Thickness-Independent Permittivity Determination of Nondispersive or Weakly Dispersive Materials Using Amplitude-Only Transmission Measurements
Bibliographic record
Abstract
This article presents an attractive microwave technique for permittivity ($\varepsilon _{r} = \varepsilon _{r}^{\prime } {-} j \varepsilon _{r}^{\prime \prime }$) extraction of nondispersive or weakly dispersive dielectric materials. The technique uses amplitude-only transmission$|S_{21}|$measurements at multiple frequencies without requiring the information of sample thickness (d). To achieve this goal, the state transition matrix (STM) was first applied for determining$|S_{21}|$, and then the least minimum square (LMS) procedure was implemented to the derived objective function for unique$\varepsilon _{r}$determination. Numerical analyses were performed to validate the proposed extraction technique and evaluate the effect of inaccurate d information on$\varepsilon _{r}$determination by other similar techniques in the literature. Its performance is examined by numerical analyses based on the different number of frequency points M within a given frequency band and based on different frequency bands for the same M. Waveguide measurements at the S-band (2.60–3.95 GHz) and the G-band (3.95–5.85 GHz) of four low-loss nondispersive or weakly dispersive samples (dioxane, cyclohexane, polyethylene, and chloroform) and two lossy dispersive samples (ethanol and dimethyl sulfoxide) with different lengths were carried out to validate the proposed extraction technique and compare its accuracy against other similar methods in the literature. From measurements of low-loss nondispersive or weakly dispersive samples, it is noted that the accuracy of our extraction method does not change much with d. For instance, extracted$\varepsilon _{r}$of the cyclohexane (chloroform) sample with three different lengths differs from the reference value by less than 1% for$\varepsilon _{r}^{\prime }$and 3% for$\varepsilon _{r}^{\prime \prime }$. Although the accuracy of the proposed method lowers for dispersive samples, it can still find applications for low-cost accurate$\varepsilon _{r}$determination of nondispersive and/or weakly dispersive dielectric samples.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".