To read the full version of this content please select one of the options below:

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.



Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited