CONSTRUCTION OF A MATHEMATICAL MODEL OF A FREQUENCY SYNTHESIZER WITH A PULSED FREQUENCY-PHASE DETECTOR USING PHASE SUBSPACES

Antonovskaya Olga Georgievna, Besklubnaya Antonina Vyacheslavovna

Mathematical modeling of the dynamics of discrete phase synchronization systems is a creative process and involves the use of mathematical models of varying degrees of complexity. Typically, the complexity of a mathematical model is mainly related to the dimension of the problem and the design of the state space. Thus, the advisability of using one or another method for its study is dictated by considerations related to the ease of application of the method and the acceptable accuracy of the resulting results. This paper presents the results of studying the dynamics of a frequency synthesizer with a pulsed frequency-phase detector using the point mapping method. This method takes into account the specifics of the system under consideration, namely: the abruptly changing nature of the structure of the equations describing the dynamics of the system. The presented mathematical model uses three phase subspaces corresponding to piecewise constancy of the control signal. Particular importance is attached to the study of possible transitions of the system trajectory between subspaces.

Keywords:discrete phase synchronization system, frequency synthesizer, mathematical model, point mapping method, phase subspace