Stability analysis of Mixed-Signal Phase Locked Loops considering nonlinear and non-ideal effects for an optimized system design

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The design of mixed-signal (MS) phase locked loops (PLL) is challenging because of the combination of the digital and analogue domain. An efficient and precise modeling of these systems is necessary, since transistor level simulations are time-consuming and a comprehensive characterization of the dynamic behavior is not easily possible. However, this characterization is necessary when targeting an optimal system design. Therefore the own preliminary studies focus on the highly efficient event-driven modeling and the stability analysis of the PLL. Furthermore, the modeling is taking typical nonlinear and non-ideal effects into account. This enables an efficient and intuitive analysis of the interdependence of these effects. Comprehensive characterizations of the preliminary studies show that the non-ideal effects within the PLL significantly affect its performance and must be considered for a robust design. Using the example of the dead zone, a more robust system design is implemented in the preliminary work showing the feasibility of the proposed design methodology.In this project, the shown methodology will be further developed in order to model more typical deterministic and stochastic non-ideal effects and to characterize their influence on the control behavior. The explored interdependence will contribute to a better understanding of the non-linear, chaotic and non-ideal PLL. Furthermore, an analytical stability analysis of the third-order phase locked loop, including non-ideal effects, will be performed. Both the indirect Lyapunov method and the general Lyapunov theory will be used. Finally, the results of the performed analysis and the analytical stability considerations, including non-ideal effects, will be used for an optimized and more robust design of the third order mixed-signal PLL. In addition, the investigated approaches can also be used for PLL with higher orders.