THEORY OF THREE-ELECTRODE VACUUM TUBE CIRCUITS 525 



where 



_ 1 d-I 



"* 7n ! dE^^ 



and has to be evaluated at the operating point.^ 

 We have further: 



E,^ g + e, Ep = p + v. (3) 



The equations (3) are obtained by applying the circuital laws to the 

 network external to the tube. 



We now proceed to a solution of equations (2) and (3) by means of 

 a method of successive approximations. Let 



J = II Ji, g= ILgu e = X, eu (4) 



111 



00 00 



P = HPu V = ^v. 



and let us define the relations between the terms in the series (4) as 

 follows : 



Ji = Piif^ei + i^i), Eg = gi + ei, Ep = pi + Vi, (5) 



J2 = Px{ne2 + V2) + P2(//ei + z;i)2, (6) 



= g2 + 62, = /?2 + V2, 



Jz = PiC^es + ^3) + 2i'2(M^i + z^i)(m^2 + v^ + P3(/xei + ^'l)^ (7) 



= g3 + ^3, = ^3 + Vz, 



Ji = Piiixei + Vi) + P2{tie2 + ^2)^ + 2P2{fj.ei + t'OC^^s + Vz) 



+ 3PzifJie2 + V2){uie, + v,y + P4()uei + ^;l)^ (8) 



= g4 + ^4, = ^4 + ^4, 



and so forth for subsequent terms. ^ 

 If we now let 



^0 = ^^, (9) 



' Loc. cit. 



^ The procedure of finding these equations is as follows: By substituting the first 

 term in each of the series (4j into (2) and (3j and neglecting all terms higher than 

 the first order equations (5) are obtained. By substituting the first two terms in 

 each of the series (4) into (2) and (3), and neglecting terms of higher order than the 

 second and by noting (5) equations (6) are found and so on for the remaining equa- 

 tions. 



