Limitations of PLL simulation: hidden oscillations in MatLab and SPICE

Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of numerical approach is discussed and it is shown that, e.g. hidden oscillations may not be found by simulation. Corresponding examples in SPICE and MatLab, which may lead to wrong conclusions concerning the operability of PLL-based circuits, are presented

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Limitations of the classical phase-locked loop analysis

Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified dynamical models and the application of simulation may lead to wrong conclusions concerning the operability of PLL-based circuits