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UDC 621.01.512

QUASISYNCHRONOUS MODES OF PHASE SYSTEM

S. S. Mamonov, PhD (physics and mathematics sciences), full professor of the department of mathematics and methods of teaching mathematical disciplines RSU named after S.A. Esenin, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.
A. O. Kharlamova, post-graduate student of the department of mathematics and methods of teaching mathematical disciplines RSU named after S.A. Esenin, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.

We considered the mathematical model of a system frequency phase-locked loop with the second-order filters. The conditions of existence of FPLL system quasi-synchronous modes are obtained. The analysis according to the frequency-amplitude characteristics of quasisynchronous mode from the low-pass filter settings is given. The aim is to develop a numerical and analytical approach to determine the conditions of existence of quasi-synchronous mode phase systems, to define the conditions of occurrence of bifurcation of the first kind of limit cycle, to develop an algorithm for finding unstable limit cycles, to study the characteristics of different types of self-oscillations excited in FPLL system with a second-order filters depending on the system parameters.

Key words: phase system, quasi-synchronous modes, limit cycles, timing, vector field rotation frequency amplitude of the fixed point, shift operator along trajectories.

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