A qualitative simulation approach for verifying PLL locking property
Bibliographic record
Abstract
Simulation cannot give a full coverage of Phase Locked Loop (PLL) behavior in presence of process variation, jitter and varying initial conditions. Qualitative Simulation is an attracting method that computes behavior envelopes for dynamical systems over continuous ranges of their parameters. Therefore, this method can be employed to verify PLLs locking property given a model that encompasses their imperfections. Extended System of Recurrence Equations (ESREs) offer a unified modeling language to model analog and digital PLLs components. In this paper, an ESRE model is created for both PLLs and their imperfections. Then, a modified qualitative simulation algorithm is used to guarantee that the PLL locking time is sound for every possible initial condition and parameter value. We used our approach to analyze a Charge Pump-PLL for a $0.18\mu m$ fabrication process and in the presence of jitter and initial conditions uncertainties. The obtained results show an improvement of simulation coverage by computing the minimum locking time and predicting a non locking case that statistical simulation technique fails to detect.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".