Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2009, Article ID 473616, 18 pages doi:10.1155/2009/473616 Research Article Analysis of a Coaxial Waveguide with Finite-Length Impedance Loadings in the Inner and Outer Conductors Feray Hacıvelio ˘ glu and Alinur B ¨ uy ¨ ukaksoy Department of Mathematics, Gebze Institute of Technology, P.O. Box. 141, Gebze, 41400 Kocaeli, Turkey Correspondence should be addressed to Alinur B ¨ uy ¨ ukaksoy, alinur@gyte.edu.tr Received 30 November 2008; Revised 2 March 2009; Accepted 10 May 2009 Recommended by Mohammad Younis A rigorous Wiener-Hopf approach is used to investigate the band stop filter characteristics of a coaxial waveguide with finite-length impedance loading. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener- Hopf equations whose formal solution is obtained by using the factorization and decomposition procedures. The solution involves 16 infinite sets of unknown coefficients satisfying 16 infinite systems of linear algebraic equations. These systems are solved numerically and some graphical results showing the influence of the spacing between the coaxial cylinders, the surface impedances, and the length of the impedance loadings on the reflection coefficient are presented. Copyright q 2009 F. Hacıvelio ˘ glu and A. B ¨ uy ¨ ukaksoy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Coaxial discontinuity structures are widely used as an element of microwave devices, and in the permeability and permittivity measurement for materials 1–3. Hence, the diffraction at discontinuities in coaxial waveguides is a very important topic in microwave theory and have been subjected to numerous past investigations. Most simple types of discontinuities such as steps in inner or outer conductors see, e.g., 4–7 and wall impedance discontinuities 8, 9 were analyzed and characterized. For example, in 8, 9 the scattering of a shielded surface wave in a coaxial waveguide by a wall impedance discontinuity in the inner cylinder has been analyzed. These classical results are related mostly with isolated discontinuities, and fail when there are several of them close enough to interfere with each other. The aim of the present work is to consider a new canonical scattering problem consisting of the propagation of the dominant TEM mode at the finite-length impedance discontinuities in the inner and outer conductors of a coaxial waveguide see Figure 1. The contributions from the successive