Two-dimensional equations for the analysis of microstrip line dispersion and step discontinuities
Bibliographic record
Abstract
It is shown how the two-dimensional equations for microwave planar circuits, which are in fact a generalization of the one-dimensional telegraphists' equations, can be derived through a rigorous theory based on Maxwell's equations. These equations are used in the thesis to calculate the dispersion of the fundamental and of the higher-order modes of propagation on microstrip lines, the losses on microstrip lines, and the components of the equivalent circuit for symmetric, asymmetric, and cascaded microstrip lines. The quasistatic parameters, necessary in the calculation of the modal dispersion, are determined using a new hybrid analytical-numerical approach. Four methods were developed, two of them being variational methods, together with theorems for the lower and upper bound of capacitance. Thus, the error in calculating the quasi-static parameters can be controlled. The results obtained in calculating the dispersion are within the error of measurement range for experimental data. The proposed dispersion model permits also the inclusion of losses in the initial formulation. Thus, the attenuation and the phase constants can be obtained simultaneously. Using the same model, the dispersion of the higher-order modes of propagation is obtained with an error of less than 1% when compared to the more accurate full-wave solution. For symmetric and asymmetric step discontinuities, simple formulas for the components of the equivalent circuit are obtained. The results are in good agreement with those from the fullwave solution, the error being less then 1.5%. In the case of cascaded microstrip lines, the proposed method reduces drastically the computation time while giving acceptable accuracy. The two-dimensional equations can be successfully used up to the cutoff frequency of the first 'TM' mode, well within the operation range of the microstrip lines.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".