The Bell System Technical Journal 



October, 1934 



An Extension of the Theory of Three-Electrode 

 Vacuum Tube Circuits 



By S. A. LEVIN and LISS C. PETERSON 



The relations between input voltage and output current of the three- 

 electrode vaccum tube are discussed when arbitrary feedback is present 

 between grid and plate circuits. Fundamental assumptions are that the 

 amplification factor is constant and conductive grid current absent. The 

 relations developed in the present paper are generalizations of those given 

 by J. R. Carson in I. R. E. Proc. of 1919, page 187. The use of the theory is 

 illustrated by application to a simple modulator circuit. The numerical cal- 

 culations in this case indicate that neglecting the effects of interelectrode 

 tube capacitances may introduce serious'errors. 



Introduction 



THE relations between input voltage and output current of the 

 three-electrode vacuum tube when connected to impedances in 

 both input and output circuits have been the subject of several papers. 

 One of the first more extensive treatments of this problem was given 

 by J. R. Carson,^ using a method of successive approximations. The 

 theory was further extended by F. B. Llewellyn,^ E. Peterson and 

 H. P. Evans,^ and J. G. Brainerd.* The theories given by these 

 authors did not take into account any feedback between input and 

 output circuit except in the first approximation. 



The aim of the present paper is to extend the theory of the three- 

 electrode vacuum tube to include the effects of feedback between 

 input and output circuits not only in the first but also in the second 

 and higher approximations. The assumptions underlying Carson's 

 treatment, constancy of the amplification factor and absence of con- 

 ductive grid current, will be maintained. The extension of the present 

 theory to such cases as treated by Llewellyn, Peterson-Evans and 

 Brainerd still remains to be done. 



1 J. R. Carson: I. R. E. Proc, April, 1919, page 187. 



2 F. B. Llewellyn: B. S. T. J., July, 1926, page 433. 



3 E. Peterson and H. Evans: B. S. T. J., July, 1927, page 442. 

 < J. G. Brainerd: /. R. E. Proc, June, 1929, page 1006. 



523 



