Search results for "phase-locked loop"
showing 10 items of 36 documents
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…
Stability of charge-pump phase-locked loops : the hold-in and pull-in ranges
2020
The problem of design and analysis of synchronization control circuits is a challenging task for many applications: satellite navigation, digital communication, wireless networks, and others. In this article the Charge-Pump Phase-Locked Loop (CP-PLL) electronic circuit, which is used for frequency synthesis and clock generation in computer architectures, is studied. Analysis of CP-PLL is not trivial: full mathematical model, rigorous definitions, and analysis still remain open issues in many respects. This article is devoted to development of a mathematical model, taking into account engineering aspects of the circuit, interpretation of core engineering problems, definition in relation to m…
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…
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…
Power System Oscillations with Different Prevalence of Grid-Following and Grid-Forming Converters
2022
The oscillatory behaviour of the power system is an aspect that is significantly affected by the increasing integration of converter-based generation sources. Several works address the impact of non-synchronous generation on the operation of the system from different points of view, but only a few studies focus on power-frequency oscillations with a prevalence of generation sources interfaced through power electronics. A lack of research can be found in particular in the comparative analysis of the two main control strategies for power converters, namely grid-following and grid-forming. The article aims to contribute to this direction, starting from a theoretical analysis of the two control…
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 highfrequency 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 the…
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…
Synchronization techniques for power quality instruments
2004
The measurement of voltage characteristics in power systems requires the accurate estimation of the power supply frequency and signal synchronization, even in the presence of disturbances. The authors developed and tested two innovative techniques for instrument synchronization. The first is based on signal spectral analysis techniques performed by means of the Chirp-Z transform analysis. The second is a phase-locked loop (PLL) software based on a time-domain coordinate transformation and an innovative phase-detection technique. To evaluate how synchronization techniques are adversely affected by the application of a disturbing influence, experimental tests were carried out, taking into acc…
A Phase-Locked Loop for the Synchronization of Power Quality Instruments in the Presence of Stationary and Transient Disturbances
2007
Power quality instrumentation requires accurate fundamental frequency estimation and signal synchronization, even in the presence of both stationary and transient disturbances. In this paper, the authors present a synchronization technique for power quality instruments based on a single-phase software phase-locked loop (PLL), which is able to perform the synchronization, even in the presence of such disturbances. Moreover, PLL is able to detect the occurrence of a transient disturbance. To evaluate if and how the synchronization technique is adversely affected by the application of stationary and transient disturbing influences, appropriate testing conditions have been developed, taking int…
Integration of DC power source in micro-grid using VSI with PLL technique
2015
The looming energy crisis is becoming the greatest challenge to the world today. As a consequence of this there is an increasing attention for alternative renewable energy resources. In future, renewable energy sources will be integrated with energy storage and it will require a proper converter for integrating with the grid. In order to achieve this, various power electronics topologies have to be incorporated between the grid and the renewable source(s). This paper presents the simulation and experimental implementation of DC power source integration in micro-grid using single phase ‘Voltage Source Inverter’ (VSI) with ‘Phase Locked Loop’ (PLL) topology. Firstly the appropriateness of the…