9-9] 



ANGLE TRACKING LOOP MECHANIZATION 



493 



harmonics. Ordinarily the phase shift produced by a low-pass noise filter 

 would be detrimental, but because the track loop bandwidth is low the 

 filter has little effect on the track loop stability. The demodulator selected, 

 however, should have a low d-c drift. To provide the proper allocation of 

 the total space error components into the correct channels, the demodulator 

 reference voltage must have the correct phase with respect to the incoming 

 voltage. If this phase is not adjusted properly, part of the azimuth error 

 will be directed into the elevation channel, and part of the elevation error 

 will be introduced into the azimuth channel. The cross coupling of the 

 azimuth and elevation channels due to this carrier frequency phase shift 

 is shown graphically in Fig. 9-9 for a typical two-channel control loop. As 



Elevation 



[G{cos/3 +G)~| _ r 

 l+2Gcos^+Gj '^° |i" 



rG(cosg+G)n r 



' ll+2Gcos/3 +gJ M 



G sin 



1+2 G cos /3 +C' 



Re 



G sin 



l+2Gcos^+G' 



Fig. 9-9 Cross-Coupling Due to Carrier Frequency Phase Shift /5: Block Diagram 

 and Equations. 



indicated in the equations, normal individual control of each loop is 

 obtained only when the phase shift error /3 is equal to zero. However, 

 when /3 is other than zero, the input of each loop affects each output. This 

 cross coupling effectively modifies the normal loop transfer ratio G by the 

 function G' which is described in Fig. 9-10. As indicated, G' introduces 

 phase lag proportional to sin^ /3 at the normal crossover frequency Wc of the 

 control loop. Actually, when /3 is equal to the phase margin of the loop, 

 (tt - 0c) at ojc, the additional phase shift due to the cross coupling is also 

 equal to (-r — 4>c). This reduces the normal phase margin to zero and the 

 loop becomes unstable. 



