Full-Wave Analysis for Ground Via Placement with Layered Media Integral Equations
Bibliographic record
Abstract
As signaling rates exceed 40 Gbps, detailed electromagnetic analysis of the Ground Return Vias (GRVs) becomes essential. Incorrect GRV placement, whether too far apart or poorly arranged in a ball-grid array, can cause a signal via's insertion loss (IL) to increase substantially. Historically, signal integrity (SI) engineers have placed GRVs near signal layer transitions following conventional practices, often without a precise understanding of the optimal quantity and spacing required. This paper proposes accurate full-wave electromagnetic analysis framework for via placement optimization. The method solves the layered medium Mixed Potential Integral Equation (MPIE) coupled with the Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE), making it suitable for analyzing composite 3D metal/dielectric structures within layered substrates encountered in GRV placement problems.
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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".