Решение Укороченных Уравнений Синхронизированного Автогенератора

Рапин, Владимир Васильевич

doi:10.20535/s0021347019060037

Cited by 1 publication

(2 citation statements)

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“…However, we take into account that the parameters and are antiphase. First of all, according to [13], it is necessary to determine positions of the differential oscillator operating points.…”

Section: Nonlinear Characteristic Of the Equivalent Oscillator Amplif...mentioning

confidence: 99%

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Theoretical investigation of injection-locked differential oscillator

Rapin¹

2022

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A preliminary analysis of published works on this topic showed that at present there is no sufficiently substantiated theory of such devices, and the approximate approaches used are rough and do not always meet the requirements of practice. The proposed transition from a differential self-oscillator to an equivalent single-circuit oscillator has not received a convincing justification. This article presents a methodology for studying a synchronized differential oscillator using rigorous methods. A mathematical model of such oscillator is presented in the form of nonlinear differential equations obtained on the basis of Kirchhoff's laws. Their analysis made it possible to substantiate the transition to the model of a single circuit LC oscillator, equivalent to a differential one. A technique for such a transition is proposed, including the procedure for determining the nonlinear characteristics of the amplifying element of this self-oscillator, based on the nonlinear characteristics of two amplifying elements of the differential oscillator. The mathematical model of an equivalent oscillator is represented by a non-linear differential Van der Pol equation in a dimensionless form, it is simple and accurate. This form of representation made it possible to single out a small parameter and estimate its value. In the case of small values of the small parameter, as is known, traditional methods can be used for its analysis. Thus, the task of studying the synchronization process of a differential oscillator is reduced to the study of the synchronization process of a Van der Pol oscillator. The presented results can be useful in the development of various devices based on synchronized differential oscillators.

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Section: Nonlinear Characteristic Of the Equivalent Oscillator Amplif...mentioning

confidence: 99%

“…The above problems, solved for an autonomous differential oscillator [13], are partially used in this paper.…”

Section: Introductionmentioning

confidence: 99%