SIMULATION OF NONLINEAR ELECTRIC CIRCUITS VIA VARIABLE TRANSFORMATION METHOD

Abstract

The article presents an analytical approach to modeling nonlinear electrical circuits based on the method of variable transformation. Special attention is given to the problem of capacitor discharge through a nonlinear load that models an electrolyzer with a volt-ampere characteristic incorporating both activation and concentration components. As a result, a generalized second-order differential equation is obtained, describing the voltage dynamics on the capacitor, accounting for the nonlinear current-dependent resistance. A method is proposed for transforming this equation into a linear one with constant coefficients by introducing a new variable, which enables a complete analytical solution of the system.

The study demonstrates that such a transformation not only simplifies the analysis but also preserves the geometric structure of the phase space, which is particularly important for modeling oscillatory and unstable operating modes. The proposed method also allows for error control and retains the physical interpretability of parameters during numerical solution. The practical significance of the approach is illustrated using an example of an electric circuit with a capacitive source and nonlinear electrolytic load, reproducing key characteristics of the transient process, including the phase portrait, energy losses, and hysteresis effects.

In addition, the possibility of applying the variable transformation method to the modeling of electrochemical processes-such as metal deposition in galvanic baths-is substantiated. In such systems, reaction kinetics and concentration dependencies lead to complex nonlinear dynamics. In this context, the introduction of new variables enables the reduction of equations to a linear form and facilitates accurate analysis of both steady-state and transient regimes. The results presented can be applied to the modeling of electronic devices with nonlinear V-I characteristics, in power engineering, automated control systems, and in physico-chemical technologies involving electrochemical transformations.

Keywords: nonlinear electrical circuits, symplectic structure, variable transformation method, electrolyzer, electrochemical processes, metal deposition.