REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 639 

 RECEIVED POWER VERSUS DISTANCE 



If antenna size and wavelength are specified, (12) gives for two dis- 

 tances, ai and aa , 



Pri I Cl-iX 60 \0l 



(19) 



For a-i = 2ai , (19) gives for different values of a/di 



oc/di = 0.5 1 2 4 



Pri/ Pin = 270 (24 db) 197 (23 db) 138 (21.5 db) 104 (20 db) 



Fig. 1 in Biillington's paper,^ which gives the median signal level in 

 decibels below the free space value as a function of distance, shows an 

 18 db increase in attenuation when the distance is doubled. This cor- 

 responds to a ratio of received powers of 18 + 6 = 24 db. The examples 

 in the table abo\'e give an average increase in attenuation of 22 db. 



RECEIVED POWER VERSUS ANTENNA SIZE 



Equation 14 can be used to calculate the effect on received power of 

 changing simultaneously the size (and, hence, the beamwidths) of the 

 antennas used for transmitting and receiving, the wavelength and dis- 

 tance remaining fixed. 



n, /«A"-_^ '\e) (20) 



Pr2 \OLl/ 9 I ^ r /«2\ 



" ^ d '' \d ) 



where P^i and P^o are the received powers corresponding to the antenna 

 l)eamwidths ai and a^ respectively. 



As an example, let a2 be constant and eciual to 4° and let d be 1°, 

 corresponding to a 200-mile circuit. The table below gives the ratio 

 Pri/Pr2 as ai is varied. 



ai 4° 2° 1° 0.5° 0.25° 



Pri/Pr2 (db) 10 18.5 25.7 31.4 



Change in db 10 8.5 7.2 5.7 



Since a is inversely proportional to the antenna dimensions, the table 

 shows that continued doubling of the antenna dimensions results in less 

 and less increase in output power. The increase varies from 10 to 5.7 db 



