678 



BELL SYSTEM TECHNICAL JOURNAL 



Horizontal Plane Directivity 

 Due to the cancellation effect of the reflections of horizontally po- 

 larized waves from a perfect ground, the horizontal plane diagram, for 

 a horizontal antenna, is merely a point. The way to view directivity is 

 properly in its solid form, but the calculations and plotted representa- 

 tions are somewhat laborious. The designer is in real need of knowing 

 the horizontal width of the major lobe of the directional characteristic 

 as would be seen from a plan view. This angular width, as measured 

 between null points, is not altered by ground effects; therefore a useful 

 simplification of the calculations may be had by ignoring the cancella- 

 tion effect of the ground reflection. It should be pointed out that the 

 amplitudes are slightly erroneous when this is done, but the null point 

 locations are accurate. If this is done, we obtain the following equa- 

 tion: 



lR=k' 



1 + cos /3 



r\ _J_ g-i'^T'^ sin (.^+/3)/X-| . rj _|_ Q-i2TTl sin (0-/3)/Xn 



cos^ — sin^ /3 



where, as shown in Fig. 14, 



/3 = wave angle in horizontal plane. 

 = tilt angle of elements. 

 / = element length in wave-lengths. 

 k' — proportionality factor. 



It. 



receiver current. 



20 30 40 50 60 70 

 TILT ANGLE <Sf IN DEGREES 



Fig. 18 — Plan view design chart. 



* In the'second and third bracketed quantities use, in the ± sign, — when / is an 

 even integral multiple of X/2 and -|- when / is an odd integral;multiple of X/2. 



