High-resolution time-to-digital converters (TDCs) with a bidirectional encoder

A high-resolution time-to-digital converter (TDC) based on wave union (four-edge WU A), dual-sampling, and sub-TDL methods is proposed and implemented in a 16-nm Xilinx UltraScale+ field-programmable gate array (FPGA). We combine WU and dual-sampling techniques to achieve a high resolution. Besides, we use the sub-TDL method and the proposed bidirectional encoder to suppress bubbles and encode four-transition pseudo thermometer codes efficiently. Experimental results indicate the proposed TDC achieves a 0.4 ps resolution with a 450 MHz sampling clock and a less than 9 ps RMS precision from 0 ns to 100 ns (achieving a 3.06 ps RMS precision in the best-case scenario). These characteristics make this design suitable for particle physics, biomedical imaging (such as positron emission tomography, PET), and general-purpose scientific instruments.