  For TOF positron emission tomography (TOF PET) 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
multi-channels 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 multi-channels
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 FPGA chip and fully
evaluated its performance. Code density tests show that the obtained resolution
results lie in the range of (23 ps ~ 37 ps), the differential nonlinearity
(DNL) results lie in the range of (-0.4 LSB ~ 0.4 LSB) and the integral
nonlinearity (INL) results lie in the range of (-0.7 LSB ~ 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.
