582 BELL SYSTEM TECHNICAL JOURNAL 



the case of negative-grid triodes and referred to Fig. 8, these equations 

 take the general form : 



F, + /zF„ = /p2p, (1) 



V,- vV^= I,z„, (2) 



where 



At = 



(Zi + Z2) - (Z2 + Z3 + Z,) 



(Z2 + Z3 + Z.)Z, + (Zi + Z2)Ze 



(3) 



Z2 + Z3 + Z, 



(Z2 + Z3 + Zc)Z, + (Zi + Z2)Ze 

 ^^ " Z2 + Z3 + z. 



and the Z's may be expressed in terms of the tube geometry and d-c. 

 current or voltage by means of equations (80)-(84) in the reference. 

 In these relations the currents, Ip and Ig, denote the total current 

 reaching plate or grid, respectively, and hence include both the 

 conduction current carried by the electrons themselves and the dis- 

 placement current arising from the change of electric force. With 

 this meaning of current, (1) and (2) contain the complete description 

 of the performance of the tube, and separate consideration of the 

 grid-plate current, usual in low-frequency methods, is unnecessary 

 because that current is already included in /p in (1). 



The equivalent network represented by (1) and (2) is shown in 

 Fig. 8. Only two currents are involved, Ip and Ig, but, also two 

 internal generators, nVg and vVp, are required. For some purposes, 

 an equivalent network which corresponds more nearly with the usual 

 low-frequency delta arrangement is desirable. Such an equivalent 

 may be obtained from (1) and (2) in conjunction with Fig. 9 which 

 shows the relation between currents in a delta network and those of 

 Fig. 8. In Fig. 9 no restriction is yet placed upon the three currents, 

 7i, I2 and 1 3, so that in general they all may be allowed to include 

 both conduction and displacement components. From Fig. 9 



Ip = h + h, (4) 



Ig = h-h. (5) 



Here are two equations expressing the three unknowns, /i, I1 and 73, 

 in terms of the currents Ip and Ig, which are assumed to be known. 



