DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 387 



the current through it in the Kirchoff equations of the original network, 

 these quantities will be replaced by U' , and Cl' -, respectively, in the Kirchoff 

 equations of the dual network. The quantities II' , and Bl' , represent the 

 current through an inductance of value L' given by (4) and the voltage across 

 it. 



The argument just given can equally well be interpreted to mean that 

 the dual of an inductance L is a capacitance C, the value of which is given 

 by 



(5) C = L/r', 



so that every Bl and II in the Kirchoff equations of the original network 

 are replaced by ic , and ec , respectively, in the Kirchoff equations of the 

 dual network. 



The dual of a resistance R is found in the same way. The equation ap- 

 plicable to a resistance is 



(6) e = Ri, 



which, with the substitution of ri' for e and e'/r for i, becomes 



(7) i' = e'l{rVR). 



Thus it is seen that a resistance R transforms into a resistance R! where 



(8) R! = r^lR. 



Also, Cr and Ir in the Kirchoff equations of the original network are replaced 

 by iff' , and eR> , respectively, in the Kirchoff equations of the dual net- 

 work. 



The dual of a temperature sensitive resistance which changes value with 

 changes in average signal level can be found by exchanging the labels on 

 the axes of an E-I plot of its characteristic. This shows that the dual of a 

 resistance which has a positive temperature coefficient, and hence increases 

 in resistance with increase in signal level, is a resistance with a negative 

 temperature coefficient of resistance which decreases in resistance with 

 increase in signal level. Similarly, the dual of a short-circuit-stable negative 

 resistance is an open-circuit-stable negative resistance. 



The equations applicable to an ideal transformer of impedance ratio 

 llo^are 



(9) ei — ae\ , and 



ii = ii/ot. 



Making the substitutions previously indicated leads to 



(10) ii — ail , and 



€2 = e-Ja. 



