%0 Journal Article %1 demenko2009analysis %A Demenko, Andrzej %A Wojciechowski, Rafał %D 2009 %E Demenko, Andrezej %I Emerald %J COMPEL - The international journal for computation and mathematics in electrical and electronic engineering %K 65h10-systems-of-nonlinear-algebraic-equations 78a55-optics-electromagnetic-theory-technical-applications 78m10-optics-electromagnetism-finite-element-method 94c05-analytic-circuit-theory %N 3 %P 691–699 %R 10.1108/03321640910940945 %T Loop analysis of multi‐branch, multi‐node non‐linear circuits using singular formulation %U https://www.emerald.com/insight/content/doi/10.1108/03321640910940945/full/html %V 28 %X Purpose The purpose of this paper is to find effective methods of loop analysis of multi‐branch and multi‐node non‐linear circuits using a singular formulation. Design/methodology/approach The classical loop analysis and the loop analysis using a singular formulation have been compared. The non‐linear systems of equations have been considered and iterative procedures of solving non‐linear equations have been applied. Special attention has been paid to the Newton‐Raphson method combined with successive over relaxation and incomplete Cholesky conjugate gradient methods. The convergence of the methods has been discussed. Findings It has been shown that in the case of the loop analysis of non‐linear circuits it is not necessary to form fundamental loops. The system of loop equations with a singular coefficient matrix can be successfully solved iteratively. Using a singular formulation one of the infinitely many solutions can be found quicker than the only one resulting from a classical method with a non‐singular coefficient matrix. Therefore, in the case of the analysis of multi‐branch and multi‐node non‐linear circuits using iterative methods, it is beneficial to introduce superfluous loops. This results in more economical computation and faster convergence. Originality/value The presented methods of solving multi‐branch and multi‐node non‐linear circuits using a singular formulation are universal and may be successfully applied both in circuit analysis and the FE analysis using edge elements for non‐linear problems with a large number of unknowns.

@article{demenko2009analysis, abstract = { Purpose The purpose of this paper is to find effective methods of loop analysis of multi‐branch and multi‐node non‐linear circuits using a singular formulation. Design/methodology/approach The classical loop analysis and the loop analysis using a singular formulation have been compared. The non‐linear systems of equations have been considered and iterative procedures of solving non‐linear equations have been applied. Special attention has been paid to the Newton‐Raphson method combined with successive over relaxation and incomplete Cholesky conjugate gradient methods. The convergence of the methods has been discussed. Findings It has been shown that in the case of the loop analysis of non‐linear circuits it is not necessary to form fundamental loops. The system of loop equations with a singular coefficient matrix can be successfully solved iteratively. Using a singular formulation one of the infinitely many solutions can be found quicker than the only one resulting from a classical method with a non‐singular coefficient matrix. Therefore, in the case of the analysis of multi‐branch and multi‐node non‐linear circuits using iterative methods, it is beneficial to introduce superfluous loops. This results in more economical computation and faster convergence. Originality/value The presented methods of solving multi‐branch and multi‐node non‐linear circuits using a singular formulation are universal and may be successfully applied both in circuit analysis and the FE analysis using edge elements for non‐linear problems with a large number of unknowns.}, added-at = {2024-04-18T02:59:03.000+0200}, author = {Demenko, Andrzej and Wojciechowski, Rafał}, biburl = {https://www.bibsonomy.org/bibtex/2cd4d10b7f32aa2c043ae82c4eb072047/gdmcbain}, doi = {10.1108/03321640910940945}, editor = {Demenko, Andrezej}, interhash = {69dfd968b0dc1da846630c14183525c1}, intrahash = {cd4d10b7f32aa2c043ae82c4eb072047}, issn = {0332-1649}, journal = {COMPEL - The international journal for computation and mathematics in electrical and electronic engineering}, keywords = {65h10-systems-of-nonlinear-algebraic-equations 78a55-optics-electromagnetic-theory-technical-applications 78m10-optics-electromagnetism-finite-element-method 94c05-analytic-circuit-theory}, month = may, number = 3, pages = {691–699}, publisher = {Emerald}, timestamp = {2024-04-18T02:59:03.000+0200}, title = {Loop analysis of multi‐branch, multi‐node non‐linear circuits using singular formulation}, url = {https://www.emerald.com/insight/content/doi/10.1108/03321640910940945/full/html}, volume = 28, year = 2009 }