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BELL SYSTEM TECHNICAL JOURNAL 



of unity divide the circle into n equal parts (Fig. 8). Analytically w6 

 have 



1 =0, 



^m = — 



'm — ^ 



2mir 



cos 9„ 



m — I, 2, 3, 



i} Iniir 



n — \, 



(21) 



^When z — \, -s/^ is evidently a principal maximum. Other maxima 

 of smaller magnitude, the so-called subordinate or subsidiary maxima, 

 occur approximately half way between the null points. The general 



ff 



IJ) IN RADIANS 



Fig. 9 — The field strength V^ as a function of i/- for w = 5. The principal maximum is 

 reduced to unity. 



behavior of the field strength can readily be understood if we follow z 

 around the unit circle. When plotted against i/', \/<S> has the shape shown 

 in Fig. 9. This is a universal radiation characteristic which can be inter- 

 preted for any particular spacing and phasing between the elements with 

 the aid of the curve ior ^p -\- ^ = fit cos d (Fig. 10). 



It is easy to estimate the relative level of the first subordinate maximum. 

 For a fairly large number of elements, the difference in levels is deter- 

 mined largely by the distances of the maximum points from the nearest 

 null points. The distances are approximately equal to the circular arcs 

 joining the corresponding points. Since the arcs joining the first sub- 

 ordinate maximum with the nearest null points are nearly half as long as 



