Two resonances of parametric time varying circuit (review)

The theory of parametric time varying circuit is of interest as an introduction to the theory of nonlinear circuit. As follows from the principle of linear representation, which is little known in radio electronics, it is advisable to select for analysis the parametric time varying circuit in the most general form. The significance of ordinary circuit for practice is stipulated by the phenomenon of resonance that is also intrinsic) to the parametric time varying circuit. The resonance theory of the latter is not easy due to the need of sophisticated mathematical apparatus. In addition, two resonances, similar by their names, but quite different in essence manifest themselves in a parametric time varying circuit, namely, parametric resonance and the resonance of parametric time varying circuit. The parametric resonance is the characteristic of free processes in the circuit. This resonance is identified with an unstable circuit when its free process tends to rise to infinity with time. The resonance of parametric time varying circuit is a direst generalization of the resonance of ordinary circuit and represents the characteristic of forced oscillations. These two fundamentally different phenomena have similar names that is inconvenient for practice. Therefore, we propose to name the last of two resonances as “classical resonance”. Below we present an analysis of both resonances in a more general form than can be found in available literature.