10-5] PATTERN SIMULATION AS LINK 



the main lobe of a cylindrical beam, it is found convenient to use 



2VbP 



ith 



e 



521 



(10-6) 



where p is the normalized one-way power pattern, Q is angular displacement 

 from the parabola centerline, and 6 is the beamwidth. 



When a more complete description of a pattern .is needed having side- 

 lobes, one of the Bessel functions is found useful.^ For example, the second- 

 order function has first sidelobes about 25 db below the main lobe. This 

 might be considered a good design practice for a narrow-beam tracking 

 system. 



"J2( 



64 



'' J 



ith 



1.277 



e 



(10-7) 



Both of these functions are shown in 

 Fig. 10-5 as compared with measure- 

 ments on a typical pencil beam. The 

 measured pattern is for an offset 

 beam tracking antenna. This ac- 

 counts for its lack of symmetry 

 about the vertical axis, particularly 

 in the side lobes 



For any calculations within 10 db 

 of the peak of the beam such as error 

 signal sensitivity, the radiation pat- 

 tern may be fitted very nicely by the 

 exponential of Equation 10-6. With 

 this assumption, the modulation 

 sensitivity for zero target error is 

 given by^ 



4 los„ 2 

 6' = -^^^AXl00percent. 



(10-8) 



Here, A is the lobing angle between 

 extreme beam positions during the 

 cycle of conical scan (squint angle), 

 e is beamwidth, and 6" is the per cent 

 modulation per unit of angular error. 

 Another useful result derivable 

 from this pattern approximation is the db difference expression that has been 



Fig. 10-5 The Radiation Pattern of a 

 Typical Offset Feed Conically Scanning 

 Antenna as Compared with Two Pattern 

 Shape Approximations That Are Often 

 Used to Represent the Actual Antenna 

 Pattern. 



''Silver, op. cit., p. 194. 



8J. B. Damonte and D. J. Stoddard, "An Analysis of Conical Scan Antennas for Track- 



g," 1956, IRE Convention Record, Part I, Page 42. 



