Firmware-only implementation of time-to-digital converter (TDC) in field-programmable gate array (FPGA)

TLDR

The TDC relies on a delay‑chain and register‑array structure to generate fine‑time bits from a clock counter, and its FPGA implementation must guarantee predictable placement for uniform binning and compensate for temperature‑ and voltage‑induced delay variations. The paper presents a firmware‑only TDC implemented in a general‑purpose FPGA for the Fermilab CKM experiment. The design uses existing FPGA carry‑logic and logic‑expansion chains to achieve predictable placement, and applies digital compensation techniques to mitigate delay variations within the same device. Bench‑top tests demonstrate the FPGA‑based TDC’s functionality and stability.

Abstract

A Time-to-Digital Converter (TDC) implemented in general purpose field-programmable gate array, (FPGA) for the Fermilab CKM experiment will be presented. The TDC uses a delay chain and register array structure to produce lower bits in addition to higher bits from a clock counter. Lacking the direct controls custom chips, the FPGA implementation of the delay chain and register array structure had to address two major problems: (1) The logic elements used for the delay chain and register array structure must be placed and routed by the FPGA compiler in a predictable manner, to assure uniformity of the TDC binning and short-term stability. (2) The delay variation due to temperature and power supply voltage must he compensated for to assure long-term stability. We used the chain structures in the existing FPGAs that the venders designed for general purpose such as carry algorithm or logic expansion to solve the first problem. To compensate for delay variations, we studied several digital compensation strategies that can be implemented in the same FPGA device. Some bench-top test results will also be presented in this document.