668 BELL SYSTEM TECHNICAL JOURNAL 



It follows readily from (2) and (3) that 



6io = — 

 h\ = 



Up 



bn = — -^w- + '2fjLpP2 

 "^ 2r„ dEa ^ 2rr, dE^ 



^01 = ^ 

 '(7 



1 ar„ _ 



^''~ ~WdE,~ 



_l ,, 2P fl — "^g _l_ ^ff "Mg 1^ 2T 



+ M.i^2 /320 - 2i,dK^2i'.dK^ ^^ ^' 



(4) 



where P2 and 7"2 are new notations for 620 and l3o2, respectively. Similar 

 expressions may be derived for the coefficients 630, 1830, etc. 



If we now apply the circuital laws to the network external to the 

 tube, we get a number of equations, two of which are 



g + eg, 



P + Cp. 



(5) 



To obtain a solution of (1) and (5) we utilize a method of successive 

 approximations. Let 



ip = Hipk, ig = High, Cp = 'Eepk, eg = J^egk, g = 'Egk, P = Xpk, (6) 



where the summations extend from k — 1 to ^ = 00 . Let us further 

 define the terms in the series (6) by the following equations: 



Tp1p\ °p\ l^pegl 



fff = gi + egi, €p = ^1 + epi 

 rpipi — tpi = [XpCgi + Tp^bi^ep^ + hi\epxeg\ + h^ieg-^) 

 ^gigi — eg2 = iJ-gepi + rg(^2oepi'^ + jSnepiCgi + ^02egi^) 

 = ^2 + egi, = p2 -\- ep2 



Tpipz — Bpz = UpCyz + ^p[262o«piep2 + bn{epieg2 + epiCgi) + 26o2«oie»2 

 + bzoSpx^ + b2iep-^egi + b^epiegi^ + 6036^1^] 



^uhs — eg3 = Mtf^ps + rgl2^2oepiep2 + ^n{epieg2 + ep2egi) + 2^o2egieg2 

 + ^3oepi^ + ^2iepi\i + ^izCpiegi^ + jSosej,!^] 



= g3 + e„3, = />3 + ep3 

 and so forth for subsequent terms. ^ 



(7) 



(8) 



(^) 



