Page 219 - Maxwell House

Chapter 5 199

∆ (−)
( ) = sin

0
2 � (5.1)
ℎ ∆ (−)
� � = sin

0
ℎ 2
Here and is the electric current in
ℎ
vertical and horizontal dipole, respectively.
Generally, these currents have different
magnitudes and are shifted in phase , i.e.
⁄
= , | | ≤ /2 (5.2)
ℎ
Figure 5.1.1a Electric Therefore, the total vector of the E-field can
field structure be represented in the phasor form
radiated by two Figure 5.1.1b E-
orthogonal electric = ( ) + vector is linear

0
dipoles � � =

0
ℎ
(−) (5.3)
� sin + sin�
0
0
∆
Here = is the common complex amplitude. To simplify the subsequent
0
2
consideration, let us study first several elementary cases.
a = 0. E-vector is Linearly Polarized (LP) aligning with the unit vector at any spot and any
0
moment in time.
= , = . E-vector keeps linear but slant polarization (see 5.1.1b). The vector LP
orientation varies from point to point depending on coordinates and where an observer is
located. It is worth noting that this phenomenon is common for practically any type of antennas
and might complicate the communication process when an LP antenna is located on moving
object such as satellite or aircraft.
= , = −/. If so, the in-
phase component of E-vector is
equal to

= ℜ( ) =
⁄
+
sincos( − ) +
0
sinsin( − ) (5.4)
0
The graph of (5.4) in Figure 5.1.2
1
Figure 5.1.2 RHCP wave illustration demonstrates the time-space
behavior of this vector at any spot
where sin = sin. In all such directions the magnitude of -vector is constant, i.e.
+
independent of time and radial coordinate
2
2
2
2
2
| | = sin (cos ( − ) + sin ( − )) ≡ sin (5.5)
+
1 Public Domain Image, source with some editing: https://en.wikipedia.org/wiki/Circular_polarization