High-Performance Time-to-Digital Conversion on a 16-nm Ultrascale+ FPGA
Bibliographic record
Abstract
In recent years, field-programmable gate arrays (FPGAs) have emerged as promising platforms for implementing picosecond-resolution time-to-digital converters (TDCs). Tapped delay-lines (TDLs) are simple to implement but require careful design decisions for high precision and linearity. Although various implementation strategies have been explored in TDC literature across different FPGA technology nodes, the 16-nm node has only recently begun to receive attention. The goal of this study is to leverage a 16-nm FPGA for TDL-TDCs with the requirement of maintaining implementation simplicity while ensuring top-tier performance. We investigated, combined, and optimized various state-of-the-art TDL techniques using an AMD-Xilinx Zynq Ultrascale+ RFSoC. The 16-nm node offers logic buffers (CARRY8) with low propagation delay, ideal for the construction of TDLs. We designed multi-channel TDCs utilizing both single and multiple carry chain TDLs. Propagating a single signal edge allows the use of a simple, bubble-free ones-counting encoder. Buffer redundancy subdivides the bins of the code density histogram, whose linearity is further enhanced by bin decimation. The optimal placement of the TDL elements is considered, together with the sampling clock frequency and source. We demonstrate the capabilities of the TDCs in terms of full-scale range (FSR), dead time, nominal resolution (LSB), RMS precision, differential and integral nonlinearity, hardware utilization, and power consumption. This method leads to TDCs that are simple to implement yet excel in performance, linearity, and sampling rate. For example, we propose a 4-chain TDC achieving LSB < 4 ps, single shot precision (SSP) < 3 ps, DNL < 1 LSB and INL < 2 LSB.
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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 | 0.000 | 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) | 0.004 | 0.001 |
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".