Page 162 - Satellite Communications, Fourth Edition
P. 162
142 Chapter Six
of propagation. The vector relationship is shown in Fig. 6.4b, where E
represents the electric field, H the magnetic field, and k the direction
of propagation. These vectors form a right-hand set in the sense that
when one looks along the direction of propagation, a clockwise rotation
is required to go from E to H. An important practical point is that the
wavefront can be assumed to be plane; that is, E and H lie in a plane
to which k is a normal.
In the far field, the electric field vector can be resolved into two com-
ponents, which are shown in relation to the coordinate system in Fig. 6.5a.
is tangent at point P to the circular arc of
The component labeled E
radius r. The component labeled E is tangent at point P to the circle of
radius r sin
centered on the z axis (this is similar to a circle of latitude
on the earth’s surface). Both these components are functions of
and
and in functional notation would be written as E (
, ) and E (
, ). The
resultant magnitude of the electric field is given by
2 2
E 2E
E (6.1)
If E and E are peak values, E will be the peak value of the resultant,
and if they are rms values, E will be the rms value of the resultant.
The vector E shown at the origin of the coordinate system represents
0
the principal electric vector of the antenna itself. For example, for a
horn antenna, this would be the electric field vector across the aper-
ture as shown in Fig. 6.5b. For definiteness, the E vector is shown
0
aligned with the y axis, since this allows two important planes to be
defined:
The H plane is the xz plane, for which 0
The E plane is the yz plane, for which 90°
Magnetic field vectors are associated with these electric field compo-
nents. Thus, following the right-hand rule, the magnetic vector associ-
ated with the E component will lie parallel with E and is normally
denoted by H , while that associated with E will lie parallel (but point-
ing in the opposite direction) to E and is denoted by H . For clarity, the
H fields are not shown in Fig. 6.5, but the magnitudes of the fields are
related through the wave impedance Z . For radio waves in free space,
W
the value of the wave impedance is (in terms of field magnitudes)
E E
Z 120 (6.2)
W
H
H
The same value can be used with negligible error for radio waves in the
earth’s atmosphere.