# Simple, Fast, and Accurate Broadband Complex Permittivity Characterization Algorithm: Methodology and Experimental Validation from 140 GHz up to 220 GHz

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## Abstract

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## 1. Introduction

## 2. Theories and Algorithms

#### 2.1. Circuit Theory of the Sensing Device

#### 2.2. Characterization Algorithm

## 3. Device Fabrication and Measurements

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MUT | material under test |

TL | transmission line |

CPW | coplanar waveguide |

VNA | vector network analyzer |

p.u.l | per unit length |

GSG | signal-ground-signal |

TRL | thru-reflect-line |

DI | de-ionized |

FEM | finite element method |

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**Figure 1.**A transmission-line-based sensing device, with the material under test being contained in a microfluidic channel formed by SU-8 polymer walls.

**Figure 3.**On-wafer measurement setup, including the probe station, the microfluidic sensing chip, and the multiline-TRL calibration standards.

**Figure 4.**The extracted real part (

**a**) and imaginary part (

**b**) complex permittivity of de-ionized water within the broadband millimeter wave frequency range between 140 and 220 GHz, using the proposed fast and simple characterization algorithm.

**Figure 5.**Frequency dependence of the extracted per-unit-length resistance R (

**a**) and the extracted per-unit-length inductance L (

**b**) within the frequency range from 140 to 220 GHz.

**Table 1.**Coefficient values of the Double-Debye function for calculating the frequency- and temperature-dependent complex permittivity of water.

Coefficient | Value | Coefficient | Value | Coefficient | Value |
---|---|---|---|---|---|

${a}_{1}$ | 79.42385 | ${a}_{2}$ | 3.611638 | ${t}_{c}$ | 132.6248 |

${b}_{1}$ | 0.004319728 | ${b}_{2}$ | 0.01231281 | ||

${c}_{1}$ | 1.352835 × ${10}^{-13}$ | ${c}_{2}$ | 1.005472 × ${10}^{-14}$ | ||

${d}_{1}$ | 653.3092 | ${d}_{2}$ | 743.0733 |

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**MDPI and ACS Style**

Bao, X.; Wang, L.; Wang, Z.; Zhang, J.; Zhang, M.; Crupi, G.; Zhang, A.
Simple, Fast, and Accurate Broadband Complex Permittivity Characterization Algorithm: Methodology and Experimental Validation from 140 GHz up to 220 GHz. *Electronics* **2022**, *11*, 366.
https://doi.org/10.3390/electronics11030366

**AMA Style**

Bao X, Wang L, Wang Z, Zhang J, Zhang M, Crupi G, Zhang A.
Simple, Fast, and Accurate Broadband Complex Permittivity Characterization Algorithm: Methodology and Experimental Validation from 140 GHz up to 220 GHz. *Electronics*. 2022; 11(3):366.
https://doi.org/10.3390/electronics11030366

**Chicago/Turabian Style**

Bao, Xiue, Li Wang, Zeyu Wang, Jiabei Zhang, Meng Zhang, Giovanni Crupi, and Anxue Zhang.
2022. "Simple, Fast, and Accurate Broadband Complex Permittivity Characterization Algorithm: Methodology and Experimental Validation from 140 GHz up to 220 GHz" *Electronics* 11, no. 3: 366.
https://doi.org/10.3390/electronics11030366