FORMAL REALIZABILITY THEORY — I 



097 



oriented branch of the original diagram is repeated in the ideal graph, 

 similarly situated and oriented. Between those nodes which, in the 

 original diagram, were the (7V , Tr) of a 2n-pole N, is drawn a branch 

 iSr , called the r-th ideal branch of N, oriented from 7V to 7\ ■ This is 

 done for each such terminal pair. 



Kirchoff's laws now apply to this ideal graph. 



4.12* Consider a particular 2/i-pole N. Let Er be the potential of Tr , 

 Er that of Tr . Define 



Vr{t) = Er- E'r. 



Then Vrit) is the voltage across the ideal branch I3r so oriented that 

 Vr{i) > when Tr is positive relative to 7V . Let kr{t) represent the cur- 

 rent entering Tr . Then Av(0 = Ir{t), the current in /3r , so kr{l) is also 

 the current lea\-ing Tr . This is the force of the notion of ideal branch 

 and the fact which distinguishes a network which is a 2Ai-pole from an 

 arbitrary network with 2n terminals. 



4.13 For example, the network at (a) of Fig. 1 is not a 2 X 2 pole because 

 its currents are not constrained to meet the ideal branch requirement. 

 The addition of ideal transformers in either of the ways shown in (b) 

 or (c) of the figure converts it to a 2 X 2 pole. Of course in a circuit in 

 which the currents are constrained externally — as they would be, for 



T,c^— ^WV 



^WV 



■^Tj 



T.'o- 



(a) 



■OT,' 



T,o. 



—I I — ^A^^ — r — VA — I r 



T,-^-rii 



■oT, 



Jn^,- 



fC) 

 Fig. 1 — Conversions of a four pole to a 2 X 2 pole. 



* Technical paragraph as explained in Section 2.91. 



