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Journal ArticleDOI

A TE/TM modal solution for rectangular hard waveguides

06 Mar 2006-IEEE Transactions on Microwave Theory and Techniques (IEEE)-Vol. 54, Iss: 3, pp 1048-1054

AbstractA TE/TM modal solution for a longitudinally corrugated rectangular waveguide is developed. These longitudinal corrugations can be used to excite a quasi-TEM wave and form a hard waveguide by correctly choosing the impedance at the guide wall. The correctly chosen impedance is referred to as the hard boundary condition. The modal solution developed here solves the problem of longitudinal corrugations filled with a dielectric material by first finding and solving the characteristic equation for a complete TE/TM modal set. It is shown that this TE/TM mode solution can be used to achieve the hard boundary condition resulting in the quasi-TEM wave in a hard waveguide for discrete values of corrugation depth. Beyond each of these depths, a mode becomes a surface wave. The theoretical mode set is amenable to the solution of problems using the mode-matching method. A combination of the mode-matching method and the TE/TM modal solution will allow the solution of larger problems.

Topics: Transverse mode (54%), Modal analysis (53%), Boundary value problem (53%), Waveguide (52%), Surface wave (51%)

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Citations
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01 Jan 1996
Abstract: We discuss the unidirectional current screen as an asymptotic strip boundary condition (ASBC) for analysis of field problems containing metal strip grids, and we introduce a related asymptotic corrugation boundary condition (ACBC) for analysis of corrugated surfaces. The boundary conditions are asymptotic in the sense that the exact boundary conditions approach the asymptotic ones when the strip and corrugation periods approach zero. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14: 99–101, 1997.

69 citations


Journal ArticleDOI
Abstract: The coupled transcendental equations describing cutoff frequencies of TE and TM modes are deduced for a rectangular waveguide with arbitrary wall impedance. In the case of TE modes, their generalization is made to a rectangular guiding structure, which possesses both distributed wall impedance and inhomogeneous dielectric loading. Effective impedance is obtained for imperfectly conducting surface incorporating periodic rectangular corrugations along the direction of mode propagation. Circular waveguide bounded by such corrugated surface and rectangular impedance waveguide are considered as numerical examples. For these waveguides, the computations performed to determine the cutoff frequencies of TE guiding modes are validated against the results of the perturbation theory and the finite-element method.

14 citations


Cites background or methods from "A TE/TM modal solution for rectangu..."

  • ...PDET is FEM-based toolbox, which is capable of solving the eigenvalue problems (1) and (4) for arbitraryshaped waveguide with constant parameters ai and bi on its contour C ....

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  • ...Among them are the field expansion method [15], [16], the finite-element method (FEM) [4], [5], [7], [8] [10], [11], [17], and the finite-difference timedomain method [9], [12], [17], which now find use in various commercial software packages....

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  • ...For example, kx is invariant with ω in the following cases: a1 = a3 = 0 [2]–[4], [6]–[8] (kx = πn/w, n = 0, 1, 2 ....

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  • ...Among them, the best-studied case is that when two opposite walls of the rectangular waveguide possess zero surface impedance [2]–[4], [7], [8]....

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  • ...The numerical results have been validated against those followed from the perturbation theory and the FEM....

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Journal ArticleDOI
Abstract: The problem of determining the eigenmodes of a rectangular waveguide with one hard wall formed by longitudinal corrugations with grooves filled with dielectric is considered. The characteristic equation is derived by using the asymptotic boundary conditions for corrugated surfaces. It is shown analytically that if the groove depth is equal to the value 0.25 lambda/(epsilon - 1)(1/2) corresponding to the hard wall condition, the TE eigenmode spectrum of the waveguide contains an infinite set of new non-uniform quasi-TEM modes with different transverse propagation constants in the empty part and identical longitudinal propagation constants equal to the wavenumber k. Analytical solution for the case of excitation of the waveguide by a specified source is given, and an example of forming local quasi-TEM waves is considered and discussed.

9 citations


Cites background from "A TE/TM modal solution for rectangu..."

  • ...Note, that the non-uniform quasi-TEM waves described above represent a new type of the eigenmodes different from the well known uniform quasi-TEM modes existing in the waveguides and horns of rectangular (or square) cross section considered in [9–11]....

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  • ...The concept of artificial electromagnetic hard and soft surfaces or walls [1, 2], that can be realized by corrugations with grooves filled with dielectric or by strips on a grounded dielectric layer, find important applications in design of conical horn antennas [3–8] and pyramidal horn antennas [9–11]....

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Proceedings Article
23 Mar 2009
Abstract: The problem of determining the eigenmodes of a rectangular waveguide with one broad hard wall formed by longitudinal corrugations with grooves filled with dielectric is considered. The dispersion equation is derived on the basis of using the asymptotic boundary conditions for corrugated surfaces. It is shown analytically that if the groove depth is equal to the value 0.25λ/(e−1)½ corresponding to the hard wall condition, the TE eigenmode spectrum of the waveguide comprises an infinite set of degenerated quasi-TEM modes with different transverse propagation constants and identical longitudinal propagation constants equal to the wavenumber k. Such solutions are important for understanding the local waves appearing along ridges in such waveguides, that has inspired to the invention of new so-called gap waveguides.

6 citations


Cites background from "A TE/TM modal solution for rectangu..."

  • ...Note, that this is a new type of the quasi-TEM modes different from the well-known TEM mode existing in a rectangular waveguide with corrugated hard walls [13], [14]....

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Journal ArticleDOI
Abstract: The asymptotic corrugations boundary conditions (ACBCs) are used together with classical theory of vector potentials and an innovative combination of matrix systems to analyze rectangular waveguides having all four walls being longitudinally (axially) corrugated. One matrix system is composed of the ACBCs of two opposite walls, while the other comprises those of the other pair of corrugated walls. A transcendental characteristic equation is derived, from which the modal dispersion diagram can be obtained, for all three modal wave-tyoes: fast space, slow surface, and evanescent waves. From the formulation, analytical modal field functions in closed form are also acquired. Results of dispersion graphs and modal field distributions generated by this method are compared favorably with those obtained by a commercial full-wave solver.

5 citations


Cites background from "A TE/TM modal solution for rectangu..."

  • ...…may be grouped into the following categories: 1) circular waveguides that are either a) transversely [10]–[18] or b) longitudinally [9] corrugated and 2) rectangular waveguides having either a) just two opposite walls that are i) transversely [19] or ii) longitudinally [20] corrugated or b) only…...

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  • ...…so, the and components of the and fields of the TE and TM modal fields within the various grooves are stated as follow; these upcoming expressions are also more directly derived in [20]–[24]. a) Left Groove: and Right Groove: (TE and TM to ): (1a) (1b) (1c) (1d) (1e) (1f) or (1gi) or…...

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References
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Book
01 Jun 1961
Abstract: Foreword to the Revised Edition. Preface. Fundamental Concepts. Introduction to Waves. Some Theorems and Concepts. Plane Wave Functions. Cylindrical Wave Functions. Spherical Wave Functions. Perturbational and Variational Techniques. Microwave Networks. Appendix A: Vector Analysis. Appendix B: Complex Permittivities. Appendix C: Fourier Series and Integrals. Appendix D: Bessel Functions. Appendix E: Legendre Functions. Bibliography. Index.

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"A TE/TM modal solution for rectangu..." refers methods in this paper

  • ...The process begins by looking for and modes, and applies the techniques described in Harrington [15]....

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Abstract: Preface. Basic Electromagnetic Theory. Green's Functions. Transverse Electromagnetic Waves. Transmission Lines. Waveguides and Cavities. Inhomogeneously Filled Waveguides and Dielectric Resonators. Excitation of Waveguides and Cavities. Variational Methods for Waveguide Discontinuities. Periodic Structures. Integral Transform and Function-Theoretic Techniques. Surface Waveguides. Artificial Dielectrics. Mathematical Appendix. Name Index. Subject Index. About the Author.

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"A TE/TM modal solution for rectangu..." refers background in this paper

  • ...If the two guides are identical, the coupling integral becomes a test for the orthogonality of the modes within a given hard waveguide [17]....

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Journal ArticleDOI
Abstract: A transversely corrugated surface as used in corrugated horn antennas represents a soft boundary. A hard boundary is made by using longitudinal corrugations filled with dielectric material. The concept of soft and hard surfaces is treated in detail, considering different geometries. It is shown that both the hard and soft boundaries have the advantage of a polarization-independent reflection coefficient for geometrical optics ray fields, so that a circularly polarized wave is circularly polarized in the same sense after reflection. The hard boundary can be used to obtain strong radiation fields along a surface for any polarization, whereas the soft boundary makes the fields radiated along the surface zero. >

636 citations


"A TE/TM modal solution for rectangu..." refers background in this paper

  • ...I N RECENT years, there has been increasing interest in forms of spatial combining where a large number of antennas are placed in either a longitudinally corrugated dielectric-filled waveguide or a dielectric-filled waveguide meant to simulate a hard waveguide [1]....

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Journal ArticleDOI
Abstract: A theoretical parametric study is given of a TE/sub 11/-to-HE/sub 11/ mode converter consisting of a section of cylindrical corrugated waveguide with varying slot depth. The analysis makes use of modal field-matching techniques to determine the scatter marks of the mode converter from which we deduce its propagation properties. It is shown that a mode converter consisting of only five slots achieves a return loss better than 30dB over the band 2.7

187 citations


Journal ArticleDOI
TL;DR: Horn antennas with soft and hard boundaries are analyzed and the dependency between the edge taper directivity, and sidelobes is calculated based on the solution to the spherical hybrid modes in a conical horn with arbitrary wall impedances.
Abstract: Horn antennas with soft and hard boundaries are analyzed. A soft boundary which exists in classical hybrid-mode horns gives zero field intensity at the wall. A hard boundary corresponds to a uniform field distribution over the horn aperture. Soft and hard horn antennas are compared with respect to directivity, sidelobes, and beamwidth. The dependency between the edge taper directivity, and sidelobes is also calculated based on the solution to the spherical hybrid modes in a conical horn with arbitrary wall impedances. This makes it possible to study how to compromise between directivity and sidelobes. Also discussed is how the different wall impedances may be realized, and some preliminary experimental work on hard horns is presented. >

93 citations


"A TE/TM modal solution for rectangu..." refers result in this paper

  • ...Contrary to [12] and postulated previously [13], [14], TE modes can also exist, albeit in a modified form....

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