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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN Imprimir: 0040-2508
ISSN On-line: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v51.i1.110
pages 100-103

Radiative Characteristics of the TM01 Mode From a Circular Waveguide With a Spiral

K. P. Yatsuk
R. R. Shvelidze


The radiation effect from an open end of a waveguide is interest both for antenna and medical applications. A number of techniques for treating the similar problems are known, e.g. the Kirchhoff approximation, the Fourier transformation, Wiener-Hopf or integral equations etc. All these require that the current or field distribution across the aperture should be known. By applying a plane spiral to the plane of the waveguide end the current distribution across the aperture can be modified thus altering the radiation characteristics. To consider these effects we will assume a dual mode representation for the fields in the waveguide region, an integral representation for the fields outside the waveguide and an anisotropically conducting plane for the spiral.
Now the system under investigation consists of a semi-infinite waveguide of circular cross-section, radius a, and a planar logarithmic spiral in the waveguide aperture. The model is as follows. A polar coordinate system ρ, φ and z has its origin (z = 0) in the waveguide aperture plane. Of the two partial regions that can be considered one is − < z < 0 and 0 < ρ < a, with the dielectric constant of the medium ε = ε1, while the other 0 < z < and ρ < with ε = ε2. The spiral is given by ρ = ρ0 exp(φ/u), where ρ0 is the initial radius of the spiral, u = cot(ψ) is the spiral parameter and ψ - the pitch angle. The spiral and the waveguide walls are perfectly conducting and the dielectrics are lossless. Let the TM01 mode incident on the spiral from z = − be of unit amplitude. The TM01 mode reflected from the spiral and the TE01 mode excited by the spiral are of amplitudes A and B, respectively. Thus, the field in the first region is described in terms of two eigen waves. In the second region (the 0 < z < half-space), the fields are represented as integrals over a continuous spectrum involving two unknown coefficients, T (γ) and C (γ), to describe the quasi-TE and quasi-TM waves, respectively. It is assumed that the region 0 < z < , a < ρ < is not illuminated by the fields arising from the waveguide rim.

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