# Improved Design of PCB Coil for Magnetically Coupled Wireless Power Transfer

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of the Compensation Network and Coil Parameters

#### 2.1. Coupling Coil Circuit Model

_{S}is the AC power supply at the transmitting coil, I

_{1}and I

_{2}are the currents of the transmitting and receiving circuits, L

_{1}and L

_{2}are the self-inductances of the transmitting and receiving coils, and R

_{1}and R

_{2}are the coil resistances of the transmitting and receiving coils, respectively. Mutual inductance M is used to represent the degree of coupling between the two coils [22].

#### 2.2. Compensation Circuit

_{s1}and Z

_{r1}are used to represent the total impedance of the receiving circuit and the reflected impedance of the transmitting circuit. R

_{r1}and X

_{r1}are used to represent the reflected impedance and reactance at the transmitting circuit [25]. When the compensating capacitor at the receiving end is connected in series to the circuit, the total impedance and reflection impedance at the receiving transmitter can be represented by Equations (5) and (6).

_{r1}and reflection reactance X

_{r1}of the transmitting circuit are represented by Equations (7) and (8), respectively.

_{1}at the transmitting end is shown in Equation (20).

_{2}of the receiving end circuit is calculated according to Equation (1), as shown in Equation (21).

_{out}and energy transmission efficiency η of the receiving circuit can be obtained, as shown in Equations (22) and (23), respectively.

## 3. Optimization of PCB Coil Structure Parameters

_{out}is the outer diameter of the coil, D

_{in}is the inner diameter of the coil, P is the coil turn spacing, w is the coil wire width, h is the thickness of the copper wire laid on the PCB, and h

_{1}is the thickness of the PCB.

_{L}in Equation (35) is zero, and the second order partial derivative is less than zero. The following can be concluded:

_{1}Q

_{2}k

_{2}is defined as the strong coupling coefficient [29] of the coil. Equation (36) reveals that the larger the strong coupling coefficient is, the higher the transmission efficiency of the coil. Previous analysis has shown that the design of the coil must consider the degree of coupling between the coils in addition to its quality factor. The quality factor and the coupling coefficient of the coil correlate with the strong coupling coefficient. Therefore, maximizing the strong coupling coefficient has become a research goal.

_{1}and Q

_{2}are also the same. The efficiency of the coil can be simplified as:

#### 3.1. Coil Thickness

#### 3.2. Coil Turn Spacing

#### 3.3. Coil Line Width

#### 3.4. Coil Turns

## 4. Research on the Offset Characteristics of PCB Coils

#### 4.1. Coaxial Parallel Offset

#### 4.2. Coaxial Nonparallel Offset

#### 4.3. Parallel Offset of Different Axes

#### 4.4. Different Axes Are not Parallel Offset

## 5. Experimental Verification

#### 5.1. Coil Experimental Model

#### 5.2. Measurement of Coil Parameters

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Circuit figure of the bilateral compensation method: (

**a**) SS-type compensation; (

**b**) SP-type compensation; (

**c**) PS-type compensation; (

**d**) PP-type compensation.

**Figure 6.**Relationship between coil mutual inductance and transmission power and efficiency under different load resistances: (

**a**) coil transmission power; (

**b**) coil transmission efficiency.

**Figure 7.**Flat coils with different shapes: (

**a**) circular plane spiral coil; (

**b**) square plane spiral coil.

**Figure 8.**Magnetic field nephogram of plane coils with different shapes: (

**a**) circular plane spiral coil; (

**b**) square plane spiral coil.

**Figure 12.**Simulation results of different coil turn spacings: (

**a**) coil quality factor and coupling coefficient; (

**b**) strong coupling coefficient of coil.

**Figure 13.**Simulation results of different coilline width: (

**a**) coil quality factor and coupling coefficient; (

**b**) strong coupling coefficient of coil.

**Figure 14.**Simulation data of different coil turns: (

**a**) coil quality factor and coupling coefficient; (

**b**) strong coupling coefficient of coil.

**Figure 15.**Top view of the double-layer PCB coil: (

**a**) top view of the coil top layer; (

**b**) top view of the coil bottom layer in Scheme 1; (

**c**) top view of the coil bottom layer in Scheme 2.

**Figure 17.**Schematic figure of coil coaxial parallel offset: (

**a**) offset 3 cm; (

**b**) offset 5 cm; (

**c**) offset 7 cm.

**Figure 18.**Simulation data of coil coaxial parallel offset: (

**a**) coil coupling coefficient; (

**b**) coil strong coupling coefficient; (

**c**) coil transmission efficiency.

**Figure 20.**Model figure of coil coaxial nonparallel offset: (

**a**) offset 5 cm, offset 30 degrees; (

**b**) offset 5 cm, offset 60 degrees; (

**c**) offset 7 cm, offset 30 degrees.

**Figure 21.**Simulation results of coil coaxial nonparallel offset: (

**a**) coil coupling coefficient; (

**b**) coil strong coupling coefficient; (

**c**) coil transmission efficiency; (

**d**) comparison of strong coupling coefficients at different offset angles under the condition of an offset distance of 5.5 cm.

**Figure 23.**Model figure of different axes used for the parallel offset of coil: (

**a**) offset 1 cm; (

**b**) offset 2.5 cm; (

**c**) offset 4 cm.

**Figure 24.**Simulation data of coils with different parallel offset axes: (

**a**) coil coupling coefficient; (

**b**) coil strong coupling coefficient; (

**c**) coil transmission efficiency.

**Figure 26.**Model figure of coil different axes nonparallel offset: (

**a**) offset 2 cm, angle 30 degrees; (

**b**) offset 2 cm, angle 60 degrees; (

**c**) offset 4 cm, angle 30 degrees.

**Figure 27.**Simulation data of coils with different nonparallel offset axes: (

**a**) coil coupling coefficient; (

**b**) coil strong coupling coefficient; (

**c**) coil transmission efficiency; (

**d**) comparison of strong coupling coefficients at different offset angles under the condition of a 1 cm offset distance.

**Figure 28.**Physical figure of a single-layer coil: (

**a**) coil 1; (

**b**) coil 2; (

**c**) coil 3; (

**d**) coil 4; (

**e**) coil 5; (

**f**) coil 6; (

**g**) coil 7; (

**h**) coil 8; (

**i**) coil 9.

**Figure 30.**Experimental platform for coil parameter measurement: (

**a**) self-inductance measurement; (

**b**) mutual inductance measurement.

**Figure 31.**Simulation data and measurement calculation data of the strong coupling coefficient for coil offset: (

**a**) coaxial parallel offset; (

**b**) coaxial nonparallel offset; (

**c**) parallel offset of different axes; (

**d**) different axes are not parallel offset.

**Figure 33.**Oscilloscope-measured waveform: (

**a**) voltage (red) and current (blue) waveforms at the transmitting end; (

**b**) load voltage (red) and current (blue) waveform at the receiving end.

Receiving Capacitance Compensation Method | Capacitor in Series | Capacitor in Parallel |
---|---|---|

Reflective resistance R_{r} | $\frac{{\omega}^{2}{M}^{2}}{{R}_{\mathrm{L}}}$ | $\frac{{M}^{2}{R}_{\mathrm{L}}}{{L}_{2}^{2}}$ |

Reflective reactance X | 0 | $-\frac{\omega {M}^{2}}{{L}_{2}}$ |

Compensation Method | Transmitting End Compensation Capacitor C _{1} | Receiving End Compensation Capacitor C_{2} |
---|---|---|

SS | $\frac{1}{{\omega}^{2}{L}_{1}}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

SP | $\frac{{L}_{2}}{{\omega}^{2}\left({L}_{1}{L}_{2}-{M}^{2}\right)}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

PS | $\frac{{L}_{1}{R}_{\mathrm{L}}^{2}}{{\omega}^{2}\left({M}^{4}+{L}_{1}^{2}{R}_{\mathrm{L}}^{2}\right)}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

PP | $\frac{{L}_{1}-\frac{{M}^{2}}{{L}_{2}}}{\frac{{M}^{4}{R}_{\mathrm{L}}^{2}}{{L}_{2}^{4}}+{\omega}^{2}{({L}_{1}-\frac{{M}^{2}}{{L}_{2}})}^{2}}$ | $\frac{1}{{\omega}^{2}{L}_{2}}$ |

Coil Shape | Outside Diameter (cm) | Area (cm^{2}) | Inductance (uH) | Resistance (mΩ) |
---|---|---|---|---|

Circular | 11.26 | 99.58 | 3.72 | 363 |

Square | 10 | 100 | 3.58 | 393 |

**Table 4.**Self-inductance and resistance value of coil with different thicknesses (turn spacing 0.5 mm).

Coil Thickness (mm) | Self-Inductance (μH) | Resistance (mΩ) |
---|---|---|

0.035 | 5.28 | 402 |

0.05 | 5.26 | 211 |

0.07 | 5.26 | 146 |

**Table 5.**Self-inductance and resistance value of coil with different thicknesses (turn spacing 1.5 mm).

Coil Thickness (mm) | Self-Inductance (μH) | Resistance (mΩ) |
---|---|---|

0.035 | 4.1 | 368 |

0.05 | 4.1 | 189 |

0.07 | 4.08 | 131 |

**Table 6.**Self-inductance and resistance value of coil with different thicknesses (turn spacing 2.5 mm).

Coil Thickness (mm) | Self-Inductance (μH) | Resistance (mΩ) |
---|---|---|

0.035 | 3.21 | 335 |

0.05 | 3.2 | 172 |

0.07 | 3.19 | 119 |

Line Width (mm) | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 |
---|---|---|---|---|---|---|

Quality factor | 17.22 | 17.31 | 17.37 | 17.42 | 17.47 | 17.38 |

Coupling coefficient | 0.1167 | 0.1171 | 0.1175 | 0.1178 | 0.1180 | 0.1181 |

Strong coupling coefficient | 4.04 | 4.11 | 4.17 | 4.21 | 4.25 | 4.21 |

Fill Factor | 0.20 | 0.25 | 0.30 | 0.36 | 0.43 | 0.50 | 0.58 | 0.66 | 0.76 | 0.87 |
---|---|---|---|---|---|---|---|---|---|---|

Coil turns | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

Inside diameter (mm) | 60.2 | 54.2 | 48.2 | 42.2 | 36.2 | 30.2 | 24.2 | 18.2 | 12.2 | 6.2 |

Coil Type | Quality Factor | Self-Inductance (uH) | Resistance (mΩ) |
---|---|---|---|

Single-layer coil | 18.09 | 5.12 | 178 |

Scheme 1 | 21.62 | 5.13 | 149 |

Scheme 2 | 21.08 | 20.61 | 614 |

Coil Number | Thickness (mm) | Turn Spacing (mm) | Line Width (mm) | Number of Turns | Number of Layers |
---|---|---|---|---|---|

1 | 0.035 | 0.5 | 2 | 7 | 1 |

2 | 0.07 | 0.2 | 2 | 7 | 1 |

3 | 0.07 | 0.5 | 2 | 7 | 1 |

4 | 0.07 | 1 | 2 | 7 | 1 |

5 | 0.07 | 0.2 | 2.7 | 7 | 1 |

6 | 0.07 | 0.2 | 2.8 | 7 | 1 |

7 | 0.07 | 0.2 | 2.9 | 7 | 1 |

8 | 0.07 | 0.2 | 2.8 | 8 | 1 |

9 | 0.07 | 0.2 | 2.8 | 9 | 1 |

10 | 0.07 | 0.2 | 2.8 | 8 | 2 |

11 | 0.07 | 0.2 | 2.8 | 8 | 2 |

Coil Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Simulation value | 0.92 | 3.63 | 3.36 | 2.98 | 4.21 | 4.25 | 4.21 | 4.57 | 4.55 |

Measurement calculation value | 0.86 | 3.39 | 3.10 | 2.74 | 3.90 | 4.93 | 3.89 | 4.23 | 4.20 |

**Table 12.**Simulated and measured values of the coil quality factor, self-inductance, and resistance.

Parameter | Single-Layer Coil | Scheme 1 Coil | Scheme 2 Coil |
---|---|---|---|

Quality factor simulation value | 18.09 | 21.61 | 21.08 |

Quality factor measurement value | 17.44 | 20.81 | 20.33 |

Self-perception simulation value (uH) | 5.12 | 5.13 | 20.61 |

Self-inductance measurement value (uH) | 5.25 | 5.27 | 20.85 |

Resistance simulation value (mΩ) | 178 | 152 | 623 |

Resistance measurement value (mΩ) | 189 | 159 | 644 |

Strong Coupling Coefficient Standard Deviation | Single-Layer Coil | Scheme 1 Coil | Scheme 2 Coil |
---|---|---|---|

Coaxial parallel offset | 0.36 | 0.37 | 0.36 |

Coaxial nonparallel offset | 0.04 | 0.02 | 0.01 |

Parallel offset of different axes | 0.05 | 0.07 | 0.05 |

Different axes are not parallel offset | 0.06 | 0.04 | 0.03 |

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

Operating frequency | 98 kHz |

Transmitting and receiving end coil self-sensing | 20.85 uH |

Transmitting and receiving terminal coil resistance | 0.64 Ω |

Compensation capacitance at the transmitting and receiving ends | 126 nF |

Input voltage at the transmitting end | 12 V |

Receiving end load resistance | 5 Ω |

Outer Diameter of Coils | With Magnetic Cores | Operating Frequency | Maximum Transmission Efficiency | Offset Transmission Efficiency | |
---|---|---|---|---|---|

This article | 9 cm | No | 98 kHz | 83.7% | 46.6% |

Reference [34] | 12 cm | Yes | 120 kHz | 65% | 22% |

Reference [35] | 17.2 cm | Yes | 1 MHz | 95% | 41% |

Reference [36] | 4.5 cm | Yes | 200 kHz | 81% | Below 30% |

Reference [37] | 11.8 cm | No | 13.56 MHz | 81.7% | Below 30% |

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## Share and Cite

**MDPI and ACS Style**

Fu, Y.; Zhu, Y.; Jiang, D.; Ji, B.; Peng, Z.
Improved Design of PCB Coil for Magnetically Coupled Wireless Power Transfer. *Electronics* **2024**, *13*, 426.
https://doi.org/10.3390/electronics13020426

**AMA Style**

Fu Y, Zhu Y, Jiang D, Ji B, Peng Z.
Improved Design of PCB Coil for Magnetically Coupled Wireless Power Transfer. *Electronics*. 2024; 13(2):426.
https://doi.org/10.3390/electronics13020426

**Chicago/Turabian Style**

Fu, You, Yu Zhu, Dequan Jiang, Bing Ji, and Zhouhua Peng.
2024. "Improved Design of PCB Coil for Magnetically Coupled Wireless Power Transfer" *Electronics* 13, no. 2: 426.
https://doi.org/10.3390/electronics13020426