1,160 research outputs found
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
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