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Bang-bang clock and data recovery (BBCDR) circuits are severely nonlinear systems as a result of the binary phase detector's nonlinear behavior. The characteristic of the bang-bang phase detectors follows ideally the sign function, but in practice, it exhibits a finite slope across a narrow range of the input phase difference. In this brief, by considering an approximated practical model for the phase detector, the nonlinear differential equation of the system is obtained which shows that the BBCDR is a nonlinear system with memory and VOLTERRA series expansion is useful for such systems. As a result, the jitter generation of voltage-controlled-oscillator phase noise in BBCDR is specified. Behavioral simulation is used to validate the analytical results. The results show a good agreement between analytical equations and simulation results.