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Article title MINIMIZATION OF PLL SYSTEM MEAN SQUARED ERROR IN THE TRACKING MODE
Authors V.S. Plaksienko, A.R. Gaiduk
Section SECTION I. METHODS AND ALGORITHMS FOR SIGNAL PROCESSIN
Month, Year 11, 2015 @en
Index UDC 621.391.24.001.57
DOI
Abstract In the radio-electronic systems of the various purposes the wide application is found the phase-locked systems of the frequency (PLL), which basic purpose is the coordination of a frequency and a phase of the arranged generator of these systems with a frequency and a phase of a useful signal. The useful signal is usually accompanied by the random noise; therefore phase-locked systems of the frequency should suppress influence of these random noise in the maximal degree. In this article the analytical design method of the phase-locked systems of the frequency, optimal in sense of the mean squared error, is considered. As against the known method of the frequency optimization of N. Wiener the physical realizability of the PLL system in this case is provided at any characteristics of random noise with normal distribution. The basic feature of the considered design method is addition to a dispersion of a random error the complexity functional, with the purpose of maintenance of the physical realizability the PLL system, and the added the optimization circuits. The decision of the formulated optimization problem, formally, is carried out by N. Wiener"s frequency method. However the analytical expressions of this method are transferred in area of the polynomials equations with the subsequent transition to equivalent systems of the linear algebraic equations. It has allowed to exclude necessity of the frequency characteristics application, to limit there polynomials representation and to keep analytical character of the optimization method. The result of the decision optimization problems is the physically realizable transfer function of system PLL, which dependent from the parameters complexity functional. Set of the expressions resulted in work, practically, is algorithmic base of the analytical design method of systems PLL, optimal in sense of minimum the mean squared error. Efficiency of the suggested method is shown on a numerical example.

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Keywords PLL system; spectral density; mean squared error; frequency optimization; complexity functional; physical implementability; optimization circuit.
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