294 BELL SYSTEM TECHNICAL JOURNAL 



do not radiate equally in all directions in this plane, but which satisfy 

 the other conditions named above; the total directive effect is the 

 product of the individual effect multiplied by the group effect. Thus, 

 since the amplitude of the radiation in the horizontal plane from a 

 single vertical loop varies as the cosine of the angle between the 

 direction of transmission and the plane of the loop, the directive 

 diagram in the horizontal plane of an array of loops, all loops being 

 oriented the same, is the corresponding directive diagram of an 

 antenna array as presented in this paper, with the radius vector 

 multiplied by a cosine factor. 



The present discussion has been stated in terms of transmission, 

 but the directive diagrams apply equally well to the case of reception 

 by an array from a distant source. 



Each of the two sets of diagrams is presented in a rectangular 

 arrangement so as to exhibit the effect of changes both in the separation 

 between adjacent antennae, specified in wave-lengths, and in the 

 phase difference introduced between the currents in adjacent an- 

 tennae, specified in periods. These drawings were originally made at 

 the suggestion of Dr. G. A. Campbell to illustrate the application 

 of antenna arrays as a means for reducing the ratio of static to signal. 



The antenna array is analogous to the optical dift'raction grating. 

 By eliminating the transmission wires connecting together the in- 

 dividual antennae of the array and utilizing instead re-radiation 

 from suitably designed antennae, the radio system would correspond 

 more closely with this optical analogue. With this arrangement, 

 however, the phase difference cannot exceed a value in periods numer- 

 ically equal to the separation in wave-lengths, a restriction to which 

 the ordinary ruled grating is also subject. The retardation grating 

 proposed by Rayleigh ^^ and the echelon spectroscope of Michelson ^^ 

 offer more complete analogies to the antenna array in that there is 

 no theoretical limitation on the separation and phase difference. 



Two Antennae, Fig. 1 



A total of 90 directive diagrams for an array of two antennae is 

 shown by Fig. 1. The separation between antennae varies from to 2 

 wave-lengths, in steps of 1/8 wave-length; the phase difference be- 

 tween antennae varies from to 1/2 period, in steps of 1/8 period; an 

 additional set of diagrams is included with a separation of 4 wave- 

 lengths. These curves were carefully drawn with a unit circle ten 



^' Rayleigh, Collected Papers, 3, pages 106-116. 



" A. A. Michelson, Astrophysical Journal, 8, page 37, 1898. 



