Repeater Sizing and Insertion Length of Interconnect to Minimize the Overall Time Delay using a Truncated Fourier Series Approach
Bibliographic record
Abstract
Computation of accurate time domain signal waveforms in VLSI interconnects, taking into account the distributed inductance of the line, has grown in importance with increasing clock speeds. A computationally efficient truncated Fourier series method for computing time domain waveforms is summarized in this work. The method assumes excitation of the VLSI interconnect modeled in the frequency domain, by periodic trapezoidal waveforms. The problem of optimizing repeater size and interconnect insertion length to minimize time delay in long interconnects, taking into account the transmission line nature of the interconnect using this Fourier series method is developed in this work. The Nelder-Mead simplex optimization technique is used to perform the actual optimizations. At each step of the Nelder-Mead iteration, the candidate interconnect length and repeater scaling at that iteration is used to evaluate the output time response using the truncated Fourier series. The results of the optimization by this method are compared with that obtained by a fourth-order Fade approximation based optimization technique in the literature. The results of the two optimization studies show significant differences in overall optimized time delay per meter. The differences are attributable to the error in the Fade approximation of the transfer function of the interconnect and terminations
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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) | 0.000 | 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".