Simulative characterization of the stability for second order voltage switched CP-PLL

The GARDNER´s stability theory is vital for linear modeling and empirical design of the 2^nd and 3^rd order charge-pump phase locked loop (CP-PLL). This criterion is general to identify the stability boundary in the steady state. It has been particularly applied to the PLL with a conventional current switched charge-pump (CSCP). Ideally, the CSCP supplies symmetrical pump currents. In some applications a voltage switched charge-pump (VSCP) is implied, which offers design simplicity and low cost. The VSCP architecture delivers an unequal amount of pump currents to the loop filter (LF), which introduces an additional and curious non-linearity in the behavior. This peculiarity buried in the second order voltage switched CP-PLL may disqualify it in several serious applications, where a symmetrical pump current is suitable. In this paper GARDNER´s stability boundary is investigated by making iterative transient simulations using the event-driven model of the second order voltage switched CP-PLL. The simulated results near fixed point from the second order voltage switched CP-PLL show that, the stability boundary is non-conservative in such system, eradicating the overloading from the current switched charge-pump.