494 



AUTOMATIC TRACKING CIRCUITS 



Ra + eo 



-^ 



Modifying Function 



G'= 



cos (3 + G 



1+G cosjS 

 Approximate Transfer Characteristic 



(/>. is Phase of G 

 at W 



Co 



1 j sin 0c sin^ (3 [ 



I cos^ /3 cos 0c + 2 cos /3 + cos 4>^ [ 



Fig. 9-10 Cross-Coupling Transfer Function Channel Output for Same Channel 



Input. 



Therefore, as the phase of the reference voltage is shifted, the stability 

 of each track loop channel changes. The overall effect on performance is 

 that the settling time of each loop is extended, and the antenna moves in a 

 spiral toward a preset position rather than in a straight line. The nature 

 of the spiral for various amounts of reference phase shift is pictured in 

 Fig. 9-11. The loop for which these illustrations were made had a large 

 phase margin at the crossover frequency equal to 71°. The data indicate 

 that the reference phase shift variation should be under 20° for loops with 

 this large normal phase margin, and that the phase shift should be under 

 10° for loops with a small normal phase margin, because a noticeable 

 deviation from an ideal straight-line response may be noted for even a 5° 

 reference phase shift in a system having a large phase margin. 



A similar form of cross coupling between channels can come from the 

 gyros used in the space stabilization loop. The gyros are not the perfect 

 instruments that have been represented in the block diagrams. They may 

 produce voltage outputs, not only from space rates about their input axes 

 but also from space accelerations about axes orthogonal to the input axis. 

 Thus, accelerations in the elevation axis can appear as a voltage or an 

 equivalent space rate in the azimuth axis; and, conversely, accelerations in 

 the azimuth axis can create false rate signals in the elevation axis. The 



