180 REFLECTION AND TRANSMISSION OF RADIO WAVES 



+ /l2£2\ 



~r '22 £,2/ 



By the reciprocity theorem, /21 = /i2- 



An interesting theorem follows from Equation 4-18: For any given target 

 and aspect, there is a polarization of incident field which gives maximuyn echo, 

 and another which gives zero echo. This can be seen readily as follows. By 

 adjustments of the radar antenna system, the ratio EilE\ may be adjusted 

 (in magnitude and phase) until the received polarization is orthogonal to 

 that of the receiving system, so no signal will then be received from the 

 target.^ Similarly a polarization may be chosen such that the polarization of 

 the echo coincides with that of the receiver, so that a maximum echo will be 

 received. 



The radar area a also may be written in the form of a matrix by replacing 

 the quantities Imn in Equation 4-18 by 



^mn =47r|/™„|2. (4-19) 



Then 



(o"ii cri2\ 

 C2I 0'22/ 



(4-20) 



However, one could not deduce the polarization theorem above from this, 

 since the radar area is a scalar. 



4-4 MODULATION OF REFLECTED SIGNAL BY TARGET 

 MOTION 



The radar area of a complex target such as an aircraft depends on its 

 orientation, or aspect relative to the radar. An aircraft is subjected to roll, 

 pitch, and yaw motions by atmospheric turbulence. In addition, it may 

 have internal motions due to rotating propellers and surface vibrations. 

 Its gross aspect will vary with time if the target aircraft is on a noncollision 

 or maneuvering course. All of these factors will affect the instantaneous 

 radar area, so that the radar echo will have corresponding time variations. 

 Some of these effects will be considered in greater detail in Paragraphs 4-7 

 and 4-8. 



Another important effect produced by target motion is the change in 

 frequency due to the doppler effect which was discussed in Paragraph 1-5. 

 If the radar and the target have a relative approach velocity V, and the 

 transmitter frequency is/o, the echo frequency is (see Equation 1-19) 



/ = /o(l + IV I C) = /o + 2/7X0 = /o +/o. (4-21) 



Ut is possible to build a radar which transmits one polarization and receives, on two separate 

 receivers, the transmitted polarization and its orthogonal. For such a system, the theorem 

 applies to only one received polarization at a time. 



