FUNDAMENTALS OF PROPAGATION 



I') I 



1. The antenna radiation pattern, which gives the 

 relative strength of the radiation held for different 

 directions. 



2. The attenuation, proportional to 1 A'-, resulting 

 from the length of path Hz of the reflected wave. 



3. The attenuation tine to increased divergence of 

 nearly parallel rays reflected from the curved earth. 

 This is taken into account by the use of a divergence 

 factor, I), which depends on range and heights of 

 transmitter and receiver. 



4. The magnitude, p, that the coefficient of reflec- 

 tion of the ground would have if the ground were 

 plane. The reflection surface for a spherical surface, 

 F, is then equal to pD. 



5. Irregularities of the earth's surface which affect 

 the reflection coefficient. 



If E is the magnitude of the direct wave and F 

 is the magnitude of the reflection coefficient, then 

 the field strength of the reflected ray is FE - 



The phase difference between the direct and re- 

 flected fields is given by an angle 5 which is the 

 sum of: 



1. The phase difference, SP, resulting from the 

 difference in path length, R2—R1; 



2. The phase difference, 4>, suffered by the reflected 

 wave upon reflection from the ground. 



The amplitude of the resultant field for a non- 

 directive antenna is then given by GE , where 



G = Vl + F 2 + 2F cos 5 (1) 



is the earth gain factor which is illustrated in Figure 3. 



Figure 3. Phase addition of direct and reflected rays. 



A curve drawn to represent the contour of constant 

 field strength E = GE as a function of the range R t 

 and the angle of elevation (3 gives the vertical cov- 

 erage diagram for that particular field strength. Cal- 

 culation of these diagrams usually requires a con- 

 siderable amount of detailed and laborious work. 



Consider the simple case of the vertical coverage 



diagram of a horizontal dipole antenna located above 

 a plane earth in a homogeneous atmosphere. If the 

 plane of Figure 2 is perpendicular to the dipole axis, 

 the radiation pattern of the antenna is a circle of unit 

 radius. The ratio, F- 2 , of the magnitude of the re- 

 flected wave to that of the incident wave is given by 

 the magnitude, p, of the reflection coefficient. For 

 propagation to distances that are great compared 

 with the antenna elevation, the path lengths R 2 and 

 Ri are not greatly different, and the attenuation clue 

 to path length is approximately the same for both 

 direct and reflected waves. For this set of conditions 

 the resultant field is E = GE a , and equation (1) 

 reduces to 



G = Vl + P 2 + 2p cos 5 ' 



(2) 



In this form G is the plane earth gain factor and a 

 plot of the curves E = GE a = constant as a function of 

 range and angle of elevation gives the coverage dia- 

 gram. It depends only upon the magnitude of the re- 

 flection coefficient, the phase changes related to re- 

 flection and to the difference in path length R^—Ri. 



Since radar requires two-way transmission the re- 

 ceived field strength is proportional to G"-/R 2 i. Other 

 modifying factors must, however, be introduced if the 

 antenna and the target have directional radiative 

 properties 



Both the magnitude of the reflection coefficient 

 -\-F and the phase angle # by which the reflected 

 wave lags behind the incident wave are functions of 

 the frequency, the polarization of the radiation, the 

 angle of grazing with the surface, the conductivity, 

 dielectric constant, and roughness of the ground or 

 sea surface. Figure 4 illustrates the variation of 

 F( = p) and <f> for reflection from a smooth plane sea 

 surface for frequencies of 100 to 3,000 mc, for both 

 types of polarization, at different grazing angles. It 

 may be noted that for horizontal polarization p is 

 approximately unity and <j> nearly 180°, irrespective 

 of the frequency and the magnitude of the grazing 

 angle. This is the simplest situation to be encountered 

 and most nearly approximates the idealized case of 

 a perfect reflector with horizontal polarization. For 

 this case p is exactly unity, and <f> is exactly 180°. 



For vertical polarization over the sea or either type 

 of polarization over ground, both p and </> depart 

 widely from unity and 180°, respectively. Variations 

 in these quantities greatly complicate the calculation 

 of coverage diagrams. 



The reflection coefficient of microwaves is usually 

 found to be small over land. This is essentially due to 



