Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2022. №3
ContentsFull text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2022.3.1
THOMSON SELF- OSCILLATORS IN DISCRETE TIME: SYNTHESIS OF DYNAMICAL SYSTEMS
V.V. Zaitsev1, A.V. Karlov2
1 Samara National Research University, 443086, Samara, Moskovskoe shosse str., 34
2Povolzhskiy State University of Telecommunications and Informatics, 443010, Samara, L. Tolstoy str., 23
The paper was received March 08, 2022
Abstract. A combination of the finite difference method and the method of slowly varying amplitudes to discretize the differential equation of motion of the Thomson oscillator is proposed. The difference approximations of the time derivatives are chosen so as to preserve in discrete time the conservativity and fundamental frequency of the linear loop of the self-oscillating system. It also requires a match of the discrete-time difference shortened equation for the complex amplitude with the Euler approximation of the shortened equation for the auto-oscillation amplitude in the analog prototype system. It is shown that the implementation of such an approach makes it possible to form discrete mappings of Thomson-type oscillators, in particular, the van der Pol oscillator. The consistency of discrete models with analog prototypes is also confirmed by numerical experiment.
Key words: self-oscillatory system, motion equation, the discrete time, finite differences, slowly changing amplitudes, the shortened equations, the discrete mapping of Thomson self-oscillators
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For citation:
Zaitsev V.V., Karlov A.V. Thomson self-oscillators in discrete time: synthesis of dynamical systems. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №3. https://doi.org/10.30898/1684-1719.2022.3.1 (In Russian)