390 



THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 



This indicates that the dual of an ideal transformer of impedance ratio 

 lla^ is another ideal transformer of impedance ratio ol^'A, It follows that 

 the dual of a 1:1 ideal transformer is a 1:1 ideal transformer. 



The dual of a constant voltage supply E is, of course, a current supply 

 which maintains a constant current equal to 



(11) 



rf 



E/r, 



and the dual of a constant current supply / is a supply of constant voltage 

 equal to 



(12) 



£' = Ir. 



lo- 



■VW- 



r; 



+eR2'- 



-AAAr 



R2 



L2 



■o2 



eL'feL C 



1 + 



T 



ec' 



Ll'+Lc' 



3 



ei -ec'-eR,' = o 

 e2 + ec'-eR2'=o 



(a) 



'C' = 



e,/ 



(b) 



Fig. 2 — The dual of a network is found by transforming the Kirchoff equations. 



The procedure of substitution used in all the examples above can be 

 used in a straightforward way to find the dual of a more complicated net- 

 work, but, in view of what has already been said some labor can be saved 

 by writing the Kirchoflf equations in the abbreviated notation used in Fig. 

 2. The equations on the left corresponding to the original network are then 

 transformed into the equations of the dual network by making the following 

 substitutions: 



ei = iv 



ii = ev 

 Cr, = iR[ 

 iRi = eR[ 



ih = Cc' , etc. 



From these transformed equations, shown on the right hand side of Fig. 2, 

 the dual network shown above them can be drawn by inspection. 



