GENERALIZED COVERAGE DIAGRAMS 



145. 



In constructing a coverage diagram for a doublet 

 transmitter, the transmitter height, the wavelength 

 and the radio gain are known. It will be shown in 

 Section 6.8.2 that the normalized free-space distance, 

 do = do/dr, is related to the gain factor A by the 

 equation 



1 Stt , , 



— = — drA. 

 do 3X 



(49) 



The path-difference parameter R has been expressed 

 in equation (114) in Chapter 5 in terms of a height- 

 wavelength factor r which is defined by 



R = nr, (50) 



where 



2 \ 2 /ii3/2 



(51) 



The first maximum, which for horizontal polariza- 

 tion occurs when A = X/2, corresponds to ??. = 1, 

 the second minimum to n = 2, etc. Recalling the 

 discussion in Section 6.5.2, it follows that it is pos- 

 sible to construct coverage diagrams in generalized 

 coordinates with r the pattern or chart parameter 

 and do the curve parameter on a chart for which r 

 is fixed. 



6.8.2 



Determination of do 



It is possible to express do = do/d^ in terms of 

 E/Ei, the ratio of the field strength E corresponding 

 to the lobe, to the free-space field Ei at unit distance 

 from the transmitter. Since 



(52) 



The ratio Ei/E may he expressed in terms of the 

 gain factor A through the following relationships. 

 By equation (16) in Chapter 2 

 „ EM^ 



When d = 1, this gives 



Pi = ^. (53) 



45 



For a doublet receiver with matched load and ad- 



justed for maximum power transfer, equation (17)' 

 in Chapter 2 gives 



Po = 



E~ 3X^ 

 120x' St' 



Hence 





(54> 



3X 



E 8ir "^ Pa StA ' 

 Substituting the value of Ei/E from equation (54} 

 into equation (52) : 



~ drKSTA/ 



(55). 



and 



1 , /SttV , — /SttXX ,- 



Equation (56) shows that if log hi is plotted against 

 log A for fixed values of (h and X, a straight line- 

 results. These straight lines are shown in Figure 14.. 



5000- 

 4000 t 



iOO- 

 dOO- 



20 LOG A — 20 LOG A 



Figure 14. Values of do as functions of hi and 20 log A 

 — 20 log X. (See equation 56. The letters refer to cover- 

 age diagrams plotted in Figures 16 to 39.) 



If hi and E/Ei or hi, X, and A are known, do may- 

 be calculated from equations (52) or (55). Th& 



