Event Driven Modeling and Characterization of the Second Order Voltage Switched Charge Pump PLL

The charge pump phase locked loop (CP-PLL) is widely used subsystem in modern mixed-signal electronic systems that are utilized in digital and wireless applications such as clock generation, synchronization and frequency synthesis. In the classical mode, the combination of a current switched charge pump and a digital phase and frequency detector (CP-PFD) circuits produces an ideal pulse width modulated constant current during one sampling period, which permits a suitable transient performance. Nevertheless, many commercially used CP-PLL chips (e.g., 4046 family) have a voltage switched charge pump (VSCP) because the design of the constant voltage source is easier than the constant current generator and it is a low cost solution. However, the VSCP delivers a non-constant pump current, which varies during one sampling period related to the electrical load of the loop filter (LF). This effect results in a varying gain of the control system affecting significantly its tracking ability. Furthermore, due to its hybrid structure, the simulation of the CP-PLL at high frequencies is challenging and the analysis of its transient characteristics during its non-linear acquisition procedure is not easy. In this paper, a first ever exact and nonlinear model based on the phase equations of the second order voltage switched charge pump phase locked loop (VSCP-PLL) is established by using an event driven (ED) technique. This exact model is then simplified by using a step-wise quasi-constant current approximation during one sampling period to obtain the analytical phase equations. The derived ED-model is validated at transistor level simulations using 130 nm CMOS process. Furthermore, some typical nonlinear features of the VSCP-PLL are explored and the developed ED-models are compared with the quasi-time-continuous (QTC) theory.