter and receiver coil, and M

_{t}

_{34}and M

_{r}

_{34}are mutual inductances between the DD2 transmitter and the receiver coil.

#### 2.1. Simulation of the Prosed Coil Structure

#### 2.2. Small-Scale Prototype Measurements

_{X}

_{1}is the inductance of the coils connected in series under positive mutual inductance, and L

_{X}

_{2}is the inductance of the coils connected in series under the negative mutual inductance. The coupling coefficient can be calculated using:

_{1}is the self-inductance of the first coil, and L

_{2}is the self-inductance of the second coil.

## 3. IPT System with the New Coil Structure

_{1}, between the DD2 coils with k

_{2}, and between the Q coils with k

_{3}. The coupling coefficients k

_{1}and k

_{2}between the DD1 and DD2 coils are almost the same, due to the same coil size and topology. The coupling coefficient between the Q coils k

_{3}was different compared to the coefficients k

_{1}and k

_{2}. This resulted in different resonator behavior, which led to different output power transfer and efficiency.

_{o}is the DC output voltage, U

_{o}

_{1}is the DC output voltage of the first rectifier, U

_{o}

_{2}is the DC output voltage of the second rectifier, and U

_{o}

_{3}is the DC output voltage of the third rectifier.

_{L}

_{1}, R

_{L}

_{2}, and R

_{L}

_{3}are equivalent loads of each inverter, and R

_{L}is the resistance of the single load.

_{r}

_{1}is the resonant frequency of the DD1 part, f

_{r}

_{2}of the DD2 part, and f

_{r}

_{3}of the Q part. C

_{T}

_{1}and C

_{R1}are the values of the compensation capacitors of the DD1 part, C

_{T}

_{2}and C

_{R}

_{2}are the values for the DD2 part, and C

_{T}

_{3}and C

_{R}

_{3}are the values for the Q part. The values of the compensation capacitors are usually chosen so that the resonant frequency of each part is the same.

_{r}. The currents i

_{T}

_{1}, i

_{T}

_{2}, and i

_{T}

_{3}are generated by the first harmonic component of each voltage:

_{T}

_{1}, u

_{T}

_{2}, and u

_{T}

_{3}are the first harmonic components of voltage at the input of each transmitter coil, and U

_{DC}is the voltage at the input of the inverter.

## 4. Experimental Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Different coil topologies: (

**a**) Exploded double DD coil structure (2DD); (

**b**) Exploded double DDQ coil structure (2DDQ).

**Figure 3.**EM simulation of magnetic flux density B for the proposed double DDQ coil: (

**a**) Vector B, (

**b**) Complex B.

**Figure 8.**Comparison between an IPT system using 2DD and 2DDQ topology: (

**a**) Efficiency comparison; (

**b**) Output power comparison.

**Figure 9.**Misalignment tolerance of the IPT system along the x-axis: (

**a**) IPT using the 2DD coil structure; (

**b**) IPT using the 2DDQ coil structure.

**Figure 10.**Misalignment tolerance of the IPT system along the y-axis: (

**a**) IPT using the 2DD coil structure; (

**b**) IPT using the 2DDQ coil structure.

**Figure 11.**Misalignment tolerance of the IPT system using 2DDQ coils at z = 10 mm: (

**a**) in the x-axis direction; (

**b**) in the y-axis direction.

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

DD1 coil self-inductance L_{1} | 38.69 µH |

DD2 coil self-inductance L_{2} | 34.89 µH |

Q coil self-inductance L_{3} | 29.75 µH |

Coupling coefficient k_{12} (DD1, DD2) | 0.000010 |

Coupling coefficient k_{13} (DD1, Q) | −0.000873 |

Coupling coefficient k_{23} (DD2, Q) | 0.001052 |

Parameter | Transmitter | Receiver |
---|---|---|

DD1 coil self-inductance L_{1} | 44.99 µH | 44.51 µH |

DD2 coil self-inductance L_{2} | 41.06 µH | 41.47 µH |

Q coil self-inductance L_{3} | 42.55 µH | 43.9 µH |

Coupling coefficient k_{12} (DD1, DD2) | 0.01396 | 0.0277 |

Coupling coefficient k_{13} (DD1, Q) | 0.008514 | 0.01239 |

Coupling coefficient k_{23} (DD2, Q) | 0.02165 | 0.02156 |

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

Input voltage U_{DC} | 25 V |

Input current I_{DC} (max.) | 4 A |

Switching frequency f_{s} | 87 kHz |

DD1 load R_{L}_{1} | 10.7 Ω |

DD2 load R_{L}_{2} | 10.7 Ω |

Q load R_{L}_{3} | 8.1 Ω |

Distance between pads d | 2 mm–40 mm |

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**MDPI and ACS Style**

Domajnko, J.; Prosen, N.
A Wireless Power Transfer System Using a Double DD Quadrature Coil Structure. *Electronics* **2023**, *12*, 890.
https://doi.org/10.3390/electronics12040890

**AMA Style**

Domajnko J, Prosen N.
A Wireless Power Transfer System Using a Double DD Quadrature Coil Structure. *Electronics*. 2023; 12(4):890.
https://doi.org/10.3390/electronics12040890

**Chicago/Turabian Style**

Domajnko, Jure, and Nataša Prosen.
2023. "A Wireless Power Transfer System Using a Double DD Quadrature Coil Structure" *Electronics* 12, no. 4: 890.
https://doi.org/10.3390/electronics12040890