RADAR ANTENNAS 279 



elements and distributing power to it through an appropriate transmission 

 line network. If the radiation characteristics of the array are to be as de- 

 sired the electrical drive of each element must have a specified phase and 

 ampHtude. In addition each element must in itself have a satisfactory 

 characteristic and the elements must have a proper spacial relationship to 

 each other. 



Such array antennas have been extremely useful in the 'short wave' bands 

 where wavelengths and antenna sizes are many times larger than at most 

 radar wavelengths but for fixed beam radar antennas they have been largely 

 superceded by the simpler optical antennas. Where a rapidly scanning 

 beam is desired, however, they possess certain advantages which were put 

 to excellent use in the war. These advantages spring from the possibility 

 of scanning the beam of an array through the introduction of rapidly vary- 

 ing phase changes in its transmission line distributing system. 



Let us first examine certain basic conditions that must be fulfilled if an 

 array antenna is to provide a satisfactory scan. The pattern of any array 

 is merely the sum of the patterns of its elements taking due account of 

 phase, amplitude and spacial relationships. If all elements are alike and 

 are spaced equally along a straight line it is not difficult to show that a 

 mathematical expression for the pattern can be obtained in the form of a 

 product of a factor which gives the pattern of a single element and an array 

 factor. The array factor is an expression for the pattern of an array of 

 elements each of which radiates equally in all directions. Since each of the 

 elements is fixed in direction it is only through control of the array factor 

 that the scan can be obtained. 



If we excite all points of a continuous aperture with equal phase and a 

 smoothly tapered amplitude the aperture produces a beam with desirable 

 characteristics at right angles to itself and no comparable radiation else- 

 where. Similarly if we excite all elements of an array of identical equally 

 spaced circularly radiating elements with equal phase and a smoothly 

 tapered amplitude the array will produce a beam with desirable charac- 

 teristics at right angles to itself. It will also produce a beam in any other 

 direction for which waves from the elements can add up to produce a wave 

 front. Such other directions will exist whenever the array spacing is 

 greater than one wavelength. 



In order to see this more clearly let us examine Fig. 37, where line XX' 

 represents an array of elements. From each element to the line AA' is a 

 constant distance, so A A' is obviously parallel to a wave front when the 

 elements are excited with equal phase. If we can find a line BB' to which 

 the distance from each element is exactly one wavelength more or less than 

 from its immediate neighbors then it too is parallel to a wavefront, for 

 energy reaching it from any element of the array will have the same phase 



