ANTENNA ARRAYS 



37 



2. Broadside: pattern factor and beam width. For 

 illustration, suppose that the antenna consists of a 

 vertical array of rn horizontal center-fed dipoles 

 spaced s apart with all fed in phase to give a broad- 

 side beam strongly directive in the vertical plane. 

 For this arrangement the field strength in the 

 horizontal plane' is given by m times equation (27), 

 that is, 



E 



horizontal 



d 



cos 



(^^cos.) 



(28) 



sin d 



with angle d measured from the dipole axis. See also 

 equation (15) and Figure 11 (for n = 1). 



In the vertical plane, the beam is much narrower. 

 If 4> is the angle from the vertical and /3 = 90° — (j> 

 is the angle from the (horizontal) broadside direc- 

 t ion, the field in the vertical plane {6 = 90°) is given 



E 



vertical 



. ma 

 sm — 

 607, 2 



d 



(29) 



sin 



with 



2w , 2-K . 



a = — s cos © = — .s sm 

 X X 



The maximum value of equation (29), corresponding 

 to 9 = 90° and /3 = 0°, is equal to 



P 60/,: 



The relati\'e field strength is then 



ma 



i?vertical 2 



EmAx . a 



m sm — 

 2 



(30) 



(31) 



Figure 32. Cophased colinear half-wave dipoles. 



The beam width in the vertical plane is determined 

 by the angle between the half-power points, or the 

 angle between the points where the field strength is 



Line of 

 Array 



11 " 





CD — 



i» " 



^Icv.? 



<D 



Midpoint Spdcing s=X/2 

 Effect of Array Length 



c 

 "5 



o 



Q. 

 CO 



'o 



o 



Q. 



Line of Array 



o 



a. 

 en 



Array Length = 3X 

 Effect of Element Spacing 



Figure 33. Cophased colinear half-wave dipoles. (From Radio Engineers' Handbook by Termano) 



