Analysis of Clock-Jitter Effects in Continuous-Time $\Delta \Sigma $ Modulators Using Discrete-Time Models
Bibliographic record
Abstract
This paper proposes a simple discrete-time (DT) modeling technique for the rapid, yet accurate, simulation of the effect of clock jitter on the performance of continuous-time (CT) DeltaSigma modulators. The proposed DT modeling technique is derived from the impulse-invariant transform and is applicable to arbitrary-order lowpass and bandpass CT DeltaSigma modulators, with single-bit or multibit feedback digital-to-analog converters (DACs) employing delayed return-to-zero (RZ) or non-return-to-zero (NRZ) rectangular pulses. Its accuracy is independent of both the power spectrum of the clock jitter and the loop transfer function of the DeltaSigma modulator. The proposed DT modeling technique is validated (for both independent and accumulated clock-jitter errors) against accurate simulations in SIMULINK, using behavioral blocks developed to directly simulate RZ or NRZ DACs with clock jitter. It is subsequently applied to various CT DeltaSigma modulator architectures (low- pass and bandpass, with single-bit and multibit DACs) to study the relative effectiveness of different feedback-DAC pulsing schemes (NRZ, RZ, RZ with fixed on-time, and RZ with fixed off-time) in minimizing the modulator sensitivity to clock jitter. The performance of each architecture is compared as a function of clock jitter, thereby offering a valuable reference for selecting a rectangular feedback-DAC pulse shape when designing CT DeltaSigma analog-to-digital converters.
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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 | 0.001 | 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".