Analysis of Elliptical Thin Ridged Waveguide
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Analysis of Elliptical Thin Ridged Waveguide Jin Xu & Wenxiang Wang & Lingna Yue & Yubin Gong & Yanyu Wei
Received: 7 May 2007 / Accepted: 21 June 2007 / Published online: 6 July 2007 # Springer Science + Business Media, LLC 2007
Abstract Elliptical waveguides and ridged waveguides have found broad applications in many microwave structures. The elliptical waveguide with double infinite thin ridges has been formulated using the mode-matching method. Exact closed-form expressions for eigenvalue problem of all TE and TM modes are presented. Numerical results suggest that the elliptical ridged waveguides have larger bandwidth than that of circular ones. Keywords Elliptical waveguide . Mathieu function . Bandwidth . Mode-matching
1 Introduction Ridged and finned waveguides have found extensive applications in microwave and millimeter wave devices [1–4]. They offer the advantages of low cutoff frequency, wide bandwidth, and low impedance. Most previously published work was focused on circular and rectangular ridged waveguides. Elliptical waveguides have been widely used in many microwave systems such as horn antennas [5], dual-filters [6], and accelerator beam tubes [7]. Recently, the slow-wave characteristics of periodic structures involving elliptical section have been studied [8, 9]. A. A. El-Sherbiny was the first to study the elliptical ridged waveguide [10]. To simplify the analysis, the infinite thin ridges extend from the walls to the focal points along the major axis is considered in A. A. El-Sherbiny’s works. In that structure, the presence of ridges does not disturb the fields of even TM modes and odd TE modes. The dominant mode can not obtain wide bandwidth until the eccentricity is very small (ellipse degenerates to circularity gradually).
Supported in part by the National Natural Science Foundation of China under Grant 60532010, and in part by the Scientific Research Foundation for the Returned Overseas Chinese Scholars under Grant 04LXJ01.
J. Xu (*) : W. Wang : L. Yue : Y. Gong : Y. Wei National Key Laboratory of High Power Vacuum Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China e-mail: [email protected]
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Int J Infrared Milli Waves (2007) 28:733–739
In this paper, the elliptical waveguide with double thin ridges along the minor axis is studied. The eigenvalue analysis of this waveguide by using mode-matching technology at certain selected boundaries in the guide is presented here. The cutoff frequencies of all TE and TM modes disturbed by ridges, and the bandwidth for the dominant mode are given.
2 Theoretical analysis The cross section of elliptical thin ridged waveguides is shown in Fig. 1. a and b are the semimajor and semi-minor axis respectively. The constant h represents half of the distance between the foci. The ridge height is presented by DðD ¼ b d Þ. The structure is divided into two regions for analysis: 1(x∈(0, x1) and 2(x∈(x1, x0). The boundary between the two regions is selected at the confocal ellipse which passed through the edge o
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