Search results for "hidden oscillations"

Nonlinear Analysis of Charge-Pump Phase-Locked Loop : The Hold-In and Pull-In Ranges

2021

In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in and pull-in ranges related to the local and global stability. Stability analysis of the steady state for the charge-pump phase locked loop is non-trivial: straight-forward linearization of available CP-PLL models may lead to incorrect conclusions, because the system is not smooth near the steady state and may experience overload. In this work necessary details for local stability analysis are presented and the hold-in range is computed. An upper estimate o…

Hidden oscillations in SPICE simulation of two-phase Costas loop with non-linear VCO

2016

Simulation is widely used for analysis of Costas loop based circuits. However it may be a non-trivial task, because incorrect choice of integration parameters may lead to qualitatively wrong conclusions. In this work the importance of choosing appropriate parameters and simulation model is discussed. It is shown that hidden oscillations may not be found by simulation in SPICE, however it can be predicted by analytical methods. peerReviewed

Simulation of PLL with impulse signals in MATLAB: Limitations, hidden oscillations, and pull-in range

2015

The limitations of PLL simulation are demonstrated on an example of phase-locked loop with triangular phase detector characteristic. It is shown that simulation in MatLab may not reveal periodic oscillations (e.g. such as hidden oscillations) and thus may lead to unreliable conclusions on the width of pull-in range.

Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization

2011

Computation of the lock-in ranges of phase-locked loops with PI filter

2016

In the present work the lock-in range of PLL-based circuits with proportionallyintegrating filter and sinusoidal phase-detector characteristics are studied. Considered circuits have sinusoidal phase detector characteristics. Analytical approach based on the methods of phase plane analysis is applied to estimate the lock-in ranges of the circuits under consideration. Obtained analytical results are compared with simulation results. peerReviewed