Electrical skin phenomena: A fractional calculus analysis

J. A.Tenreiro MacHado, Isabel S. Jesus, Alexandra Galhano, J. Boaventura Cunha, J. K. Tar

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenom-enas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Original languageEnglish
Title of host publicationAdvances in Fractional Calculus
Subtitle of host publicationTheoretical Developments and Applications in Physics and Engineering
PublisherSpringer Netherlands
Pages323-332
Number of pages10
ISBN (Print)9781402060410
DOIs
Publication statusPublished - Dec 1 2007

Keywords

  • Skin effect
  • eddy currents
  • electromagnetism
  • fractional calculus

ASJC Scopus subject areas

  • Engineering(all)

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    MacHado, J. A. T., Jesus, I. S., Galhano, A., Cunha, J. B., & Tar, J. K. (2007). Electrical skin phenomena: A fractional calculus analysis. In Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (pp. 323-332). Springer Netherlands. https://doi.org/10.1007/978-1-4020-6042-7_22