ern properties. The pedestal distribution is representative of many reflector antennas, which have an edge taper of about -10 dB corresponding to Ea(a) = 0.316. The Gaussian dis- tribution is also important because high-performance feed horns ideally have Gaussian aperture distributions. The Fourier transform of a Gaussian taper that decreases to zero at the edge of the aperture gives a Gaussian radiation pattern, which has no sidelobes. Generic Antenna Types Table 9.2 Radiation Characteristics of Circular Apertures Electric Field Aperture Distribution 3-dB Beamwidth Level of First Sidelobe Uniform 1.02 % -17.6 dB Taper to zero at edge -24.6 dB 1 (2r) Taper on pedestal -26.5 dB 0.5 + 1 (2g) Gaussian -40 dB (p = 3) Radiation from Small Antennas Small antennas are needed for mobile communications operating at frequencies from HF to the low microwave region. Most of these are derivatives of the simple dipole (see Figure 9.6), which is an electric current element that radiates from the currents flowing along a small metal rod. The radiation pattern is always very broad, with energy radiating in all directions. An important design parameter is the impedance of the dipole, which can vary considerably depending on the exact size and shape of the rod. This means that the imped- ance matching between the antenna and the transmitting or receiving circuit becomes a major design constraint. The radiation fields from a dipole are obtained by integrating the radiation from an infinitesimally small current element over the length of the dipole. This depends on knowing the current distribution, which is a function not only of the length but also of the shape and thickness of the rod. Many studies have addressed obtaining accurate results (King, 1956; King, Mack, & Sandler, 1968). For most cases this has to be done by numerical integration. A simple case is a short dipole with length a << 1/102 when the current dis- tribution can be assumed to be triangular. This results in radiated fields of the form given in equation 9.9. Image