Cutoff Wavelengths of Elliptical Metallic Waveguides

The cutoff wavelengths lambda cmn of elliptical metallic waveguides with perfectly conducting walls are determined analytically. Two different methods are used for the evaluation. In the first, the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions. In the second, a...

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Bibliographic Details
Published in:IEEE transactions on microwave theory and techniques 2009-10, Vol.57 (10), p.2406-2415
Main Authors: Tsogkas, G.D., Roumeliotis, J.A., Savaidis, S.P.
Format: Article
Language:English
Subjects:
Analytical
Applied sciences
Attenuation
Boundaries
Circuit properties
closed-form expressions
Closed-form solution
cutoff wavelengths
Electric, optical and optoelectronic circuits
Electromagnetic fields
Electromagnetic waveguides
Electronics
elliptical metallic waveguides
Equations
Exact sciences and technology
Exact solutions
Feeds
Mathematical analysis
Mathematical models
Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits
Perturbation methods
Radar
Shape
Studies
Walls
Wave functions
Waveguides
Wavelengths
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Summary:The cutoff wavelengths lambda cmn of elliptical metallic waveguides with perfectly conducting walls are determined analytically. Two different methods are used for the evaluation. In the first, the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions. In the second, a shape perturbation method, the field is expressed in terms of circular-cylindrical wave functions only, while the equation of the elliptical boundary is given in polar coordinates. Analytical expressions are obtained for the cutoff wavelengths, when the solution is specialized to small values of the eccentricity h=c/2a, (hLt1), with c the interfocal distance of the elliptical waveguide and 2a the length of its major axis. In this case, exact closed-form algebraic expressions, free of Mathieu as well as of Bessel functions, are obtained for the expansion coefficients g mn (2) and g mn (4) in the resulting relation lambda cmn (h)=lambda cmn (0) [1+g mn (2) h 2 +g mn (4) h 4 + O(h 6 )] for the cutoff wavelengths. These expressions are valid for each m and n, namely, for the general mode. Numerical results for all types of modes and comparison with existing ones are also included.
ISSN:0018-9480
1557-9670
DOI:10.1109/TMTT.2009.2029636