Further Extensions of the Theory of Multi-Electrode 

 Vacuum Tube Circuits 



By S. A. LEVIN and LISS C. PETERSON 



The response of circuits containing vacuum tubes with any number of 

 electrodes due to impressed electromotive forces, and under such circum- 

 stances that the time of transit of the electrons is negligible, is discussed when 

 arbitrary feedback is present between the circuits connected to the elec- 

 trodes, each of which may carry conductive current. The use of the theory 

 is illustrated by obtaining first and second order eflfects in typical three- 

 electrode tube circuits. 



In a previous paper in the Bell System Technical Journal, October, 

 1934, the treatment was restricted to three-electrode tube circuits in which 

 it was assumed that the amplification factor of the tube was constant and 

 that no conductive grid current was present. In the present paper these 

 restrictions are removed. 



Introduction 



THE response in multi-electrode vacuum tube circuits due to 

 impressed electromotive forces has been the subject of several 

 papers. For the three-electrode vacuum tube circuit J. R. Carson ^ 

 has used a method of successive approximations, assuming constant 

 amplification factor and no conductive grid current. E. Peterson and 

 H. P. Evans ^ removed the restriction on the amplification factor but 

 maintained the assumption regarding the grid current, while F. B. 

 Llewellyn ^ considered the general case with both plate and grid 

 currents. Finally, J. G. Brainerd ^ has treated the general case of the 

 four-electrode tube circuit. The theories given by these authors did 

 not take into account any feedback between the circuits of the elec- 

 trodes except in the first approximation. 



In a previous paper ^ the theory given by Carson was extended to 

 include the effects of feedback between plate and grid circuits not 

 only in the first but also in the second and higher approximations. 

 The aim of the present paper is to extend similarly the other theoretical 

 work mentioned above^- ^' ^ to circuits containing tubes with three, 

 four, or any number of electrodes. 



Theory of Three-Electrode Tube Circuits 

 We shall consider the three-electrode tube circuit shown in Fig. 1 

 where Zi, Z2, and Z3 are impedances which may include inter-electrode 



1 J. R. Carson: /. R. E. Proc, April, 1919, p. 187. 



2 E. Peterson and H. P. Evans: B. S. T. J., July, 1927, p. 442. 



3 F. B. Llewellyn: B. S. T. J., July, 1926, p. 433. 



* J. G. Brainerd: /. R. E. Proc, June, 1929, p. 1006. 

 fi S. A. Levin and Liss C. Peterson: B. S. T. J., October, 1934, p. 523. 



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