Determination of the Admittance and Effective Length of Cylindrical Antennas

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 examined for from one to 30 iterations. It is shown that for β 0 α ≤ 0.1 or α/λ ≤ 0.016 (where α is the radius, β 0 = 2 π/λ 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 antenna. The more accurate the solution, the nearer the susceptance approaches infinity. A simple empirical correction is combined with the second‐order iterated value to provide a good approximation of the ideal independent susceptance of the antenna. When β 0 α ≤ 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 β 0 h e , 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.