Cutoff wave numbers of eccentric circular and concentric circular‐elliptic metallic wave guides

Abstract

The cutoff wave numbers knm and the field of two-conductor, perfectly conducting wave guides are determined analytically. Three types of wave guides are considered: Eccentric circular conductors of radii R•, R2 and distance d between their axes, elliptic inner with circular outer conductor, and circular inner with elliptic outer conductor. The electromagnetic field is expressed in the first case in terms of circular cylindrical wave functions referred to both axes in combination with related addition theorems, while in the last two cases, both circular and elliptical cylindrical wave functions are used, which are further connected with one another by well-known expansion formulas. When the solutions are specialized to small eccentricities, kd in the first case and h = ka/2 in the last two cases (where a is the interfocal distance of the elliptic conductor), exact, closed-form expressions are obtained for the coefficients gnm in the resulting relations knm(d ) = knm(0)[1 + gnm(knmd) 2 + .-.] and knm(h ) = knm(0)[1 + grim h2 + '''] for the cutoff wave numbers of the corresponding wave guides. Similar expressions are obtained for the field. Numerical results for all types of modes, comparisons, and certain generalizations are also included.

Scattering parameters representing imperfections in precision coaxial air lines

“…In this connection, Hill [5] developed perturbation expressions for the scattering parameters for a lossless circular air line. When the conductor surface exhibits transverse angular variation, Roimeliotes, Houssain and Fikioris report the effects of ellipticity and eccentricity on cutoff wave numbers [6]. …”

Efficient and Accurate Calculation of the Cutoff Wavenumbers of Coaxial Elliptical-Circular and Circular-Elliptical Metallic Waveguides

“…Thus, the circular-elliptical geometry of the present work can be considered as an extension of [13], where the roots of the corresponding matrix equations are determined. In [14], an attempt was made for the calculation of the cutoff wavenumbers in coaxial elliptical-circular and circular-elliptical metallic waveguides, but the results in that paper turn out to be ambiguous, as it can be concluded from the numerical results of this paper. This means that [14] cannot be used for the calculation of the cutoff wavenumbers in elliptical-circular and circular-elliptical waveguides, and that this paper presents the original formulas for this calculation.…”

“…In [14], an attempt was made for the calculation of the cutoff wavenumbers in coaxial elliptical-circular and circular-elliptical metallic waveguides, but the results in that paper turn out to be ambiguous, as it can be concluded from the numerical results of this paper. This means that [14] cannot be used for the calculation of the cutoff wavenumbers in elliptical-circular and circular-elliptical waveguides, and that this paper presents the original formulas for this calculation. Moreover, this paper presents an extension of [14] where only terms of the order of were used.…”

“…This means that [14] cannot be used for the calculation of the cutoff wavenumbers in elliptical-circular and circular-elliptical waveguides, and that this paper presents the original formulas for this calculation. Moreover, this paper presents an extension of [14] where only terms of the order of were used. Now terms of the order of are present, meaning that the formulation here gives more accurate results for the cutoff wavenumbers as compared to the solution.…”

Electromagnetic Scattering by a Metallic Spheroid Using Shape Perturbation Method

“…For small values of h one can set up to the order h 4 A's and D's are obtained from the solution of the sets (15) and (16) by Cramer's rule, following steps similar to the ones in [12,13]. The determinant ∆ of a's, a 's, d's and d 's is [10,12] …”