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BELL SYSTEM TECHNICAL JOURNAL 



Equations (7), (8) and (9) contain the general theory of the three- 

 electrode vacuum tube circuit. In the special case when conductive 

 grid current is absent it is only necessary to omit the second equation 



P3 



■■g [2^2oep,ep2+'9„(^p,^g2+ ^p2^g.) 

 ^i2^pieg. +^o3^g,^ 



V[2''20^p.^p2+b,,(«p,eg2*^p2^g,) 



:^g.^g2+b3„ej,,+ b^,. 



+ 2bo2eg,eg2+b3„eJ„+ b^.eJ^Sg, 



Fig. 4 — ^Equivalent circuit — third-order effects. 



in each of the equations (7) to (10), inclusive, and to omit in each of 

 the Figs. 2, 3, and 4, the branch containing Yg. If it is assumed that 

 not only conductive grid current is absent, but also that tip is constant, 

 the second plate e.m.f. in (8) reduces to TpPiicpi + Atp^oi)^ as is seen 

 from (10), and (8) thus becomes identical with the corresponding 

 equation already obtained previously.^ A similar reduction and 

 correspondence occurs for the second plate e.m.f. in (9), as well as in 

 subsequent equations. 



Application to Steady State Solutions 

 In this section the use of the theory is illustrated by obtaining first 

 and second-order effects assuming the circuit configuration to be that 

 shown in Fig. 1. To avoid unnecessary complications the discussion 

 is limited to steady-state solutions, and it is also assumed that no 

 plate e.m.f. is impressed. We shall first obtain the solutions in the 

 general case and then indicate how these are simplified in such special 

 cases which have been treated by some previous investigators.^- '*• ^ 



