Lower and upper bounds of cutoff frequencies in metallic waveguides

Gruner, L.

doi:10.1109/22.137408

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…where the prime over the summation sign in (11) excludes the term with n = 0. We assume that the infinite vector of Fourier coefficients…”

Section: Hollow Waveguide Of Arbitrary Cross Sectionmentioning

confidence: 99%

“…Polygonal metal waveguides are analyzed analytically and numerically in [10], where the authors used finite difference time domain models of microwave waveguide junctions. Conformal transformation is one of the elegant mathematical tools widely applied in the analysis of waveguides of circular [11][12][13] and rectangular cross section [14,15].…”

Section: Introductionmentioning

confidence: 99%

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High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

Vinogradova,

Smith,

Shestopalov

2024

Applied Sciences

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A method for the accurate calculation of the cut-off wavenumbers of a waveguide with an arbitrary cross section and a number of inner conductors is demonstrated. Concepts of integral and infinite-matrix (summation) operator-valued functions depending nonlinearly on the frequency spectral parameter provide a secure basis for formulating the spectral problem, and the Method of Analytical Regularization is employed to implement an effective algorithm. The algorithm is based on a mathematically rigorous solution of the homogeneous Dirichlet problem for the Helmholtz equation in the interior of the waveguide, excluding the regions occupied by the inner conductor boundaries. A highly efficient method of calculating the cut-off wavenumbers and the corresponding non-trivial solutions representing the modal distribution is developed. The mathematical correctness of the problem statement, the method, and the ability to calculate the cut-off wavenumbers with any prescribed and proven accuracy provide a secure basis for treating these as “benchmark solutions”. In this paper, we use this new approach to validate previously obtained results against our benchmark solutions. Furthermore, we demonstrate its universality in solving some new problems, which are barely accessible by existing methods.

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“…where the prime over the summation sign in (11) excludes the term with n = 0. We assume that the infinite vector of Fourier coefficients…”

Section: Hollow Waveguide Of Arbitrary Cross Sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

Vinogradova,

Smith,

Shestopalov

2024

Applied Sciences

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Waveguides

Vorst

2004

Encyclopedia of RF and Microwave Engineering

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In the electromagnetic spectrum, microwaves are the waves whose wavelengths are comparable to ordinary laboratory dimensions. Furthermore, smooth surfaces of good conductors form very perfect reflectors for them. As a consequence, an electromagnetic wave in a reflecting pipe is reflected back and forth from wall to wall, so that it can travel to large distances with small attenuation. Hence we have “waveguides” as transmission lines, dealing with electromagnetic fields in the inside of hollow regions, rather than outside wires for more conventional electric applications, or waves in free space as in optics, and the propagating electromagnetic field is confined to the finite region of the guide by reflecting walls. The present article reviews the basic theory and the different geometries used in the various applications of such hollow waveguides. It also reviews specific recent (as of 2003) developments, such as theoretical advances, waveguides with arbitrary cross section, and ridged and grooved waveguides.

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An analysis of electromagnetic waves by a complementary finite element method

Igarashi

Honma

1994

IEEE Trans. Magn.

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Lower and upper bounds of cutoff frequencies in metallic waveguides

Cited by 4 publications

References 11 publications

High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

Waveguides

An analysis of electromagnetic waves by a complementary finite element method

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