A Discrete Adjoint Variable Method for Printed-Circuit Board Computer-Aided Design
Bibliographic record
Abstract
We propose an adjoint-variable method for design sensitivity analysis of printed circuits and antennas where allowable perturbations in the design parameters are of a discrete type. We extend previous work on the sensitivity analysis of waveguide structures, where changes in the design parameters are stepwise, on-grid volumetric perturbations. Here, we explore the feasibility of such an approach in the case of printed-circuit board problems (with open boundaries) where perturbations relate to the shapes elements of infinitesimal thickness. We propose a complex-variable formulation of our approximate sensitivity analysis that improves its computational efficiency. The proposed technique offers significant increases in efficiency, accuracy, and convergence when compared to traditional sensitivity-analysis techniques. Its implementation is straightforward. The response and its gradient with respect to all possible design parameters are computed with at most two full-wave analyses—of the original and the adjoint problems. It operates on a fixed discretization grid where perturbations of grid nodes are not needed. We illustrate our technique through the sensitivity analysis of a microstrip line and a probe-fed printed patch antenna as well as the optimization of a printed Yagi antenna array.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".