240 



BELL SYSTEM TECHNICAL JOURNAL 



ard with which more useful but more complex antennas can profitably be 

 compared. 



3.7 Efect OH Pattern oj Amplitude Taper 



The — — pattern which results from an ideal wave front has undesirably 



high minor lobes for most radar applications. These minor lobes will be 

 reduced if the wave front of constant amplitude is replaced by one which 

 retains a constant phase but has a rounded or 'tapered' amplitude dis- 

 tribution. 



OFF AXIS 



\l /APERTURE 



UNIFORM PHASE 



AND AMPLITUDE 



ACROSS APERTURE 



-5n -AV\ -3n -2TT -no n 2n 3n 4tt 5n 



^ TTO SIN a 

 Fig. 1 1 — Pattern of Ideal Rectangular Antenna. 

 If such an amplitude taper is represented analytically by the function 



a'{x) = Ci + C'i cos 



ttx 



(40) 



then equation (36) is readily integrable. To integrate it we utilize the 

 identity 



cos — = 



a 2 



upon which the integral becomes the sum of three simple integrals of the 

 form 



. ka 



,an sm 



e""dx = a 



all 



ka 



y 



(41) 



