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A-2

Appendix A: Path Evaluation Information

Moseley SL9003Q

602-12016-01 Revision J

direct signal, and may tend to add to or cancel the direct signal. The extent of direct signal
cancellation (or augmentation) by a reflected signal depends on the relative powers of the

direct and the reflected signals, and on the phase angle between them.
Maximum augmentation will occur when the signals are exactly in phase. This will be the

case when the total phase delay is equal to one wavelength (or equal to any integer
multiple of the carrier wavelength); this will also be the case when the distance traveled by
the reflected signal is longer than the direct path by an odd number multiple of one-half

wavelength. Maximum cancellation will occur when the signals are exactly out of phase, or
when the phase delay is an odd multiple of one-half wavelength, which will occur when the

reflected waves travel an integer multiple of the carrier wavelength farther than the direct
waves. Note that the first cancellation maximum on a shallow angle reflective path will

occur when the phase delay is one and one-half wavelengths, caused by a path one
wavelength longer than the direct path.
The direct radio path, in the simplest case, follows a geometrically straight line from
transmitting antenna to receiving antenna. However, geometry shows that there exist an
infinite number of points from which a reflected ray reaching the receiving antenna will be

out of phase with the direct rays by exactly one wavelength. In ideal conditions, these
points form an ellipsoid of revolution, with the transmitting and receiving antennas at the

foci. This ellipsoid is defined as the first Fresnel zone. Any waves reflected from a surface
that coincides with a point on the first Fresnel zone, and received by the receiving antenna,

will be exactly in phase with the direct rays. This zone should not be violated by intruding
obstructions, except by specific design amounts. The first Fresnel zone, or more accurately

the first Fresnel zone radius, is defined as the perpendicular distance from the direct ray line
to the ellipsoidal surface at a given point along the microwave path:

F1 = 2280 × [(d1×d2) / (f × (d1+d2))]½ feet

Where,

d1 and d2 = distances in statute miles from a given point on a microwave path

to the ends of the path (or path segment).

f = frequency in MHz.

F1 = first Fresnel zone radius in feet.

There are in addition, of course, the second, third, fourth, etc. Fresnel zones, and these can
be easily computed, at the same point along the microwave path, by multiplying the first
Fresnel zone radius by the square root of the desired Fresnel zone number. All odd

numbered Fresnel zones are additive, and all even numbered Fresnel zones are canceling.

A.1.4 K Factors

The matter of establishing antenna elevations to provide minimum fading would be

relatively simple was it not for atmospheric effects. The antennas could easily be placed at
elevations somewhere between free space loss and first Fresnel zone clearance over the

predominant surface or obstruction, reflective or not, and the transmission would be
expected to remain stable. Unfortunately, the effective terrain clearance changes, due to

changes in the air dielectric with consequent changes in refractive bending.
As described earlier, the radio beam is almost never a precisely straight line. Under a given

set of meteorological conditions, the microwave ray may be represented conveniently by a
straight line instead of a curved line if the ray is drawn on a fictitious earth representation of
radius K times that of earth's actual radius. The K factor in propagation is thus the ratio of

effective earth radius to actual earth radius. The K factor depends on the rate of change of
refractive index with height and is given as: