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BELL SYSTEM TECHNICAL JOURNAL 



for freedom from instability •' applicable to an amplifier having linear 

 positive constants. 



To use this criterion, plot /x/3 (the modulus and argument vary with 

 frequency) and its complex conjugate in polar coordinates for all 

 values of frequency from to + <» . If the resulting loop or loops 

 do not enclose the point (1,0) the system will be stable, otherwise 

 not.^ The envelope of the transient response of a stable amplifier 



80 



30 



20-^^ 



1,000 IQOOO 



FREQUENCY- CYCLES 



100,000 



Fig. 6 — Gain frequency characteristics with and without feedback of amplifier of 



Fig. 2. 



always dies away exponentially with time; that of an unstable amplifier 

 in all physically realizable cases increases with time. Characteristics 

 A and B in Fig. 5 are results of measurements on two different 

 amplifiers; the amplifier having jujS-characteristic denoted A was stable; 

 the other unstable. 



The number of stages of amplification that can be used in a single 

 amplifier is not significant except insofar as it affects the question of 

 avoiding singing. Amplifiers with considerable negative feedback 



' For a complete description of the criterion for stability and instability and 

 exactly what is meant by enclosing the point (1, 0), reference should be made to 

 "Regeneration Theory" — H. Nyquist, Bell System Technical Journal, Vol. XI, 

 pp. 126-147, July, 1932. 



