“…A PLL-based circuit behaves as a nonlinear control system and its physical model in the signal space can be described by nonlinear nonautonomous difference or differential equations. In practice, numerical simulation is widely used for the analysis of PLL-based circuit nonlinear model (see, e.g., [Best, 2007, Bianchi, 2005, Goldman, 2007, Klapper, 2012, Razavi, 2003, Tranter et al, 2010 and others) since the rigorous analysis of nonlinear nonautonomous equations is often a very difficult task. However for the high-frequency signals, the explicit numerical simulation of the physical model of PLL-based circuit in the signal space is very complicated since one has to consider simultaneously both the very fast time scale of the signals and the slow time scale of phase difference between the signals.…”