Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T22:22:41.093Z Has data issue: false hasContentIssue false
  • English
  • Français

An asymptotic solution of an integro-differential equation arising in magnetic coupling through thin shield walls

Published online by Cambridge University Press:  17 February 2009

G. F. Fitz-Gerald  and
N. A. McDonald
G. F. Fitz-Gerald
Affiliation:
Department of Mathematics, RMIT, Melbourne, Vic., Australia.
N. A. McDonald
Affiliation:
Department of Communication and Electronic Engineering, RMIT, Melbourne, Vic., Australia.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An equation which has arisen in a study of the magentic coupling through a small rectangular aperture of dimension A × B in a thin shield wall is discussed. The magnetic polarisability of such an aperture in a conducting wall of zero thickness is known to be expressible as RHA3, in which RH is dimensionless and is a function of the aspect ratio α ≡ B/A. An asymptotic solution procedure of a certain variational formulation of this problem is described in the limiting case of large aspect ratio α. Explicit analytical formulase for the leading terms in the expansion are given. These analytical results justify the purely numerical procedures used previously to obtain approximate solutions of this formulation of the problem.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 4 , April 1989 , pp. 414 - 423
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions with formulae, graphs and mathematical tables (Dover, N.Y., 1972).Google Scholar
[2]Bethe, H. A., “Lumped constants for small irises”, Radiation Laboratory Report 43–22, 1943.Google Scholar
[3]Bethe, H. A., “Theory of diffraction by small irises”, Phys. Rev. 66 (1944) 163–182.CrossRefGoogle Scholar
[4]Colin, R. E., Field theory of guided waves (McGraw-Hill, N.Y., 1960).Google Scholar
[5]De Smedt, R. and Van Bladel, J., “Magnetic polarisability of some small apertures”, IEEE Trans. Antennas Propagat. AP-28 (1980) 703–707.CrossRefGoogle Scholar
[6]Fitz-Gerald, G. F. and McDonald, N. A., “An asymptotic solution of an integro-differential equation arising in magnetic coupling through thin shield walls”, RMIT, Department of Mathematics, Technical Report Series 9 (1987).Google Scholar
[7]Gradshteyn, I. S. and Ryzhik, I. M., Tables of integrals series and products (Academic Press, N.Y., 1965).Google Scholar
[8]McDonald, N. A., “Electromagnetic coupling through small apertures”, Ph.D. Thesis, University of Toronto, Canada, 1971. Also issued as Research Report 45, Dept. of Elec. Eng., Univ. of Toronto, 1971.Google Scholar
[9]McDonald, N. A. “Electric and magnetic coupling through small apertures in shield walls of any thickness”, IEEE Trans. Microwave Theory and Techniques MTT-20 (1972) 689–695.CrossRefGoogle Scholar
[10]McDonald, N. A., “Polynomial approximations for the transverse magnetic polarisabilities of some small apertures”, IEEE Trans. Microwave Theory and Techniques MTT-35 (1987) 20–23.CrossRefGoogle Scholar
[11]Muskhelishvili, N. I., Singular integral equations (Wolters-Noordhoff, Groningen, 1972).Google Scholar