Identification of Phase-Locked Loop System From Its Experimental Time Series

• Published in: IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2022-03, Vol.69 (3), p.854-858
• Main Authors: Mishchenko, Mikhail A., Bolshakov, Denis I., Vasin, Alexander S., Matrosov, Valery V., Sysoev, Ilya V.
• Format: Article
• Language: English
• Subjects: Analytical models; bandpass filter; Bandpass filters; Communications systems; First principles; Generators; Integrated circuit modeling; Mathematical models; Model accuracy; nonlinear circuit; Parameter estimation; Phase locked loops; Phase-locked loop; Reconstruction; system identification; Time series; Time series analysis; Voltage-controlled oscillators
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2021.3122892

Phase-locked loops (PLLs) are now widely used in communication systems and have been a classic system for more than 60 years. Well-known mathematical models of such systems are constructed in a number of approximations, so questions about how they describe the experimental dynamics qualitatively and quantitatively, and how the accuracy of the model description depends on the dynamic mode, remain open. One of the most direct approaches to the verification of any model is its reconstruction from the time series obtained in experiment. If it is possible to fit the model to experimental data and the resulting parameter values are close to the expected values (calculated from the first principles), the quantitative correspondence is nearly proved. In this brief, for the first time, the equations of the PLL model with a bandpass filter are reconstructed from experimental signals of the generator in various modes. The reconstruction shows that the model known from literature generally describes the experimental dynamics in regular and chaotic regimes. The relative error of parameter estimation is between 2% and 50%. The reconstructed nonlinear function of phase is not harmonic and highly asymmetric in contrast to model one.