70 BELL SYSTEM TECHNICAL JOURNAL 



frequently known as the driven antenna and the other the reflector. 

 This viewpoint is perhaps only a convenience and may not be al- 

 together correct. An array of the above type transmits and receives 

 best in a direction at right angles to its principal dimension. This 

 type is, therefore, frequently known as a broadside array. 



Directive Diagrams from Arrays and Reflectors 



In Fig. 5 is plotted a series of diagrams in a bisecting plane normal 

 to the axis of each antenna of the array for different broadside arrange- 

 ments such as are used commercially. They are systematically ar- 

 ranged horizontally in the order of the number of couplets in the array, 

 and vertically with the increased spacing between adjacent couplets. 



Several different forms of such directive diagrams are possible, 

 which may be plotted in either polar or rectangular coordinates. In 

 one form all diagrams are roughly of constant area and relative gains 

 from various antenna systems are expressed in terms of the principal 

 radius vector. In the second form the length of the principal radius 

 vector remains constant and the relative gain is roughly inversely 

 proportional to the area of the diagram. The second of these forms has 

 been adopted in this paper largely because of the relative simplicity of 

 the equation of the diagram and the facility with which properties of 

 antennas may be determined. 



In the lower left-hand corner of Fig. 5 will be found a plan showing 

 the arrangement of the elements relative to the important direction of 

 transmission. At its right is the general equation of these diagrams. 

 This formula is also given as equation (14) of the appendix where the 

 analytical theory of arrays is developed. Below each diagram is the 

 ratio of the area of the circumscribed unit circle to the area of the hori- 

 zontal diagram. Here also will be found the ratio of the area of the 

 subordinate loops to the area of the main loop. The total area may be 

 measured approximately with a planimeter or calculated more accu- 

 rately by equation (32) in the mathematical appendix. In making up 

 Fig. 5 each diagram was accurately plotted on standard polar coordin- 

 ate paper from perhaps a hundred calculated points. This was then 

 reduced photographically and the several diagrams were assembled.^ 



Inspection of the diagrams shows that increasing the number of 

 couplets increases in all cases the sharpness of the main loop and 

 hence the gain of the array. However, increasing the separation be- 



* The diagrams used in this paper were calculated by a group of the Department 

 of Development and Research of the American Telephone and Telegraph Company, 

 under the direction of Miss E. M. Baldwin. Most of the material was checked by 

 Mrs. Isabel Bemis, who assembled it in its present form and prepared the attached 

 bibliography. 



