520 ANTENNAS AND RF COMPONENTS 



on the signal returned from the antenna after a round trip between the radar 

 and target. The modulation is almost sinusoidal near zero error, but 

 becomes high in harmonics at large errors. It is found that the per cent 

 fundamental modulation of the received signal is the important quantity- 

 through which the tracking servo is linearly closed.^ That is, the amplitude 

 of the per cent fundamental modulation is proportional to target displace- 

 ment from the antenna centerline. The phase of this signal is the target 

 position around the antenna in a roll coordinate. Thus the per cent 

 fundamental modulation goes to zero with no target error and reverses sign 

 (phase) when the error goes through zero. This error curve is shown in 

 Figure 10-4(b) for several values of beam offset. Here {Et) is target error 

 normalized to beamwidth (6). For a high angular resolution, the function 

 should have a high slope and should be linear, at least in the region of zero 

 error. 



The transition of radar function from search to track is called lock-on. 

 During this period, the radar antenna is positioned manually as close as 

 possible to the correct aiming direction and then a switch is closed to change 

 the radar function. As the initial aiming error may be relatively large, it is 

 important that the error curve have at least the correct sign (even if it is 

 no longer linear) out to this initial probable error. The error signal sign 

 reversal is the limit of target lock-on; beyond this point the antenna will be 

 driven in the reverse direction by the antenna position servo and the target 

 will be lost. Finally, a false lock-on may occur at a target error other than 

 zero where the per cent fundamental modulation again goes through zero 

 with the same polarity of slope as it does on the antenna centerline. Such 

 a possibility is shown in Figure 10-4(b) for |-db crossover with a target 

 error of 1.57 beamwidths. See Paragraph 10-6 for more discussion of false 

 lock-on. 



It can be seen that fundamental modulation is important to the tracking 

 function. It can be measured by harmonic analyzer methods on an actual 

 antenna or it can be calculated from a known beam shape. In this manner 

 the system requirements can be related to the usual antenna parameters 

 such as beamwidth. For this calculation and others, an approximation to 

 the radiation pattern by a simple function is required. 



10-5 PATTERN SIMULATION AS A LINK BETWEEN 

 SYSTEM REQUIREMENTS AND ANTENNA 

 CHARACTERISTICS 



A mathematical description of the antenna pattern is a link between 

 antenna terminology and system requirements. For problems involving 



^Aeronautical Electronics Digest, 1955, IRE National Conference on Aeronautical Elec- 

 tronics, Page 13. (Also see Paragraph 5-8, above.) 



