132 



COVERAGE DIAGRAMS 



accurate knowledge of the lobe shape is required. 

 Three different solutions of this problem are given 

 in Sections 6.4, 6.5, 6.6, and 6.7. They are 



1. The p-q method for horizontal polarization only. 



2. The u-v method, which may be used for both 

 horizontal and vertical polarization. 



3. Lobe-angle method which has the ad\^antage of 

 determining the lobe angles directly and is used for 

 either polarization. 



where T) replaces K in equation (46) in Chapter 5, 

 since for horizontal polarization p = 1 and since 

 we are neglecting any effect due to the antenna 

 radiation pattern. For this expression, D and Q are 

 certain functions of the antenna heights hi and /jo as 

 well as d which were considered earlier (see Sec- 

 tions 5.2.4 and 5.5.6). For a given transmitter, h, 

 Cn, do, and X are given, so that for a given gain 

 contour the only variables in equation (12) are d and 



ll/2' 



i/a 



126 160 192 ZZA 



d DISTANCE IN IMLOMETERS 



Figure 3. Vertical coverage diagram. 



6.4 



6.4.1 



THE p-q METHOD 

 (HORIZONTAL POLARIZATION) 



Outline of Method 



This method consists in plotting the locus of 

 points having a constant range d and locating those 

 points on this curve which are at such a distance 

 from the transmitter that the phase shift caused by 

 path difference corresponds to the required range. 

 The range corresponding to a total phase shift fi 

 is given by 



d = VGirfo V C.l - ^y- + -l^ sih^ 



n 



(12) 



/!2. The difficulty of the problem consists in the fact 

 that equation (12) provides an extremely complicated 

 relation between hi and d which cannot be solved 

 explicitly for either coordinate. 



Under such circumstances, the natural procedure 

 is to introduce new coordinates which make the 

 handling of equation (12) easier. The method de- 

 scribed in the following makes use of the variables 



p = — and q = 

 dx d 



discussed in Sections 5.5.5 and 5.5.7, and the pro- 

 cedure will be called the p-q method. 



