THEORY OF MULTI-ELECTRODE VACUUM TUBE CIRCUITS 677 



■n M6a 

 i5i = , 



B2 ) 



rb 



B, = 



2rb^ dEb n dEb 



^'-JFb-dK^Wb'dEb^'''^^' 



„ _ 1 5^6p ^6p 5^6p 



Vb-dEb^^^'^' 



Tb SEp Yb dEp 



+ l^bafJ'bpBh 



(32) 



The circuital laws applied to the external network furnish a number 

 of 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 



fpl'pl 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 that 

 given in Fig. 6. 



We get further for second-order quantities 



?'p*p2 ~ Sp2 = IJ-pa&ai + fJ'pbSbi + ^pL 



Taiai — ea2 = P-abebi + llapepQ. + TaM 



rbibi — eb2 = tlba^ai + Mbp^p2 + ^6-^^ 



= ^2 + ea2i = 62 + ^62, = p2 -{- 6p2, 



(36) 



