38 



ANTENNAS 



0.707 of the maximum. Thus, equation (31) is set 

 equal to 0.707 and 13 determined. The beam width is 

 equal to 2/3^ 



To illustrate, let s = X/2. For m = 2,3,4,8,12,16 

 dipoles in the array, the corresponding beam widths 

 are 60°, 36.4°, 26.4°, 12.8°, 8.5° and 6.3°. A few field 

 patterns are illustrated in Figure 30A and gains are 

 shown in Figure 31. 



3. Colinear array (see Figure 32). For )i equal 

 cophased currents, equally spaced, 



sm- 



na 



Ee = E,i (6, (t>) 



a 

 sm- 



where 



a = S cos d . 



X 



(32) 



(33) 



For center-fed half-wave dipoles, from equation (3), 



£' , = 



607, 



cos I 



(34) 



sin e 



The patterns for various array lengths and spacings 

 are given in Figure 33. 



If s = X/2, equation (32) for half-wave dipoles 

 reduces to equation (18). 



3.4.6 



Unidirectional Broadside 

 and Colinear Arrays 



If an array is backed up with a similar array, the 

 latter may serve to concentrate the radiation in one 

 direction, provided the currents in the arrays are 

 properly adjusted in magnitude and phase. Patterns 

 for the unidirectional broadside and colinear arrays 

 are given in Figure 34. 



The broadside array is a collection of unidirec- 

 tional couplets of the type illustrated in Figiu'e 26. 

 Increasing the number of couplets n appreciably 

 narrows the beam width. 



A similar impro\'ement is obtained in the colinear 

 combination. 



3.4.7 



Multidimensional Arrays 



Enough has already been given to show that it is 

 not difficult to extend the principles of summation 

 of fields from elements to cover two- and three- 

 dimensional arravs. 



^^ * Binomial Arrays 



Most array patterns show, in addition to the main 

 maximum, secondary maxima (side lobes) which are 

 inconvenient in radar work. Side lobes are practi- 

 calh' eliminated in the binomial array. 



Q-n/2 



B 



(B) Colinear 



Figure 34. Unidirectional broadside and colinear array. 



Consider first a two-element half-wave dipole 

 broadside array with equal cophased currents and 

 elements spaced a half wavelength apart. See equa- 

 tions (21) and (22). Theni/' = 0, s = X/2, a = ircoscj). 

 Then with 



Ee' {d) = 



cosf 

 60/ V 



— cos d I 



1 L 



sin 6 



(35) 



E = Ea (e^" + c'^- 



This gives the broadside field in Figure 26 which has 

 only two equal major lobes. There are no side lobes. 

 Now consider the equation 



E = Ea {e''+ c-'^Y , 



(36) 



= Ea (1 + 2c-''' + le:'-"). 



This represents three half-wave dipoles in broadside, 

 spacing .s = X/2, currents in phase but with relative 

 magnitudes 1 : 2 : 1. The pattern has no side lobes. 



