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A new approach to steady state analysis of nonlinear electrical circuits

Tadeusz Sobczyk (Institute of Electromechanical Energy Conversion, Cracow University of Technology, Krakow, Poland)
Michał Radzik (Technical Institute, State Higher Vocational School in Nowy Sącz, Nowy Sącz, Poland)



The purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain.


An iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants.


This study found a novel differential operator for periodic functions and its application in the steady-state analysis.

Research limitations/implications

This approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems.

Practical implications

The complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach.


This study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.



This research has been carried out in the frame of project E-2/581/2016/DS founded by the Polish Ministry of Science and Higher Education.


Sobczyk, T. and Radzik, M. (2017), "A new approach to steady state analysis of nonlinear electrical circuits", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 3, pp. 716-728.



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