RADAR ANTENNAS 233 



the antenna. The amplitude, phase and polarization of the electric intensity 

 in portions of the wave are determined by the currents in the antenna and 

 thus by the details of the antenna structure. This advancing wave can be 

 called the 'wave front' of the antenna. 



When the wave front of an antenna is known its radiation characteristics 

 may be calculated. Each portion of the wave front can be regarded as a 

 secondary or 'Huygens' source of known electric intensity, phase and polari- 

 zation. At any other point in space the electric intensity, phase and polari- 

 zation due to a Huygens source can be obtained through a simple expression 

 given in the next section. The radiation characteristics of the antenna can 

 be found by adding or integrating the effects due to all Huygens sources of 

 the wave front. 



This procedure is based on the assumption that the antenna is transmit- 

 ting. A basic law of reciprocity assures us that the receiving gain and radia- 

 tion characteristics of the antenna will be identical with the transmitting 

 ones when only linear elements are involved. 



This resolution of an antenna wave front into an array of secondary 

 sources can be justified within certain limitations on the basis of the induc- 

 tion theorem of electromagnetic theory. These limitations are discussed in 

 a qualitative way in section 3.13. 



3.1 The Huygens Source 



Consider an elementary Huygens source of electric intensity £opolarized 

 parallel to the X axis with area dS in the XY plane (Fig. 8). This can be 

 thought of as an element of area dS of a wave front of a linearly polarized 

 plane electromagnetic wave which is advancing in the positive z direction.^ 

 From Maxwell's Equations we can determine the field at any point of space 

 due to this Huygens Source. The components of electric field, are found 

 to be 



Ee = t — — e (1 + cos 6) cos <^ , , 



Tkr (l5) 



Ea, = —I — - — e (1 -1- cos 6) sm </> 



2Kr 



where X is the wavelength. 



We see at once that this represents a vector whose absolute magnitude 

 at all points of space is given by 



\E\ =^(l-^cose). (16) 



^ S. A. Schelkunoff, Loc. Cit., Chap. 9. 



