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This paper presents a phase noise analysis of charge-pump phase-locked-loops. Fundamental results from the theory of discrete-time systems are employed to derive closed-form expressions of noise transfer functions and design guidelines. The proposed expressions allows predicting the PLL in-band noise and spurs induced by VCO internal white and flicker noise sources and by external interferences coupled to VCO most sensitive nodes. To verify the correctness of the presented theoretical results, a simulation method is developed, which takes into account the time-varying nonlinear characteristics of the VCO and which is much more efficient than transistor-level noise simulations.