Derivation and Design of In-Loop Filters in Phase-Locked Loop Systems
Bibliographic record
Abstract
This paper addresses the concept of in-loop filters in phase-locked loop (PLL) systems. The in-loop filters are derived from an optimization perspective, and an analytical method to design the controlling parameters of a PLL with in-loop filters is also presented. Such filters can also be selected as conventional window functions in which case they can be tuned to reject certain frequency components similar to the discrete Fourier transform. In this paper, a rigorous method to introduce the concept of in-loop filters and window functions into PLL systems is presented. This method enables smoother estimation of the signal parameters such as phase angle, frequency, and amplitude in the presence of noise and harmonics. The in-loop filters can be adjusted to completely remove specific harmonics. The method is first developed for a single-phase enhanced PLL system and is then extended to three-phase PLLs including the well-known synchronous-reference-frame PLL. Simulation and experimental results are also included.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".