A two-stage time-stretching TDC with discrete components

This paper presents the design and testing of a time-stretching-based time-to-digital converter (TDC) implemented with discrete components. The TDC utilizes capacitor charging and discharging to achieve a time resolution of under 100 ps using a 100 MHz clock counter on a low-power, low-cost FPGA, achieving a time amplification factor of over 100. A two-stage time-stretching architecture is employed to reduce the conversion time to below 300 ns for a 10 ns input range. An onboard calibration system, including a pulse generation circuit, is implemented, and calibration results are presented. This system serves as a proof-of-concept platform for circuit optimization toward an ASIC implementation of a front-end TDC targeting future 4D pixel detectors at hadron colliders, with goals of sub-50 ps resolution and power consumption at the $\mu$W/channel level. Additionally, the design offers a modular, low-cost solution for extracting signal arrival times with 100 ps precision in particle physics experiments, such as photoelectron timing extraction for photodetector readout in neutrino experiments.