BELOW THE INTERFERENCE REGION 



111 



For antennas at, or very close to, zero height, the 

 gain-factor ratio depends on AiFs. While F^ gi^'es 

 greater attenuation (lower gain) for horizontal than 

 for vertical polarization, the difference between the 

 two lies principally in the values of Ai. For X = 1 

 meter, the ratio is 64,000 to 1 in favor of vertical 

 polarization. For X = 10 meters, the ratio is about 

 8.6 X 10". 



However, as the antennas are raised above the 

 ground, the strength of a horizontally polarized 

 field increases much more rapidly than does the 

 corresponding vertically polarized field, for a given 



which, as in Section 5.7.3, can be written 



A = 1.77 X 10'' 



— 1a,p', 



cH (188) 



or 



F. 



20 log /I = -]35 + 201og— ^ +201ogA 



(srf)'' 



+ 20 log p'd + 20 log f. (189) 



Since F^ has a graphical representation which de- 

 pends on the wavelength, it is necessary to assume 

 a particular value of X; equation (188) then becomes 



25 



20 



15 



10 



0.06 0. 



0.2 



0.4 0.6 I 



fh 



4 6 



10 



20 



Figure 47. Height-gain function H^ versus //(, for low antenna heiglits. [See equation (1.52.)] 



o 



wavelength up to a certain height above which the 

 field is substantially independent of polarization. 

 For example, above a height of 3 meters for X = 1 

 meter, and above 77 meters for X = 10 meters, the 

 two fields are practically equal. 



6. Parameter A. As in Section 5.7.3, curves can 

 be drawn in terms of the parameter A where 



^ for h > i/l, 



ihgg')i 



Al 



— for h < -i/l. 



(186) 



Equation (185), including the correction for 

 d < 50/p', becomes 



A = I ^^ (Aip'd) {gg'hUgg'h),, (187) 

 2 a- 



a relation between A, di, and Ih, and Figures 48, 49, 

 and 50 for X = 1, 3, 6 meters are in terms of these 

 coordinates. The height-gain function of the trans- 

 mitter gi can be found from Figure 41. 



7. Illustrative example: Communication. A com- 

 munication set used in ship-to-ship work has a wave- 

 length of 1 meter, a receiver sensitivity of 10 micro- 

 volts \vith a resistance of 50 ohms across the input 

 terminals and a transmitter power output of 100 

 watts. The transmitter and receiver antennas are 

 vertical half- wave dipoles at an elevation of 30 meters. 

 The range is to be found. 



To produce a voltage of 10 microvolts across 

 50 ohms, a power of 



Pi = 



F2 100 X 10 



R 



-12 



50 



■ watt = 2 X 10 ''- watt, 



