The idealized behavior of finite-length dipoles

The author shows how, in the case of a thin, finite-length, center-fed, radiating dipole, supported by a sinusoidal current distribution, it is possible to approximate the far-field behavior of the dipole by the behavior of an idealized omnidirectional element. Typically, the radiation-intensity factor of the idealized element is that of a simple sine term, raised to some exponent (power). It has been common practice in the past to approximate, where possible, the behavior of such dipoles by the behavior of an idealized element, with an integer value for the exponent. This has allowed for ease of integration in determining the parameters of interest to the designer, such as the dipole radiation resistance and directivity. The determination of these parameters would otherwise require the numerical evaluation of a combination of sine-integral and cosine-integral terms, which, although straightforward, is tedious. It is shown here that, for dipoles not exceeding about one wavelength, it is more appropriate to represent the behavior of the dipole by that of an idealized model, with non-integer values for the exponent. Such an approach would not normally circumvent the numerical integrations but, in the light of previous discoveries, it is possible to produce approximate results for the radiation resistance, the directivity, and the half-power beamwidth that are very close to their exact values. Furthermore, these results can be determined with ease for a variety of different dipole lengths, using only a hand-held, non-programmable pocket calculator.