John,
In regard to your question about power coupling and take-off
angles (TOA) of antennas, power coupling is greatest when the E-
field from an antenna is parallel to the geomagnetic field and the
least when the two are perpendicular to each other. Good examples
of the two circumstances are, first, propagation in all directions
from a vertical antenna at one of the magnetic poles where the
field is vertical and, second, E-W propagation from a vertical
antenna at the geomagnetic equator where the field is horizontal
and in the N-S direction.
Numerically, power coupling is calculated by finding the degree
to which the radiation field at a radiation angle has an E-field
component parallel to the magnetic field. It involves the
elliptically polarized waves propagated in the field and the
geometry of the waves relative to the antenna. In short, the
numerical factor by which power coupling affects the signals
entering or leaving the lower ionosphere is largely geometrical
in origin.
Of course, there is an infinity of antenna situations and a
similar degree of multiplicity when it comes to magnetic field
inclinations and radiation angles. By way of illustration, the
vertical variation of signal intensity from a simple vertical
antenna over a perfect ground plane and power coupling are given
below for propagation of signals to the north and south of Omaha,
NE, where the field points 4.7 degrees east, is at 20.4 degrees
with the zenith and directed down into the ground:.
Angle RF Coupling Coupling
(deg) (vert. ant) (to North) (to South)
3 0.997 0.963 0.748
6 0.989 0.971 0.737
9 0.976 0.981 0.722
12 0.957 0.991 0.704
15 0.933 0.998 0.685
18 0.905 1.000 0.666
21 0.872 0.996 0.647
24 0.835 0.985 0.629
27 0.794 0.969 0.612
30 0.750 0.947 0.596
33 0.703 0.921 0.582
36 0.655 0.893 0.568
39 0.604 0.864 0.556
42 0.552 0.834 0.546
45 0.500 0.804 0.536
Couplings are given as numerical factors, not in logarthmic
notation, and the relative signal strength from the vertical at
a given radiation angle is the product of the RF and coupling
factors. It is seen that the coupling is greatest to the north at
18 degrees elevation, close to the inclination I of the magnetic
field. To the south, the coupling factor at that angle is 0.666,
because the field to the south is tilted AWAY from the direction
of propagation.
In any event, the angular variation is slower for the power
coupling than the radiation pattern. That is because power
coupling depends just on differences in angles whereas the
radiation intensity depends on interference, because of path
differences between direct and ground-reflected rays.
73,
Bob, NM7M
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