Imperfectly Conducting Dipoles

Abstract

For many purposes the conductivity σ of copper is sufficiently high so that no significant differences exist between the distributions of current and the admittances of copper antennas and the physically unavailable but mathematically convenient perfectly conducting antennas. The discussion and the tables in Section 2 assume σ = ∞ or z ⁱ = r ⁱ + jx ⁱ = 0, where z ⁱ is the internal impedance per unit length. In this section the properties of cylindrical antennas with nonzero values of z ⁱ are considered. The basis of the results presented is given in three papers.^1,2,3 The impedance per unit length of the cylindrical antenna is conveniently expressed in terms of the dimension-less real parameter

$$\Phi_i = 2\lambda r^i/\zeta_0$$

where r ⁱ is the resistance per unit length, λ is the wavelength in air, and ζ₀ ≐ 1207π ohms. Typical graphs of the distributions of current along cylindrical antennas that are a half wavelength and a full wavelength long when perfectly conducting are shown in Figs. 3.1 and 3.2, with Φ_i as the parameter. Typical graphs of the admittance of resistive dipoles are shown in Fig. 3.3, and graphs of the impedance in Fig. 3.4. The efficiency is shown in Fig. 3.5. Tables 3.1 and 3.2 give numerical values of the admittance and the impedance, respectively, of resistive dipoles for a wide range of values of h/λ and Φ_i.