104 



CALCULATION OF RADIO GAIN 



For the dielectric earth, S > > 1. See equation (,193). 

 If both antennas are low {h < 30X"'^) equation (172) 

 and the accompan3ang figures (Figures 31 to 41) are 

 valid for all distances d such that 



c^ >> 



2hJh 



(173) 



If one or both antennas are elevated, equation (172) 

 is valid only well within the diffraction region of the 

 transmitter, i.e., for 



d>> dL. (174) 



The following quantities required to find 20 log A 

 are given in Figures 31 to 41 : 



s as a function of X is given in Figure 31. 



20 log Fs versus sd in Figures 32 and 33. 



20 log d can be found by using Figure 34. 



e as a function of X by Figure 35. 



20 log g versus eh is given by Figures 36 and 41. 



When one anlenna is low, h < 30X"''^, and the other 

 quite elevated, h > 1,200X"''^, a result valid for hz near 

 the line of sight can be foiuid from the formula and 

 graphs in Section 5.7.5, obtained by summing several 

 modes. 



A more general method of finding the gain near 

 the line of sight is to use equation (172) well below 

 the line of sight to obtain a curve of A versus h^ and 

 by constructing a similar curve for the optical region 



eh ^o log q 



20 log h 



note: 



h scale is 

 being multiplied 

 by 10, therefore 

 'value given by 

 ehj must be 

 multiplied by 10 



- 20 log h:4l.3 



Figure 42. Illustrating use of Figure 41. Note: (eh 

 represents ehg{5)); [e/i2 = 12.3] represents [ehog(5) = 

 12.3]. 



by the method of Chapter 6, "Coverage Diagrams." 

 By joining the tw'o curves into a smooth overall 

 curve, it is possible to estimate A in the transition 

 region near the line of sight. 



For the case of short distances and receiver below 

 the interference region, see Section 5.1.7. 



2. For h < 4/1. Vertical polarization. A more 

 accurate result can be obtained by replacing the 

 height-gain {gh) hj H^/l or in decibels by 20 log H^^ 

 — 20 log I. Hi^ is given by Figure 47 and I by 

 Figure 4G (.see Table 3) . 



3. Graphical aids {continued). 



A. Definition of A. Figures 31 to 36 can be com- 

 bined into a form more convenient for nimierical 

 computation. In Figure 37, a curve parameter A is 

 introduced, defined by 



A 



A = 



Jhgi 



(175) 



where gi is a function of e/ii- This may also be ex- 

 pressed in the form 



20 log i = 20 log .4 - 201og/hgi. 



(176) 



(For h, < 4/1, 20 log A = 20 log A - 20 log H^ -|- 20 

 log I.) 



Equation (172) can be written as 



.1 = 1.77 X 10"' —lA 

 (srf)- 



(177) 



or 



20 log A 



where 



135 + 20 log ^ -I- 20 log -A, (177a) 

 (sd)- 



"A = (eh)g2, 



\\-ith (72 a function of e/jo. Note that Fs/isd)" is a 

 function of sd only and is independent of height. 

 While hi usually represents the transmitter antenna 

 height and h-< that of the rccei\'er, the role of hi and 

 /h in equations (176) and (177) may be interchanged. 



To facilitate the use of Figure 37, three nomograms 

 ha-\'e been added (Figure 40 gi\'es sd when X and d 

 are given. Figure 41 gives chi, 20 log h and 20 log g 

 when X and h are known. Figure 43 gives the modi- 

 fied height h' and distance d' for given /;, d, and k.) 

 To find sd for a value of d which is not on the nomo- 

 gram, say 120 km, find sd corresponding to a distance 

 100 times smaller (i.e., 1.2 km) and multipl}' result- 

 ing sd by 100. Proceed similarly for ch. 



B. Both antennas low. In the case of both an- 

 tennas low, hi and hi < 30 X"'^, the contours 20 log A 



