Stabilized Feedback Oscillators 



By G. H. STEVENSON 



The author presents a mathematical consideration of the con- 

 ditions which insure constant frequency of the vacuum tube 

 oscillator under changes of electrode potentials or of the cathode 

 temperature. It has already been shown that the grid and plate 

 resistances may enter into the determination of the frequency. 

 The problem is treated here in the manner suggested in the recent 

 studies of feedback amplifiers. The conditions necessary for sta- 

 bility are developed in terms which are independent of particular 

 circuit configurations and are applicable to certain dissipative 

 circuits as well as to purely reactive systems. 



THE frequency deviations that accompany changes of the electrode 

 potentials or of the cathode temperature in many types of 

 vacuum tube oscillators have been recognized for some time as having 

 their origin in the variation of the internal resistances of the tube. 

 Llewellyn has shown ^ that both the grid and plate resistances may 

 enter into the determination of the frequency and, by treating the prob- 

 lem as one of network design, has demonstrated the possibility of mak- 

 ing the frequency substantially independent of the tube resistances. 

 He also devised a large number of oscillator circuits stabilized in this 

 way and established the conditions necessary for stabilization in each 

 case. 



The problem is treated here in a somewhat more general manner sug- 

 gested by recent studies of feedback amplifiers. ^ The conditions neces- 

 sary for stability are developed in terms which are independent of 

 particular circuit configurations and which permit their application to 

 certain types of dissipative circuits as well as to purely reactive systems. 

 While no new fundamental principles are presented, it is thought that 

 the restatement of the known principles in broader terms may be of 

 interest. 



The mathematical theory will be developed for the case of the single- 

 tube oscillator circuit, since this is the form most generally used. The 

 extension of the theory to multiple stage circuits presents little or no 

 difiliculty. The principal assumptions made are, first, that all of the 



1" Constant Frequency Oscillators," F. B. Llewellyn, Bell Sys. Tech, Jour., 

 January 1932. 



2 " Regeneration Theory," H. Nyquist, Bell Sys. Tech. Jour., January 1932; 

 "Stabilized Feedback Amplifier," H. S. Black, Bell Sys. Tech. Jour., January 1934. 



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