Page 164 - Satellite Communications, Fourth Edition

144 Chapter Six

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

2
E
(6.3)
Z W
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 Z in ohms.
W
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 hypothet-
ical, it can be made 100 percent efficient, meaning that it radiates all the
power fed into it. Thus, referring back to Fig. 6.1a, P rad P . By imagin-
S
ing 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

P S
(6.4)
i
4 r 2
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:

M
G (6.5)
i
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