# Discrepancies of Measured SAR between Traditional and Fast Measuring Systems

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## Abstract

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## 1. Introduction

- Why do discrepancies appear for the estimation of SAR by different fast measuring systems?
- Can we say fast measuring systems generate biased estimations if they differ appreciably from the traditional SAR measuring system?
- Which of the traditional measuring system and the fast measuring system is the more accurate?

## 2. Traditional SAR Measuring System

- Area scan: measure fields according to a two-dimensional coarse grid, the distance of which to the phantom surface is fixed, to locate the local maxima of the amplitude of electric fields.
- Zoom scan: a three-dimensional scanning within cubes centered at the location of local maxima, the grid step being smaller than that in the area scan.
- Interpolation and extrapolation: linear interpolation and cubic spline interpolation (and extrapolation) are used as necessary to deduce the amplitude at the points in a finer grid.
- Peak spatial-average SAR: obtained by performing numerically the integration in (1) based on the interpolated and extrapolated amplitude.

## 3. Fast SAR Measuring System Based on Field Reconstruction

#### 3.1. Plane-Wave Expansion (PWE)

#### 3.2. Field Reconstruction Making Use of More High-Frequency Components

## 4. Numerical Results

#### 4.1. Configurations

#### 4.2. Verification of Post-Processing Procedures

#### 4.3. Problem in Field Reconstructions

#### 4.4. Uncertainty of Factors

#### 4.5. Comparison between the Traditional and Fast Measuring Systems

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Field reconstruction with respect to the fourth case. ${E}^{\mathrm{PWE}}$ and ${E}^{\mathrm{Ref}}$ denote the reconstructed field and the reference field, respectively.

**Figure 4.**Estimation of peak 1 $\mathrm{g}$ and 10 $\mathrm{g}$ SAR based PWE field-reconstruction method by assigning four different values to $\delta $.

**Figure 5.**Field reconstruction with respect to the seventh case, $\left|E\right|$ denotes the amplitude of electric field, $\left|F\right|$ the amplitude of spectrum, and the superscript “PWE”, “Ref” indicate the reconstructed field and the reference field, respectively.

**Figure 6.**Box plots of estimated values of peak 1 g SAR for the 4th case, fields are reconstructed with the PWE approach by setting various values of $\delta $.

**Figure 7.**Comparison of estimated peak sSAR by traditional measurement approach (with linear and spline interpolations) and the fast method based on field reconstructions with PWE.

Area scan | maximum grid spacing | 20 mm if $f<$ 3 GHz and $60/f$ mm otherwise |

maximum distance between probe and surface of phantom | 5 mm if $f<$ 3 GHz and $\delta ln2/2$ mm otherwise | |

Zoom scan | horizontal grid spacing | $\le min\{24/f,8\}$ mm |

minimum scan size | $30\text{}\mathrm{mm}\text{}\times 30\text{}\mathrm{mm}\text{}\times 30\text{}\mathrm{mm}$ if $f<$ 3 GHz and $22\text{}\mathrm{mm}\text{}\times 22\text{}\mathrm{mm}\text{}\times 22\text{}\mathrm{mm}$ otherwise | |

maximum distance between probe and surface of phantom | 5 mm if $f<$ 3 Ghz and $\delta ln2/2$ mm otherwise |

Index | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|

f (MHz) | 850 | 1800 | 1900 | 2450 | 5500 | 5800 | 750 | 1950 | 750 | 835 | 1750 |

${\u03f5}_{r}$ | 42.23 | 40.45 | 40.28 | 39.37 | 33.30 | 32.64 | 42.47 | 40.20 | 42.47 | 42.26 | 40.53 |

$\sigma $ (S/m) | 0.89 | 1.39 | 1.45 | 1.87 | 5.18 | 5.55 | 0.85 | 1.49 | 0.85 | 0.88 | 1.35 |

10g SAR | 0.58 | 0.48 | 0.48 | 0.43 | 0.29 | 0.28 | 0.28 | 0.41 | 0.66 | 0.65 | 0.52 |

**Table 3.**Description and distribution of input variables. $\mathcal{U}(a,b)$ denotes the uniform distribution with limits a and b, and $\mathcal{N}(\mu ,\tau )$ denotes the normal distribution with mean $\mu $ and standard deviation $\tau $.

Variable | Description | Distribution |
---|---|---|

${x}_{p},{y}_{p},{z}_{p}$ (mm) | Cartesian coordinates of the probe position | ${a}_{p}^{\mathrm{Ref}}+\mathcal{U}(-0.1,0.1)$, a being x, y, or z |

${\u03f5}_{r}$ | relative permittivity | ${\u03f5}_{r}^{\mathrm{Ref}}+{\u03f5}_{r}^{\mathrm{Ref}}\mathcal{U}(-0.1,0.1)$ |

$\sigma $ (S/m) | conductivity | ${\sigma}^{\mathrm{Ref}}+{\sigma}^{\mathrm{Ref}}\mathcal{U}(-0.1,0.1)$ |

c (dB) | coupling coefficient | ${c}^{\mathrm{Ref}}+\mathcal{U}(-2,2)$ |

$\left|E\right|$ | amplitude of electric field | ${\left|E\right|}^{\mathrm{Ref}}+{\left|E\right|}^{\mathrm{Ref}}\mathcal{N}(0,0.025)$ |

$\angle E$ (radian) | phase angle of electric field | $\angle {E}^{\mathrm{Ref}}+\angle {E}^{\mathrm{Ref}}\mathcal{N}(0,0.025)$ |

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**MDPI and ACS Style**

Liu, Z.; Allal, D.; Cox, M.; Wiart, J. Discrepancies of Measured SAR between Traditional and Fast Measuring Systems. *Int. J. Environ. Res. Public Health* **2020**, *17*, 2111.
https://doi.org/10.3390/ijerph17062111

**AMA Style**

Liu Z, Allal D, Cox M, Wiart J. Discrepancies of Measured SAR between Traditional and Fast Measuring Systems. *International Journal of Environmental Research and Public Health*. 2020; 17(6):2111.
https://doi.org/10.3390/ijerph17062111

**Chicago/Turabian Style**

Liu, Zicheng, Djamel Allal, Maurice Cox, and Joe Wiart. 2020. "Discrepancies of Measured SAR between Traditional and Fast Measuring Systems" *International Journal of Environmental Research and Public Health* 17, no. 6: 2111.
https://doi.org/10.3390/ijerph17062111