A MATHEMATICAL THEORY OF LINEAR ARRAYS 



91 



those for the principal maximum, the tirst subordinate maximum of the 

 held strength is about one-quarter of the principal maximum. In other 

 words, the subordinate maximum is approximately 12 decibels below the 

 principal maximum. 



Fig. 10 



A more accurate value for this difference in levels can be obtained by 

 first rewriting (20) in the form 



V^ = 



r2 _ 



2^ — 2~ 



sm 



n\p 



sm- 



(22) 



and then substituting successively ^p = Q and 4/ = — , one for the principal 



n 



maximum and the other for the first subordinate. Accordingly we obtain 



\/*(0) 



Hi) 



In 



(23) 



If n is large sin -— is approximately equal to -— and the field strength 

 2n 2n 



ratio becomes 



3i 



4.71. This ratio corresponds to the diflference in 



levels equal to 13.5 decibels. 



