# A Magnetic Field Containment Method for an IPT System with Multiple Transmitting Coils Based on Reflective Properties

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## Abstract

**:**

## 1. Introduction

## 2. Reflective Segmentation Basic

#### 2.1. Equivalent Circuit of the IPT System with Unified Passive Compensation Network

_{D}is the DC input voltage. Q

_{1}–Q

_{4}are four switches, which form a full bridge inverter; u

_{AB}and i

_{AB}represent its instantaneous output voltage and current, respectively. The compensation networks are composed of one or more inductors or capacitors. L

_{P}, R

_{P}are the inductance and parasitic resistance of the transmitting coil, respectively. L

_{S}and R

_{S}are the inductance and parasitic resistance of the receiving coil, respectively. M represents mutual inductance between the coils, which is described as $M=k\sqrt{{L}_{\mathrm{P}}{L}_{\mathrm{S}}}$, where k is the coupling coefficient. D

_{1}−D

_{4}are four diodes that constitute a rectifier; u

_{ab}and i

_{ab}represent its instantaneous input voltage and current, respectively. The capacitance C

_{F}is the filter, and R

_{L}is the load.

_{AB}, I

_{AB}, U

_{ab}, and I

_{ab}are, respectively, the root mean square (RMS) values of the fundamental harmonics of u

_{AB}, i

_{AB}, u

_{ab}, and i

_{ab}. I

_{P}and I

_{S}are the RMS values of the current flowing through the transmitting and receiving coils, respectively. Then, the output voltage U

_{AB}of the inverter can be calculated by Equation (1).

_{ab}and current I

_{ab}of the rectifier can be obtained [15].

_{L}are equivalent to the load R

_{eq}of the secondary side, which can be expressed by Equation (3).

_{P1}, Z

_{P2}and Z

_{P3}are the impedance of a single compensation inductor or capacitor in the primary compensation network. Z

_{S1}, Z

_{S2}and Z

_{S3}are the impedance of a single compensation inductor or capacitor in the secondary compensation network. Here, Z

_{pi}= jX

_{Pi}+ R

_{Pi}, Z

_{Si}= jX

_{Si}+ R

_{Si}, (i = 1,2,3), where X

_{Pi}and X

_{Si}represent the reactance of the compensation inductor or capacitor, R

_{Pi}and R

_{Si}represent the parasitic equivalent series resistance (ESR) of the compensation inductor or capacitor.

#### 2.2. Reflective Properties and Performance Figures

_{P}is the impedance of the primary side when k = 0. Z

_{S}, Z

_{r}and Z

_{in}represent the secondary side impedance, reflected impedance and input impedance, respectively. ω = 2πf is the angular frequency of the power source, where f represents the frequency. The currents for each branch can be obtained, as shown in Equation (5).

_{0}is defined as the maximum coupling coefficient of the system. Z

_{r,k}is the reflective impedance when the coupling coefficient is k. Z

_{in,k}is the input impedance when the coupling coefficient is k. When $0<k\le {k}_{0}$, the current flowing through the transmitting coil is

_{0}. ${\dot{I}}_{\mathrm{P},\mathrm{un}}$ is the transmitting coil current when k = 0. When the voltage U

_{AB}is constant, the transmitting coil current can be adjusted by the input impedance. The parameter configuration method designed in this paper is as follows. When k = 0, the input impedance of the system is ${Z}_{\mathrm{in},\mathrm{un}}$, i.e., ${Z}_{\mathrm{P}}$, which is inductive and the maximum. When k = k

_{0}, the input impedance of the system is ${Z}_{\mathrm{in},\mathrm{k}0}$, which satisfies the relation ${Z}_{\mathrm{in},\mathrm{k}0}=\mathrm{Re}[{Z}_{\mathrm{r},\mathrm{k}0}]$. Here, $\mathrm{Re}[{Z}_{\mathrm{r},\mathrm{k}0}]$ represents the real part of the reflected impedance ${Z}_{\mathrm{r},\mathrm{k}0}$. When 0 < k < k

_{0}, the input impedance of the system is ${Z}_{\mathrm{in},\mathrm{co}}$, which is closely related to the coupling coefficient k.

## 3. Proposed Topology and Operation

#### 3.1. Receiver Design

_{11}, Z

_{12}, Z

_{21}and Z

_{22}are the Z parameters of the two−port, and ${\dot{U}}_{\mathrm{S}}$ is the induced voltage of the secondary side, i.e., ${\dot{U}}_{\mathrm{S}}=\mathrm{j}\omega M{\dot{I}}_{\mathrm{P}}$. The impedance Z

_{S}, the voltage ${\dot{U}}_{\mathrm{ab}}$ and the current ${\dot{I}}_{\mathrm{ab}}$ can be obtained, as shown in Equation (11).

_{C}C

_{S}ω

^{2}, B = R

_{eq}C

_{S}ω. According to Equation (11), when the real part of the denominator for I

_{ab}is zero, the output current is independent of the load. The output current and frequency can be obtained, as shown in Equation (12).

_{S}/L

_{C}. According to Equation (11), when the imaginary part of the denominator for ${\dot{U}}_{\mathrm{ab}}$ is zero, the output voltage is independent of the load. The output voltage and resonant angular frequency are given as Equation (13).

_{S}of the LCL compensation topology can be written as Equation (14).

_{S}, L

_{S}and L

_{C}.

#### 3.2. Transmitter Design

_{0}and M

_{0}represents the coupling coefficient and mutual inductance in the condition of perfect alignment, respectively, and satisfies the relation ${M}_{0}={k}_{0}\sqrt{{L}_{\mathrm{P}}{L}_{\mathrm{S}}}$. X

_{r,k0}is the reflected reactance when k = k

_{0}.

_{AB}is constant, the transmitting coil current depends on the input impedance. According to the definition of SR in Equation (9) and impedance values in Equations (16) and (18), the SR of the IPT system can be calculated as Equation (21).

_{S}/R

_{eq}. Therefore, the SR can be adjusted by α and Q according to actual need.

## 4. System Design and Analysis

#### 4.1. Transmitter Design

_{P}= L

_{S}= 270 μH, k

_{0}= 0.3, f = 85 kHz. The IPT systems of the three topologies are nominally designed to transfer about 60 W to the load, and the compensation parameters are shown in Table 1.

_{0}/2 and k = k

_{0}. As shown in Figure 7a, the transmitting coil current with the LCC−P topology is constant at the operating point of 85 kHz, which means that the SR is equal to 1. As can be seen from Figure 7b, the transmitting coil current with the S−P topology in the uncoupled state is the smallest at the operating frequency, which means that the SR is less than 1. For the S−LCL topology, the maximum current of the transmitting coil in the uncoupled state is shifted further from 85 kHz, resulting in a lower current of the standby transmitting coils (as shown in Figure 7c). Therefore, the proposed S−LCL topology achieves the purpose of “field focusing” compared with the LCC−P and S−P topologies.

_{P}is the quality factor S−P topology, which is defined as Q

_{P}= R

_{eq}/ωL

_{S}. The S−LCL topology provides an extra degree of freedom over the S−P topology. By choosing appropriate α and Q, the desired SR can be obtained, as shown in Figure 8.

#### 4.2. Power Transfer and Efficiency Considerations

## 5. Experimental Validation

_{D}= 25 V, L

_{P}= L

_{S}= 270 μH, k

_{0}= 0.3 and f = 85 kHz, respectively. The output power is different under different α and Q, and the maximum output power of the prototype is about 100 W. The other parameters of the experimental prototype are listed in Table 2.

_{rms1}, I

_{rms1}are input DC voltage and current, U

_{rms2}, I

_{rms2}are output DC voltage and current. P

_{1}and P

_{2}represent input and output power, respectively; η

_{1}and L

_{oss1}represent the efficiency and losses of the system. As shown in Figure 12a,b, the phase angle between the voltage and current waveforms of the inverter is almost zero. It indicates that the input impedance of the system is pure resistance in the fully coupled state. When the system works in the uncoupled state, the phase angle between the voltage and current waveforms of the inverter is almost 900 (as shown in Figure 12c), indicating that the input impedance of the system is inductance, which is consistent with the theoretical analysis in Section 3.

_{D}is reduced from 25 V to 23 V in the theoretical calculation. The measured results of the transmitting coil current are basically consistent with the theoretical calculation. The measured results of the power transfer are smaller than the calculated value (under high coupling coefficients). The reason for this mismatch is that the losses of power electronic devices and the losses of parasitic resistances are ignored in theoretical calculations.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Transmitter coil current as a function of k and f. (

**a**) LCC−P topology; (

**b**) S−P topology; (

**c**) S−LCL topology.

**Figure 12.**Measured waveforms and results of the IPT system with α = 3. (

**a**) k = k

_{0}, Q = 2. (

**b**) k = k

_{0}, Q = 4. (

**c**) k = 0.

**Figure 14.**Simulated magnetic flux density of the transmitting coils. (

**a**) The completely coupled state. (

**b**) The uncoupled state.

**Figure 15.**The theoretical and experimental measurements of transmitting coil currents with respect to k under α = 3, Q = 4.

**Figure 16.**The theoretical and experimental measurements of output power with respect to k under α = 3, Q = 4.

**Figure 17.**The system loss and efficiency measurements with respect to the coupling coefficient k under α = 3, Q = 4.

Parameters | LCC−P Topology | S−P Topology | S−LCL Topology |
---|---|---|---|

U_{D} | 50 V | 22.5 V | 22.5 V |

L_{P1} | 72 μH | −−− | −−− |

C_{P1} | 48.71 nF | 14.27 nF | 14.76 nF |

C_{P2} | 17.71 nF | −−− | −−− |

C_{S} | 12.99 nF | 12.99 nF | 51.95 $\mathrm{n}$F |

L_{C} | −−− | −−− | 90 $\mathsf{\mu}$H |

R_{eq} | 200 Ω | 200 Ω | 36 Ω |

Parameters | α = 2, Q = 2 | α = 3, Q = 2 | α = 3, Q = 4 |
---|---|---|---|

C_{P} | 15.02 nF | 14.76 nF | 14.76 nF |

C_{S} | 38.96 nF | 51.95 nF | 51.95 nF |

L_{C} | 135 $\mathsf{\mu}$H | 90 $\mathsf{\mu}$H | 90 $\mathsf{\mu}$H |

R_{eq} | 72 Ω | 72 Ω | 36 Ω |

I_{P,k0} | 3.10 A | 6.69 A | 3.45 A |

I_{P,un} | 1.01 A | 1.12 A | 1.12 A |

SR | 3.07 | 5.97 | 3.08 |

P_{in} | 68.4 W | 135.6 W | 80.2 W |

P_{out} | 57.9 W | 101.8 W | 66.2 W |

P_{loss} | 10.2 W | 33.8 W | 13.9 W |

η | 84.6% | 75.1% | 82.6% |

P_{idle−loss} | 0.69 W | 0.85 W | 0.85 W |

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## Share and Cite

**MDPI and ACS Style**

Yang, X.; Yang, J.; Fan, J.; Wang, B.; Li, D.
A Magnetic Field Containment Method for an IPT System with Multiple Transmitting Coils Based on Reflective Properties. *Electronics* **2023**, *12*, 653.
https://doi.org/10.3390/electronics12030653

**AMA Style**

Yang X, Yang J, Fan J, Wang B, Li D.
A Magnetic Field Containment Method for an IPT System with Multiple Transmitting Coils Based on Reflective Properties. *Electronics*. 2023; 12(3):653.
https://doi.org/10.3390/electronics12030653

**Chicago/Turabian Style**

Yang, Xu, Junfeng Yang, Jing Fan, Bao Wang, and Dingzhen Li.
2023. "A Magnetic Field Containment Method for an IPT System with Multiple Transmitting Coils Based on Reflective Properties" *Electronics* 12, no. 3: 653.
https://doi.org/10.3390/electronics12030653