Exact Solution of Propagation Constant of Cylindrical Waveguide with Finite Conductivity

Wei-Dong WANG  Minoru ABE  Toshio SEKIGUCHI  

IEICE TRANSACTIONS on Electronics   Vol.E78-C   No.10   pp.1419-1426
Publication Date: 1995/10/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Electromagnetic Theory)
propagation constant of cylindrical waveguide,  hybrid mode,  transcendental equation,  continued fraction,  Bessel function,  

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An exact solution of the propagation constant of a cylindrical waveguide has been obtained in the event of the conductivity of the waveguide-composing 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 in-guide electromagnetic wave, and calculation of Jn-1(z)/Jn(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 TE01 wave that has conventionally been used as a millimeter-wave 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 102 [S/m].