Modeling of Jitter Characteristics for the Second Order ‎Bang-Bang CDR ‎

Bang-Bang clock and data recovery (BBCDR) circuits are hard nonlinear systems due to the ‎nonlinearity introduced by the binary phase detector (BPD). The specification of the CDR frequency ‎response is determined by jitter tolerance and jitter transfer. In this paper, jitter transfer and jitter tolerance ‎of the second-order BBCDR are characterized by formulating the time domain waveforms. As a result, a ‎new equation is presented to obtain corner frequency. Also, the jitter tolerance is expressed in closed form ‎as a function of loop parameters. The proposed method is general enough to be used for designing ‎BBCDR. The analysis is verified using behavioral simulations in MATLAB. Simulation results ‎demonstrate the validity of the result obtained by analytical equations.‎