Abstract
THE VAN DER POL OSCILLATOR WITH A TUNNEL DIODE
Yefim Berkovich*
ABSTRACT
The Van der Pol oscillator is a classical example of a circuit in whichself-oscillations occur. They are the Hopf-Andronov oscillationscaused by the presence in the circuit of a nonlinearity of the amplifyingelement. The present paper considers changes in behavior of these selfoscillationswhen into the circuit another essentially nonlinear elementsuch as a tunnel diode is inserted. Three forms of realization of theoscillator have been analyzed – two simplified ones and one in theform of computer model of its complete physical diagram with atransistor serving as an amplifier. As concerns the first approximaterealization of the oscillator in the form of a pure mathematical model, the paper quotes thedetailed results of previous research, which later are compared to the results of the two otherrealizations. If the first approximate realization of the oscillator is described by its differentialequations, which cannot be descriptions of any electronic circuit, the second approximaterealization of the oscillator is a concrete circuit whose computer model has also beenanalyzed in detail. And, finally, the third most complete realization of the oscillator gives atrue description of the oscillations in the twice nonlinear diagram of the Van der Poloscillator. A comparison of the analyses of these three models demonstrates that each of themis an independent object with characteristics proper only to it. The most adequate model ofthe oscillator might be a model of its complete electrical circuit that shows the character ofthe changes in auto-oscillations and a possibility of their synchronization. An energy criterionensuring the possible synchronization has been considered.
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