Broadband Dielectric Spectroscopy with a Microwave Ablation Antenna
Abstract
:1. Introduction
2. Materials and Methods
2.1. Antenna Model and Numerical Simulation Settings
2.2. De-Embedding Models for Reconstructing Dielectric Properties
- capacitance represents the fringing field in the dielectric core of the probe; it is the capacitance between the inner and outer conductor of the probe,
- capacitance represents the fringing field in the outer dielectric material (MUT); capacitance represents the fringing field in free space (when no MUT is located at the probe’s aperture),
- conductance represents the radiation conductance of the probe; conductance is the radiation conductance in free space.
- S&S model
- M&E model
- S&S model
- M&E model
- is the normalized radiation conductance,
- is the difference in reflection coefficients, ρi.j is the measured reflection coefficient when the probe is immersed in one of the known calibration standards (i, j = 1, 2, 3), ρm is the measured reflection coefficient when the probe is immersed in the MUT,
- is the input probe admittance when it is immersed in one of the known calibration standards (j = 1, 2, 3).
- and are the real and imaginary parts of reference complex permittivity of the MUT at the given frequency,
- and are the real and imaginary parts of the calculated complex permittivity, obtained using a specific de-embedding model and a combination of calibration standards.
Dielectric Properties of Selected Materials
- ε∞ is the infinite permittivity (at a very high frequency),
- εs is the static permittivity,
- τ is the relaxation time constant,
- ω is the angular frequency,
- α is an empirical parameter for broadening the dispersion,
- σi is the ionic conductivity,
- ε0 is the permittivity of the vacuum.
3. Results
3.1. Validation of The Numerical Model of the Antenna
3.2. De-Embedding Models’ Comparison
- OC, 0.1 mol and 2 mol NaCl,
- DW, 0.1 mol and 2 mol NaCl,
- DW, 1 mol NaCl and 2 mol NaCl.
- DW, 1 mol NaCl and EG70.
- OC, DW, 0.1 mol and 2 mol NaCl,
- DW, EG70, 1 mol NaCl and 2 mol NaCl,
- DW, EG70, 0.1 mol NaCl and 2 mol NaCl.
3.3. Antenna Sensitivity Analysis
3.3.1. Transversal Dimension Influence
3.3.2. Longitudinal Dimension Influence
3.4. Analysis of the Insertion Depth Influence
4. Discussion
- The optimal de-embedding model and calibration for reconstructing dielectric properties of MUT.
- Sensing region of the antenna.
- Immersion depth limitation.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Design Parameter | Parameter Value [mm] |
---|---|
Antenna: structure | |
2 | |
7.7 | |
1.75 | |
0.55 | |
5.28 | |
100 | |
50 | |
Antenna: cross-section | |
0.15 | |
0.485 | |
0.595 | |
0.795 | |
1.095 | |
1.295 | |
MUT block (cube) | |
Cube edge | 100 |
Material | |||||
---|---|---|---|---|---|
Liver [15] | 44.32 | 5.32 | 11.55 | 0.25 | 36.115–j13.799 |
DW at 25 °C [24] | 78.36 | 5.2 | 8.27 | / * | 72.268–j20.213 |
0.1 mol NaCl (at 20 °C) [25] | 78.1 | 5.22 | 9.1 | 0.96 | 70.879–j22.071 |
1 mol NaCl (at 20 °C) [21] | 67.9 | 5.22 | 8.53 | 7.81 | 62.377–j41.971 |
2 mol NaCl (at 20 °C) [21] | 59.4 | 5.22 | 8.13 | 13.29 | 55.028–j55.944 |
EG70 (at 25 °C) [26] | 53.96 | 3.99 | 58.34 | / * | 19.175–j15.080 |
Measurement Sensitivity | ||||
---|---|---|---|---|
3–10 GHz Range | @5.8 GHz | |||
Calibration Option | ||||
OC, 0.1 mol and 2 mol NaCl | 13.15 | 40.59 | 6.61 | 32.30 |
DW, 0.1 mol and 2 mol NaCl | 12.95 | 26.11 | 13.52 | 33.13 |
DW, 1 mol and 2 mol NaCl | 15.44 | 33.84 | 7.57 | 23.22 |
DW, 1 mol NaCl and EG70 | 0.85 | 3.09 | 0.07 | 1.09 |
Measurement Sensitivity | ||||
---|---|---|---|---|
In the 3–10 GHz Range | At 5.8 GHz | |||
Calibration Option | ||||
OC, DW, 0.1 mol and 2 mol NaCl | 12.75 | 20.70 | 13.35 | 11.52 |
DW, EG70, 1 mol and 2 mol NaCl | 3.28 | 6.61 | 2.46 | 0.14 |
DW, EG70, 0.1 mol and 2 mol NaCl | 1.48 | 6.57 | 1.42 | 3.20 |
Measurement Sensitivity | ||||
---|---|---|---|---|
In the 5–6 GHz Range | At 5.8 GHz | |||
100 × 100 | 0.29 | 1.33 | 0.07 | 1.09 |
90 × 100 | 0.30 | 1.26 | 0.04 | 1.02 |
80 × 100 | 0.08 | 1.85 | 0.29 | 1.42 |
70 × 100 | 0.28 | 1.34 | 0.06 | 1.02 |
60 × 100 | 0.28 | 1.46 | 0.10 | 1.56 |
50 × 100 | 0.39 | 1.38 | 0.26 | 1.39 |
40 × 100 | 0.33 | 1.48 | 0.10 | 1.50 |
30 × 100 | 2.13 | 4.74 | 1.56 | 2.55 |
20 × 100 | 4.28 | 4.48 | 6.36 | 3.46 |
15 × 100 | 6.17 | 37.37 | 3.04 | 17.55 |
10 × 100 | 58.22 | 79.88 | 45.76 | 121.88 |
Measurement Sensitivity | ||||
---|---|---|---|---|
In the 5–6 GHz Range | At 5.8 GHz | |||
Antenna Immersion [mm] | ||||
50 | 0.29 | 1.33 | 0.07 | 1.09 |
45 | 2.00 | 7.89 | 1.61 | 7.06 |
40 | 1.55 | 7.33 | 1.66 | 8.64 |
30 | 5.57 | 17.21 | 0.66 | 20.08 |
20 | 24.98 | 20.15 | 7.81 | 21.97 |
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Vidjak, K.; Hessinger, C.; Cavagnaro, M. Broadband Dielectric Spectroscopy with a Microwave Ablation Antenna. Sensors 2023, 23, 2579. https://doi.org/10.3390/s23052579
Vidjak K, Hessinger C, Cavagnaro M. Broadband Dielectric Spectroscopy with a Microwave Ablation Antenna. Sensors. 2023; 23(5):2579. https://doi.org/10.3390/s23052579
Chicago/Turabian StyleVidjak, Klementina, Carolin Hessinger, and Marta Cavagnaro. 2023. "Broadband Dielectric Spectroscopy with a Microwave Ablation Antenna" Sensors 23, no. 5: 2579. https://doi.org/10.3390/s23052579
APA StyleVidjak, K., Hessinger, C., & Cavagnaro, M. (2023). Broadband Dielectric Spectroscopy with a Microwave Ablation Antenna. Sensors, 23(5), 2579. https://doi.org/10.3390/s23052579