92 



BELL SYSTEM TECHNICAL JOURNAL 



Directivity of Arrays 



The "decomposition theorem" of the preceding section throws consider- 

 able hght on directive properties of arrays. The number of elements in the 

 array is one greater than the number of virtual couplets. Hence to secure 

 the greatest possible directivity with a given number of elements, the virtual 

 couplets must be properly combined. 



Fig. 11 — The null points of several three-element arrays. The spacing between the 

 elements is X/4 and the progressive phase delay is r/4 {T equals period). 



14.0° 160° 



Fig. 12 — Comparison of directivity of several three-element arrays. The spacing between 

 the elements is X/4; the direction of principal radiation is = 0°. Curve (A) 

 refers to the uniform array, (B) to an array with nulls at P and B (see Fig. 11), 

 and Curve (C) refers to an array with its nulls at B and M. 



For example, the null points of a uniform array of three elements, one- 

 quarter wavelength apart, are at P and Q (Fig. 11). If ?? = 7r/2, the range 

 of z consists of the lower half of the unit circle and principal radiation takes 

 place in the direction = 0. Evidently, the virtual couplet with its null 



