Page 241 - Maxwell House

Chapter 5 221

Here the integral is normalized to the surface of a sphere enclosing the antenna. Meanwhile,
according to (5.37), the noise temperature is proportional to the noise power. Therefore,

2

2
= 1 ∫ ∫ |(, )| (, )sin (5.39)

4 0 0
The worst occurrence is when a directed antenna located on satellite or airplane picks up signals
from the sources on the Earth’s surface, or the ground antenna tries to get a signal from
directions close to the sun.
5.2.9 TEM Waves in Far field Zone

Recall that we proved in Chapter 4 (see (4.66)) a rather surprising fact that the expanding
wavefront of waves emitted by any antennas is practically spherical. Moreover, studying the
elementary radiators we found that the E- and H-far fields have a TEM structure, i.e. they are
normal to each other while resting on a plane tangential to the spherical wavefront. It means
that neither E- nor H-far field vector itself possesses the radial components, i.e. in the direction
of wave propagation. We can, therefore, expect that the same must be true for any antenna that
emits the far away fields with a spherical wavefront. The conventional approach proving this
fact is to put (4.69) into the second equation from (4.66), find the magnetic field vector and
then evaluate the electric field vector from Maxwell’s equation:

1
= ×
� (5.40)
0
1
= ×

The essential mathematical transformations are not very complicated but cumbersome since
they are based on curl operations in the spherical coordinate system. The final result is that the
far away fields emitted by any antenna are practically very close to the TEM structure and
depends on field polarization while

≅ ≅ 0

� (5.41)
→ 0 1

� ~
→ 0

5.2.10 Directivity and Gain
Directivity (D) and Gain (G) are two antenna parameters showing how good the antenna is in
comparison with the ideal free-of-loss isotropic radiator (see Figure 5.2.6a). Both parameters
demonstrate the antenna’s ability to deliver a larger portion of total radiated power in the desired
direction or pick up the maximum energy from a particular direction in a noisy environment.
Notice that we treat any antenna as a passive device, and there is no way to increase the signal
power in it. Such gain, sometimes called passive gain, just means that the directional antennas
are capable of better focusing the emitted energy in the specified direction or better collect
energy from the particular direction at the expense of other parts of space. For simplicity, we
will discuss the directivity and gain of transmit antennas only. Due to Lorentz’s reciprocity
theorem (see Chapter 3) all that can be said is right for the same antenna in receiving mode.