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(b) Figure 6.5
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(a) The electric field components E and E in the far-field region. (b) The reference vector E0 at the origin.
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6.5 Power Flux Density The power flux density of a radio wave is a quantity used in calculating the performance of satellite communications links. The concept can be understood by imagining the transmitting antenna to be at the center of a sphere. The power from the antenna radiates outward, normal to the surface of the sphere, and the power flux density is the power flow per unit surface area. Power flux density is a vector quantity, and its magnitude is given by E2 ZW (6.3)
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Here, E is the rms value of the field given by Eq. (6.1). The units for are watts per square meter with E in volts per meter and ZW in ohms. Because the E field is inversely proportional to distance (in this case the radius of the sphere), the power density is inversely proportional to the square of the distance. 6.6 The Isotropic Radiator and Antenna Gain The word isotropic means, rather loosely, equally in all directions. Thus an isotropic radiator is one which radiates equally in all directions. No real antenna can radiate equally in all directions, and the isotropic radiator is therefore hypothetical. It does, however, provide a very useful theoretical standard against which real antennas can be compared. Being hypothetical, it can be made 100 percent efficient, meaning that it radiates all the power fed into it. Thus, referring back to Fig. 6.1a, Prad PS. By imagining the isotropic radiator to be at the center of a sphere of radius r, the power flux density, which is the power flow through unit area, is PS
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(6.4)
Now the flux density from a real antenna will vary with direction, but with most antennas a well-defined maximum occurs. The gain of the antenna is the ratio of this maximum to that for the isotropic radiator at the same radius r: G
(6.5)
A very closely related gain figure is the directivity. This differs from the power gain only in that in determining the isotropic flux density, the
Antennas
actual power Prad radiated by the real antenna is used, rather than the power PS supplied to the antenna. These two values are related as Prad APS , where A is the antenna efficiency. Denoting the directivity by d gives G Ad. Often, the directivity is the parameter which can be calculated, and the efficiency is assumed to be equal to unity so that the power gain is also known. Note that A does not include feeder mismatch or polarization losses, which are accounted for separately. The power gain G as defined by Eq. (6.5) is called the isotropic power gain, sometimes denoted by Gi. The power gain of an antenna also may be referred to some standard other than isotropic. For example, the gain of a reflector-type antenna may be stated relative to the antenna illuminating the reflector. Care must be taken therefore to know what reference antenna is being used when gain is stated. The isotropic gain is the most commonly used figure and will be assumed throughout this text (without use of a subscript) unless otherwise noted. 6.7 Radiation Pattern The radiation pattern shows how the gain of an antenna varies with direction. Referring to Fig. 6.3, at a fixed distance r, the gain will vary with and and may be written generally as G( , ). The radiation pattern is the gain normalized to its maximum value. Denoting the maximum value simply by G [as given by Eq. (6.5)] the radiation pattern is g( , ) G( , ) G (6.6)
The radiation pattern gives the directional properties of the antenna normalized to the maximum value, in this case the maximum gain. The same function gives the power density normalized to the maximum power density. For most satellite antennas, the three-dimensional plot of the radiation pattern shows a well-defined main lobe, as sketched in Fig. 6.6a. In this diagram, the length of a radius line to any point on the surface of the lobe gives the value of the radiation function at that point. It will be seen that the maximum value is normalized to unity, and for convenience, this is shown pointing along the positive z axis. Be very careful to observe that the axes shown in Fig. 6.6 do not represent distance. The distance r is assumed to be fixed at some value in the far field. What is shown is a plot of normalized gain as a function of angles and . The main lobe represents a beam of radiation, and the beamwidth is specified as the angle subtended by the 3-dB lines. Because in general the beam may not be symmetrical, it is usual practice to give the beamwidth in the H plane ( 0 ), as shown in Fig. 6.6b, and in the E plane ( 90 ), as shown in Fig. 6.6c.
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