Analytical Expressions for Spherical Wire Antenna Quality Factor Demonstrating Exact Agreement Between Circuit-Based and Field Integration Techniques
Bibliographic record
Abstract
Properties of spherical wire antennas are revisited using a circuit analysis approach. This methodology yields the exact quality factor and axial ratio of coupled-mode spherical radiators as analytical expressions. The new circuit-based equations are compared to field integration predictions for quality factor, and both are found to agree for a general multipole expansion of the electromagnetic fields. These two predictions of stored energy inside a spherical wire antenna are shown to be equivalent via direct analysis, while predictions of stored energy outside the spherical wire antenna are compared by way of mathematical induction. Additionally, the circuit analysis reveals general relations between supplied current and radiated power of spherical wire antennas, resonance conditions of coupled-mode systems, and analytical quantification of the trade-off between the quality factor and axial ratio for TM1m–TE1mradiators. New and simple expressions for the minimum quality factor of circular, near-circular, linear, and general elliptical polarizations are provided.
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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 | 0.003 |
| 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 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".