On the effect of gap width on the admittance of solid circularcylindrical dipoles

A center-fed, solid, circular cylindrical dipole of radius a with feed gap of width 2d radiating in a circular waveguide of radius b terminated in infinite ground planes is rigorously analyzed by applying both the conservation-of-complex-power technique and the multiple-reflections technique. The analysis begins by studying the dependence of the dipole admittance on its feed gap width and on its length, 2l, as well as on b, with ka (k=2π/λ is the number) as a parameter. From the decreasing amplitudes of the almost periodic oscillations of these input admittances as b/λ is increased, the input admittances of dipoles radiating in free space (b→∞) are estimated using a variable-bound approach. The effect of gap width (d/a⩽5) for different lengths of dipoles (0.2⩽2l/λ⩽1) in free space and for different thicknesses (ka⩽0.2) is then established. The feed gap dependence for a half-wave dipole is also examined in detail for d /a⩽10 and ka⩽0.14     

The Input Admittance of Thin Prolate Spheroidal Dipole Antennas with Finite Gap Widths

The input admittance of a thin prolate spheroidal dipole antenna of major and minor axes a, b and fed by a gap of finite width 2d operating at the wavelength λ (k=2π/λ) is expressed as a very slowly convergent sum of symmetric prolate spheroidal angle and radial modal functions whose computation in this paper is facilitated by a novel method for evaluating radial functions of the second kind for small and large order with high accuracy. Then, by using Infeld's (1947) method of replacing a sum by an integral, the slowly convergent part of the admittance is evaluated. Three different types of distributions for the gap electric field are considered, and numerical results for the admittance are given as a function of the spheroidal dipole's length (0⩽2a⩽λ) with its thickness (2b⩾2×10^-5 λ), as well as the gap ratio d/b, as parameters     

Quasi-translational addition expressions of prolate scalar wavefunctions for thin prolate spheroids

The conventional, translational addition theorems for both spherical and prolate spheroidal wave functions applied to incoming or outgoing waves possess a well-known convergence sphere near which the addition series fail to converge rapidly. To overcome this deficiency the quasi-translational addition expressions for prolate wave functions are developed by using a physical-geometrical transformation which allows the separation in the azimuthal direction in the translated prolate spheroidal coordinate system. These quasi-translational addition expressions are valid everywhere and, in particular, exhibit a fast convergence characteristics for thin spheroids which are commonly used in physical and engineering applications     

Effect of gap length on the input admittance of center fed coaxial waveguides and infinite dipoles

The input admittance of a coaxial waveguide fed by a gap of length2din the center conductor is evaluated using the dyadic Green's function of the guide and a band of equivalent magnetic surface current proportional to the gap's axial electric field via the equivalence principle. The axial electric field is expressed in terms of a rapidly convergent series of ultraspherical polynomials whose weighting function satisfies the edge conditions at each end of the gap. If the inner and outer radii of the coaxial guide areaandb, respectively, then the limiting case ofb rightarrow inftyis an infinite dipole in free space. Numerical results for the admittance are given as a function ofka (0.01 leq ka leq 0.50)with parameterb/a = 2, 5,10and 50 for the coaxial guide. For the infinite dipole the admittance is presented as a function ofd/a (10^{-3} leq d/a leq 10)withkaas a parameter (0.001 leq ka leq 0.1).     

The static electric field distribution between two semi-infinite circular cylinders: A model for the feed gap field of a dipole antenna

The static electric field distribution in the gap between two solid perfectly conducting semi-infinite cylinders is obtained in terms of a Fourier-Bessel eigenfunction series. For dipole antennas whose cylinder diameter2aand gap length2dare both much less than the operating wavelengthlambda, this field can serve as the quasistatic excitation field in the gap of the dipole. However, the Fourier-Bessel series is slowly convergent. It is transformed into a rapidly convergent series of ultrasphetical polynomials whose weighting function explicitly satisfies the Meixner edge condition. Numerical results are presented graphically for both the axial electric field on the gap surface and the associated potential distribution. Gap ratios ofd/afrom 0.01 to 10.0 are considered and it is shown that asd/a rightarrow 0the solution approaches the two-dimensional solution obtainable by conformal mapping.