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Low-frequency dispersion characteristics of a multilayered coaxial cable
Linnæus University.
Linnæus University.
Linnæus University.
Jönköping University, School of Engineering, JTH, Physics.
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2013 (English)In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 83, no 1, 169-184 p.Article in journal (Refereed) Published
Abstract [en]

This paper provides an exact asymptotic analysis regarding the low-frequency dispersion characteristics of a multilayered coaxial cable. A layer-recursive description of the dispersion function is derived that is well suited for asymptotic analysis. The recursion is based on two well-behaved (meromorphic) subdeterminants defined by a perfectly electrically conducting (PEC) and a perfectly magnetically conducting termination, respectively. For an open waveguide structure, the dispersion function is a combination of two such functions, and there is only one branch point that is related to the exterior domain. It is shown that if there is one isolating layer and a PEC outer shield, then the classical Weierstrass preparation theorem can be used to prove that the low-frequency behavior of the propagation constant is governed by the square root of the complex frequency, and an exact analytical expression for the dominating term of the asymptotic expansion is derived. It is furthermore shown that the same asymptotic expansion is valid to its lowest order even if the outer shield has finite conductivity and there is an infinite exterior region with finite nonzero conductivity. As a practical application of the theory, a high-voltage direct current (HVDC) power cable is analyzed and a numerical solution to the dispersion relation is validated by comparisons with the asymptotic analysis. The comparison reveals that the low-frequency dispersion characteristics of the power cable is very complicated and a first-order asymptotic approximation is valid only at extremely low frequencies (below 1 Hz). It is noted that the only way to come to this conclusion is to actually perform the asymptotic analysis. Hence, for practical modeling purposes, such as with fault localization, an accurate numerical solution to the dispersion relation is necessary and the asymptotic analysis is useful as a validation tool.

Place, publisher, year, edition, pages
2013. Vol. 83, no 1, 169-184 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-23044DOI: 10.1007/s10665-012-9616-3Local ID: JTHövrigtISOAI: oai:DiVA.org:hj-23044DiVA: diva2:686122
Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2014-03-04Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
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  • sv-SE
  • Other locale
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Output format
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