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BELL SYSTEM TECHNICAL JOURNAL 



of the earth. The latter have specifically been omitted in this dis- 

 cussion. 



Fig. 20 shows roughly the calculated directional characteristics of 

 a typical stacked array incorporating both horizontal and vertical 

 directivity. The planes passed through the diagram serve only as 

 convenient references to assist in visualizing the horizontal and vertical 

 diagrams. Earth effects of course, have been ignored. 



Appendix 



A general case of linear arrays which includes those used exten- 

 sively in short-wave radio work, consists of a number of sources equi- 

 spaced and equiphased along each of the three principal coordinate 

 axes such that the space between sources is made up of rectangular 

 parallelopipeds with the individual sources located at each corner. 

 This may be regarded as A^ parallel planes each made up of N parallel 

 columns where each column is made up of n individual radiating ele- 

 ments. The arrangement is made more evident by Fig. 21. The 



Fig. 21— General case of linear antenna arrays. 



usual conventions for representing three-dimensional space have been 

 adopted. We may designate the spacing between elements along the 

 X, y, and z axes, respectively, by a\, A\, and A\ and their corresponding 

 phase displacements between adjacent elements along the three princi- 

 pal axes by bT, BT and BT. 



The distance from any point in space to a particular radiator is 



i?„jv^ = R - (N - l)A\ cos 6 (1) 



— {N — 1)AX cos (p sin 6 — {n — l)aX sin 6 sin 0. 



