Speaker
Description
The waveform sampler in the CMS ETROC2 chip for LGAD gain aging monitoring is a 2.56-GS/s 12-bit 8x-Interleaved ADC that consists of a coarse SAR stage, and a fine stage. This architecture delivers high performance on a relatively modest 65 nm process, while requires finding up to 24 calibration constants through calibration. We developed an automatic calibration method using charge injection test data. After calibration, the baseline random error is reduced by a factor of 2.5–3 compared to the default calibration, and a 5% charge measurement precision is achieved in 15 fC charge injection tests.
Summary (500 words)
The waveform sampler integrated into the CMS ETROC2 ASIC is designed to monitor the evolution of LGAD gain aging in the radiation environment during CMS operation. The waveform samplers are powered on periodically during the years of operation as LGAD pixels accumulate radiation doses, enabling the measurement of detector gain changes. These gain variations provide essential input for adjusting high-voltage settings and fine-tuning parameters in the time-walk correction algorithm. The waveform sampler is operated via both slow and fast command links, allowing users to combine collected waveforms with TDC data captured by the DAQ system, thus supporting a wide range of detailed studies.
The sampler is a 2.56 GS/s, 12-bit, 8×-interleaved ADC comprising three main stages: a 6-bit SAR (Successive Approximation Register) as the first stage, a dynamic residue amplifier (RA), and a 7-bit SAR as the second digitization stage. Eight 320 MHz ADC channels operate in an interleaved fashion to achieve an effective 2.56 GHz sampling rate. Each channel employs the two-stage coarse-fine SAR architecture, enabling high performance on a relatively modest 65 nm process. To fully exploit the ADC’s capabilities, an extensive calibration process is needed, requiring the determination of up to 24 constants (coarse-to-fine gain ratios, DC offsets, and overall gains for each channel).
To address this, we developed an automatic calibration scheme that leverages charge conservation and minimizes the roughness of the discharge curve, significantly reducing the number of free parameters down to 7. This approach substantially lowers computational complexity, making on-line calibration practical.
In this calibration method, the coarse-to-fine gain ratios for channels 2 through 8 (with channel 1 fixed) are selected as free parameters. In each iteration pass, charge conservation is used to determine the gains of all eight channels, while DC offsets are calculated from baseline data points. A brute-force nested looping strategy is employed to explore the parameter space thoroughly and avoid local minima. Although non-optimal, this method—requiring approximately two million iterations—can still be completed within a few minutes on a typical notebook computer.
Using this calibration, the baseline random error is reduced by a factor of 2.5 to 3 (from 0.18 to 0.06 coarse-stage LSBs) compared to default constants. The smoothness of the calibration is sufficient for applications like visualization, and further digital filtering is not necessary for these tasks. In charge injection tests with 15 fC input, a 5% charge measurement precision is achieved.
Preliminary beam tests with LGAD pixel detectors bump-bonded to ETROC2 ASICs have been conducted. Waveform data from particle hits have been successfully collected and are currently undergoing further analysis.
(See attached supporting document for performance details.)