102 BELL SYSTEM TECHNICAL JOURNAL 



For a quarter wavelength separation between the elements \p — t and this 

 ratio is equal to 



V2(w - 1) 



so that the drop in the radiation intensity becomes [10 Logio (« — 1) + 3] 

 decibels. On the other hand, for a long uniform array the corresponding 

 drop is independent of n and is equal to 4 decibels. 



Another consequence of equispacing the null points in the range of z 

 consists in substantial suppression of subsidiary radiation lobes. The first 

 subordinate maximum is situated approximately halfway between the first 



two null points where \l/ = —-- — ^--r ; thus the field strength there, relative 



2{n — 1) 



to the principal maximum, is 



^ . ^ .3^ . (2n - 5)^ 



sm — — sm — sm — — • • • sm -— — - 



_ Ajn — 1) 4(w - 1) 4(w - 1) ^{n — 1) 



^ ~ . ^ . 2^ . 3i^ . (w - l)iA 



sm — TT sm —. -r sm — -: • • • sm — —. 



2{n-\) 2{n-\) 2{n - \) 2{n - \) 



For a quarter wavelength separation this field strength becomes 



sm 



^ ^{n - 1) 



X 2n— 3 /r» oN 



(48) 



sm 



4(w - 1) 



/W-, 7T • 2(w — 3)7r 



V2(» - 1) sm j^^^j^ 



When n is sufficiently large, we have approximately 



^ " 4U - 1) ^W^^ ^^^^ 



and the subsidiary maximum is [30 Logio (« — 1) + 5] decibels below the 

 principal maximum. Each time the number of elements is doubled, the 

 level of the subsidiary maximum is diminished by about 9 decibels. Thus 

 an array of the type (37) with ^ = 2/3f has very sharp directive properties. 



