NIK C-VI.Cl l.\TIO\ OK \KKTIC\K CO\KKA<;K 



167 



DIRECT RAY 



ANTENNA 



IMAGE 



„T~ n CENTER LINE OF 

 S" ANTENNA PATTERN 



Figure 68. Earth curvature effect on direct and image patterns. Note: GH horizontal at the antenna; CE horizontal at 



the reflection point 6 = 



ka 



the base of the antenna. Because of diffraction at a 

 cliff edge the modified antenna pattern f(y) is unsym- 

 metrical as in Example 18. The lines GH are parallel 

 to the horizontal at the antenna. The line CE is 

 horizontal at the reflection point and makes an angle 

 6 with GH. The target is at an angle y with respect 

 to GH. The incident and reflected rays make the 

 angle y — d with CE. It will be noted that the 

 direct ray makes the angle y ~ /3 with the centerline 

 of the antenna pattern, and the reflected ray makes 

 the angle y — 20. 



15616 Coefficient of Reflection 



The coefficient of reflection of the reflecting surface 

 is in general complex. That is, both the magnitude 

 and phase of the reflected wave are affected. The 

 reflection coefficient varies with the conductivity and 

 dielectric constant of the reflector and with the 

 frequency, polarization, and angle of incidence. 

 Careful consideration should be given to the rough- 

 ness of the surface, and a substantial reduction in 

 the coefficient should be made when the height of 

 roughness is comparable to that computed from 

 equation (16). In general the reflection obtained 

 with microwaves is of minor importance. 



The magnitude and phase angle of the reflection 



coefficient are plotted as functions of the angle of 

 reflection, SP in Figures 69 and 70. Curves are given 

 for horizontal and vertical polarization and for the 

 extreme conditions of sea water and dry soil. For 

 dry soil the reflection coefficient is not sensitive to 

 frequency changes, and the 100-mc curve may also 

 be used for 3,000 mc. 



For most purposes the reflection coefficient for 

 horizontal polarization may be taken as unity, and 

 the phase angle as 180°. The use of these values 

 simplifies computations. 



The coefficients of reflection and phase angle for 

 vertical polarization vary rapidly with frequency 

 and angle of reflection for sea water and more 

 gradually for dry land. The minimum point of the 

 curves in Figure 69 is known as the pseudo-Brewster 

 angle corresponding to a similar angle in optics. 



Cases not covered by Figures 69 and 70 may be 

 computed from the following equations. 



Vertical Polarization: 



pexp (-7</>) = 



e f sin^ — \/e r — cos 2 ^ 

 e c sin ty + -v/e c — cos 2 ^ 



Horizontal Polarization: 



P exp(-j4>) = 



\/e c — cos 2 ^ — sin <^ 

 y/ € c — cos 2 ^ + sin SI' 



(95) 



(96) 



