OPERATION OF THERMIONIC VACUUM TUBE CIRCUITS 437 



inipt'dance in ihc plate circuit, as an explicit limction of e, a variable 

 \()llaii;e applied in series with a general impedance in the grid circuit. 



Special Case 



The following special case will make the detailed derixation, where 

 complex quantities are considered, more intelligible. 



For this special case consider a vacuum tube connected in circuits 

 containing only pure resistances. Let the resistance in the grid circuit 

 be denoted by Q and that in the plate circuit be denoted by Z. Fig. 1 

 illustrates this circuit. Let ip and ig be determined to satisfy the 

 following series : 



«^=aigg+a2^g^+ ... (11) 



i^ = t^e-\-b2e--\- . . . (12) 



(11) and (12) are valid since (4) and (5) are formally power series. 

 As seen from Fig. 1, e represents a variable voltage impressed in 

 series with the resistance, Q, on the grid (A the tube. 



© 



Hh 



Fig. 1 — Fundamental circuit diagram 



These equations will give the plate and grid currents as explicit 

 function of the voltages Cg and e, respectively, if we can evaluate 

 the a's and b's. To do this, we have the relation 



ep=—ipZ. (13) 



Substituting (11) in (4) and equating coefificients of like powders 

 of Cg, we may evaluate a^ and ao and thus express ip as an explicit 

 function of eg-. 



{rp+Z) 



e,+ 



-M%/'/+)u^(r/-Z^) + ^(/'/.+z/ 



{rp+zy 



(14) 



