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evaluated on this basis for a plate impedance Zp equal to a pure 

 resistance at all frequencies, it can be shown that the currents so 

 obtained are identical with the corresponding currents given by 

 equations (4) and (6) in the paper referred to. 



Finally, if we assume finite values for Zi, Z2, and Z3, no conductive 

 grid current, and constant yip, we have the case treated in the previous 



paper. 



Theory of Four-Electrode Tube Circuits 



Circuits with tubes having more than three electrodes can be treated 

 by a process similar to that adopted above, as will be made clear by 

 outlining the theory for the four-electrode tube circuit. 



The circuit to be considered is shown in Fig. 5 where Zi to Ze are 



Fig. 5 — Four-electrode vacuum tube and circuit. 



impedances which may include inter-electrode admittances. On the 

 electrodes denoted by a, b, and p are impressed the variable electro- 

 motive forces €a, 66, and Cp in series with the impedances Za, Zb, and 

 Zp, respectively. The significance of the quantities Ep, Epo, Cp, Ip, Ipo, 

 ip and the corresponding quantities with indices a and b, is obvious 

 from the preceding discussion of the three-electrode tube circuit. 

 Let a, b, and p be the incremental voltages across the impedances Za, 

 Zb, and Zp. As before, instantaneous values are implied. 

 For the currents we get the expansions 



ip = PiCa + PiCb + PsCp -f Piea" + P.eb'' + PeBp" 



+ PygaCb + PsCaBp + P^ebSp + • • • 



ia = AiBa -\- A2eb + AsBp -\- AteJ -^ A^Cb^ -\- A^ep^ ^ 



-{■ A^eaeb + AsCaep + AgebCp -\- • • • 



ib = BiCa + B^Bb + B^Cp + B^ea^ + Bi.eb'^ + B^ep^ 



+ B^eaeb -f BsCaep + Bgebep + • • • 



