Page 242 - Maxwell House

222 ANTENNA BASICS

First of all, we need to estimate the power radiated by an ideal isotropic point-size radiator at
distance r in a far field zone. From the energy conservation law, it follows that the total power
radiated by this free-of-loss antenna is equal to the power = delivered to it by the
Σ
Σ
source generator. It is reasonable to assume that the surrounding antenna medium is free-of-
loss. Then the total power accumulated within any of sphere shown in Figure 5.2.6a is
Σ
constant and independent of the radius of sphere. Eventually, the radial component of
Poynting’s vector crossing the unit area of the sphere and the radiated power

1 2
=

0 2 � (5.42)
4 2
= ∯ ∘ = 0
Σ

2
Here 4 is the whole sphere surface and = . is the intensity of electric field
created in point by an isotropic radiator. Therefore, according to (5.42)
2 Σ 0 (5.43)
=
4
The total power radiated by some free-of-loss directional antenna is defined by the integral in
(3.18) and the equity (5.30). Using both we obtain

2 2 2
0 2 |(,)| 0 2
2
2
= ∯ ∘ = ∫ ∫ sin = ∫ ∫ |(, )| sin (5.44)
Σ
0 0 0 2 0 0 0
If so, the square of electric field intensity emitted and arrived at to the same observation spot is
2
= 2 Σ 0 (5.45)
0
2
∫ ∫ |(,)| sin
0 0
Note that in (5.30) was chosen as the peak magnitude of the antenna main beam. Now we
0
can estimate how good a direction antenna is by comparing (5.43) with (5.45) and introducing
the antenna peak directivity D as the ratio
2
0 4
= = 2 (5.46)
2
2 ∫ ∫ |(,)| sin
0 0
On the other hand, antenna directivity can be defined in any arbitrary direction ( , ) as
0
0
2 2
4|( 0 , 0 )| 2|( 0 )|
( , ) = 2 = (5.47)
0
0
∫ ∫ |(,)| 2 sin ∫ |()| 2 sin
0 0 0
Here the second more simple equation describes the directivity of the antenna with rotationally
symmetrical around z-axis pattern, i.e. independent on -coordinate. Evidently, the
dimensionless parameter demonstrates how much more power some antenna delivers to the
observation point in comparison to an isotropic antenna emitting the same power as a
directional antenna. Note that the directivity in (5.47) is regularly measured in decibels relative
to isotropic or in shorthand [dBi]
[dBi] = 10 log 10 (5.48)
Since the relative directivity of the isotropic radiator is 1 or 0 dBi, any antenna with > 1 can
be defined as directional. The elemental electric or magnetic dipole are slightly directional