626 BELL SYSTEM TECHNICAL JOURNAL 



ing device, the transfer stiffness in this case appearing in the jS circuit. 

 If d is regarded as the output, then /3 = —St * and the transfer characteristic 

 is, for high loop gain, 



..A = | = c,.. 



where Ct — \/St . Thus the over-all characteristic between input voltage 

 and angular displacement is simply a transfer compliance constant. In 

 Fig. 7 a tachometer monitor is used. Regarding angular speed d as the 

 output, then jS = —Rt, the transfer resistance of the tachometer. The 

 transfer equation is thus 



where gt{= l/Rt) is a transfer conductance. 



3. Design of Simple Linear Servo Systems 



The majority of servo systems in use, while often greatly extended in 

 space and frequently including highly diversified transmission elements, 

 may be represented by one essential feedback loop. However, a well 

 designed servo often will incorporate numerous subsidiary or local feedback 

 loops around stages of the system, in order to obtain a desired degree of 

 linearity or performance with easily obtainable circuit components. Com- 

 mon examples of such local feedback loops are electrical feedback around 

 vacuum tube amplifiers, and tachometer (velocity) feedback around motor- 

 drive systems. These subsidiary feedback loops are almost always designed 

 so that they are individually stable when the over-all feedback loop is 

 opened (assuming the method employed for opening the over-all loop does 

 not disturb the impedance terminations of the local feedback stages). 

 If it is thus assumed that any subsidiary loops are individually stable, then 

 the primary servo loop design may be treated simply as that of a single loop, 

 whose over-all loop transmission is obtained by taking the product of the 

 external transfer ratios of the various stages. 



The design of a single loop serv'o may be divided into the design of the 

 loop transmission n^, and one of the remaining parts, /x or (3. As previously 

 described, it is usually desirable to fix /3 according to the required basic 

 input-output relationship of the ser\^o, thus leaving mjS as a single charac- 

 teristic to be chosen. 



* It is assumed here that the transmission of the n circuit is basically positive. The 

 negative signs associated with St of Fig. 6 and R, of Fig. 7 are then introduced (by poUng) 

 to make the loop transmission n0 essentially negative. This stipulation ensures what is 

 commonly called "negative feedback," when the loop delay is zero. 



