Jitter Minimization in Digital PLLs with Mid-Rise TDCs

This paper analyzes the absolute jitter performance of digital phase-locked loops and compares the case when either a multi-bit time-to-digital converter with mid-rise characteristic or a bang-bang phase detector is adopted. The linear equivalent model of the PLL and expressions for random-noise and limit-cycle jitter are first derived for the case of a 2-bit time-to-digital converter with a mid-rise characteristic, and the optimal TDC resolution is determined. The analysis, which account for TDC mismatches, shows that, compared to the 1-bit one, the 2-bit time-to-digital converter can substantially reduce the quantization noise in the case of dominant random-walk noise at the TDC input. Moving to the Nb-bit midrise TDC case, the quantization noise can be further reduced at the cost of higher complexity and finer time resolution. The choice of Nb=2 seems to be the best compromise between jitter reduction and complexity increase. Time-domain simulations assess the theoretical framework and demonstrate the validity of the assumptions made throughout the paper.