EQUIVALENT CIRCUITS OF NETWORKS 



605 



It can be shown that the network representation of Fig. 12 is consistent with 

 (19). This network representation suffers from two obvious disadvantages. 

 One is that the ' 'passive network" is determined by only one short-circuit 

 driving-point admittance of the complete network. The other short-circuit 

 driving-point admittance of the "passive part" appears to be unrelated to 

 any simple admittance which may be found from measurements at the 

 output terminals of the complete network. The second disadvantage is 

 that the coefficient of the current in the impressed force is of a complicated 

 nature, since a driving-point admittance enters. Moreover, a closer 

 investigation shows that in this network representation the "passive part" 

 besides preserving the driving-point admittance (3n and the feedback ad- 

 mittance /3i2 , also preserves the quantity A^ = i3iij322 — i3 12/321 of the complete 

 network. 



-/3, 



■y32. 



/3i 



1 



Ai+/3i2 



' _ y3i2-H/32i-H/3„ \ I, 



Fig. 12 — Equivalent circuit of an active four-pole; current impressed at the output. 



By proceeding from (19) in a way similar to that used in (17) the network 

 in Fig. 12 transforms into another in which the impressed force appears on 

 the input side. Many other networks can also be found. 



The networks discussed were based on (14), which expressed the fact of 

 current equilibrium and leads rather naturally to 11 networks together with 

 an impressed current source. On the other hand, starting with the four- 

 pole equations which express voltage equilibrium, one encounters T networks 

 together with impressed electromotive forces. These networks must now 

 also be considered. In regard to the details involved in their derivation we 

 may be very brief since the methods are similar to those already employed. 



The four-pole equations expressing voltage equilibrium may be written 

 as 



Fi = Zn/i -f Z12/2 

 V2 = Z2.1I I + Z22/2, 



(20) 



where current and voltage directions are assumed to be taken in accordance 

 with the conventions of Fig. 1. 



