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BELL SYSTEM TECHNICAL JOURNAL 



— /xjS exhibits gain and phase margins of the order of 10 db and 50 decrees 

 resoectively, the transient response of the modifying factor to a step function 

 will be well-damped and generally not overshoot more than about 25%. 

 If the gain margin is sufficient, the phase margin usually will be the dominant 

 factor in determining the size of the initial overshoot. The required phase 

 margin for critical damping depends upon the exact shape of m/^O'cj), but 

 in general is about 60 degrees. The gain margin needed in a particular 

 design will depend upon the expected variability of the loop transmission. 

 Radar tracking loops should usually have gain margins of the order of 15 



0.3 0.4 0.6 



TIME IN SECONDS -► 



Fig. 9 — Transient response of illustrative servo system. 



db or more because of the large number of factors which may cause the loop 

 gain to vary. 



While the polar diagram gives a clear picture of stability considerations, 

 it is usually more convenient for design purposes to plot the gain and phase 

 of — ;u;S as separate curves on a logarithmic frequency scale, for positive 

 values of w. This is illustrated in Fig. 10, for the sample servo system. 

 Under two commonly met conditions, the requirement for single loop" 

 stability on this type of plot is simply that the absolute value of phase shift 

 be less than 180 degrees at zero db gain (| M)3 | = 1). The conditions are 

 that the connective polarity be such as to make — /xjS positive when the 



" Again, multiple loop systems ma\' be included if all subsidiary loops are individually 

 stable. 



