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For time-of-flight positron emission tomography detectors, time-to-digital converters (TDCs) are essential to resolve the coincidence time of the photon pairs. Recently, an efficient TDC structure called ring-oscillator-based (RO-based) Vernier TDC using carry chains was reported by our team. The method is very promising due to its low linearity error and low resource cost. However, the implementation complexity is rather high especially when moving to multichannels TDC designs, since this method calls for a manual intervention to the initial fitting results of the compilation software. In this paper, we elaborate the key points toward implementing high performance multichannels TDCs of this kind while keeping the least implementation complexity. Furthermore, we propose an efficient fine time interpolator construction method called the period difference recording which only needs at most 31 adjustment trials to obtain a targeted TDC resolution. To validate the techniques proposed in this paper, we built a 32-channels TDC on a Stratix III field programmable gate array chip and fully evaluated its performance. Code density tests show that the obtained resolution results lie in the range of (23-37 ps), the differential nonlinearity results lie in the range of [-0.4-0.4 least significant bit (LSB)] and the integral nonlinearity results lie in the range of (-0.7-0.7 LSB) for each of the 32 TDC channels. This paper greatly eases the designing difficulty of the carry chain RO-based TDCs and can significantly propel their development in practical use.

Toward Implementing Multichannels, Ring-Oscillator-Based, Vernier Time-to-Digital Converter in FPGAs: Key Design Points and Construction Method