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Loop analysis of multi-branch, multi-node non-linear circuits using singular formulation

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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.
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Keywords: Circuits; Electromagnetic fields; Finite element method

Document Type: Research Article

Publication date: May 8, 2009

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