CAIN OF DIRECTIVE ANTENNAS 69 



passing it is also of interest to note that the diagram of the coil or 

 frame aerial as generally used is intermediate between Figs. 3c and 

 3d. Its diagram would not differ essentially from its neighbors, Figs. 

 3d, 3e, or 3f , except for scale. This scale may conveniently be regarded 

 as a measure of the impedance of the device, or possibly its radiation 

 efficiency, but not necessarily a measure of its usefulness. 



Fig. 4 shows similar diagrams resulting from 16 antennas for vari- 

 ous phase and space relations. As in Fig. 3, diagrams in the top and 

 bottom rows corresponding respectively to phases of and K^ T are 

 symmetrical about both the horizontal and vertical axes. The dia- 

 grams in the top row are in general bidirectional, while the bottom row 

 has one bidirectional diagram corresponding to phase and space 

 differences both equal to >^. It is of interest that for the most part 

 cases where the phase and space separations are numerically equal 

 correspond to unidirectional diagrams. However, these diagrams are 

 only moderately sharp and thus far such arrays have not been used 

 extensively in practice. 



Referring again to the diagrams in the top row corresponding to 16 

 antennas all driven in phase, we note that directivity becomes progres- 

 sively sharper as the spacing is increased until in the vicinity of 15/16X 

 appendages develop which soon surpass in magnitude the desired lobes. 

 This effect is present in the commercial array, and limits, as we shall 

 later see, the gain that may be derived from a given number of elements. 

 The diagrams shown in Fig. 4 for 16 antennas are typical of others 

 where the number of antennas in linear array is fairly large. 



The Linear Array and Reflector 



One type of array now in commercial use consists of two parallel 



linear arrays of equiphased elements where the two parallel arrays are 



spaced M wave-length and differ in relative phase by }/ii period. It is 



convenient to regard such a device either as two independent linear 



arrays, each having a directional characteristic as shown in the top 



row of Fig. 4, or as an array of couplets, each couplet of which has by 



itself a heart-shaped characteristic. Both antennas of the couplet may 



be independently driven at their prescribed phase separation of 3i 



period, or one may derive its power from that radiated by the other, in 



which case the proper phase relation is automatically approximated •* 



and the same practical result is obtained. In the latter case one is 



^ The problem of the reflecting antenna has been considered by Wilmotte and 

 McPetrie, Jour. I. E. £., 66, 949, Englund and Crawford, Proc. I. R. E., 17, 1277; 

 August, 1928, and Palmer and Honeyball, Jour. I. E. E., 67, 1045. Their conclusions 

 indicate that the optimum separation between a single antenna and its reflector to 

 give maximum forward radiation is roughly X/3. However, it appears that when 

 several antennas and reflectors are involved a separation more nearly X/4 is optimum. 



