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BELL SYSTEM TECHNICAL JOURNAL 



where Rq is the internal resistance of the tube, equations (5), (6), (7) 

 and (8) may be rewritten as : 



RoJi — vi = nei, Eg = gi + ei, Ep = pi + vi, 

 R0J2 - vi = ixei + RoPiiixei + ViY, 



= g2 + 62, = ^2 + V2, 



(10) 



(11) 



RJz -vz = nez + 2RoP2(fJiei + Vi)(fjLe2 + V2) + R^Pzinei + v^Y (12) 

 Q = gz + ez, Q = pz + Vz, 



R0J4 — Vi = ixei + RoPiiixe^ + v^Y + IRaPiiiiei + z;i)(/ie3 + Vz) 



+ 3RoPz{uie2 + V2) {ixei + v^f + RoP^ifJiei + Vi)', (13) 

 = g4 + ei, = pi -{- Vi, 



and so forth. 



Equations (10) to (13) admit of simple physical interpretations. 

 Referring first to equations (10) it is clear that the equivalent circuit 

 corresponding to Fig. 1 for first order quantities is given by Fig. 2. 

 Similarly Fig. 3 is the equivalent circuit of Fig. 1 for second order 

 effects and Fig. 4 for third order effects. Higher order effects corre- 

 spond to similar circuits. 



JiJ|ro 



er 



Fig. 2 — Equivalent circuit, first order effects. 



The equivalence expressed by Fig. 2 is the familiar circuit which 

 has found such wide application, for instance, in amplifier and oscil- 

 lator work; while the equivalent circuits in Figs. 3 and 4 represent 

 the second and third order effects. With no feedback, that is when 

 Z2 is infinite, they reduce to the equivalences given by Carson.^ Com- 

 paring now any two equivalent circuits for same order effects with and 

 without feedback we find different values of the electromotive forces 

 appearing in series with the internal tube resistance Rq. Otherwise 



1 Loc. cit., equations (23) and following. 



