New methods, for the design of different block diagrams of PLL, using the asymptotic analysis of high-frequency periodic oscillations, are suggested. The PLL description on three levels is made: 1)â€¦ (More)

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (orâ€¦ (More)

New method for the rigorous mathematical analysis of electronic synchronization systems is suggested. This method allows to calculate the characteristics of phase detectors and carry out a rigorousâ€¦ (More)

Methods of harmonic linearization & describing function, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of periodic oscillations of controlâ€¦ (More)

New method for the rigorous mathematical nonlinear analysis of PLL systems is suggested. This method allows to calculate the characteristics of phase detectors and carry out a rigorous mathematicalâ€¦ (More)

The terms hold-in, pull-in (capture), and lock-in ranges are widely used by engineers for the concepts of frequency deviation ranges within which PLL-based circuits can achieve lock under variousâ€¦ (More)

Discovery of undesirable hidden oscillations, which cannot be found by simulation, in models of phase-locked loop (PLL) showed the importance of development and application of analytical methods forâ€¦ (More)

The analysis of the stability and numerical simulation of Costas loop circuits for highfrequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneouslyâ€¦ (More)