BELOW THE INTERFERENCE REGION 



115 



so that this is the minimum detectable power. The 

 vakie of Pi/Pi ior the given power output of 100 

 watts is 



-12 



2_21i^ = 2X10- 

 100 



and 



lOIog— =3+ (-140) = -137. 

 ■Pi 



This is to be changed to 20 log A by equation (3). The 



gain of a half -wave dipole over a doulslet is 1.09 



(see Sections 2.2.2 and 3.2.3), so that r^i = G. = 1.09 

 or 0.4 dl), 



20 log A = - 137 -0.8 ^ - 138 db. 



In changing from 20 log A to 20 log A it must be 

 determined which of the relations in equation (186) 

 is required by comparing the transmitter height of 

 30 meters with 4/1. The value of I as given by 

 Figure 46 is 0.4. Hence the value of 4/1 is 10, which 

 is less than 30. Then 



20 log i = 20 log A 

 = - 138 - 



= - 168. 



-201og30-201oggs', 

 30-0, 



Referring to the chart for X = 1, Figure 48, we 

 lind that for h-, = 30 meters and 20 log A = - 168, 

 the distance d is 53 kilometers. This then is the 

 maximum theoretical range between the two sets. 



5.7.5 



Radio Gain Near the Line of Sight 



For d much greater than d^, the first mode is 

 sufficient, as given in Sections 5.7.3 and 5.7.4. For 

 d nearly equal to d^, i.e., the receiver near the line of 

 sight, a formula [equation (190)] can be given which 

 takes into account several modes and still permits 

 the use of graphical aids. This formula is valid only 

 when the elevated antenna is very high, i.e., 

 h > 1,200X"^^ and the other antenna is low, i.e., 

 /) < 30X''^. (Otherwise the transition curve near 

 the line of sight must be sketched in graphicalh^, as 

 indicated by the broken portion in Figure 7.) 



Denoting by Hi^i the height-gain of the low antenna 

 at height hi, 



A = 2A,Hli M{S) 



'{sdf 

 . 2e}u. 



i/-t 



Fi{A) 



(190) 



1. sd and eh are given in Figures 40 and 41. 6 is 

 given in Section 5.7.6. 



2. A = V^) [sd - V2e/h). 



3. g{5) = 1, except for the VHF range, vertical 

 jiolarization, over sea water. The values are given in 

 Table 9. 



Table 9. Values of ■\1 g{8) for VHF (sea water). 



123456789 10 meters 



Vff(5) 0.98 0.97 0.95 0.94 0.93 0.91 0.90 0.88 0.86 0.84 



A = l[g(S) (sd-^Zeh^) 



F(A) 



0.1 



0.01 



0.001 



0.0001. 



-10 

 -20 



-30 

 DB 



-40 



^-50 



•60 



0.1 



1.0 



10 



-70 



-80 



Figure 51. F{A) [repreKeiiting /''2(A)] versiw A for use in 

 equation (190). 



4. F^iiA) is given Ijy Figure 51. 



5. M(S) for vertical polarization is given b]i- 

 Figure 52 as a function of 8 ^vhich can he found from 

 Figures 53 and 54. 



For horizontal polarization 



M(S) ^ 



vui 



where //2 and F^ii^) refer to the elevated antenna. 



\27rfca/ Vj 

 \2,rA-a/ \/( 



1 I 

 1 



iy-+ (60<rX)- 



. (191) 



