496 



AUTOMATIC TRACKING CIRCUITS 



Tracking Loop Network and Amplifier. The frequency character- 

 istics and the gain of the track loop shown in Fig. 9-8 are obtained with a 

 shaping network and amplifier indicated by d in Fig. 9-3. To obtain this 

 function, an amplifier may be cascaded with a simple, passive RC network 

 such as that shown in Fig. 9-12. For reference purposes the frequency 



s 



Frequency Characteristic 

 a), 



■ 1.0 



Flow Diagram 



Transfer Function 



s Rj(Cj+C2)+l 



CiCjRjRo+slCjRo + CjRi+CiRiJ + l 



Design Formulas 



Let Ro = l (Resulting Values May Be Adjusted to Any 

 Impedance Level) 



Then C = -^ + -77 - rr 1 



Kc, ^' 

 Fig. 9-12 Passive RC Tracking Network. 



characteristic, a flow diagram, the transfer function, and useful design 

 formulas are given. Note that the design formulas are expressions for 

 deriving the parameter values directly in terms of the corner frequencies 

 desired in the transfer function. This eliminates a cut-and-try procedure 

 in the design synthesis. Although this is a simple network, it has some 

 disadvantages: (a) the parameter values, particularly the capacitor C2 

 may become quite large for loops with narrow bandwidths, and (^) a change 

 in amplifier gain will create a corresponding change in track loop band- 

 width. 



These objections can be largely eliminated by using an active network, 

 the operational amplifier shown in Fig. 9-13. It should be noted that the 

 transfer function is essentially the same as that of the passive network 

 except that the input resistor value is modified by the amplifier gain. 

 Consequently, the lower lag corner is also a function of amplifier gain; and 

 if the gain of the amplifier changes, the low-frequency corner will change 

 inversely. Thus the bandwidth, stability, and noise transmission of the 

 tracking loop will not be altered. It should be noted that the low-frequency 

 corner is achieved by using feedback which permits the use of smaller 

 parameters, and the output impedance of the active network is much less 

 than that of the passive network. This reduces the problem of loading, but 

 the output impedance still will not be zero and its value must be considered 

 if the impedance of a device following the network is low. 



