Tertinek, StefanStefanTertinekFeely, OrlaOrlaFeely2012-05-012012-05-012011 IEEE2011-06IEEE Transactions on Circuits and Systems Part II1549-7747http://hdl.handle.net/10197/3594Bang-bang phase-locked loops (BBPLLs) are inherently nonlinear systems due to the binary phase detector (BPD). While they are typically used for clock and data recovery, the ongoing trend toward digital loop implementations has resulted in several digital BBPLLs (DBBPLLs) suitable for frequency synthesis. This brief investigates the effect of nonaccumulative reference clock jitter (due to white phase noise) in second-order DBBPLLs, comparing the output jitter with that of first-order DBBPLLs. For small clock jitter, the nonlinear loop behavior is modeled as a two-dimensional Markov chain, and the output jitter is smaller than but close to that of a first order loop. For large clock jitter, the BPD nonlinearity is linearized, and the output jitter is larger than that of a first order loop; it is proportional to clock jitter and inversely proportional to the square root of the stability factor—the ratio of the proportional path gain to the integral-path gain of the digital loop filter.179677 bytesapplication/pdfenPersonal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Phase-locked loopBang-bangMarkov chainTiming jitterBinary phase detectorPhase-locked loopsMarkov processesPhase detectorsJournal Article58633133510.1109/TCSII.2011.2149650https://creativecommons.org/licenses/by-nc-sa/1.0/