Bang-bang phase detector model revisited

The operation of bang-bang phase detectors (BBPDs) in clock and data recovery circuits (CDRs) is typically modeled in terms of the phase difference between their inputs; however, this approach is not sufficient to describe their dynamic behavior completely. This paper introduces a more comprehensive model of the operation of BBPDs that takes into account phase as well as frequency differences between their inputs. Numerical simulations of the operation of a CDR have been carried out to evaluate the validity of the model.