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In this paper a fairly complete mathematical model of CP-PLL, which reliableenough to serve as a tool for credible analysis of dynamical properties ofthese circuits, is studied. We refine relevant mathematical definitions of thehold-in and pull-in ranges related to the local and global stability. Stabilityanalysis of the steady state for the charge-pump phase locked loop isnon-trivial: straight-forward linearization of available CP-PLL models may leadto incorrect conclusions, because the system is not smooth near the steadystate and may experience overload. In this work necessary details for localstability analysis are presented and the hold-in range is computed. An upperestimate of the pull-in range is obtained via the analysis of limit cycles. Thestudy provided an answer to Gardner's conjecture on the similarity of transientresponses of CP-PLL and equivalent classical PLL and to conjectures on theinfinite pull-in range of CP-PLL with proportionally-integrating filter.

Nonlinear analysis of charge-pump phase-locked loop: the hold-in and pull-in ranges