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Phase-locked loop (PLL), conceived in 1932 by H. Bellescize, has been the basic electronic component in the development of communication technology from the early analog radio receptors to modern digital civil and military facilities.…

Systems and Control · Electrical Eng. & Systems 2024-11-28 José Roberto Castilho Piqueira , Felipe Freitas , Luis Antonio Aguirre

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…

Dynamical Systems · Mathematics 2015-11-17 N. V. Kuznetsov , O. A. Kuznetsova , G. A. Leonov , P. Neittaanmaki , M. V. Yuldashev , R. V. Yuldashev

Charge pump phase-locked loop with phase-frequency detector (CP-PLL) is an electrical circuit, widely used in digital systems for frequency synthesis and synchronization of the clock signals. In this paper a non-linear second-order model of…

Signal Processing · Electrical Eng. & Systems 2019-03-12 Nikolay Kuznetsov , Marat Yuldashev , Renat Yuldashev , Mikhail Blagov , Elena Kudryashova , Olga Kuznetsova , Timur Mokaev

Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system…

Systems and Control · Computer Science 2015-08-21 Vera Smirnova , Anton Proskurnikov , Natalia V. Utina

In the present work the model of PLL with impulse signals and active PI filter in the signal's phase space is described. For the considered PLL the lock-in range is computed analytically and obtained result are compared with numerical…

Dynamical Systems · Mathematics 2016-04-01 K. D. Aleksandrov , N. V. Kuznetsov , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

Synchronous reference frame phase-looked loop (SRF-PLL) techniques are widely used for interfacing and control applications in the power systems and energy conversion at large. Since a PLL system synchronizes its output with an exogenous…

Systems and Control · Electrical Eng. & Systems 2025-09-24 Michael Ruderman , Elia Brescia , Paolo Roberto Massenio , Giuseppe Leonardo Cascella , David Naso

In current MIMO mobile communication systems, phase noise can significantly impair performance. To allow for compensation of these impairments, accurate phase noise modeling is necessary. Numerical modeling of the phase noise process at a…

Signal Processing · Electrical Eng. & Systems 2026-04-10 Carl Collmann , Ahmad Nimr , Gerhard Fettweis

Modern communication and computer systems require rapid (Gbps), efficient and large bandwidth data transfers. Agressive scaling of digital integrated systems allow buses and communication controller circuits to be integrated with the…

Hardware Architecture · Computer Science 2012-01-10 Zainab Ashari , Anis Nurashikin Nordin

In this paper we discuss the application of the harmonic balance method for the global analysis of the classical phase-locked loop (PLL) circuit. The harmonic balance is non rigorous method, which is widely used %,often without rigorous…

Dynamical Systems · Mathematics 2017-05-09 E. V. Kudryashova , N. V. Kuznetsov , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

A number of popular measures of dependence between pairs of band-limited signals rely on analytic phase. A common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input…

Neurons and Cognition · Quantitative Biology 2018-03-26 Christopher K. Kovach

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…

Signal Processing · Electrical Eng. & Systems 2021-07-30 N. V. Kuznetsov , A. S. Matveev , M. V. Yuldashev , R. V. Yuldashev

The Costas loop is a modification of the phase-locked loop circuit, which demodulates data and recovers carrier from the input signal. The Costas loop is essentially a nonlinear control system and its nonlinear analysis is a challenging…

Dynamical Systems · Mathematics 2017-05-09 N. V. Kuznetsov , O. A. Kuznetsova , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

In the present work PLL-based circuits with sinusoidal phase detector characteristic and active proportionally-integrating (PI) filter are considered. The notion of lock-in range -- an important characteristic of PLL-based circuits, which…

Dynamical Systems · Mathematics 2016-03-29 K. D. Aleksandrov , N. V. Kuznetsov , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

This paper introduces a conversion matrix method for linear periodically time-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling that offers precise and computationally efficient results to enable rapid design iteration…

Signal Processing · Electrical Eng. & Systems 2024-07-01 Hongyu Lu , Patrick P. Mercier

The phase locking value (PLV) is a widely used measure to detect phase connectivity. Main drawbacks of the standard PLV are it can be sensitive to noisy observations and does not provide uncertainty measures under finite samples. To…

Methodology · Statistics 2025-09-09 Shonosuke Sugasawa , Takeru Matsuda , Tomoyuki Nagakawa

A simulation of an atomic force microscope operating in the constant amplitude dynamic mode is described. The implementation mimics the electronics of a real setup including a digital phase-locked loop (PLL). The PLL is not only used as a…

Atomic and Molecular Clusters · Physics 2007-05-23 Laurent Nony , Alexis Prof. Baratoff , Dominique Schaer , Oliver Pfeiffer , Adrian Wezel , Ernst Meyer

Non-contact scanning probe microscopy (SPM) has developed into a powerful technique to image many different properties of samples. The conventional method involves monitoring the amplitude, phase or frequency of a cantilever oscillating at…

Mesoscale and Nanoscale Physics · Physics 2015-06-16 Manan Mehta , Venkat Chandrasekhar

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…

Dynamical Systems · Mathematics 2015-09-15 R. E. Best , N. V. Kuznetsov , O. A. Kuznetsova , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

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…

Other Computer Science · Computer Science 2016-11-15 G. Bianchi , N. V. Kuznetsov , G. A. Leonov , M. V. Yuldashev , R. V. Yuldashev

Many speech and music analysis and processing schemes rely on an estimate of the fundamental frequency $f_0$ of periodic signal components. Most established schemes apply rather unspecific signal models such as sinusoidal models to the…

Sound · Computer Science 2021-12-23 Volker Hohmann
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