Dispersion modeling and analysis for multilayered open coaxial waveguides

Nordebo, Sven; Çınar, Gökhan; Gustafsson, Stefan; Nilsson, Börje

doi:10.48550/arxiv.1401.4978

Cited by 1 publication

(4 citation statements)

References 23 publications

(41 reference statements)

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“…The integral operator defined on the left-hand side of ( 17) can be continued to the complex α-plane taking the branchcut (defined by the square root κ = √ k 2 − α 2 ) into proper account, and hence defines an analytic operator-valued function A(α) where A(α)E(ρ, α) = F (ρ, α). The solution to (17) can be expressed as the sum of discrete modes (residues at poles), plus an integration along the branch-cut [5]. In practice, the branch-cut contribution can often be neglected [17].…”

Section: B Fourier Analysismentioning

confidence: 99%

“…The solution to (17) can be expressed as the sum of discrete modes (residues at poles), plus an integration along the branch-cut [5]. In practice, the branch-cut contribution can often be neglected [17].…”

Section: B Fourier Analysismentioning

confidence: 99%

“…where C n is a small closed contour enclosing the point β+n 2π p , f (α) is a function which is analytic inside C n and δ nq denotes the Kronecker delta. By applying the residue theorem ( 20) to (17), the following integral equation is obtained for E mn (ρ)…”

Section: The Floquet Theoremmentioning

confidence: 99%

“…When there are sources present, the modes (the discrete set of eigenfunctions) can be obtained as the residues of the poles and the non-discrete set is manifested as an integration along the branch-cut [5]. In practical circumstances, the branch-cut contribution can often be neglected [17].…”

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confidence: 99%

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On the natural modes of helical structures

Nordebo¹,

Gustafsson²,

Kristensson³

et al. 2015

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Natural modes of helical structures are treated by using the periodic dyadic Green's functions in cylindrical coordinates. The formulation leads to an infinite system of onedimensional integral equations in reciprocal (Fourier) space. Due to the twisted structure of the waveguide together with a quasistatic assumption the set of non-zero coefficients in reciprocal space is sparse and the formulation can therefore be used in a numerical method based on a truncation of the set of coupled integral equations. The periodic dyadic Green's functions are furthermore useful in a simple direct calculation of the quasistatic fields generated by thin helical wires.Index Terms-High-voltage power cables, helical waveguides, dispersion relations, open waveguides, volume integral equations. I. INTRODUCTIONT he purpose of this paper is to formulate a volume integral equation for the determination of the natural modes of helical structures. Low-frequency applications are of particular importance where it can be anticipated the existence of twisted modes of a particularly simple structure. The presented problem formulation is largely motivated by the need of being able to accurately model the field distribution and losses inside twisting three-phase high-voltage power cables at 50 Hz, see e.g., [8,9]. The approach could also potentially be useful for analyzing the wave propagation characteristics of the so called litz wires.Helical waveguide structures have been treated previously such as e.g., with helical sheaths [5,15], and approximations for wire helices [16,26]. Presently, there are also very promising numerical techniques being developed that are based on Finite Element Modeling [8,9] and the Method of Moments [22]. However, to our knowledge there has not been any general presentation regarding analytical modeling of the natural modes of helical structures.

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Section: B Fourier Analysismentioning

confidence: 99%