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BELL SYSTEM TECHNICAL JOURNAL 



the wave referred to the direction of the array axis the array factor 

 represents a surface of revolution. Figures 4 and 5 show merely axial 

 cross sections which, for a horizontal array, may be considered vertical 

 plane patterns. 



Equation (3), as well as Figs. 4 and 5, shows that the sharpness of 

 the principal lobe depends upon the total length of the array in wave- 



lAl 



|A| 



10 15 20 25 30 



EARTH ANGLE 6, IN DEGREES 



40 



Fig. 4 — Plots of the array factor for a 45-wave-length horizontal end-on array. 



lengths, i.e., upon Na, while the angular spacing of adjacent principal 

 lobes depends inversely upon the spacing "a." Thus, a single lobed 

 pattern results if the array consists of a large number of closely 

 spaced units. 



A single lobed pattern is desirable, but to obtain it by using a large 

 number of unit antennas ^^ with separate transmission lines and phase 



13 The reader may observe that the reduction of the spacing would, if carried so 

 far as to make "a" a fraction of a wave-length, violate the assumption that there is 

 negligible reaction or coupling between unit antennas. As stated, this assumption 

 is made in the interest of simplicity. It is theoretically possible to compensate for 

 coupling between antennas so that (1), (2), and (3) still hold. 



