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11-42 Broadcast Transmission Systems

Where:
a = the actual radius of the earth
dn/dh = the rate of change of the refractive index with height

Through the use of average annual values of the refractive index gradient, k is found to be 4/3 for
temperate climates.

Stratification and Ducts

As a result of climatological and weather processes such as subsidence, advection, and surface
heating and radiative cooling, the lower atmosphere tends to be stratified in layers with contrast-
ing refractivity gradients [20]. For convenience in evaluating the effect of this stratification,
radio refractivity N is defined as N = (n – 1) 

×  10

6

 and can be derived from:

(11.2.25)

Where:
P = atmospheric pressure, mbar
T = absolute temperature, K
e = water vapor pressure, mbar

When the gradient of N is equal to –39 N-units per kilometer, normal propagation takes place,

corresponding to the effective earth’s radius ka, where k = 4/3.

When dN/dh is less than –39 N-units per kilometer, subrefraction occurs and the radio wave is

bent strongly downward.

When dN/dh is less than –157 N-units per kilometer, the radio energy may be bent downward

sufficiently to be reflected from the earth, after which the ray is again bent toward the earth, and
so on. The radio energy thus is trapped in a duct or waveguide. The wave also may be trapped
between two elevated layers, in which case energy is not lost at the ground reflection points and
even greater enhancement occurs. Radio waves thus trapped or ducted can produce fields
exceeding those for free-space propagation because the spread of energy in the vertical direction
is eliminated as opposed to the free-space case, where the energy spreads out in two directions
orthogonal to the direction of propagation. Ducting is responsible for abnormally high fields
beyond the radio horizon. These enhanced fields occur for significant periods of time on overwa-
ter paths in areas where meteorological conditions are favorable. Such conditions exist for signif-
icant periods of time and over significant horizontal extent in the coastal areas of southern
California and around the Gulf of Mexico. Over land, the effect is less pronounced because sur-
face features of the earth tend to limit the horizontal dimension of ducting layers [20].

Tropospheric Scatter

The most consistent long-term mode of propagation beyond the radio horizon is that of scatter-
ing by small-scale fluctuations in the refractive index resulting from turbulence. Energy is scat-
tered from multitudinous irregularities in the common volume which consists of that portion of
troposphere visible to both transmitting and receiving site. There are some empirical data that
show a correlation between the variations in the field beyond the horizon and 

∆N, the difference

5

2

77.6

3.73 10

P

e

N

T

T

=

+

×

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Propagation

Propagation 11-43

between the reflectivity on the ground and at a height of 1 km [21]. Procedures have been devel-
oped for calculating scatter fields for beyond-the-horizon radio relay systems as a function of
frequency and distance [22, 23]. These procedures, however, require detailed knowledge of path
configuration and climate.

The effect of scatter propagation is incorporated in the statistical evaluation of propagation

(considered previously in this chapter), where the attenuation of fields beyond the diffraction
zone is based on empirical data and shows a linear decrease with distance of approximately 0.2
dB/mi (0.1 dB/km) for the VHF–UHF frequency band.

11.2.3g

Atmospheric Fading

Variations in the received field strengths around the median values are caused by changes in
atmospheric conditions. Field strengths tend to be higher in summer than in winter, and higher at
night than during the day, for paths over land beyond the line of sight. As a first approximation,
the distribution of long-term variations in field strength in decibels follows a normal probability
law.

Measurements indicate that the fading range reaches a maximum somewhat beyond the hori-

zon and then decreases slowly with distance out to several hundred miles. Also, the fading range
at the distance of maximum fading increases with frequency, while at the greater distances where
the fading range decreases, the range is also less dependent on frequency. Thus, the slope of the
graph N must be adjusted for both distance and frequency. This behavior does not lend itself to
treatment as a function of the earth’s radius factor k, since calculations based on the same range
of k produce families of curves in which the fading range increases systematically with increas-
ing distance and with increasing frequency.

Effects of the Upper Atmosphere (Ionosphere)

Four principal recognized layers or regions in the ionosphere are the E layer, the F1 layer, the F2
layer (centered at heights of about 100, 200, and 300 km, respectively), and the D region, which
is less clearly defined but lies below the E layer. These regular layers are produced by radiation
from the sun, so that the ion density—and hence the frequency of the radio waves that can be
reflected thereby—is higher during the day than at night, The characteristics of the layers are dif-
ferent for different geographic locations and the geographic effects are not the same for all lay-
ers. The characteristics also differ with the seasons and with the intensity of the sun’s radiation,
as evidenced by the sunspot numbers, and the differences are generally more pronounced upon
the F2 than upon the F1 and E layers. There are also certain random effects that are associated
with solar and magnetic disturbances. Other effects that occur at or just below the E layer have
been established as being caused by meteors [24].

The greatest potential for television interference by way of the ionosphere is from sporadic E

ionization, which consists of occasional patches of intense ionization occurring 62 to 75 mi (100
to 120 km) above the earth’s surface and apparently formed by the interaction of winds in the
neutral atmosphere with the earth’s magnetic field. Sporadic E ionization can reflect VHF sig-
nals back to earth at levels capable of causing interference to analog television reception for peri-
ods lasting from 1 h or more, and in some cases totaling more than 100 h per year. In the U.S.,
VHF sporadic E propagation occurs a greater percentage of the time in the southern half of the
country and during the May to August period [25].

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Propagation

11-44 Broadcast Transmission Systems

11.2.4 References

1.

Bullington, K.: “Radio Propagation at Frequencies above 30 Mc,” Proc. IRE, pg. 1122,
October 1947.

2.

Fink, D. G., (ed.): Television Engineering Handbook, McGraw-Hill, New York, N.Y., 1957.

3.

Eckersley, T. L.: “Ultra-Short-Wave Refraction and Diffraction,” J. Inst. Elec. Engrs., pg.
286, March 1937.

4.

Norton, K. A.: “Ground Wave Intensity over a Finitely Conducting Spherical Earth,” Proc.
IRE, pg. 622, December 1941.

5.

Norton, K. A.: “The Propagation of Radio Waves over a Finitely Conducting Spherical
Earth,” Phil. Mag., June 1938.

6.

van der Pol, Balth, and H. Bremmer: “The Diffraction of Electromagnetic Waves from an
Electrical Point Source Round a Finitely Conducting Sphere, with Applications to Radio-
telegraphy and to Theory of the Rainbow,” pt. 1, Phil. Mag., July, 1937; pt. 2, Phil. Mag.,
November 1937.

7.

Burrows, C. R., and M. C. Gray: “The Effect of the Earth’s Curvature on Groundwave
Propagation,” Proc. IRE, pg. 16, January 1941.

8.

“The Propagation of Radio Waves through the Standard Atmosphere,” Summary Technical
Report of the Committee on Propagation, vol. 3, National Defense Research Council,
Washington, D.C., 1946, published by Academic Press, New York, N.Y.

9.

“Radio Wave Propagation,” Summary Technical Report of the Committee on Propagation
of the National Defense Research Committee, Academic Press, New York, N.Y., 1949.

10.

de Lisle, E. W.: “Computations of VHF and UHF Propagation for Radio Relay Applica-
tions,” RCA, Report by International Division, New York, N.Y.

11.

Selvidge, H.: “Diffraction Measurements at Ultra High Frequencies,” Proc. IRE, pg. 10,
January 1941.

12.

McPetrie, J. S., and L. H. Ford: “An Experimental Investigation on the Propagation of
Radio Waves over Bare Ridges in the Wavelength Range 10 cm to 10 m,” J. Inst. Elec.
Engrs., pt. 3, vol. 93, pg. 527, 1946.

13.

Megaw, E. C. S.: “Some Effects of Obstacles on the Propagation of Very Short Radio
Waves,” J. Inst. Elec. Engrs., pt. 3, vol. 95, no. 34, pg. 97, March 1948.

14.

Dickson, F. H., J. J. Egli, J. W. Herbstreit, and G. S. Wickizer: “Large Reductions of VHF
Transmission Loss and Fading by the Presence of a Mountain Obstacle in Beyond-Line-of-
Sight Paths,” Proc. IRE, vol. 41, no. 8, pg. 96, August 1953.

15.

Bullington, K.: “Radio Propagation Variations at VHF and UHF,” Proc. IRE, pg. 27, Janu-
ary 1950.

16.

“Report of the Ad Hoc Committee, Federal Communications Commission,” vol. 1, May
1949; vol. 2, July 1950.

17.

Epstein, J., and D. Peterson: “An Experimental Study of Wave Propagation at 850 Mc,”
Proc. IRE, pg. 595, May 1953.

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Propagation

Propagation 11-45

18.

“Documents of the XVth Plenary Assembly,” CCIR Report 563, vol. 5, Geneva, 1982.

19.

Bean, B. R., and E. J. Dutton: “Radio Meteorology,” National Bureau of Standards Mono-
graph 92, March 1, 1966.

20.

Dougherty, H. T., and E. J. Dutton: “The Role of Elevated Ducting for Radio Service and
Interference Fields,” NTIA Report 81–69, March 1981.

21.

“Documents of the XVth Plenary Assembly,” CCIR Report 881, vol. 5, Geneva, 1982.

22.

“Documents of the XVth Plenary Assembly,” CCIR Report 238, vol. 5, Geneva, 1982.

23.

Longley, A. G., and P. L. Rice: “Prediction of Tropospheric Radio Transmission over Irreg-
ular Terrain—A Computer Method,” ESSA (Environmental Science Services Administra-
tion), U.S. Dept. of Commerce, Report ERL (Environment Research Laboratories) 79-ITS
67, July 1968.

24.

National Bureau of Standards Circular 462, “Ionospheric Radio Propagation,” June 1948.

25.

Smith, E. E., and E. W. Davis: “Wind-induced Ions Thwart TV Reception,” IEEE Spec-
trum, pp. 52—55, February 1981.

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