622 BELL SYSTEM TECHNICAL JOURNAL 



may be written by inspection. Referring to Fig. 2b, the transfer admittance 

 of a motor with resistance and inertia load may be written as 





where 



Rm + Rn 



(3) 



COr 



/ 



com is the reciprocal of the time-constant of the motor and control mesh, 

 and is 2x times the "corner" frequency at which the inertia! impedance just 

 equals the apparent mechanical resistance. Writing the transfer charac- 

 teristic in terms of shaft position, rather than speed, 



For values of w small compared with com , d/E is proportional to l/;aj . 

 This factor has a phase shift of —90 degrees and approaches infinity as w 

 approaches zero. This is merely a statement in frequency analysis language 

 that the motor shaft angle is the time integral of the applied voltage, for 

 slowly changing voltage. For more rapidly varying voltage, such that co 

 is large compared to co™ , d/E is proportional to l/O'w)- or — l/co-, the angular 

 variation being shifted —180 degrees with respect to the voltage variation. 

 The transfer ratio of the potentiometer, Fig. 3a, may be written as 



^-St^ (4.1) 



while for the tachometer, Fig. 3c, 



E 



= Rt, (4.2) 



or 



^=jo^Rt. (4.3) 



a 



Usually at some point in the system a compensating or "equalizing" 

 network will be included to modify the transfer ratio of the basic com- 

 ponents to the desired over-all transmission characteristic. Frequently 

 this equalizer is incorporated in the electrical section of the servo because 



