Analysis of nonlinear electrical circuits using bernstein polynomials |
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Authors: | M Arounassalame |
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Affiliation: | Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Puducherry 605 014, India |
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Abstract: | In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either
voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems.
In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems
of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However,
because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based
on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of
function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We
propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk
operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three
circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB
based solver and found that our proposed algorithm is more efficient and fast. |
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Keywords: | Nonlinear circuit analysis Bernstein polynomials Krawczyk operator interval analysis polynomial system |
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