A GRAPHOANALYTICAL METHOD FOR ANALYZING THE PARAMETRIC CONVERTERS OF UHF

Abstract

The considered circuits of parametric converters belong to linear and nonlinear radio engineering circuits with variable parameters. The mathematical problems arising at the analysis of such schemes was first formulated by Euler in 1772, examining the equations of motion of the Moon and proposed methods for solving them. Since then, these problems have been the object of study of many researchers, including Lyapunov, Hill, Mathieu, Krylov, Taft, Van der Pol and others. The problems of parametric excitation of oscillations in electrical engineering arose for first time in 1907, thanks to the theoretical works of Poincare, and in the1930s-thanks to the works of an entire school of scientists, to which Mandelstam Papaleksi, Andronov, Migulin and others belong. The merit of this school is that they were the first to show the possibility of amplification and generation of electrical signals, developed the theory of parametric resonance confirmed by numerous experiments, including also in the radio frequency range. In the 1950s, in connection with the rapid development of semiconductor devices and the simplicity of electrical control of their parameters with frequencies up to the UFH, the works in the theory and application of parametric amplifiers and converters with controlled reactivity reached the top of development. It is known that at analyzing the parametric converters of UHF, it is necessary to determine the Fourier components for non-linear functions of charge q (u) and current i (u) approximating the volt-coulomb and current-voltage characteristics (WSS and CVC) of the active element. The calculation of integrals, even at an impact of a dual frequency signal on a non-linear element is connected with certain difficulties. From an engineering point of view, a graphical-analytical method of analysis acceptable for any nonlinear active element of arbitrary characteristics is prposed. As a result, the calculation error is about 5%, which is acceptable from a practical point of view for the analysis and synthesis of parametric converters of UHF.