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5-5 Appendix
NXE1-20 Digital Radio 602-95555-01 Rev A
5.1.1.4 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:
K = 157/157+ dN/dh
Where,
N is the radio refractivity of air.
dN/dh is the gradient of N per kilometer.
The radio refractivity of air for frequencies up to 30 GHz is given as:
N = (77.6 P/T ) + (3.73 x 10
5
)( e/T
2
)
Where,
P = total atmospheric pressure in millibars.
T = absolute temperature in degrees Kelvin.
e = partial pressure of water vapor in millibars.
The P/T term is frequently referred to as the "dry" term and the e/T
2
term
as the "wet" term.
K factors of 1 are equivalent to no ray bending, while K factors above 1 are equivalent to ray
bending away from the earth's surface and K factors below 1 (earth bulging) are equivalent to ray
bending towards the earth's surface. The amount of
earth bulge at a given point along the path
is given by: