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Mathematical Problems in Engineering
Volume 2010, Article ID 976930, 24 pages
Research Article

A Perturbative Method for Calculating the Impedance of Coils on Laminated Ferromagnetic Cores

Program of Postgraduates and Research in Electrical Engineering, Instituto Tecnológico de Morelia, Avenida Tecnológico 1500 Col. Lomas de Santiaguito, 58120 Morelia, MICH, Mexico

Received 24 February 2010; Revised 11 August 2010; Accepted 6 September 2010

Academic Editor: Francesco Pellicano

Copyright © 2010 Serguei Maximov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new set of formulas for calculating the self and mutual impedances of coils on straight and closed laminated ferromagnetic cores of circular cross-section has been derived. The obtained formulas generalize the well-known formulas for impedances of coils on homogeneous ferromagnetic cores, for the case of laminated cores, and improve the previously known formulas for laminated cores. The obtained formulas are fully consistent with Maxwell's equations and, therefore, offer an excellent accuracy. The perturbation theory and the average field technique are used to solve Maxwell's equations inside and outside the core. The solution inside the core can also be used in the analysis of thermal effects occurring inside the laminated core.