THEORY OF THREE-ELECTRODE VACUUM TUBE CIRCUITS 527 



the two circuits are identical except that for one the impedance Z2 is 

 finite and for the other infinite. 



By the aid of the equivalent circuits given, that is by using equations 

 (10), (11), (12), (13) and so forth, the terms in the series (4) can be 

 calculated. These series formally satisfy equations (2) and (3) and 

 are the solutions if they converge. 



Fig. 3 — Equivalent circuit, second order effects. 



2R0P2 O^e, + Vi)(jjLe2 + V2)+ [(^ 

 RoP3(>xe,^vy 



Fig. 4 — Equivalent circuit, third order effects. 



For the purpose of fixing our ideas we assumed at the start a definite 

 circuit to which the tube was connected. It is obvious, however, 

 that no matter how complicated the linear network is to which the 

 input and output terminals of the tube are connected the procedure 

 given above can be followed. 



Application to a Modulator Circuit 



As an illustration of the theory just presented we shall calculate 

 the steady state second order effect assuming the circuit configuration 

 to be that given in Fig. 1. In so doing we shall assume that no variable 



