Normalized geometrical analysis: unified theory and derivation of natural trajectories for basic dc-dc topologies
Bibliographic record
Abstract
This paper introduces a generalized derivation and equation that represents the behavior of the basic dc-dc topologies (namely buck, boost, and buck-boost converters) in a normalized geometrical domain. The establishment of a unified theory is an important step towards understanding the natural trajectories and physical limits of power converters. A comprehensive insight into geometrical characteristics allows for the derivation and benchmarking of high-performance controllers, which results in enhanced dynamic responses. The contribution of the normalized geometrical domain analysis relates to the understanding of the highly non-linear nature and large-signal characteristics of converters not covered by small-signal, linearized modeling around a quiescent operating point. Experimental results of buck, boost, and buck-boost converters are provided to illustrate the geometrical behavior described by a unified equation and the benefits of the state-plane analysis.
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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 | 0.001 |
| 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".