Determination of the Admittance and Effective Length of Cylindrical Antennas

Abstract

The apparent admittance of a cylindrical antenna depends critically on the structure of the conductors near the junction of the antenna and the feeding line. For thin cylinders and closely spaced lines an ideal admittance can be defined in the hypothetical limit of "zero" line spacing. The approximate theoretical equivalent is the admittance seen by a delta-function generator with the infinite susceptance of the knife-edge capacitance subtracted.The iterated theoretical admittance of a cylindrical antenna with a delta-function generator is examin':d for from one to 30 iterations. It is shown that for fJ0a EO 0.1 or a/>.. .E; 0.016 (where a is the radms, fJo = 21T/ >.. the wave number) the conductance converges rapidly, but the susceptance increases continually with the added iterations by an amount proportional to the circumference of the ante!l~a-The m~re _accurat~ the s?lution, the nearer t~e susceptance appro~ches infinity. A simple empmcal correctiOn IS combmed With the second-order Iterated value to provide a good approximation of the ideal independent susceptance of the antenna. When f30 a EO 0.1, the second-order corrected admittance is essentially the same when calculated with either the exact kernel for the tubular antenna or the commonly used average kernel.Tables of the admittance Y, impedance Z, radian effective length fJohe, and directivity D are given.When combined with the terminal-zone network for a particular transmission line, the measurable apparent admittance and impedance of a cylindrical antenna are obtained with essentially as great an accuracy as is possible in terms of an "independent" admittance for the antenna. More accurate values depend on the individual analysis of each transmission-line-antenna configuration.

On the combination of the method of auxiliary sources with reaction matching for the analysis of thin cylindrical antennas

“…The computed values of the current at z ¼ 0 are illustrated in Figure 4 for an increasing N up to L=ð2aÞ ¼ 50: Note that the incorporation of the terminal monopoles yields a remarkably stable solution, since practically unchangeable results are obtained for a very small N: On the contrary, in the absence of the terminal monopoles, a significantly larger N is needed to attain a comparable stability. It should be also noted that a similar behaviour is observed when the MoM is used, as long as, for small N, the computed current distribution from (19) is practically equal to the one obtained by invoking the magnetic field boundary condition of (16) and (17). However, as N tends to and becomes larger than L=ð2aÞ; the magnitudes of the auxiliary sources currents near z ¼ AEL=2 oscillate with increasing amplitude with N; which leads to a non-physical current distribution as computed from (19).…”

“…It should be also noted that a similar behaviour is observed when the MoM is used, as long as, for small N, the computed current distribution from (19) is practically equal to the one obtained by invoking the magnetic field boundary condition of (16) and (17). However, as N tends to and becomes larger than L=ð2aÞ; the magnitudes of the auxiliary sources currents near z ¼ AEL=2 oscillate with increasing amplitude with N; which leads to a non-physical current distribution as computed from (19). Although this phenomenon was perceived many years ago, an in depth analysis of it was only recently appeared in the open literature [5][6][7].…”

“…The presented results were calculated with N þ 1 ¼ dL=ð2aÞe: The addition of the terminal monopoles was found to lead to small but not insignificant differences in the predicted input admittance for small N; which become smaller as N increases. The computed results are compared to available tabulated data obtained after subtracting the admittance term of the knife-edge capacitance associated with the delta-gap generator (which tends to infinity) from the well-known King-Middleton variational method [19] and very close agreement is observed. It is noted that the small differences between the results obtained with and without the terminal monopoles is due to the fact that they were computed for quite large N: For small N; the differences between the curves are more significant.…”

Alternative Representation of Green's Function for Electric Field on Surfaces of Thin Vibrators

“…One may also understand that the errors defined by the kernel approximation and excitation model by a concentrated load cannot always be separated. Although the analysis of these issues is beyond the scope of this paper, we can state that if the analytical methods of the integral Equation (9) solution are used, the simulation results for exact and approximate equations kernel are practically identical [27]. We will use this property in the next section.…”

On Digital Computer Solutions of Fredholm Integral Equations of the First and Second Kind Occurring in Antenna Theory

“…'rhe purpose of this paper is to present two techniques for solving of certain Fredholm integral equations using digital computers. The open-ended, iterative technique, which is discussed, was developed at Sandia Laboratory and recently employed in iterating the King-Middleton integral equation 30 times for the current distribution along a symmetrical center-driven ·antenna (King, Aronson, and Harrison, 1966). The problem treated, which yields a diverging solution, was not· a good one to instill confidence in the validity of the method.…”