LINEAR SERVO THEORY 



623 



of the comparative ease with which electrical circuit components may be 

 assembled in desired combinations. The transfer characteristic of the 

 equalizer may be simple or complicated, but in general may be written in 

 the form, 



M» 



(jo) + oJi)(icj + C03) 

 O'co + aj2)(ico + C04) 



(5) 



where the constants cci , 0^2 , etc. may be real or complex. The synthesis of 

 equalizing networks is a well known art and will not be discussed here, 

 particularly since most of the equalization characteristics used in present 

 ser\-o systems can be realized with simple networks. 



2.3 Simple Servo System {Single Loop) 



The simple serv^o system may be divided into two basic parts, an amplify- 

 ing circuit and a monitoring or comparison circuit. Such a division is 



f,(t! 



F, +PF2 



PF2 



fp(t) 



LOOP TRANSMISSION-ijp 

 TRANSFER CHARACTERISTIC: 



F - — tL_F 



Fig. 4 — Simple servo system. 



indicated in Fig. 4, where 11 and /3 are the transfer characteristics of the am- 

 plifying and monitoring parts, respectively. Fi and F2 represent typical 

 sinusoidal components of the total input and output quantities /i(/) and 

 /2(/),'* while ju and /3 are comple.x-valued functions of 70; as described in the 

 previous section. 



The return signal ^I'^ from the monitoring circuit is added to the servo 

 input Fi to form a net /z circuit input Fi -f /3F2 . The servo transfer char- 

 acteristic is found by setting 



F2 = fJiiFi + ^Fs), 



from which 



Fo = 



1 -M^ 



Fi. 



(6) 



* That is, Fi and F2 are complex quantities employed in the same fashion as / in equa- 

 tion (2). 



