A Highly Linear and Flexible FPGA-Based Time-to-Digital Converter

Time-to-digital converters (TDCs) are major components for the measurements of time intervals. Recent developments in field-programmable gate array (FPGA) have enabled the opportunity to implement high-performance TDCs, which were only possible using dedicated hardware. In order to eliminate empty histogram bins and achieve a higher level of linearity, FPGA-based TDCs typically apply compensation methods either using multiple delay lines consuming more resources or postprocessing, leading to a permanent loss of temporal information. In this article, we propose a novel TDC with a single delay line and without compensation to realize a highly linear TDC by encoding the states of the delay lines instead of the thermometer code used in the conventional TDCs. The experimental results show our states-based approach achieves an improved differential nonlinearity of [ <tex-math notation="LaTeX">$-$</tex-math> 0.998, <tex-math notation="LaTeX">$-$</tex-math> 1.533] for time resolution of 5.00 ps, [ <tex-math notation="LaTeX">$-$</tex-math> 0.44, 0.49] for 10.04 ps, [ <tex-math notation="LaTeX">$-$</tex-math> 0.16, 0.19] for 21.65 ps, [ <tex-math notation="LaTeX">$-$</tex-math> 0.10, 0.11] for 43.87 ps, [ <tex-math notation="LaTeX">$-$</tex-math> 0.06, 0.07] for 64.12 ps, and [ <tex-math notation="LaTeX">$-$</tex-math> 0.07, 0.05] for 87.73 ps, whilst no empty bins have been observed. To the best of authors’ knowledge, the achieved raw linearity together with the zero empty bins and a simple delay line structure exceeds previously reported of the FPGA-based TDCs.