Development of the analitical method for nonlinear circuits analysis with the use of the admittance and resistance orthogonal components

摘要

A method for the nonlinear electric circuit analysis with the use of the orthogonal components of instantaneous admittance and resistance is proposed. The mechanism of the generation of the admittance orthogonal components of a nonlinear electric circuit is demonstrated. The analytical expressions for the components of instantaneous admittance and resistance are given and analyzed. The balance equations for the components of instantaneous admittance and resistance are analyzed. On their basis, the harmonic components of the current of the nonlinear electric circuit consisting of an active linear and nonlinear resistance, connected in series, are determined. The accuracy and adequacy of the developed method are proved by the comparative analysis of the current harmonic components calculated with the use of the proposed method and the ones obtained as a result of the numerical calculation of the researched circuit mathematical model. The advantages of the proposed method include its versatility in the use, the possibility to assess the circuit parameters influence on the current spectrum composition, good adaptation to the automation of the calculations in the frequency domain, the ability to obtain the predicted result independently of the degree of the approximating polynomial and the number of the analyzed harmonics.