Development of Matrix-Exponential-Based Methods for Transient Analysis of Circuits with Nonlinear Resistors
DOI: 10.21293/1818-0442-2026-29-2-189-198
Abstract: Relevance. The development of new methods for transient analysis of electrical circuits is relevant despite the availability of numerous well-known methods and computer programs. The reason is that practical tasks impose a set of requirements that existing methods do not always fully satisfy. As a result, they give significant inaccuracy or even qualitatively incorrect results, or require excessive computational time and become very complicate or completely inapplicable. The methods should be suitable for stiff, oscillatory, and stiff-oscillatory circuits with a wide range of parameters; highly accurate (order of accuracy of at least 3); computationally efficient; be L-stable (this eliminates false oscillations and restrictions on the integration step); adapted for calculating nonlinear circuits and circuits with frequent switching; simple and convenient, without requiring configuration, preliminary calculations and evaluations. The purpose of the study. To expand the set of methods previously proposed by the author for calculating transients in linear electrical circuits on circuits with nonlinear resistors. Methods. The presented work is based on a new set of high-precision implicit numerical methods for calculating transients in linear electrical circuits. The new methods are based on decomposition of the Padé approximation of the matrix exponential into elementary partial fractions and satisfy all the requirements listed above. They are very well adapted to the structure of electrical-circuit equation systems, and they are much simpler than other high-precision methods. Nonlinear equations are solved using the method of simple iterations and current interpolation within the integration interval. Scientific novelty. New effective methods for calculating transients in linear circuits have been adapted to the calculation of circuits with nonlinear resistors. An original, high-precision linearization of the resistor current-voltage characteristic is proposed, together with a method for calculating currents within the integration interval. All results presented in this study were obtained personally by the author. Results. The proposed new methods make it possible to calculate arbitrary modes of circuits containing nonlinear resistors with an error several orders of magnitude smaller than that of the trapezoidal rule integration, one of the most commonly used for this purpose. Practical significance. Calculations of dynamic processes in circuits with nonlinear elements have numerous practical applications. In particular, they are required for the design of power semiconductor inverters, digital equipment, power supply systems, electronic and radio engineering devices and their components.
Keywords: electrical circuits, nonlinear resistors, transient processes, L-stable methods, high precision methods, matrix exponential, Padé approximation
For citation:
Burtsev Yu. A. Development of Matrix-Exponential-Based Methods for Transient Analysis of Circuits with Nonlinear Resistors. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2026, vol. 29, no. 2, pp. 189–198. DOI: 10.21293/1818-0442-2026-29-2-189-198
Authors and copyright holders:
- Burtsev Yu. A. , Platov South-Russian Polytechnic University (NPI)
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