Bubble-Proof Algorithm for Wave Union TDCs

Nowadays state-of-the-art time-to-digital converters (TDCs) are commonly implemented in field-programmable gate array (FPGA) devices using different variations of the wave union method. To take full advantage of this method many design challenges need to be overcome, one of which is an efficient data encoding. In this work, we describe in detail an effective algorithm to decode raw output data from a newly designed multisampling wave union TDC. The algorithm is able to correct bubble errors and detect any number of transitions, which occur in the wave union TDC output code. This allows us to reach a mean resolution as high as 0.39 ps and a single shot precision of 2.33 ps in the Xilinx Kintex-7 FPGA chip. The presented algorithm can be used for any kind of wave union TDCs and is intended for partial hardware implementation.