PARABOLIC ELEMENTS 



43- 



For the paraboloid of revolution or the truncated 

 paraboloid, a simple source of radiation at the focus 

 is used. Often this is a half-wave dipole, sometimes 

 combined with a parasitic dipole which acts as a 

 reflector (Section 3.5.2). 



In other types, the energy is brought to the focal 

 point by a wave guide and is then reflected back onto 

 the parabolic surface. 



If the wavelength is small compared with the 

 dimensions of the parabolic reflector, the following 

 approximate formula holds for the radiation pattern 

 produced by a parabola: 



E = constant ■ 



ttD 



■kD sin e/\ 



(1 



cos 



m 



sm & = y ^ . 



(41) 



Avhere D is the aperture of the reflector and 6 the 

 angle from the axis. The half-power points corre- 

 spond approximateh^ to 



0^2X 

 D 



These formulas correspond to the case of nearly 

 uniform illumination of the reflector from the source 

 at the focus. In practice a source that concentrates 

 the field toward the center of the parabola is used 

 in order to reduce the magnitude of the side lobes. 



ELECTRIC 

 FIELD 



7 



WAVE-CUIDE 



V 



Figure 44. Sectoral horn. 



</>^30" 



4>--90° 



Figure 45. Radiation pattern for a sectoral horn hav- 

 ing various flare angles. 



The half-power angle is then more nearly equal to 

 e = 0.6X/D. 



The maximum gain of a parabolic reflector is 



G 



(fTi 



(42) 



For D = 2 meters and X = 0.1 meter, the gain is 

 approximately 1,000. 



II 



o 



80 

 70 

 60 

 50 



o> 30 



o 

 0. 



20 



10 



10 20 30 40 50 



Flore Angle, Degrees 



70 



60 



II 



50 



c 

 o 



V 



o 

 0. 



40 



30 



20 



10 



B 



2 4 6 8 10 15 20 30 



Horizontal Aperture in X 



Figure 46. Gain of sectoral horn with TEi,o wave. 

 (These curves are for a vertical aperture ratio a /X = 1. 

 For other ratios the gain given should be multiplied by 

 a /X.) (From Radio Engineers' Handbook by Terman.) 



