Asymptotic Limits of Negative Group Delay in Active Resonator-Based Distributed Circuits
Bibliographic record
Abstract
In this paper the asymptotic limits of negative group delay (NGD) phenomena in multi-stage RLC resonator-based circuits are discussed. A NGD-bandwidth-product limit is derived as a function of the number of stages and the out-of-band gain, which is independent of the circuit topology and can include active gain compensation. The limit is verified experimentally at microwave frequencies using a gain-compensated NGD circuit employing a parallel RLC resonator in the feedback path of a high-frequency op-amp. It is shown that, in the asymptotic limit, the NGD-bandwidth-product is proportional to the square root of the number of stages, and also to the square root of the logarithm of the out-of-band gain. The relation between the time-domain transient amplitude and the out-of-band gain is analyzed for finite-duration modulated signals, indicating an exponential increase in transient amplitudes with the square of NGD. Analysis shows that any attempt to increase the NGD of a finite-duration modulating waveform, by cascading more stages, is thwarted by the transients.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".