Page 159 - Satellite Communications, Fourth Edition
P. 159
Antennas 139
A B
E
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A B
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Figure 6.2 The reciprocity theorem.
A number of important consequences result from the reciprocity the-
orem. All practical antennas have directional patterns; that is, they
transmit more energy in some directions than others, and they receive
more energy when pointing in some directions than others. The reci-
procity theorem requires that the directional pattern for an antenna
operating in the transmit mode is the same as that when operating in the
receive mode.
Another important consequence of the reciprocity theorem is that the
antenna impedance is the same for both modes of operation.
6.3 Coordinate System
In order to discuss the directional patterns of an antenna, it is neces-
sary to set up a coordinate system to which these can be referred. The
system in common use is the spherical (or polar) coordinate system illus-
trated in Fig. 6.3. The antenna is imagined to be at the origin of the coor-
dinates, and a distant point P in space is related to the origin by the
coordinates r,
, and . Thus r is the radius vector, the magnitude of
