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An elegant analytical method for the derivation of the non-linear mathematical model of classical Costas electric circuit with non-sinusoidal signal waveforms is presented. Resulting model is similar to classical phase-locked loop (PLL) with special waveform of the phase detector characteristic. Phase detector characteristic can be computed analytically using Fourier series representation. The method...
In 1963 E.Lorenz discovered strange attractors, which correspond to the turbulence in liquids and atmosphere. In the second half of the 20-th century these attractors were described in electromechanical and electronical systems. In this time the well-known scientists created the methods of estimates of attractor dimension in the theory of dynamical systems and differential equations. Lyapunov function...
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...
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.
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...
Phase-controlled systems described by differential and integro-differential equations are considered. Such systems are widely applied in television, in radio communications, in remote cosmic communications as well as in the control of electric motors[1-12]. Frequency-domain criteria for global stability of phase-controlled systems are obtained.
The problem of entrainment (capture, synchronization) of the trajectories of nonlinear oscillatory system driven by an external periodic signal is reconsidered. The frequency-domain conditions of capture (global synchronization)are established extending the previous results (dealing with the harmonic excitation) to the case when external excitation is a multiharmonic signal, i.e. sum of a finite number...
Rigorous nonlinear analysis of the physical model of Costas loop is very difficult task, so for analysis, simplified mathematical models and numerical simulation are widely used. In the work it is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis may lead to wrong conclusions concerning the operability of Costas loop.
Nowadays simplified mathematical models and numerical simulation are widely used for the analysis of QPSK Costas loop. In the work it is shown that the use of simplified mathematical models and the application of non-rigorous methods of analysis may lead to wrong conclusions concerning the operability of real model of QPSK Costas loop.
In the present work for checking conjecture on pull-in range of two-phase Costas loop, a number of numerical experiments in MatLab Simulink has been made. In addition, the analytical approach to the proof of the conjecture is presented.
A modification of BPSK Costas loop, where low pass filters are applied separately from the loop, is considered. Such modification of the loop can work with non-sinusoidal signals or with some special phase detectors instead of multipliers. In this paper a general approach to the analytical computation of phase detector characteristic of the loop for general periodic signal waveforms is demonstrated...
Nonlinear analysis of BPSK Costas loop is a difficult task, so for its analysis simplified mathematical models and their simulation are widely used. In the work it is shown that the use of simplified mathematical models and the application of non-rigorous methods of analysis may lead to wrong conclusions concerning the operability of real model of BPSK Costas loop. Corresponding examples of BPSK Costas...
An effective analytical methods for computation of phase detector characteristics are suggested. For high-frequency oscillators new classes of such characteristics are described. Approaches to a rigorous nonlinear analysis of PLL are discussed.
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