250 BELL SYSTEM TECH NIC A L JOURNA L 



7. Basic Design Formulation 



Certain design factors are common to almost all radar antennas. Because 

 of their importance it would be well to consider these factors in a general 

 way before proceeding with a study of particular antenna techniques. 



Almost every radar antenna, regardless of how it is made, has a well de- 

 fined aperture or wave front. Through wave front analysis we can often 

 examine the connections between the Huygens sources in the antenna aper- 

 ture and the radiation characteristics of the antenna. We can, in other 

 words, use wave front analysis to study the fundamental antenna design 

 factors, provided the analysis does not violate one of the conditions of 

 section 3.13. 



7.1 Dimensions oj the Aperture 



The dimensions of the aperture of a properly designed antenna are related 

 to its gain by simple and general approximate relations. If the aperture is 

 Uniphase and has an amplitude distribution that is not too far from constant 

 the relation 



^ 47ryl 



is useful in connecting the gain of an antenna with the area of its aperture. 

 The effective area is related to the area of the aperture by the equation 



A = rjS 



where ij is an efficiency factor. In principle 77 could have any value but in 

 practice for microwave antennas 77 has always been less than one. Its value 

 for most Uniphase and tapered amplitude antennas is between 0.4 and 0.7. 

 In special cases, e.g. for cosecant antennas or for some scanners its value 

 may be less than 0.4. 



The necessary dimensions for the aperture may be determined from the 

 required beam widths in two perpendicular directions. Beam widths are 

 usually specified as half power widths, that is by the number of degrees 

 between directions for which the one way response is 3 db below the maxi- 

 mum response. Figure 11 shows that for an ideal rectangular antenna with 



uniform phase, polarization and amplitude ap/2= 51 - degrees where a^/o == 



a 



half power width in degrees, a = aperture dimension and X = wavelength. 



The relation ap/2 = 65 - degrees is more nearly correct for the majoritv of 

 a 



practical antennas with round or elliptical apertures and with uniform phase 



and reasonably tapered amplitudes. 



