Analytical-numerical methods for nonlinear analysis and synthesis of phase-locked loops
Lobachev, Mikhail (2024-09-21)
Väitöskirja
21.09.2024
Lappeenranta-Lahti University of Technology LUT
Acta Universitatis Lappeenrantaensis
School of Engineering Science
School of Engineering Science, Tuotantotalous
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In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of Lappeenranta-Lahti University of Technology LUT's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_ standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink.
Julkaisun pysyvä osoite on
https://urn.fi/URN:ISBN:978-952-412-112-5
https://urn.fi/URN:ISBN:978-952-412-112-5
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Tiivistelmä
Nowadays, various types of phase-locked loops (PLLs) are used for synchronization of signals in modern electronic, electromechanical, and electrical systems. Nonlinear study of PLL models allows evaluation of the circuit’s parameters at an earlier stage of design, providing wider pull-in and lock-in ranges, which are among the key PLL stability characteristics.
In engineering practice, the pull-in and lock-in ranges are mostly analyzed by linear and approximate methods. However, such approach can lead to wrong results and lack of synchronization, because the pull-in and lock-in ranges are inherently nonlinear concepts requiring the whole phase space to be examined.
In this dissertation, analytical, numerical, and combined analytical-numerical methods are applied to various nonlinear PLL models in order to estimate the pull-in and lock-in range and suggest solutions to related engineering problems in PLL analysis. The direct Lyapunov method, method of small parameter, and computer simulation are used for analysis of the pull-in range and global stability boundaries of PLL models. Analytical integration of trajectories on the linear segments of piecewise-linear PLL models and phase-plane analysis allow to obtain the exact lock-in range for continuous models, whereas additional application of the theory of differential inclusions extends the results for discontinuous piecewise-linear PLL models. All theorems have strict mathematical proofs and are confirmed by numerical simulation.
In engineering practice, the pull-in and lock-in ranges are mostly analyzed by linear and approximate methods. However, such approach can lead to wrong results and lack of synchronization, because the pull-in and lock-in ranges are inherently nonlinear concepts requiring the whole phase space to be examined.
In this dissertation, analytical, numerical, and combined analytical-numerical methods are applied to various nonlinear PLL models in order to estimate the pull-in and lock-in range and suggest solutions to related engineering problems in PLL analysis. The direct Lyapunov method, method of small parameter, and computer simulation are used for analysis of the pull-in range and global stability boundaries of PLL models. Analytical integration of trajectories on the linear segments of piecewise-linear PLL models and phase-plane analysis allow to obtain the exact lock-in range for continuous models, whereas additional application of the theory of differential inclusions extends the results for discontinuous piecewise-linear PLL models. All theorems have strict mathematical proofs and are confirmed by numerical simulation.
Kokoelmat
- Väitöskirjat [1186]