DIRECTIVE DIAGRAMS OF ANTENNA ARRAYS 295 



inches in diameter, so that, on the reduced scale of reproduction, the 

 accuracN- should leave nothing to l)e desired. For a sending array the 

 specified phase difference is the lag of the current in the right-hand 

 antenna behind the current in the left-hand antenna; for a receiving 

 array it is the lag introduced in the current from the right-hand 

 antenna. In each case the line of the array is parallel to the hori- 

 zontal axis of the diagram. 



Reversing the sign of the phase difference reflects the directive 

 diagram about its vertical axis, that is, the right and left sides are 

 interchanged. With increasing phase difference the diagrams repeat 

 cyclically, those from |r to fT being the same as those from -^T 

 to hT, and so on. 



In the first column, that is, for zero separation, all diagrams are 

 circles, since the two antennae are coincident, and thus the array 

 radiates uniformly in all directions. For zero phase difference the 

 directive diagram is the unit circle, since the radiations from the 

 two antennae reenforce each other without interference. As the 

 phase difference is increased, this circle grows smaller, due to in- 

 creasing interference, until, for a phase difference of a half period, 

 the two radiations completely neutralize each other, the directive 

 diagram shrinking down to a null circle. 



The diagrams in the first row, that is, for zero phase difference, 

 are symmetrical about the vertical axis In addition to being sym- 

 metrical about the horizontal axis. In every case the amplitude is 

 unity along the vertical axis, that is, in a direction perpendicular 

 to the line of the array. As the separation is increased from zero, 

 the amplitude along the horizontal axis diminishes, until it reaches 

 zero for a separation of |X, it then increases to unity at X, it diminishes 

 to zero at UX, it reaches unity at 2X, and so on. 



The diagrams in the bottom row, that is, for a phase difference of a 

 half period, are also symmetrical about the vertical axis. In every 

 case the amplitude is zero along the vertical axis. For small separa- 

 tions, the directive diagram is approximately a pair of tangent circles, 

 which increase in size as the separation is increased. When the 

 separation reaches |X, the amplitude along the horizontal axis reaches 

 unity, it then falls off to zero as the separation is increased to X, 

 it rises to unity at 1|X, it falls to zero at 2X, and so on. 



The diagram for (|X, IT) is particularly interesting in that there is 

 a single direction of unit amplitude w^th zero amplitude in the oppo- 

 site direction. This array was proposed by Blondel, as stated above, 

 and it is the basis of the Alexanderson barrage.^^ The diagrams 



15 E. F. \V. Alexanderson, Proceedings of the I. R. E., 7, pages 363-378, 1919. 



