106 



CALCULATION OF RADIO GAIN 



are given by Figure 39. If both antennas are so low, 

 saj^ hi and h < -i/l (see Table 4) that it is desired 

 to use Hl for greater accuracy for vertical polariza- 

 tion (Figure 47), then for 20 log A we take 20 log A 

 + 20 log I - 20 log Hl (see Section 5.7.3) and 

 instead of eh in Figure 39, we use as ordinate eHL2/l- 

 Then for given sd, Figure 39 would give the value 

 of eHL2/l. If the frequency is given, e/l is known 

 (Figures 35 and 46), and we must find the value of 

 Ihi which corresponds to a known value of H12 (Fig- 

 lu-e 47) for the appropriate value of = er/'GOaX. 

 From Uh, Ih is found by dividing by I. 



If only one antenna height is less than -i/l, then de- 

 fine 20 log A as 20 log A + 20 log I - 20 log H^ for 

 that antenna and ho then refers to the other antenna. 



C. Non-standard atmosphere, k 7^ 4/3. The pre- 

 ceding graphs are all based on fc = 4/3. If /v 9^ 4/3, 

 /ii, /12, d, and A should be replaced by /i/, hJ , d' , and 

 A', where 



A' = .1 



or 



20 log A' = 20 log .1 + 



201og(fJ^ 



(178) 



The change of h,d, A to the primed values can be 

 made with the aid of Figure 43, i.e., if h,d are known, 

 change to h',d', then Figure 37 will give A' , which 

 in turn will give A', and this with the aid of Figure 43 

 will give A . 



D. Change to dimcnsionlcss coordinates. In the op- 

 tical region, convenient coordinates are (see Section 

 6.5) 



d _d 



11 = 



-^21:^111 



/)2 



/(I 



For these coordinates, equation (175) becomes 

 A 



A = 



Writing 



hig(e) 



e = ehi, 



s = .sV2A-a/(i, 



(179) 



(180) 



it follows that 



eh« = eu, 

 sv = sd, 

 and, using equations (150) and (159), 

 s- = 2e. 



Consequently, Figure 37 can be used with sv 

 replacing sd, eu replacing eho, and A is defined in 

 equation (179). 



Caution: In using the graphs, care must he exercised 

 when one or both antennas are elevated to see that the 

 receiver antenna is well within the diffraction region, 

 i.e., 



d>>dL. (181) 



E. Illustrative problems; diffraction formula; di- 

 electric earth. In Section 5.6, four types of problems 

 were considered for the optical-interference region. 

 The same four types are given here, for a receiver 

 below the optical-interference region. A dielectric 

 earth is assumed so that the figures in Section 5.7.3 

 are applicalDle. These require supplementing b}^ 

 equations (3) and (5). 



For one-way transmission the radio gain is 



10 log — = 20 log A + 10 log (r/jf;,). (182) 



f 1 



For two-way transmission the radar gain is 



10 log — = 40 log A + 10 log (GiGn) 



^^ + 7.5 -F 10 log 0- - 20 log X. (183) 



Type I. The heights and distance apart of the 

 transmitter and recei\'er antennas and the wave- 

 length are known. The radio gain is to be found. 



An early-warning set has a horizontal antenna, 

 located 118 meters above sea level. A receiver is 

 located in an airplane 1,520 meters above sea level, 

 at a distance of 300 km. The wavelength is 3 meters. 

 The gain of the radar antenna is 96 db and its power 

 output 100 kw. (a) The power received by the air- 

 plane receiver, assuming a gain of 10 db, is to be 

 found, (b) The power returned to the radar by the 

 airplane, assuming that the airplane has a radar 

 cross section o- of 40 square meters, is to be found. 



One-way: From Figure 2, d^ = 205 km. Hence 

 the receiver may be assumed well within the diffrac- 

 tion region. 



From Figure 40, sd = 9.3, with fib) = 1. 



From Figure 41, eh^ = 12.3, with g{b) = 1. 



From Figure 37, 20 log i = - 213. 



