Theory of Nonuniform Waveguides: the crosssection method
2: Public University of Navarra, Pamplona, Spain
3: Department of Electrical Engineering, TelAviv University, TelAviv, Israel
4: University of Karlsruhe, Karlsruhe, Germany
This book presents and develops the mathematical tools required to effectively examine and analyse propagation processes of waves of various natures using the cross section method, in artificial and nonartificial waveguides. These techniques are used in the solution of practical situations in various fields, such as plasma heating in nuclear fusion, materials processing and radar and satellite communication systems.
Inspec keywords: transmission line matrix methods; finite difference methods; finite element analysis; waveguide theory
Other keywords: mode converters; crosssection method; polarisers; cutoff and resonant frequencies; fibre optic communications; wave propagation; natural waveguides; transmission line matrix formalism; tapers; finite element analysis; nonuniform waveguide theory; fully threedimensional analysis; transmission lines components; nonuniform oversized tubular metallic waveguides; overmoded transmission lines; antenna synthesis; bends; finite difference; magnetically confined nuclear fusion; electrodynamic problems; numerical analysis; electromagnetic wave transmission; absorbing surface design; microwave radio links; finite integration
Subjects: Waveguide and cavity theory; Differential equations (numerical analysis); Transmission line theory; Waveguides and microwave transmission lines; Finite element analysis
 Book DOI: 10.1049/PBEW044E
 Chapter DOI: 10.1049/PBEW044E
 ISBN: 9780852969182
 eISBN: 9781849193979
 Page count: 272
 Format: PDF

Front Matter
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1 The method of small nonuniformities
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The simplest nonuniformity is the small nonuniformity, limited to a small area and having little effect on the waveguiding properties. There are three kinds of principal nonuniformity: waveguide curvature, variation of waveguide filling or impedance and variation of waveguide cross section. The corresponding small nonuniformities are the small angle tilt, a small step of the waveguide filling parameters ε and μ or of impedance and a small step of waveguide cross section, respectively. The electrodynamic problems corresponding to wave scattering from the small nonuniformities mentioned above are considered in the three sections of this Chapter, namely the scattering from ajunction of two halfinfinite uniform waveguides different by one of the following features: by the directions of their axes, by their filling media, their impedance or by their cross sections. The analysis of the solutions obtained for small nonuniformities leads to the calculation of the field scattered by a nonuniform waveguide sec tion of finite length, where the parameter variations are not small at all.

2 The crosssection method
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The basic idea of the crosssection method is that the electromagnetic fields in an arbitrary nonuniform waveguide cross section are represented as a superposition of the waves of different modes propagating in forward and backward directions along an auxiliary straight uniform waveguide of the same cross section and with the identical distribution of ε and μ. The coefficients of this superposition satisfy firstorder ordinary differential equations. The general problem of the field derivation in a nonuniform waveguide is reduced in such a way to the problem of the fields in a uniform waveguide and to the solution of coupledwave ordinary differential equations. Further, this method is employed for the basic types of nonuniform waveguides and for the more general case of combined nonuniformities.

3 Special cases: cutoff cross sections andresonance frequencies
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Generally, if waveguide properties vary slowly, coupling coefficients have small values and if there is no mode degeneracy, only one equation for each parasitic mode remains from the coupledwave eqns. 2.9 and 2.46. Their solutions have the form of eqns. 2.35,2.75 and 2.37, respectively. However, if a wavenumber A, is small or equal to zero, the values of S_{jm} and F_{jm/r} are not small even for very small v_{ο} and a/r, despite slowly varying parameters. The socalled cutoff cross section can exist in a straight waveguide with varying h_{j} along its axis. There, h_{j} = 0 at a given frequency and h_{j} is small. For the case of bent waveguides with constant cross section, h_{j} can be small only in a narrow frequency band near the socalled resonance frequency, i.e. h_{j} = 0. In the first three sections of this chapter special conditions which are valid when critical cross sections exist or the frequency is near the resonance is studied.

4 Straight nonuniform waveguides
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The mathematical technique developed in previous chapters is employed in this chapter to solve some real problems of wave propagation in straight nonuniform waveguides. Examples illustrate different features of the cross section method.

5 Bent waveguides
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In this chapter, the crosssection method is applied to calculations on bent rectangular and circular waveguides.

6 Mode converters with periodicallynonuniform waveguide walls
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Highpower millimetre microwave sources as gyro devices operate in higher order modes of circular waveguides. For interfaces of these devices to high power microwave transmission lines operating in waves with simple field struc ture, for feeding of gyro and Cherenkov amplifiers and for low power (cold test) measurements of electrodynamic circuits of such high power tubes, mode converters for higherorder modes are required (Thumm, 1993).

Back Matter
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