STABILIZED FEEDBACK OSCILLATORS 



459 



circuit elements except the tube resistances are linear and of lumped 

 character and, second, that modulation effects arising from the non- 

 linearity of the tube resistances may be neglected. The validity of the 

 second assumption is discussed in the appendix to the article by 

 Llewellyn noted above. Its use permits the treatment of the system 

 as though the resistances were actually linear but variable in magni- 

 tude in response to variations of the oscillation amplitude. 



Theory 

 The essential features of the single-tube feedback oscillator are shown 

 in Fig. 1. The feedback network B is unrestricted in its configuration 



Fig. 1 — Elements of a single tube feedback oscillator. 



and complexity and may include the vacuum tube electrode capaci- 

 tances in addition to the external elements. The impedance system of 

 the tube is reduced to the plate and grid resistances Ri and i?2 with uni- 

 lateral coupling between them, the latter being indicated by the inclu- 

 sion of a generator in series with the plate resistance. The voltage Ei 

 generated in the plate circuit is proportional to the voltage £2 between 

 the grid and the cathode and, when the system is oscillating, the latter 

 voltage is produced entirely by Ei as the result of the coupling through 

 the feedback network. 



The condition for the existence of self-sustained oscillations is ex- 

 pressed very concisely by the familiar equation 



M^ = 1, 



(1) 



wherein ix and /3 denote the voltage transfer ratios in the vacuum tube 

 and in the feedback path respectively. The factor n is the negative of 

 the amplification constant of the tube, the negative sign taking account 

 of the phase reversal inherent in a simple triode. The transfer ratio j8 

 represents the ratio of £2 to Ei for transmission through the feedback 

 network. 



