0000000000158449
AUTHOR
Renat V. Yuldashev
showing 13 related works from this author
Nonlinear Analysis of Phase-locked Loop-Based Circuits
2013
Main problems of simulation and mathematical modeling of high-frequency signals for analog Costas loop and for analog phase-locked loop (PLL) are considered. Two approachers which allow to solve these problems are considered. In the first approach, nonlinear models of classical PLL and classical Costas loop are considered. In the second approach, engineering solutions for this problems are described. Nonlinear differential equations are derived for both approaches.
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.
Nonlinear analysis of classical phase-locked loops in signal's phase space
2014
Abstract Discovery of undesirable hidden oscillations, which cannot be found by the standard simulation, in phase-locked loop (PLL) showed the importance of consideration of nonlinear models and development of rigorous analytical methods for their analysis. In this paper for various signal waveforms, analytical computation of multiplier/mixer phase-detector characteristics is demonstrated, and nonlinear dynamical model of classical analog PLL is derived. Approaches to the rigorous nonlinear analysis of classical analog PLL are discussed.
Tutorial on dynamic analysis of the Costas loop
2016
Abstract Costas loop is a classical phase-locked loop (PLL) based circuit for carrier recovery and signal demodulation. The PLL is an automatic control system that adjusts the phase of a local signal to match the phase of the input reference signal. This tutorial is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed. Acquisition is most conveniently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations all these parameters have been derived (many of them are approximations, some even crude approximations), this has not…
A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis
2015
Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop ph…
Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large
2015
The analysis of the stability and numerical simulation of Costas loop circuits for high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal?s phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of th…
On the Gardner Problem for the Phase-Locked Loops
2019
This report shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loops systems. The development of analogs of classical stability criteria for the cylindrical phase space made it possible to obtain analytical estimates of the lock-in range for third-order system.
Nonlinear analysis of phase-locked loop
2010
Abstract 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 mathematical analysis of transient process and stability of the system.
Analytical methods for computation of phase-detector characteristics and PLL design
2011
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.
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
Computation of lock-in range for classic PLL with lead-lag filter and impulse signals
2016
For a classic PLL with square waveform signals and lead-lag filter for all possible parameters lock-in range is computed and corresponding diagrams are given. peerReviewed
The Egan problem on the pull-in range of type 2 PLLs
2021
In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …
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