A Closed-Form Full-Wave Model for the Reflection Coefficient of an Open-Ended Coaxial Probe for Real-Time Dielectric Spectroscopy
Bibliographic record
Abstract
Dielectric spectroscopy using open-ended coaxial probes characterizes the permittivity of a material based on its interference with a transmitted electromagnetic wave, offering many applications spanning from human health to non-destructive testing. The permittivity is uniquely tied to the material's reflection coefficient, that is, the ratio between the magnitude of the reflect wave to that of the incident wave. Various models have been proposed to relate the permittivity of the material to the measured reflection coefficient, but they all suffer from a common trade off: When they favour simplicity, they neglect higher order modes and become inaccurate. When using full-wave analysis, they are indeterminate, computationally intensive with no closed-form solution, and cannot be used in real-time. In this paper we introduce for the first time a novel full-wave, closed-form model for the reflection coefficient of an open-ended coaxial probe. Our novel model combines full-wave analysis with a Taylor series expansion to reduced the forward problem to a simple matrix inversion, significantly reducing the computational costs of full-wave analysis, while maintaining unparalleled accuracy. The proposed model is validated experimentally through 200 measurements in methanol and with extended permittivity ranges over 1800 simulations in Ansys. The average modelling errors compared to experimental and simulation results are 0.92 % and 1.5 %, respectively, making this model a significant step towards full-wave real-time spectroscopy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".