GAIN OF DIRECTIVE ANTENNAS 67 



and troughs are represented respectively by solid and dotted lines. 



At points where either two crests or two troughs arrive simultaneously 



the resultant wave is greatly enhanced, whereas at certain other points 



crests and troughs arrive together, thereby neutralizing each other's 



effects. At certain intermediate points these interfering effects are 



only partially complete. Accompanying each figure is a directive 



diagram (lb and 2b), plotted in polar coordinates, which shows the 



effectiveness of the wave in each direction. The circle drawn outside 



each diagram indicates the effect if the radiation had proceeded from 



a single non-directional source similar to each of the above. The 



ratio between the areas of the circle and the inscribed diagram gives 



roughly the power improvement of such a device as manifested in the 



intensity of the radiated wave. A more exact calculation of this 



improvement requires an integration of the force components over a 



unit sphere. 



Linear Antenna Arrays 



Most directive antenna systems now in general use for short 

 waves may be regarded as special applications of the linear array. 

 This type consists of two or more antennas all having currents of equal 

 amplitude, equispaced along the same straight line. The properties 

 of such arrays have been treated very generally by Foster,^ whose 

 paper included several hundred directive diagrams, taken in a bi- 

 secting plane perpendicular to the axis of each antenna of the array, 

 and typical of the results which may be expected from two antennas 

 and from arrays consisting of 16 antennas. A portion of these dia- 

 grams have been reproduced in Figs. 3 and 4 below. The same 

 principles are applicable to both transmission and reception. 



In Fig. 3 are shown diagrams resulting from two antennas as the 

 separation is increased from to 1 wave-length in steps of 3^ wave- 

 length and the phase increased from to >2 period in steps of }4 

 period. The line or axis of the array is assumed to be horizontal and 

 the specified phase difference is such that the current in the right- 

 hand antenna is lagging for a transmitting system and leading for a 

 receiver. It will be noted that for phase differences of both and }4T 

 the diagrams are symmetrical about both the horizontal and vertical 

 axes of the figure, whereas for other phases the figures are asymmetrical 

 about the vertical axis except for certain limiting cases. Of these 

 asymmetrical diagrams, that corresponding to phase and spacial sepa- 

 rations both of I'i (Fig. 3b) is of particular importance and forms 

 the basis of the so-called reflector effect. This particular combination 

 of two sources is referred to later as a unidirectional couplet.^ In 



2 Loc. cit. 



* In this, and in other cases in this paper, radiation is referred to as unidirectional 

 when sensibly more power is propagated in one direction than in others. 



