176 REFLECTION AND TRANSMISSION OF RADIO WAVES 



process. F may be a function of the range and other parameters of the 

 particular situation at hand. Thus, the radar equation becomes 



The quantity a is variously called the radar area, radar cross section, echoing 

 area, and back-scattering cross section. 



It is sometimes useful to relate a to another quantity known as the radar 

 length, designated by /. This is a phasor which represents the ratio, in 

 amplitude and phase, of the back-scattered field-at-unit-distance to the 

 incident field strength. Its relation to cr is 



(T = 47r|/r". (4-2) 



The radar length bears a relation to the received field strength similar to 

 that of radar area to received power in Equation 4-1. Thus, the received 

 field strength Er is given by 



Er = IE,F-'- '-^- (4-3) 



where E^ = the transmitted field at unit distance (the far field extrapolated 

 to unit distance from the transmitting antenna) 



K = Itv l\ = phase constant which expresses the relationship 

 between distance and the phase angle of a transmission 

 of wavelength X. 



The radar area a may be very much larger than the actual projected area 

 of the target. This may be shown in the following way. If the target is 

 large relative to the wavelength, then it is essentially correct to consider 

 that it intercepts a power P' equal to the product of its projected area A' 

 and the incident power density Wi, 



P' = A'JV,. (4-4) 



The currents set up in the target by the intercepted field will produce a far 

 field which has a certain directive characteristic, just as if the target were 

 an antenna with such a current distribution. Hence the target will have a 

 directive gain which is a function of angle. If we call the directive gain in 

 the radar direction G', then the effective power reradiated backwards will be 



P'G' = A'G'lVi = ctJV,. (4-5) 



Hence 



a - A'G'. (4-6) 



It is obvious that if G' is large, then a will be large relative to the actual 

 projected area A' . As an example, consider a target in the form of a flat 



