es. It is one of the most significant parameters for small antennas, where the problem is often matching very dissimilar impedances. A receiving antenna is both a spatially selective filter (measure by the radiation pattern) and a frequency selective filter. The bandwidth measures the frequency range over which the antenna operates. The upper and lower frequencies can be specified in terms of a number of possible parameters: gain, polarization, beamwidth, and impedance. A communications link consists of a transmitting antenna and a receiving antenna. If the transmitter radiates Pt watts, then the received power, Pri at a distance, r, is given by equation 9.2, where Gt and Gr are the transmitter and receiver antenna gains, respectively. (9.2) This formula is known as the Friis transmission equation. It assumes that the antennas are impedance and polarization matched. If this is not the case, then extra factors must be mul- tiplied to the equation to account for mismatches. Generic Antenna Types Antenna design is based on several generic antenna types. These include apertures, small antennas, and array antennas. The properties of each are considered in this section. Generic Antenna Types Fig. 9.4 Radiation aperture in a ground plane. Radiation from Apertures The radiation from apertures illustrates most of the significant properties of pencil beam antennas. The radiation characteristics can be determined by simple mathematical relation- ships. If the electric fields across an aperture (see Figure 9.4) are Ea(x, y), then the radiated fields, Ep(O, Q), are given by equation 9.3, where f(0, Q) is given by equation 9.4 (Olver, 1986; Milligan, 1985). (9.3) (9.4) For high- or medium-gain antennas, the pencil beam radiation is largely focused to a small range of angles around O=0. In this case it can be seen from equation 9.3 that the distant radiated fields and the aperture fields are the Fourier transformation of each other. Fourier transforms have been widely studied, and their properties can be used to under- stand th