This paper proposes a rigorous stability criterion for the 2nd order digital phase locked loop (DPLL),with a charge pump phase frequency detector (CP-PFD) component. The Stability boundary is determined using piecewise linear methods to model the non-linear nature of the CP-PFD component block. It calculates the control voltage, after a predetermined number of input reference signal sampling periods, to a small initial voltage offset. Using this piecewise linear model an exact closed form stability criterion is proposed for the second order system. The 2nd order stability boundaries, as defined by the proposed technique, are compared to that of existing linear theory stability boundaries, and display a significant improvement.