. The Bell System technical journal . , 2/1 ^ ~ 2r„ a£p ^ 2;^ aE; ^ ^ . _ 1 (9Map , Map ^Mab , ^ . Ta drLb Ta drLa 1 dHal + ro d£p ^a dEa flab dfiap . ^ . S (31) THEORY OF MULTI-ELECTRODE VACUUM TUBE CIRCUITS 677 ■n M6ai5i = , B2 ) rb B, = 2rb^ dEb n dEb ^-JFb-dK^WbdEb^^^ „ _ 1 5^6p ^6p 5^6p Vb-dEb^^^^ Tb SEp Yb dEp + l^bafJbpBh (32) The circuital laws applied to the external network furnish a numberof equations, three of which are ^a = a -\- Ca, ib = h -{- Bb, ^p — P -\- ^P- Let now ip 2^^pfc> P = Zpk, ib = ^ibk Cb = Y.^bk - (33) (34) We then obtain the equations fplpl Bp\ f^pa^al 1 l^pb^b
. The Bell System technical journal . , 2/1 ^ ~ 2r„ a£p ^ 2;^ aE; ^ ^ . _ 1 (9Map , Map ^Mab , ^ . Ta drLb Ta drLa 1 dHal + ro d£p ^a dEa flab dfiap . ^ . S (31) THEORY OF MULTI-ELECTRODE VACUUM TUBE CIRCUITS 677 ■n M6ai5i = , B2 ) rb B, = 2rb^ dEb n dEb ^-JFb-dK^WbdEb^^^ „ _ 1 5^6p ^6p 5^6p Vb-dEb^^^^ Tb SEp Yb dEp + l^bafJbpBh (32) The circuital laws applied to the external network furnish a numberof equations, three of which are ^a = a -\- Ca, ib = h -{- Bb, ^p — P -\- ^P- Let now ip 2^^pfc> P = Zpk, ib = ^ibk Cb = Y.^bk - (33) (34) We then obtain the equations fplpl Bp\ f^pa^al 1 l^pb^bX faial — Cal = flab^bl + Mop^pl Ca = ^1 + ^al, eb = &l + ^61, «p = ^1 + ^pl. (35) which show that the equivalent circuit for first order effects is thatgiven in Fig. 6. We get further for second-order quantities ?p*p2 ~ Sp2 = IJ-pa&ai + fJpbSbi + ^pL Taiai — ea2 = P-abebi + llapepQ. + TaM rbibi — eb2 = tlba^ai + Mbp^p2 + ^6-^^ 0 = ^2 + ea2i 0 = 62 + ^62, 0 = p2 -{- 6p2, (36) 678 BELL SYSTEM TECHNICAL JOURNAL. ©; 1^ °^ ($)| Eb i$)V;,9i ^ Ec Fig. 6—Equivalent circuit—first-order effects. where rpL= {P^ea^-\-Phebl^+P&ep^+P^ealehl-\-Piealep^-\-P^ehlepl)rpraM={Aieai^+A5ebi^-]-A6epi^-^A7eaiebi+Aseaiepi-]-A9ebiepi)rarbN= {Bieal+Bieb^ -\-B6epi-t-B7eaiebi-\-B8eaiepi+B9ebiepi)rbwhich in view of (30), (31) and (32) may be written T T, / r I \2 I 1 / dfipa . dHpa\ „ TpL = rpPeiiipaCai + Mpb^bi + ^pv + 2 \ d£ ^^^ d£ / I 1 / dfJLpb , \ „ 2 j_ ( . dfJ,pa\ -^-dEp^dEp , 1 / dHap , ^Map \ 2 I ^^° « o 1 / ^Mt dfJLba Cal- (37) (38) (39) (40) THEORY OF MULT I-ELECTRODE VACUUM TUBE CIRCUITS 679 From (36) it now follows that the equivalent circuit for second-ordereffects for the four-electrode tube circuit is as indicated in Fig. 7.
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
