Recent improvements in microwave techniques have resulted in precise measurements which indicate that the conventional constants K1 = 79°K/mb and K22?=4,800°K in the expression for the refractivity of air, N=(n-1) 106=[K1/T](p+ K2'e/T) should be revised. Various laboratories appear to have arrived at this conclusion independently. In much of radio propagation work the absolute value of the refractive index of the atmosphere is of small moment. However, in some work it is important and it seems highly desirable to decide upon a particular set of constants. Through consideration of the various recent experiments this paper arrives at a relation 77.6 e N = ~ p + 4,810-T T where p=total pressure in millibars e=partial pressure of water vapor in millibars T=absolute temperature=°C+273 This expression is considered to be good to 0.5 per cent in N for frequencies up to 30,000 mc and normally encountered ranges of temperatures, pressure and humidity.

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The Constants in the Equation for Atmospheric Refractive Index at Radio Frequencies

Completely general formulas are given for computing at any point above a plane earth of finite conductivity the vector electric field for a source which may be a combination of vertical and horizontal electric dipoles or a loop antenna with its axis parallel or perpendicular to the earth. As illustrations of the above general methods, formulas are derived for the ground-wave radiation from (1) a grounded vertical antenna carrying a sinusoidal current distribution and (2) elevated vertical and horizontal half-wave antennas. The "effective height" of the grounded vertical antenna is determined as a function of the ground constants, and this formula is then used to determine the effect of the ground constants on the groundwave field intensity in the neighborhood of a quarter-wave antenna. The formulas are also used to show the influence of antenna height on the attenuation of high and ultra-high frequencies. The forward tilt, i.e., E r /E z , which occurs for the electric vector lying in the vertical plane passing through the antenna, is also easily computed from the formulas given and is shown graphically. An expression for the Poynting vector is derived, and it is shown that a part of the energy in the wave near the ground flows downward into the ground.

The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere

Diffraction propagation over hills and ridges at VHF and UHF is commonly estimated using Fresnel knife edge diffraction. This approach has the advantage of simplicity, and for many geometries yields accurate results. However, since it neglects the shape and composition of the diffracting surface, it can in some cases yield results which are in serious disagreement with measurements. To remedy this, attempts have been made to approximate the diffracting hill or ridge by other shapes, most notably cylinders. These approaches have not been widely adopted, due in large part to their greater numerical complexity. In this paper it is proposed to apply wedge diffraction in the format of the geometrical theory of diffraction (GTD), modified to include finite conductivity and local surface roughness effects. It is shown that, for geometries with grazing incidence and/or diffraction angles, significant improvement in accuracy is obtained. Further, the GTD wedge diffraction form used is based on the Fresnel integral, so that it is only slightly more complex numerically than knife edge diffraction. Finally, the GTD includes reflections from the sides of the ridge (wedge faces), and can be extended to multiple ridge diffraction and three-dimensional terrain variations.

Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss

Radio-wave transmission over the surface of the Earth is a subject of enquiry going back to the beginning of the century. In this review, an attempt is made to describe the ground-wave mechanism that is omni-present. We first call attention to the early analytical contributions of Zenneck and Sommerfeld, based on a flat-Earth model. The subsequent controversies, particularly with regard to the role of the Zenneck surface wave, are outlined. Further developments by other pioneers, such as van der Pol, Fock, Bremmer, Norton, and Millington, are reviewed, and an attempt is made to put these in a modern context. We also show that the trapped surface wave can be a significant contribution to the total ground-wave field, when the Earth boundary is sufficiently inductive. Mixed-path theory and confirming model tests by Ray King are described briefly, along with calculated propagation curves for twoand three-section paths. The bibliography includes references to related topics, such as tropospheric refraction and topographic influences.

The ancient and modern history of EM ground-wave propagation

The paper discusses a simplified solution to the problem of multiple diffraction of microwaves over knife-edge obstacles. The path loss is obtained directly and quickly by alignment of distances and heights, adequately selected from a path profile. A theoretical study shows good agreement between the simplified approach and a complete mathematical analysis made by G. Millington in 1962. When the diffraction loss reaches a maximum which might be in excess of 50 dB, the approximate value exceeds the theoretical one by 2 to 5 dB. Predictions are in good agreement, too, with the results of experiments conducted both in France and in the United States. Out of ten examples reported in the paper, nine indicate an error equal or smaller than 3 dB.

Multiple knife-edge diffraction of microwaves

Part I of this paper first describes a method of measuring attenuation and field strength in the ultra-short-wave range. A resume of some of the quantitative experiments carried out in the range between 17 megacycles (17 meters) and 80 megacycles (3.75 meters) and with distances up to 100 kilometers is then given. Two cases are included: (1) "Optical" paths over sea water and (2) "Nonoptical" paths over level and hilly country. An outstanding result is that the absolute values of the fields measured were always less than the inverse distance value. Over sea water, the fields decreased as the frequency increased from 34 megacycles (8.7 meters) to 80 megacycles (3.75 meters), while the opposite trend was found over land. As a rule, the signals received were very steady, but some evidence of slow fading was obtained for certain cases when the attenuation was much greater than that for free space. Part II gives a discussion of reflection, diffraction, and refraction as applied to ultra-short-wave transmission. It is shown, (1) that regular reflection is of importance even in the case of fairly rough terrain, (2) that diffraction considerations are of prime importance in the case of nonoptical paths, and (3) that refraction by the lower atmosphere can be taken into account by assuming a fictitious radius of the earth. This radius is ordinarily equal to about four thirds the actual radius.

Ultra-Short-Wave Propagation

Part I of this paper first describes a method of measuring attenuation and field strength in the ultra-short wave range. A resume of some of the quantitative experiments carried out in the range between 17 mc. (17 meters) and 80 mc. (3.75 m.) and with distances up to 100 km. is then given. Two cases are included: (1) “Optical” paths over sea-water and (2) “Non-optical” paths over level and hilly country. An outstanding result is that the absolute values of the fields measured were always less than the inverse distance value. Over sea-water, the fields decreased as the frequency increased from 34 mc. (8.7 m.) to 80 mc. (3.75 m.) while the opposite trend was found over land. As a rule, the signals received were very steady, but some evidence of slow fading was obtained for certain cases when the attenuation was much greater than that for free space.

C. R. Burrows

Papers

Ultra-Short-Wave Propagation

Ultra-short wave propagation