#
Optimized NFC Circuit and Coil Design for Wireless Power Transfer with 2D Free-Positioning and Low Load Sensibility^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. The WPT System Overview

## 3. Coil Design and Optimization of Its Dimensions

#### 3.1. Coil Design

_{AC}and a capacitor C

_{p}in parallel. Figure 3 illustrates the circuit.

#### 3.1.1. Coil Inductance

#### 3.1.2. AC Resistance

#### 3.1.3. Parasitic Capacitance

#### 3.1.4. RL Equivalent Circuit

#### 3.2. Optimization of Coil Dimensions by Maximizing the Efficiency

#### 3.2.1. Circuit Analysis

#### 3.2.2. Optimization Procedure

^{®}2020b (The MathWorks, Inc., Natick, MA, USA) are suitable options for the purpose of this work.

^{®}was executed with $13.56\text{}\mathrm{MHz}$ as the operating frequency, with a threshold efficiency of ${\mathsf{\eta}}_{\mathrm{th}}=82\%$, operating separation between coils of ${\mathrm{z}}_{\mathrm{gap}}=5\text{}\mathrm{mm}$, charging surface of $12\text{}\mathrm{cm}\text{}\times 8\text{}\mathrm{cm}$, and the dimensions of the receiver limited to 4$\text{}\mathrm{cm}\text{}\times 4\text{}\mathrm{cm}$ maximum. The conductor’s width and spacing between turns might vary between 0.3$\text{}\mathrm{mm}$ and 1.2$\text{}\mathrm{mm}$, the conductor was set to copper with thickness of 35$\text{}\mathsf{\mu}\mathrm{m}$, and the number of turns was set to a minimum of two. Some constrains were defined, such as a maximum quality factor of 90, maximal inductance of $3\text{}\mathsf{\mu}\mathrm{H}$, positive internal dimensions, and minimal self-resonance frequency. Table 1 illustrates the dimensions of the coils calculated by the algorithm.

^{®}(ANSYS, Inc., Canonsburg, PA, USA), the optimized system was modelled (Figure 7a) and the efficiency was simulated. The result is illustrated in Figure 7b, but thanks to the symmetry, instead of simulating the whole surface, only a quadrant is sufficiently representative. The simulated efficiency ranges from $83.3\%$ (on the center) to $87.3\%$. The simulation results present a minimal discrepancy regarding the theory, which can be justified by the approximations made on (4).

## 4. System Optimization Proposition

#### 4.1. Optimization of Dimensions through Figure of Merit Maximization

#### 4.2. Receiver’s Circuit Design and Optimization

#### 4.3. Transmitter’s Circuit Design and Optimization

## 5. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 6.**MATLAB

^{®}optimization results (efficiency in %) are represented as (

**a**) a 3D plot of efficiency vs. the x and y axis; (

**b**) 2D plot of the efficiency seen by the top. The coordinates x and y represent the center position of the receiver. The dashed red line represents the Rx contour in an extreme position (its “center” is located at x = 4 cm and y = −2 cm).

**Figure 7.**(

**a**) 3D Model representing the optimized coils and the representation of the charging surface; (

**b**) electromagnetic simulation results of the efficiency (%) of the optimized coils.

**Figure 8.**(

**a**) The manufactured transmitter and receiver prototypes; (

**b**) the experimental efficiency (%) results of the optimized coils for all charging area. Only positions inside the effective charging area were measured.

**Figure 10.**Theoretical results of the S, P, and SP topologies are represented as plots of (

**a**) efficiency vs. load resistance; (

**b**) current gain (ratio between the current through the load and the current thought the Tx coil) vs. load resistance.

**Figure 12.**Theoretical transmitter’s load impedance caused by receivers of type S, P, and SP is represented as (

**a**) real part vs. receiver’s load; (

**b**) imaginary part vs. receiver’s load.

**Figure 13.**(

**a**) Theoretical transmitter’s transconductance vs. resistance of the transmitter’s load for four values of reactance of the transmitter’s load. (

**b**) Delivered power to the receiver’s load vs. receiver’s load for the three types of compensation and the sinusoidal voltage supply set to 8 V of amplitude.

**Figure 14.**Measurement setup for the new prototypes are shown: (

**a**) top view: receiver at horizonal position with VNA connections; (

**b**) side view: separation $\left({Z}_{gap}=10\text{}\mathrm{mm}\right)$, trimmers, and SP compensation network.

**Figure 15.**Efficiency measurements for a fixed load of $50\text{}\mathsf{\Omega}$ with the input always adapted to $50\text{}\mathsf{\Omega}$: (

**a**) 3D plot of efficiency vs. the x and y axes; (

**b**) 2D plot of the efficiency seen from the top. The coordinates x and y represent the center position of the receiver. The dashed line represents the Rx contour in an extreme position (its “center” is located at x = 4 cm and y = −2 cm).

**Figure 16.**Efficiency vs. load resistance for four different positions of the receiver. The Rx is connected to an SP compensation network and the Tx is always adapted to $50\mathsf{\Omega}$.

$\mathbf{N}$ | $\mathit{a}\left(\mathbf{cm}\right)$ | $\mathbf{b}\left(\mathbf{cm}\right)$ | $\mathbf{w}\left(\mathbf{mm}\right)$ | $\mathbf{g}\left(\mathbf{mm}\right)$ | |
---|---|---|---|---|---|

Tx | 3 | 11.27 | 7.65 | 0.3 | 0.9 |

Rx | 4 | 4 | 4 | 0.4 | 1 |

**Table 2.**Comparative table of the theoretical, simulation, and experimental results of the efficiency and electrical parameters at $13.56\text{}\mathrm{MHz}$.

${\mathit{\eta}}_{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{\eta}}_{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{R}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Tx}\right)$ | ${\mathit{L}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Tx}\right)$ | ${\mathit{R}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Rx}\right)$ | ${\mathit{L}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Rx}\right)$ | |
---|---|---|---|---|---|---|

Theory | 82.2% | 87.2% | 2.93 Ω | 2.83 µH | 1.17 Ω | 1.24 µH |

Simulation | 83.3% | 87.3% | 2.78 Ω | 2.88 µH | 1.07 Ω | 1.27 µH |

Measurements | 81.7% | 87.0% | 2.88 Ω | 2.99 µH | 1.23 Ω | 1.30 µH |

$\mathbf{N}$ | $\mathit{a}\left(\mathbf{cm}\right)$ | $\mathbf{b}\left(\mathbf{cm}\right)$ | $\mathbf{w}\left(\mathbf{mm}\right)$ | $\mathbf{g}\left(\mathbf{mm}\right)$ | |
---|---|---|---|---|---|

Tx | 3 | 11.4 | 7 | 1.2 | 0.9 |

Rx | 5 | 4 | 4 | 1.2 | 0.4 |

**Table 4.**Comparative table of theoretical results, simulations, and measurements of the electrical parameters and quality factor at $13.56\text{}\mathrm{MHz}$.

${\mathit{R}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Tx}\right)$ | ${\mathit{L}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Tx}\right)$ | $\mathit{Q}\text{}\left(\mathbf{Tx}\right)$ | ${\mathit{R}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Rx}\right)$ | ${\mathit{L}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{Rx}\right)$ | $\mathit{Q}\text{}\left(\mathbf{Rx}\right)$ | |
---|---|---|---|---|---|---|

Theory | 846 mΩ | 2.08 µH | 210 | 527 mΩ | 1.36 µH | 220 |

Simulations | 836 mΩ | 2.17 µH | 221 | 628 mΩ | 1.40 µH | 190 |

Measurements | 978 mΩ | 2.33 µH | 202 | 663 mΩ | 1.41 µH | 181 |

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**MDPI and ACS Style**

Buchmeier, G.G.; Takacs, A.; Dragomirescu, D.; Alarcon Ramos, J.; Fortes Montilla, A.
Optimized NFC Circuit and Coil Design for Wireless Power Transfer with 2D Free-Positioning and Low Load Sensibility. *Sensors* **2021**, *21*, 8074.
https://doi.org/10.3390/s21238074

**AMA Style**

Buchmeier GG, Takacs A, Dragomirescu D, Alarcon Ramos J, Fortes Montilla A.
Optimized NFC Circuit and Coil Design for Wireless Power Transfer with 2D Free-Positioning and Low Load Sensibility. *Sensors*. 2021; 21(23):8074.
https://doi.org/10.3390/s21238074

**Chicago/Turabian Style**

Buchmeier, Guilherme Germano, Alexandru Takacs, Daniela Dragomirescu, Juvenal Alarcon Ramos, and Amaia Fortes Montilla.
2021. "Optimized NFC Circuit and Coil Design for Wireless Power Transfer with 2D Free-Positioning and Low Load Sensibility" *Sensors* 21, no. 23: 8074.
https://doi.org/10.3390/s21238074