A MATHEMATICAL THEORY OF LINEAR ARRAYS 



85 



This array consists of three elements with amphtudes proportional to 1, 

 2, 1. If the elements of the original couplet are one-quarter wavelength 

 apart and 90° out of phase, the couplet is "unidirectional". The space 

 factor of such a couplet is depicted by Curve A in Fig. 4. The space 

 factor of the triplet represented by (8) is shown by Curve B. In the 

 directions in which the couplet radiates half as much or a third as much 

 power as in the principal direction, the triplet radiates correspondingly 

 only a quarter or a ninth of the power radiated in the principal direction. 

 The above considerations suggest a simple method for suppressing 

 subsidiary radiation lobes. It is well known that in a uniform linear array^ 



"{¥ 



Fig. 4 — Space Factors — Curve A is the space factor of a unidirectional couplet in which 

 ^ = X/4. Curve (B) represents the space factor of an array with amplitudes pro- 

 portional to 1, 2, 1. 



the difference in levels of the principal maximum of radiation and the first 

 subsidiary is substantially independent of the number of elements, pro- 

 vided this number is sufficiently large. Thus in the limit, the first sub- 

 ordinate maximum is 13.5 decibels below the principal maximum. Con- 

 sequently for the array with its space factor equal to the square of the 

 space factor of the uniform array, the limiting difference in levels must 

 be 26.9 decibels. 



Since the uniform array is represented by 



V$ = I 1 + z + 32 -f- 



+ 2"-l I, 



(9) 



^ A "uniform" array is an array made up of sources of equal strength with a uniform 

 progressive phase delay. 



