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Dynamics of self-oscillators with fractional communications

Keywords:

V.V. Zaitsev – Ph. D. (Phys.-Math.), Professor, Department of Radiophysics, Samara State University. E-mail: zaitsev@ssu.samara.ru Ar.V. Karlov – Leading Design Engineer, JSC «Concern «Automation». E-mail: arkarlov@oao-avtomatika.ru


The article discusses two schemes of radio electronic self-oscillators of the Thomson type with fractional chains in the feedback loop. Equations of motion of the self-oscillators for the scheme with fractional excitation and for the scheme with fractional feedback, con-taining a left-sided derivative of Liouville are obtained. Solutions of the equation of motion which correspond to the transitional regime and the steady-state self-oscillations are obtained in the quasi-harmonic approximation. Despite the fact that the fractional derivative includes in the equation of motion for the scheme with fractional feedback more compli-cated than in the equation of motion for the scheme with fractional excitation, considered schemes of the self-oscillators have identical characteristics in the quasi-harmonic approximation. It is shown that isochronism, characteristic for a standard oscillator, is retained in fractional oscillator of the Thomson type. It is con-cluded that the fractionality of the excitation circuit degrades the energy characteristics of the self-oscillator. Considered fractional self-oscillators primarily represent model objects of nonlinear dynamics. However, fractional communications may be formed in the environment, as well as a side effect in radio electronics due to the widening variety of electronic components used.
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