Simple Analytical Dispersion Equations for the Shielded Sievenpiper Structure
Bibliographic record
Abstract
Closed form expressions for the dispersion curves of the shielded Sievenpiper structure are derived in terms of the geometric and electromagnetic parameters of the structure. A compact form of the dispersion equation is presented in this paper, arrived at by using multiconductor transmission-line theory and assuming that the series loading capacitor and shunt loading inductor are added to the per-unit length impedance and admittance matrices in a continuous (homogeneous) manner. This approximate model is shown to yield excellent agreement with the full model (in which the loading parameters are not incorporated in a continuous manner), under suitable conditions. The dispersion curve provided by this model is analyzed and it is shown that there exists a frequency band (stopband) supporting complex modes. Analytical expressions for the edges of this complex-mode band are derived, and the variation of these expressions as functions of the geometry is explored
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".