Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics1090810.18469/1810-3189.2022.25.4.27-32Research ArticleDiscrete time model of self-oscillations with spectral line wideningZaitsevValery V.<p>Candidate of Physical and Mathematical Sciences, professor of the Department of Optics and Spectroscopy</p>zaitsev@samsu.ruhttps://orcid.org/0000-0003-2544-8197KarlovAlexander V.<p>Candidate of Physical and Mathematical Sciences, associate professor of the Department of Theoretical Foundations of Radio Engineering and Communication</p>a.v.karlov@gmail.comAlalvanHusamuldin K.-M.<p>second-year master student</p>comphysics@samsu.ruSamara National Research UniversityPovolzhskiy State University of Telecommunications and Informatics31122022254273225122022Copyright © 2022, Zaitsev V.V., Karlov A.V., Alalvan H.K.2022<p>An algorithm for generating quasi-harmonic self-oscillations with a uniformly widened spectral line is presented. The algorithm is based on the equation of motion of the Thomson-type DT-oscillator, which introduced a random effect in the form of band-pass white noise. Two types of effects are implemented: additive and parametric. Spectral characteristics of generated self-oscillations were analyzed by numerical experiment. The additive algorithm is shown to generate self-oscillations with amplitude-frequency fluctuations. Frequency fluctuations set the Lorentz (resonant) shape of the central part of the self-oscillation power spectrum, amplitude fluctuations form a noise pedestal of the spectral line. Based on the analysis of statistical characteristics of fluctuations in the frequency of the DT-oscillator with additive noise impact, a parametric algorithm for generating quasi-harmonic self-oscillations is proposed. In it, the resonance frequency of the oscillating system of the Thomson DT-oscillator is subject to random perturbations. The results of numerical experiments with generators of quasi-harmonic oscillations are given.</p>автоколебанияспектральная линияоднородное уширениефлуктуации частотыдискретное времяразностное уравнение автоколебанийслучайные возмущенияself-oscillationspectral lineuniform wideningfrequency fluctuationsdiscrete timedifference equation of self-oscillationsrandom perturbations[Zvelto O. Principles of Lasers. 4th ed. Saint Petersburg: Lan’, 2008, 720 p. (In Russ.)][Stratanovich R.L. Selected Questions of the Theory of Fluctuations in Radio Engineering. Moscow: Sovetskoe radio, 1961, 558 p. (In Russ.)][Malakhov A.N. Fluctuations in Self-Oscillatory Systems. Moscow: Nauka, 1968, 660 p. (In Russ.)][Rytov S.M. Introduction to Statistical Radiophysics. Moscow: Nauka, 1966, 404 p. (In Russ.)][Lemb U. Theory of Optical Masers. Quantum Optics and Quantum Radiophysics. Moscow: Mir, 1966, 452 p. (In Russ.)][Yariv A. Quantum Electronics. 2nd ed. Moscow: Sovetskoe radio, 1980, 488 p. (In Russ.)][Zaytsev V.V. Discrete van der Pol oscillator: finite differences and slow amplitudes. Izvestiya vuzov. PND, 2017, vol. 25, no. 6, pp. 70–78. DOI: https://doi.org/10.18500/0869-6632-2017-25-6-70-78 (In Russ.)][Zaytsev V.V., Karlov A.V. Thomson oscillators in discrete time: synthesis of dynamical systems. Zhurnal radioelektroniki, 2022, no. 3. DOI: https://doi.org/10.30898/1684-1719.2022.3.1 (In Russ.)][Vaynshteyn L.A., Vakman D.E. Separation of Frequencies in the Theory of Oscillations and Waves. Moscow: Nauka, 1983, 288 p. (In Russ.)][Gardiner K.V. Stochastic Methods in the Natural Sciences. Moscow: Mir, 1986, 528 p. (In Russ.)][Zaytsev V.V., Nuraev D.B., Shilin A.N. Van der Pol, Rayleigh, Duffing oscillators in dynamics with discrete time. Vestnik Samarskogo gosudarstvennogo aerokosmicheskogo universiteta imeni akademika S.P. Koroleva (natsional’nogo issledovatel’skogo universiteta), 2016, vol. 15, no. 1, pp. 187–196. DOI: https://doi.org/10.18287/2412-7329-2016-15-1-187-196 (In Russ.)]