636 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



f{oc/e) 



0.5 



1.0 



1.5 



2.0 



2.5 



a/d 



3.0 



3.5 



4.0 



4.5 



5.0 



\ 



Fig. 9 — The function / (a/O). 



with aspect ratio one, 



A = 



a'- 



(11) 



Substituting (7), (10) and (11) in (5) gives for identical transmitting 

 and receiving antennas with aspect ratio one, 



Pu = P: 



M>^_1_ 1 



^+e 



-Al 



(12) 



For actual antennas, a may be taken to be the half-power beam-width. 

 In the following sections, (12) will be used to derive some of the gen- 

 eral properties of propagation beyond the horizon. 



* K. Bullington has suggested that a useful form for equation (12) is 



Pr = 





e \d 



a 



where the first term in brackets represents the power that would be received in 

 free space, the second term involves the characteristics of the troposphere, an<l 

 the third term is a correction factor for narrow beam antennas. 



