Frequency-Domain Study of Lock Range of Non-Harmonic Oscillators With Multiple Multi-Tone Injections
Bibliographic record
Abstract
This paper presents a frequency-domain study of the lock range of non-harmonic oscillators with multiple multi-tone injections. By representing non-harmonic oscillators with a set of harmonic oscillators, the intrinsic relation between the lock range of harmonic oscillators and that of non-harmonic oscillators is obtained. We show non-harmonic oscillators with a multi-tone injection exhibit a larger lock range as compared with that with a single-tone injection. We further show non-harmonic oscillators with multiple single-tone injections exhibit a larger lock range as compared with that with a single single-tone injection. The condition upon which non-harmonic oscillators with multiple single-tone injections exhibit a larger lock range as compared with those with a single-tone injection is derived. The condition upon which non-harmonic oscillators with multiple multi-tone injections exhibit a larger lock range as compared with those with a single multi-tone injection is also derived. The theoretical findings are verified using a dual-comparator relaxation oscillator designed in an IBM 130 nm 1.2 V CMOS technology and analyzed using Spectre from Cadence Design Systems with BSIM4 device models.
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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) | 0.001 | 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".