CALCULATIONS FOR OPTICAL-INTERFERENCE REGION 



83 



7. Q = mr = 5.9 [see equation (116)], 



- = 2.95, 

 2 



sin^ - = 0.035.3. 

 2 



8. To use equation (110), the value of the free- 

 space gain factor Ao is needed. Figure 3 in Chapter 2 

 gives 



20Iog Ao = - 118. 

 Substituting in equation (110), 



20 log A = 201og Ao + 10 log (0.0025 + 0.1342) 

 = -118-8.64^ -127 

 By equation (3), using gains of 20 db, 



10 log— = -127 + 40 = -87. 

 ■Pi 



Accordingly the radio gain is —87 db and the received 

 power is given bj^ 



p, = Piio-*-^ 



Suppose the receiver has a minimum detectable 

 power of 10^^° watt, then the required minimum 

 power output under the given conditions would be 



Pi = F2 X 10®'' 



= 10"" X 10*-''= 10"^-^ watts. 



Radab 



Suppose that, instead of a receiver, there is a target 

 at the same position mth a radar cross section of 

 o- = 50 square meters. The value of P2/P1 at the 

 radar receiver can be found from equation (5) using 

 the value of A found above and the given vakies 

 of a- and X. If the radar uses the same antenna for 

 transmitting and recei\-ing, G\ = C2, which in this 

 case is 100 or 20 db, and tlie radar gain 



10 log ~ = 20 log G'l + 10 log — + 10 log a 

 Pi 9 



+ 40 log A - 20 log X, 

 = 40 + 7.5 + 17 - 254 - 0, 

 = - 189.5 db 



This gives Pi = 10^'^ watts, which obviously is unat- 

 tainable. 



Effect of Vertical Polarization 



The general value for K in equation (108), when 

 the reflection coefficient p differs from — 1 and 

 F2/P1 = 1 is (see Section 5.3.1) 



K = pD. (128) 



Q in equation (108) is no longer given by equation 

 (116) but is the sum of two phase shifts, one caused 

 by path difference, (R/r)ir = mr, while the other is 

 4>' = (f> — IT, the difference between the phase of the 

 reflection coefficient and that for perfect reflection. 

 Hence 



„ R 



> 



(129) 



The lobe variable (for imperfect reflection) is 

 now A^, defined by 



9. = Nt (130) 



rather than n = R/r. The relation between N and n 

 is derivable from equation (129), giving 



-4> 



N = 71 



(131) 



The propagation is assumed to take place over 

 sea water. The angle between the reflected wave 

 and the earth is given bj' equation (107) or Figure 24, 

 and is 



^ = 0.582°. 



From Figures 14 and 15 in Chapter 4, 



(j) = 168°, p = 0.76. 



The lobe variable A'^, in terms of the old lobe variable 

 (for p = 1,</) = 180°), by equation (131), is 



N = 1.88 - — = 1.81, 

 180 



- = 163°, 

 2 



sin2 - = 0.085. 

 2 



The fact that N < n signifies that the lobe for 

 vertical polarization (other things being equal) has a 

 greater angle of elevation than the lobe for hori- 

 zontal polarization. 



The value of 10 log 



(1 



K = pD = 0.76 X 0.95 = 0.722 



KY + 4A'sin'^-1 

 = 10 log 0.322 = -5. 

 Therefore, for vertical polarization, 



20 log A = -118 - 5 = -123, 



which may be compared with the value 20 log A 

 = —127, obtained for horizontal polarization with 

 P = 1. 



