242 



BELL SYSTEM TECHNICAL JOURNAL 



over an aperture —a/2 < x < a/2 then 36 becomes a simple integral of 

 the form (41) and we obtain 



sin xp" „ ira . kia . . 



/' (a) = a —777— where \f/ — — sm a — --- (43) 



yp A 2 



The physical interpretation of^(43) is simply that the pattern is identical to 

 the pattern of an antenna with constant amplitude and uniform phase but 

 rotated through an angle 6 where 



sm 6 = — — 

 27r 



- 2"n 



-non 

 u,_ no SIN a 



2rr 



Fig. 13 — Pattern of Tapered Rectangular Antenna. 



Simple examination shows that the new direction of the radiation maximum 

 is at right angles to a uniphase surface, as we would intuitively expect. This 

 phenomenon has particular relevance to the design of scanning antennas. 



3.9 Effect on Pattern of Square Law Phase Variation 



If we assume a constant amplitude and a square law phase variation 



(t)'{x) = —kix 

 over the aperture a/2 < x < a/2 then the substitution 



27r . 



X = 



1 



i2 L 



sm a 



X + 



2k 



2 _ 



(44) 



