484 AUTOMATIC TRACKING CIRCUITS 



of the stabilization and angle track loops in Fig. 9-3 can also be simplified 

 as an aid to the analysis and understanding of the tracking function. This 

 simplified diagram is shown in Fig. 9-4. 



The block Gi comprises the radar receiver (including the automatic range 

 tracking circuit discussed in Paragraph 9-11 and the common track 

 demodulator, voltage amplifiers, and bandwidth shaping circuits). The 

 block Gi contains a power amplifier, actuating motor, and antenna structure 

 with associated mechanical resonances. The block Gz represents the rate 

 gyro and possibly a network and an attenuator as shown in Fig. 9-3. 



The transfer function of the open stabilization loop (assuming the angle 

 track loop is not closed) will be equal to the product of G^Gz. This was 

 described in Paragraph 8-23. The transfer ratio Gt for the angle tracking 

 loop will be equal to the product of Gi and the closed-loop transfer function 

 of the stabilization loop. 



Vii 1 + G2G; 

 G1G2 



(9-2) 



In Fig. 9-4 the transfer functions for the simplified blocks Gi, G2, and G3 

 are shown in Laplace transform notation. Note that numerical values are 

 dependent upon the design specifications which are themselves determined 

 from the target and interceptor information available, and that the 

 mechanized system transfer functions may differ in numerical value in 

 different systems. Actually, the functions become much more complex if 

 high-frequency terms are included. However, the functions will have the 

 basic form shown in the figure, and this may be readily synthesized, 

 especially at low frequencies, by networks which compensate for undesirable 

 corner frequencies inherent in the physical components used in the mecha- 

 nization. 



Consideration in Specifying Control Loops. The control system 

 specifications may be determined from the output required, the type of 

 inputs that can be anticipated, and the necessary accuracy. Two charac- 

 teristics generally used to specify control-loop performance are frequency 

 responses and time responses. To obtain satisfactory results, both will be 

 used to obtain the control system characteristics in the next paragraph. 



In general, the gain at specific frequencies and the bandwidth (unity 

 crossover) of the control-loop response (unity gain of the loop transfer 

 ratio) will be used. By specifying the gain at various frequencies, the errors 

 in the system will be maintained within the desired limits; by specifying 

 the bandwidth and the gain constants or error constants, the necessary 

 speed of response to aperiodic inputs will be provided, and the magnitude 



