Direct Energy, 2018a

70 4.2 Electromagnetic Radiation
Infinitesimal
Antenna
r
Effective
Receiver
Area
Figure 4.2: Illustration of power radiating from an isotropic antenna.
or receive a signal [15,ch. 10]. A plot of the strength of the eld radiated
from a transmitter as a function of the angles θ and φ is called a radiation
pattern plot. Similarly,a plot of the strength of the signal received by
a receiving antenna as a function of angles θ and φ assuming a uniform
eld strength is also called a radiation pattern plot. Consider two identical
antennas,one being used as a transmitter and the other as a receiver. The
radiation pattern plots will be the same for these two antennas.
Regardless of the idea of reciprocity,it is often a bad idea to swap the
transmitting and the receiving antennas of a system because a transmitter
may be designed to handle much more power than a receiver [15,p. 479]. A
receiving antenna of eective area A at a distance r from an antenna which
transmits uniformly in all directions receives at most only the fraction
A
4πr 2
of the transmitted power [49,p. 4].
A
P rec = P trans
(4.3)
4πr 2
For example,consider an antenna that transmits 20 kW of power uniformly
in all directions. Assume a receiving antenna has an eective area
of 10 cm 2 and covers a portion of a spherical shell as shown in Fig. 4.2.
What is the power received assuming that the antenna is at a distance of
r =1m,and what is the power received assuming a distance of r =1km?
The surface area intercepted by the receiver is 10 cm 2 =10 −3 m 2 . In
the rst case,this surface area is the fraction 10−3 of the surface sphere of
4π·1 2
radius 1 m. At most,the antenna can receive this fraction of the power.
P =20· 10 3 ·
10 −3
=1.6 W (4.4)
4π · 12