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BELL SYSTEM TECHNICAL JOURNAL 



the null points are evenly spaced in the range of z, appropriate to each sep- 

 aration between the elements. 



If the elements of the array are directive, the null points should be dis- 

 tributed with due reference to the directive pattern of the elements in order 

 •that a further increase in directivity could be secured. 



i¥ 



20° 40° 60° 80° 100° 120° 140° 160° 180° 



Fig. 18 — Directive properties of linear arrays with total length equal to X/4. (A), n= 2, 

 t = V4; (B), n = 3J = X/8; (C), n = 5, ^ = V16. 



Multi-Dimensional Arrays 



The simplest method of constructing multi-dimensional arrays is to take a 

 linear array as an element of another linear array. The axis of the second 

 array may be chosen to make any angle with the axis of the first array. 

 In this way only a special class of multi-dimensional arrays can be formed. 

 Analytical expressions for the radiation intensities of more general arrays 

 can be formulated in terms of two or more complex variables. These 

 variables, however, will not be independent and a given direction in space 

 will be represented by a group of related points, one point on each circle 

 representing the particular complex variable. At this time we shall not be 

 concerned with any developments applicable to such general multi-dimen- 

 sional arrays. 



Arrays with Prescribed Space Factors 



If the minimum separation between the elements does not exceed X/2, 

 it is theoretically possible to design a linear array with a space factor given 

 by an arbitrary function /(^i/) or F(6) of direction of radiation. Naturally 

 the number of required elements will be usually infinite; with a finite number 

 of elements the space factor may only be approximate. 



