Regeneration Theory and Experiment * 

 By 



E. PETERSON, J. G. KREER, AND L. A. WARE 



A comprehensive criterion for the stability of linear feed-back circuits 

 has recently been formulated by H. Nyquist, in terms of the transfer factor 

 around the feed-back loop. The importance of any such general criterion 

 lends interest to an experimental verification, with which the paper is 

 primarily concerned. 



The subject is dealt with under five principal headings. The first sec- 

 tion reviews some of the criteria for oscillation to be found in the literature of 

 vacuum tube oscillators. The second describes the derivation of Nyquist's 

 criterion somewhat along the lines followed by Routh in one of his investiga- 

 tions of the stability of dynamical systems. The third part deals with two 

 experimental methods used in measuring the transfer factor. The fourth is 

 concerned with the particular amplifier circuit used in the test of Nyquist's 

 criterion. The last section applies the criterion to a nonlinear case, and to 

 circuits including two-terminal negative impedance elements. 



IN a comparatively recent paper on "Regeneration Theory," ^ Dr. 

 Nyquist presented a mathematical investigation of the conditions 

 under which instability ^ exists in a system made up of a linear ampli- 

 fier and a transmission path connected between its input and output 

 circuits. The results of the investigation are of interest because of 

 their obvious application to amplifiers provided with feed-back paths,^ 

 as well as to the starting conditions in oscillators. As a result of his 

 general analysis. Dr. Nyquist arrived at a criterion for stability, ex- 

 pressed in particularly simple and convenient form, which is not re- 

 stricted in its range of application to particular amplifier and circuit 

 configurations. 



The great value attached to a criterion as precise and as general as 

 Nyquist's makes it desirable to submit the criterion to an experimental 

 test. One particularly striking conclusion drawn from this criterion is 

 that under certain conditions a feed-back amplifier may sing within 

 certain limits of gain, but either reduction or increase of gain beyond 

 these limits may stop singing. A feed-back amplifier satisfying these 

 conditions was set up, and the experimental results were found to be in 

 agreement with this conclusion. 



* Published in Proc. I. R. E., October, 1934. 



1 Bell. Sys. Tech. Jour., vol. XI, p. 126. 



2 Instability is used in the sense that a small impressed force, which dies out in 

 course of time, gives rise to a response which does not die out. 



^Electrical Engineering, July, 1933; Bell Sys. Tech. Jour., p. 258, July, 1933. 



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