70 



CALCULATION OF RADIO GAIN 



Figure 12 shows 



^ 



(1 - A')-^ + iKsin- 



as a function of K for various values of sin n/2 and 

 maj' be used to calculate E. 



The value of (Vi to be used in equation (46) may 

 be found from the antenna specifications for a given 

 set. The free-space field Eo at distance d from a 

 transmitting doublet with power output Pi is equal to 



Efj = 



3V5 VPi 



(47) 



100 500 1000 



d IN METERS 



5000 10,000 



Figure 13. Free-space range d as a function of field 

 strength Eo and transmitter power Pi. 



Figure 13 shows Eo in decibels above 1 microvolt 

 per meter as a function of d for various values of 

 transmitted powder. The free-space field at distance 

 of d meters expressed in decibels above 1 microvolt 

 per meter for Pi watts radiated is 



Decibels = 20 logK 



3 V5 VPi" 



10 --"rf J 



(48) 



5.4 



PLANE EARTH 



^* ' Use of Plane Earth Formula 



It will Ije shown in Section 5.5.5 that under cer- 

 tain conditions calculations based upon the assump- 

 tion of a plane earth yield satisfactory results. Cal- 

 culations for propagation over a plane earth are 

 given in this section. 



5.4.2 



Path Difference 



It follows from equation (29) that when p = 1 

 and ({) = 180 degrees, the received field depends 



only upon the phase lag caused by path difference. 



Referring to Figure 8, 



r. = V rf= + (h - hY- = d-y/l -I- (~^y , 



(49) 



(50) 



2/)i/io 



If 



2d' ^ 

 Ih' + hi 



(51) 



2d2 



<< 1, 



A ^ 



2M2 



IT ' 



(52) 



The phase lag caused by the path difference A is 

 equal to 



\d 

 w'here X is the wavelength of the radiation. 



S^2^(2_hhA=^lh}b, (53) 



\\ d / \d 



5.4.3 



Field Strength Equations 



When p = 1 and (j> = 180°, equation (26) may be 

 used. Substituting equation (53) for 5 into equation 

 (26) gives 



E = 2Eo sin 



. f2TrIhh.\ 



m I I . 



\ \d / 



If 6/2 < 10°, sin (5/2) -^ 6/2 and 



E = E, 



■iirhJh 

 \d 



(54) 



(55) 



When hi or h^ equals 0, equation (55) indicates that 

 the received field intensity is equal to zero, which is 

 contrary to fact. For this case the diffraction field 

 must therefore be calculated and included as ex- 

 plained in Section 5.1.7. 



In the general case (p < 1), equation (44) may 

 be applied with K = {F^/Fi) pD. A refinement may 

 be added to the calculation by taking into account 



