A fast improved fat tree encoder for wave union TDC in an FPGA

Up to now, the wave union method can achieve the best timing performance in FPGA-based TDC designs. However, it should be guaranteed in such a structure that the non-thermometer code to binary code （NTH2B） encoding process should be finished within just one system clock cycle. So the implementation of the NTH2B encoder is quite challenging considering the high speed requirement. Besides, the high resolution wave union TDC also demands that the encoder convert an ultra-wide input code to a binary code. We present a fast improved fat tree encoder （IFTE） to fulfill such requirements, in which bubble error suppression is also integrated. With this encoder scheme, a wave union TDC with 7.7 ps RMS and 3.8 ps effective bin size was implemented in an FPGA from Xilinx Virtex 5 family. An encoding time of 8.33 ns was achieved for a 276-bit non-thermometer code to a 9-bit binary code conversion. We conducted a series of tests on the oscillating period of the wave union launcher, as well as the overall performance of the TDC; test results indicate that the IFTE works well. In fact, in the implementation of this encoder, no manual routing or special constraints were required; therefore, this IFTE structure could also be further applied in other delay-chain-based FPGA TDCs.