  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.
