Abstract This paper presents a study of classical circuit of differential oscillator using rigorous methods of nonlinear theory of electrical oscillations. It is proposed a mathematical model of such oscillator based on the Kirchhoff’s laws application. It is implemented by pass to the model of single-circuit LC oscillator, equivalent to a differential one. A method is developed for such transition with development of nonlinear characteristic of the amplifying element of the equivalent based on nonlinear characteristics of the amplifying elements of a differential oscillator. The mathematical model of the equivalent oscillator is simple and accurate. In case of small values of a small parameter, the traditional method can be used for its analysis, for example, the method of slowly varying amplitudes. For insufficiently small values of a small parameter, expressions are obtained to describe the changes in the amplitude and frequency in oscillations establishing process. The results presented can be useful in the development of various devices based on a differential self-excited oscillator.
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