514 ANTENNAS AND RF COMPONENTS 



50 per cent of the physical cross section normal to the transmission direc- 

 tion. Antenna directivity D, as previously defined, is simply related to 

 the effective aperture^ A^, at a wavelength X by 



Z) = ^ ^e. (10-2) 



This expression shows that the directivity of an antenna increases in direct 

 proportion to its effective area expressed in square wavelengths. 



Thinking of the antenna, now, as a transmitter, if the actual physical 

 aperture is fed in such a manner as to contain a wave of constant phase and 

 amplitude, then the physical aperture is equal to the effective aperture in 

 the above relation for directivity. Generally, however, a variation from a 

 plane wave in phase and amplitude may exist across such an aperture. 

 For example, an amplitude distribution which is much lower at the edges 

 of the aperture is usually required in practice to improve some antenna 

 characteristics. Thus the effective aperture may be smaller than the 

 physical cross section A^^ by a factor which is called illumination effective- 

 72ess. 



ile ^ ^iUumin ation -^p- (ACs 'W 



effectiveness ^ ' 



Antenna gain is closely related to directivity. It is usually defined, 

 however, for an actual antenna which is not perfectly matched to its load 

 and which is not dissipationless. Gain is less than directivity because of 

 these two losses: 



(j ^^ ^dissipation X ^matching ^- CSCS A.\ 



efficiency efficiency ^ ' 



In many practical radar antennas, ^matching will be essentially unity, 



efficiency 



^dissipation will be greater than 0.9, and ^illumination will be greater than 0.5. 



efficiency effectiveness 



Thus, gain is nearly equal to directivity and it is within 50 per cent of 

 47r/X2 times the antenna physical cross-section area. 



Finally, the antenna beam shape is described by certain terms such as 

 beamwidth, sidelobe level, etc. The sidelobes, such as those in Fig. 10-1 

 are an inherent but generally undesirable characteristic of the antenna. 

 They are described by their magnitude and direction relative to the main 

 lobe. The pattern in Fig. 10-1 has 0.05 or —13 db sidelobes at zb6 deg 

 azimuth. 



3H. T. Fris and W. D. Lewis, "Radar Antennas," Bell System Tech. J., p. 229 (April, 1947). 



