Page 38 - Antennas for Base Stations in Wireless Communications

Fundamentals of Antennas 11

where, Ω 1r is the half-power beamwidth in one plane (radians) and Ω 2r is
the half-power beamwidth in a plane at a right angle to the other (radi-
ans). The same approximation can be used for angles given in degrees
as follows:

180  2
 
D ≈ 4π  π  = 41253 (1.18)
Θ Θ 2 d Θ Θ 2 d
1
1
d
d
where Ω 1d is the half-power beamwidth in one plane (degrees) and Ω 2d
is the half-power beamwidth in a plane at a right angle to the other
(degrees). In planar arrays, a better approximation is 6
32400
D ≈ (1.19)
Θ Θ
1 d 2 d
Gain as a parameter measures the directionality of a given antenna.
An antenna with low gain emits radiation with about the same power
in all directions, whereas a high-gain antenna will preferentially radiate
in particular directions. Specifically, the gain, directive gain, or power
gain of an antenna is defined as the ratio of the intensity (power per unit
surface) radiated by the antenna in a given direction at an arbitrary dis-
tance divided by the intensity radiated at the same distance by a hypo-
thetical isotropic lossless antenna. Since the radiation intensity from a
lossless isotropic antenna equals the power into the antenna divided by
a solid angle of 4p steradians, we can write the following equation:

4π U
G = (1.20)
P
in
Although the gain of an antenna is directly related to its directivity,
antenna gain is a measure that takes into account the efficiency of the
antenna as well as its directional capabilities. In contrast, directivity is
defined as a measure that takes into account only the directional prop-
erties of the antenna, and therefore, it is only influenced by the antenna
pattern. If, however, we assume an ideal antenna without losses, then
antenna gain will equal directivity as the antenna efficiency factor
equals 1 (100% efficiency). In practice, the gain of an antenna is always
less than its directivity.

4π U 4π U
G = = e = e D (1.21)
P in cd P r cd
Equations 1.20 and 1.21 show the relationship between antenna gain
and directivity, where e cd is the antenna radiation efficiency factor, D the