Self-oscillations of a third order PLL in periodic and chaotic mode and its tracking in a slave PLL |
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| Affiliation: | 1. Physics Department, Burdwan University, Burdwan 713104, WB, India;2. Physics Department, Bidhan Chandra College, Asansol 713304, WB, India;1. School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, PR China;2. Research Center on Logistics optimization and Prediction of Engineering Technology, Ji’nan, Shandong 250014, PR China;1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, PR China;2. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China;3. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China;4. School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, PR China;1. Departamento de Matemáticas, Centro de Investigación de Física Teórica y Matemática FIMAT, University of Huelva, 21071 Huelva, Spain;2. Departamento de Matemática Aplicada II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;1. Dep. of Electrical Engineering (TEE), Fluminense Federal University (UFF), 24210-240 Niterói, RJ, Brazil;2. Engineering Department, LIGHT S.E.S.A., Rio de Janeiro, RJ, Brazil;1. Monell Chemical Senses Center, 3500 Market Street, Philadelphia, PA 19104, USA;2. Institut de Mathématiques et de Sciences Physiques, B.P. 613, Porto-Novo, Benin;3. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain;1. Macedonian Academy of Sciences and Arts, Skopje, Macedonia;2. BioCircuits Institute, University of California, San Diego, La Jolla, CA 92093-0402, USA |
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| Abstract: | The dynamics of a third order phase locked loop (PLL) with a resonant low pass filter (LPF) has been studied numerically in the parameter space of the system. The range of stable synchronous operating zone of the PLL, expressed in terms of system and signal parameters, is estimated. The obtained results are in agreement with the analytically predicted results in the literature. The PLL dynamics in the unstable region is found to have a sequence of period doubling bifurcation and chaos. In the master–slave mode of operation of two 3rd order PLLs, the slave PLL can track the periodic as well as chaotic dynamics of the master PLL for a narrow range of effective frequency offset when other design parameters are within the stable zone as predicted for an isolated PLL. The synchronization of the master and slave PLLs in this condition is proved to be a generalized one using the auxiliary slave system approach. Experimental observations on prototype hardware circuits for an isolated PLL and for a master–slave PLL arrangement are also given. |
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| Keywords: | Third order PLL Chaos Sychronization Stability |
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