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Exact Solution of Propagation Constant of Cylindrical Waveguide with Finite Conductivity
WeiDong WANG Minoru ABE Toshio SEKIGUCHI
Publication
IEICE TRANSACTIONS on Electronics
Vol.E78C
No.10
pp.14191426 Publication Date: 1995/10/25 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Issue on Electromagnetic Theory) Category: Keyword: propagation constant of cylindrical waveguide, hybrid mode, transcendental equation, continued fraction, Bessel function,
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Summary:
An exact solution of the propagation constant of a cylindrical waveguide has been obtained in the event of the conductivity of the waveguidecomposing conductor being finite. The said analysis has been reduced to a problem to solve a transcendental equation concerning an eigenvalue of the individual modes of the inguide electromagnetic wave, and calculation of J_{n1}(z)/J_{n}(z) by using of Bessel function becomes necessary. With a large conductivity the absolute value of the complex number z becomes excessively large, and none of calculation method with high accuracy has been found with the aid of a computer. This paper has solved the problem by using a continued fraction for the calculation with regard to which a recurrence formula is utilized. With the TE_{01} wave that has conventionally been used as a millimeterwave guide, it is cleared that it is sufficient to select the number of the calculation terms of the continued fraction to the extent of approximately 1000 in the accuracy in accordance with this calculation method. It is also cleared that the approximation solution obtained by a method of perturbation coincides with the exact solution for the conductivity σ 10^{2} [S/m].

