INTRODUCTION 



61 



The free-space field, in terms of the transmitted 

 power Pi, is given by 



Vg^^o = ?^^^Wg; 



(8) 



for a point in the direction of maximum radiation. 

 In terms of the power P^ dehvered to the load circuit 

 of a receiving antenna, with matched load and 

 oriented for maximum pickup, the field at any point in 

 space is equal, from equation (17) in Chapter 2, to 



K (-T2 



It is sometimes convenient to express E in terms of 

 the (radiation) field at one meter from the trans- 

 mitter, whence -Eo = Ei/d and, from equation (6), 



E=^^I'G,A,■ (10) 



5.1.3 



Factors Affecting Attenuation 

 and Gain 



The above definitions are quite general. In the 

 absence of the earth, there remains only the free- 

 space attenuation which results from the spreading 

 out of the radiated energy as it moves away from 

 the transmitter. At a distance which is several times 

 larger than the wavelength, the field strength varies 

 inversely as the distance from the antenna. 



The presence of the earth affects the field through 

 two sets of quantities. One set is geometric and 

 includes the heights of the antennas and their dis- 

 tance apart, the curvature of the earth, and shape 

 of terrain features. The other set is electromagnetic 

 and depends on the dielectric constant and con- 

 ductivity of the earth and of its atmosphere, the 

 polarization and the wavelength of the radiation. 



5.1.4 



Simplifying Assumptions 



The present chapter is mainly concerned with the 

 computation of the field-strength distribution of a 

 transmitter for certain idealized standard condi- 

 tions, so chosen as to give a fair average picture 

 of propagation conditions for very high-frequency 

 radiation. The reasons for this limitation are stated 

 in Chapter 1. In substance, the limitations are 

 imposed by the great complexity of the general 

 problem, which makes it necessary to proceed in 

 successive steps. Thg first step is to consider propa- 



gation under standard conditions, which will be 

 defined farther on. Successive steps take into 

 account diffraction by terrain, that is, by trees, 

 hills, mountain ranges, or shore lines, or by non- 

 standard propagation effects in the atmosphere. 



The fundamental importance of a knowledge of 

 propagation under standard conditions is first of all 

 due to the fact that in a large number of cases condi- 

 tions do not differ significantly from standard. On the 

 other hand, when they do deviate significantly, the 

 standard solution sets up a criterion for the discov- 

 ery of deviations and the evaluation of the influence 

 of the nonstandard conditions upon propagation. 



The basic assimiptions which define what we have 

 been calling standard propagation conditions will 

 now be given. 



1. Standard atmosphere. It is assumed that the 

 index of refraction of the atmosphere has a uniform 

 negative gradient with increasing elevation. As has 

 been pointed out in Chapter 4, the influence of such 

 an atmosphere upon propagation is equivalent to 

 that of a homogeneous atmosphere over an earth of 

 radius ka, where A; is a constant that usually is taken 

 equal to 4/3. 



2. Smooth earth. The earth is assumed to be 

 perfectly smooth. It can be considered sufficiently 

 smooth if Rayleigh's criterion is satisfied, that is 

 when the height of surface irregularities times the 

 grazing angle (in radians) is less than X/16 (see 

 Section 4.2.10). 



3. Ground constants. The dielectric constant and 

 conductivitjr of the earth are assumed uniform. For 

 wavelengths less than one meter this assumption is 

 particularly valid since in this case propagation is 

 largely independent of the ground constants. In 

 the VHF (1 to 10 m) range, the same is true with the 

 important exception of vertically polarized radiation 

 over sea water. For the \'HF range, the assumption 

 of uniform earth constants is unsatisfactory for 

 paths partly over land and partly over sea water, or 

 over sea water with large land masses near-by (see 

 Chapters 8 and 10). 



4. Doublet antenna and antenna gain. For the 

 formulas of this chapter, the radiating system is 

 assumed to be a doublet antenna (i.e., a straight 

 wire, short compared to the wavelength). Actual 

 antennas have radiation patterns different from 

 that of a doublet, usually having greater directivity. 

 The antenna gain of a half- wave dipole is 1.09 times 

 (or 0.4 db greater than) that of a doublet, the field 

 maximiun being the same in the two cases. This 



