Modeling and Design of Multilevel Bang–Bang CDRs in the Presence of ISI and Noise

Multilevel clock-and-data recovery (CDR) systems are analyzed, modeled, and designed. A stochastic analysis provides probability density functions that are used to estimate the effect of intersymbol interference (ISI) and additive white noise on the characteristics of the phase detector (PD) in the CDR. A slope detector based novel multilevel bang-bang CDR architecture is proposed and modeled using the stochastic analysis and its performance compared with a typical multilevel Alexander PD-based CDR for equal-loop bandwidths. The rms jitter of the CDRs are predicted using a linear jitter model and a Markov chain and verified using behavioral simulations. Jitter tolerance simulations are also employed to compare the two CDRs. Both analytical calculations and behavioral simulations predict that at equal-loop bandwidths, the proposed architecture is superior to the Alexander type CDR at large ISI and low signal-to-noise ratios.