116 



CALCULATION OF RADIO GAIN 



'^*' General Solution for Vertical 

 (or Horizontal) Dipole 

 Over a Smooth Sphere 



1. Field strength of dipole. The vertical component 

 of the electrical field of a vertical dipole radiating 

 in a homogeneous atmosphere o^'er a sphere of 

 radius Ay; (or horizontal component in the case of a 

 horizontal dipole) is given by equation (192). The 

 solution is \-alid provided the distance between 

 receiver and transmitter and the radius of the 



For horizontal polarization, 



14.2X10' ^,, , 4 



= ^^2^3 (e, - l)torA- =-. 



d. i" = sd, 

 where 



\Xfc-aV 



MISI 



+ 20 



+10 



0.01 0.02 0.05 0.1 0.2 0.5 1JD 2 5 1 20 50 100 200 500 1000 



ISI 



Figure 52. il/(5) versus | 5 | for use in equation (190), vertical polarization. 



sphere are much greater than a wavelength, condi- 

 tions which are fulfilled in any practical application 

 of short waves. 



fnihO-LUh) 



E =2£o(2irf)''- 



V 



tr( s + 2i 



(192) 



a. hi and h^ are antenna heights, 



b. £"0 is the value of E for a doublet in free space, 



c. 5 is the ground parameter which depends on 

 the complex dielectric constant e^, = e^—jQOa-^. 



For vertical polarization, 



.2/3 , _ 1 



-m 



14.2 X 10^ tc 



\ 



2/3 



— for fc = - . 

 3 



(193) 



or 



= 4.43 X 10 



■--'{£)" 



(194) 



e. Tn are complex numbers which characterize 

 the indi\-idual terms (modes) in equation 

 (192). They are a function of 5. 



f- fnihi) and fi.ih-z) are height-gain functions 

 for the nth mode. 



2. The complex ground parameter 5. 5 depends on 

 the wavelength and the electrical constants of the 

 ground. (The dielectric constant is referred to air 

 as unity.) 5 is large for horizontally polarized waves, 

 but for vertically polarized waves it may vary con- 

 siderably, as may be seen from Figure 53. In Figure 

 54, the phase of 5 is given. For wavelengths less 



