Journal IssueDOI

# Numerical calculation of analytic solutions for higher order modes in conical lines

01 Jan 2009-International Journal of Rf and Microwave Computer-aided Engineering (Wiley Subscription Services, Inc., A Wiley Company)-Vol. 19, Iss: 1, pp 99-109
TL;DR: In this article, a full analytical study of higher order modes in conical transmission lines is presented, and methods for the evaluation of these solutions are presented which combine a number of mathematical techniques and results.
Abstract: This article presents a full analytical study of higher order modes in conical transmission lines. Full analytical field solutions and modal cutoff equations are included, and methods for the evaluation of these solutions are presented which combine a number of mathematical techniques and results. Calculated numerical results and field distributions of some higher order modes in conical lines are shown. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.
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Dissertation
01 Dec 2007

8 citations

### Cites background from "Numerical calculation of analytic s..."

• ...• A proof of the cutoff wavelength equation, • Information on the numerical computation of the cutoff wavelengths [17], • Analytical field plots of some higher order modes which are unavailable in the literature....

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Proceedings ArticleDOI
18 Oct 2010
TL;DR: In this article, a study on the constraints on the size of conical line power combiners is presented, where the constraints are imposed by the occurrence of higher order modes which cause unpredictable behavior in electrically large structures.
Abstract: A study is presented on the constraints on the size of conical line power combiners. The constraints are imposed by the occurrence of higher order modes which cause unpredictable behavior in electrically large structures. A simple method is presented to estimate the maximum size of the combining structure to ensure predictable transverse electromagnetic mode behavior.

4 citations

### Cites background or methods from "Numerical calculation of analytic s..."

• ...It also shows a comparison of the exact cutoff radius, computed with the procedure given in [3], [6], with the approximate cutoff radius calculated using (1)....

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• ...Due to the complexity of the calculations required to calculate the exact cutoff radius, the exact procedure will not be repeated here, but the reader is referred to [3], [5], [6]....

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• ...In conical lines the cutoff of a mode is dependent on the radius as well as the frequency [3]–[6]....

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Dissertation
01 Mar 2015

2 citations

### Cites background from "Numerical calculation of analytic s..."

• ...1) is still not satisfied, however, accurate results are still obtained due to the gradual cutoff exhibited by conical transmission lines [38]....

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##### References
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Book
01 Jan 1989
TL;DR: In this article, the authors introduce the notion of circular cross-section waveguides and cavities, and the moment method is used to compute the wave propagation and polarization.
Abstract: Time--Varying and Time--Harmonic Electromagnetic Fields. Electrical Properties of Matter. Wave Equation and Its Solutions. Wave Propagation and Polarization. Reflection and Transmission. Auxiliary Vector Potentials, Contruction of Solutions, and Radiation and Scattering Equations. Electromagnetic Theorems and Principles. Rectangular Cross--Section Waveguides and Cavities. Circular Cross--Section Waveguides and Cavities. Spherical Transmission Lines and Cavities. Scattering. Integral Equations and the Moment Method. Geometrical Theory of Diffraction. Greena s Functions. Appendices. Index.

5,693 citations

Book
01 Jun 1961
TL;DR: In this paper, a revised version of the Revised edition of the book has been published, with a new introduction to the concept of plane wave functions and spherical wave functions, as well as a detailed discussion of the properties of these functions.
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.

5,655 citations

Reference BookDOI
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Abstract: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.

4,083 citations

### "Numerical calculation of analytic s..." refers background in this paper

• ...The associated Legendre function of the first kind is defined as [13]...

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• ...It is shown in [13], that for complex degrees, orders and arguments, when Re(m) 20....

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Book
01 Jan 1951

2,353 citations

Book
01 Jan 1996
TL;DR: Bernoulli and Euler Numbers Orthogonal Polynomials Gamma, Beta, and Psi Functions Legendre Functions Bessel Functions Modified Bessel Function Integrals of Bessel function Spherical Bessel functions Kelvin Functions Airy Functions Struve Functions Hypergeometric and Confluent Hypergeometrical Functions Parabolic Cylinder Functions Mathieu Functions Spheroidal Wave Functions Error Function and Fresnel Integrals Cosine and Sine Integrals Elliptic Integrals Exponential Integrals Summary of Methods for Computing Special Functions Appendices Indexes as mentioned in this paper.
Abstract: Bernoulli and Euler Numbers Orthogonal Polynomials Gamma, Beta, and Psi Functions Legendre Functions Bessel Functions Modified Bessel Functions Integrals of Bessel Functions Spherical Bessel Functions Kelvin Functions Airy Functions Struve Functions Hypergeometric and Confluent Hypergeometric Functions Parabolic Cylinder Functions Mathieu Functions Spheroidal Wave Functions Error Function and Fresnel Integrals Cosine and Sine Integrals Elliptic Integrals and Jacobian Elliptic Functions Exponential Integrals Summary of Methods for Computing Special Functions Appendices Indexes.

481 citations