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The analysis of physical processes of nonlinear parametrical zone system as versions of the nonlinear resonator


G.P. Sinjavsky, L.V. Cherkesova, A.N. Zaichenko

Research and application in practice of the phenomenon and the processes occurring in nonlinear oscillatory systems at parametrical generation and strengthening of electromagnetic oscillations (i.e. at excitation of self-oscillations and strengthening of signals for the account of energy of the rating delivered in oscillatory systems by periodic modulation of parametres of power-intensive elements – dynamic reactance), represents the special scientific interest caused by the big possibilities of technical application of the phenomenon of parametrical resonance in devices of new generation of radio-electronic equipment microwave ranges. Doubtless advantage of the nonlinear parametrical zone system (NPS) is the possibility of transition from one zone of instability of oscillations in another, by changing of amplitude or frequency of rating. Researching NPS, functioning on ultraharmonics in the higher zones of instability of oscillations is perspective. In article is carried out the analysis of physical processes in NPS with variable reactance – the inductive and capacitor types which are a version of nonlinear resonators. Characteristic example of similar nonlinear resonant system is the parametrical generator, working in the higher zones of instability of oscillations. The differential and nonlinearity dynamic characteristics – dynamic inductance and its derivatives, coefficient of attenuation and its derivatives, instant values of own frequency of the resonant contour are investigated. The analytical parities are received, algorithms and computer programs for calculation of dynamic parametres of NPS are developed, tabular and graphic dependences of these parametres on the normed time are received, interaction of the internal and external forces operating on investigated system is shown. Computer modelling of dynamic characteristics of nonlinearity NPS is spent. The results received by program, are checked up by means of systems of computer mathematics Maple and MathCAD. It is proved, that by the developed program DYNAMIC PARAMETRES which is the component of program complexes for further researching NPS, working on ultraharmonics in the higher zones of instability of oscillations, shows authentic results, on which basis it is possible to explain the mechanism of intensive resonant interaction of resonant contour of NPS with external influence of a rating. All results are confirmed by experiment. That fact is found out, that sizes of peak value of pressure of the generator of rating and phase parities in more degrees influence on the changing of dynamic parametres, than changing of other parametres. The process of changing of condition of system with change of coefficient of attenuation that explains the mechanism of parametrical strengthening, excitation (generation) and attenuation of oscillations in the system is analysed. That fact is established, that at work NPS in the higher zones of instability of oscillations, occurs accelerated (in comparison with the lowest zones of instability) transition from the raised condition to attenuation of oscillations. With growth of intensity of external influence of rating on NPS, the own frequency of aresonant contour increases owing to saturation of material of the core and reduction of inductance of a contour. Thus the increasing of coefficient of attenuation is accompanied by increasing in losses. Distinctive line of investigated processes is influence of inductive character of resonant chain, that the period of change of inductance leads to phase shift of change of inductance in relation to the rating, and accordingly, the instant frequency of the resonant contour, twice above exciting influences. These factors open the parametrical mechanism of excitation of the NPS oscillations. Researching of the character of changing of dynamic parametres allows to define the condition of NPS. The received results show the qualitative picture of proceeding processes and find application at calculation and designing of radio-electronic equipment of new generations, working on the basis of resonant schemes – generators, amplifiers-modulators, etc., on ultraharmonics, in the higher zones of instability of oscillations, in microwave ranges.

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