Cylindrical Waveguide Mode Converters: Analysis, Design & Filter Principle via Mode Matching

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本文档深入探讨了圆柱波导模式转换器的分析与设计，主要焦点在于模式匹配法的应用。模式匹配法是一种在电磁波传播领域中用于优化和设计器件的技术，它确保波的能量在不同介质或结构之间有效传递，同时保持特定模式的完整性。文章首先介绍了基本概念，如边界条件，其中提到当满足 EZ=0 和 Br(ro)=0 或 J.((ro))=0 的条件时，涉及到的是 TE (横电磁场) 和 TM (纵电磁场) 模式的分离。在讨论 m=0 的情况下，作者对比了不同的方程组，揭示出这些方程对应于 TE 部分的 B 和 Bq 的合成，以及 TM 部分的 Bq。然而，在实际设计中，通常只考虑最后一个项，因为它对应于波导截面保持常数的情况（即 TE1 模式），以及在圆柱波导中 r=r1(y) 也是常数的情况（对应 TM0 模式）。这种模式下，磁场和电场的边界条件 B,=Ew=0 定义了可以插入金属墙壁而不会干扰场分布的区域。作者引用了两篇重要的文献，Cap 和 Deutsch 的研究，他们分别在1978年和1980年关于toroidal resonators（圆筒形共振器）对电磁波的应用，这些共振器是模式匹配法在微波理论和技术中的具体应用实例。Zagrodzinski 的论文可能提供了关于模式转换器设计中的数学模型和理论基础。通过这种方式，本文不仅阐述了圆柱波导模式转换器的设计原则，还展示了如何利用模式匹配法解决实际问题，如确定理想的工作区域和共振特性，这对于通信、雷达和其他微波技术设备的设计至关重要。读者可以从中学到如何通过数学建模和分析来优化这些转换器的性能，确保信号在不同频率和模式间的高效传输。

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. MIT-29, NO. 10, OCTOBER 1981

1059

boundary condition EZ = O

Br(ro)=O=E,(ro) or J.(~~rO) =0. (76)

We consider now the case m =0. Comparing (64), (66),

(68), (71), (73), and (75) with (52)-(54) we find that the

latter solution corresponds to a superposition of the TE

parts’ of B, and B= and the TM part of Bq. We use,

however, only the last term giving from rBv = const for the

“mode” k= f)

r~l ( yr ) = const (77)

(corresponding to a waveguide with cross section r=const)

and for k= 1 (TMOI mode) we obtain

~~1(~~).osz=const

(78)

which describes the surfaces on which B,= Ew = O and into

which metallic walls may be inserted without disturbing the

field patterns.

[1]

[2]

[3]

[4]

REFERENCES

F. Cap and R. Deutsch, “Toroidal resonators for electromagnetic

waves;

IEEE Trans. Microwaue Theory Tech., vol. MTT-26, pp.

478-486, Jdy 1978.

_ “Toroidaf resonatorsfor electromagneticwavesfl LEEE

Trans.

Micro;ave Theo~ Tech., vol

MTT-28, pp. 70G703, July 1980.

J. Zagrodzinski,

J. Phys. A: Math. Gen. vol. 10, pp. 823-831, 1977.

F. Cap, “Some

remarks on toroidaf problems: Beitr. Plasmaphys.

vol.

18,no. 4, pp. 207–217, 1978.

[5]

[6]

[7]

[8]

J. Jager and B. Schnitzer, “Characteristic values of dominant modes

within an empty torus computed by mesh method,” Institut ftir

theoretische Physik, Technische Universitat Graz, Rep. ITPR-8001 1,

June 1980.

D. Nielsen,

“The calculation of electromagnetic field modes in

toroidat cavities of rectangular cross section; Inst. Plasma Research,

Stanford Univ., SU-IPR Rep. 647, Dec. 1975.

S. Przezdziecki, “TE and TM fields inorthogonat coordinate systemsj”

Bull. A cad. Pol. Sci. vol. 8, nr. 8,

pp. 429-436, 1960.

American Institute

of Physics Handbook, New York: McGraw-Hill,

various editions.

Ferdinand Cap was born in 1924 near Viema,

Austria. He ~tudied physics, mathematics, and

chemistry from 1942– 1946 at the University of

Vienna, Vienna, Austria.

He became a Lecturer at the University of

Innsbruck, Innsbruck, Austria, in 1949 after a

stay at the Zttrich Technical University. He was

promoted to Assistant Professor in 1955, Associ-

ate Professor with tenure in 1957, and Fnlf Pro-

fessor in 1960. In 1967 he was Guest Professor

for plasma physics in New York. In 1971 he

became a Senior Research Associate of NASA at Goddard SDace Center

and in 1979 he was a visitor at the Princeton Plasma Physics “Laboratory.

For 10 years he was Austria’s Scientific Representative at the UN in New

York. He has published more than 100 papers in physics and severat

textbooks about nuclear reactors and plasma physics.

Analysis and Design of TE1l-to-HE1l

Corrugated Cylindrical Waveguide Mode

Converters

GRAEME L. JAMES

A bstract— A theoretical parametric study is given of a TE ~l-to-HE II wavegnide) with the HE,1 mode in the balanced condition at ka = 2.9. The

mode converter consisting of a section of cytindricaf corrugated wavegnide

prdlcted resssfts are in very good agreement with experimental data.

with varying slot depth. The anatysis makes use of modat field-matching

“ tecluiaues to detersnine the scatter matrix of the mode converter from

I. INTRODUCTION

which we deduce its propagation properties. It is shown that a mode

converter consisting of only five slots achieves a return loss better than 30

N DESIGNING corrugated horns which use a section

dB over the band 2.7 <ka< 3.8 (where a is the intemaf radius of the

of cylindrical corrugated waveguide at the input, it is

necessary to study the transition from a smooth-walled

Manuscript received January 1, 1981; revised April 10, 1981.

cylindrical waveguide supporting the TE, ~ mode to a cor-

The author is with the Division of Radiophysics, CSIRO, P.O. Box 76,

rugated cylindrical waveguide where the HE ~, hybrid mode

Epping, N.S.W. 2121,Australia.

is supported. With the corrugated surface represented by

0018-9480/81 /1000- 1059$00.75 01981 IEEE

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