REFLECTION THEORY — PROPAGATION BEYOND THE HORIZON 637 

 RECEIVED POWER VERSUS ANGLE d 



The angle 6 is the angle between the lower edge of the idealized an- 

 tenna pattern and the straight line joining the terminals (see Fig. 7). 

 The minimum value of 6 is determined by the profile of the transmission 

 path. If X, a and a are constants, (12) can be used to calculate the ratio 

 of the powers, P ri and Pr2 , received at two different angles, di and do , 



Equation (13) shows the importance of having the angle 6 as small as 

 possible. For example, for di = a and 62/ di = 1.25, the power ratio is 

 3.4 (5 db). Thus in an actual circuit the antenna pattern should be close 

 to the horizon plane. 



RECEIVED POWER VERSUS WAVELENGTH 



Consider a given path in which a and 9 are specified. Equation (12) 

 can be used to calculate the ratio of received powers, Pm and Pro , cor- 

 responding to two different wavelengths, Xi and X2 . 



^ = [?)[-) -^^ (14) 



-I R2 



where ai and a2 are the beamwidths of the antenna patterns at wave- 

 lengths Xi and X2 respectively. 



Case I. Equal antenna gains at the two wavelengths. 

 For this case, ai = 0:2 and equation (14) reduces to 



Pr\ /Xi 



3 



P R2 \X2/ 



In free space the power ratio would be 



Pr, 



Pr2 



or 



Pr\/Pr2 (Beyond-Horizon) _ Xi 

 Pri/Pr2 (Free Space) X2 



=©■ 



(15) 



(16) 



(17) 



