80 BELL SYSTEM TECHNICAL JOURNAL 



If the array is divided into four sections the rotation may extend 

 over a range of perhaps 9 deg., while for eight sections it may be 15 deg. 

 The final case of 16 sections of one couplet each permits of considerable 

 flexibility such as would be useful in operating with several distant 

 stations in the same general direction. It should be pointed out, how- 

 ever, that the problem of making 16 phase adjustments each time a 

 station wishes to change its direction of transmission is of considerable 

 magnitude. For the particular case illustrated above it appears that 

 the maximum rotation of the projected radiation is more or less pro- 

 portional to the number of sections into which the array is divided. 

 It may readily be seen from the two top rows of diagrams in Fig. 15 

 that continued addition of phasing amounts effectively to negative 

 rotation. This may also be seen from an analysis of the equation of the 

 diagram. 



Fields of Linear Arrays 



The successful use of an array of couplets to give unidirectivity 

 suggests that the use of more than two parallel linear arrays might 

 further be employed to advantage.^ Obviously many such combina- 

 tions are possible, but one of some interest has been investigated 

 below. As a concrete example of this variation of gain with arrange- 

 ment of arrays, a series of diagrams for 36 elements has been plotted 

 in Fig. 16. The condition of spacing and phase intervals between 

 columns of each of 34X has been chosen. The horizontal character- 

 istic is given for separations between rows of both }4 and 34 wave- 

 length. The vertical characteristic common to these two separations 

 is also shown. The equation of the diagram is given in formula (17) 

 of the mathematical appendix below. 



It will be observed from Fig. 16 that the horizontal directivity is 

 for the most part only moderate, but approaches a maximum for the 

 condition where a long broadside array prevails, whereas the vertical 

 directivity is increased by increasing the number of columns in the 

 field. A substantial loop will be found near the rear of diagrams corre- 

 sponding to an odd number of columns. It is of further interest that, 

 as far as horizontal directivity alone is concerned, the optimum may 

 be derived either from a single array of 36 elements or from 18 couplets. 

 Considerations of both minimum interference and total gain, however, 

 make the latter preferable. These conclusions may also be reached by 

 more direct analysis.'^ 



« U. S. Patent 1,643,323, John Stone Stone, September 27, 1927. 

 ' Wilmotte, "General considerations of the directivity of beam systems," Jour. 

 I. E. E., 66, 955. 



