DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 385 



show that over a fairly wide range of values the tube currents are roughly 

 linear functions of the voltages. When the tube is connected into an external 

 circuit, the circuit imposes a second set of algebraic relationships between 

 vacuum tube currents and potentials and the performance of the circuit as 

 a whole represents a simultaneous solution of these two sets of relationships. 

 Now if the vacuum tube is replaced by a transistor and the external circuit 

 is left unchanged, then the relationships internaUy imposed are markedly 

 changed while the relationships imposed by the external circuit are left 

 unaltered. Ordinarily this will lead to a completely different simultaneous 

 solution for the two sets of conditions and hence to completely different 

 circuit performance. 



If circuit performance (with respect to the terminals of the tube or transis- 

 tor) is to be maintained after substituting a transistor for a vacuum tube 

 then the external circuit must be modified. One might suppose, for example, 

 that it should be possible to find a new external circuit such that the collec- 

 tor voltage in the new circuit would behave exactly as did the plate voltage 

 in the original circuit. To a certain extent this is possible, but this procedure 

 meets with a serious difficulty. Although transistor voltages are fairly well 

 behaved, roughly linear single-valued functions of transistor currents over 

 fairly wide ranges of values, transistor currents are relatively more non- 

 hnear, often double valued, functions of the voltages. This means at once 

 that if circuit performance is to be maintained for large signals, non-linear 

 elements will be needed in the external circuit. This approach seems very 

 much less promising than another to which we now come. 



The new approach is to seek a transistor circuit in which every current 

 behaves like a corresponding voltage in a known vacuum tube circuit and 

 every voltage behaves like a corresponding current. This approach is rela- 

 tively simple because, as has already been shown, half the problem is solved 

 simply by exchanging transistor for vacuum tube. The remaining part of 

 the problem is to find an external circuit which will impose the same rela- 

 tion between transistor potentials and currents as the original circuit im- 

 posed between vacuum tube currents and potentials. This amounts to say- 

 ing that if the vacuum tube is to be replaced by a device in which the roles 

 of currents and voltages are just interchanged then the external network 

 should also be replaced by a new network which accomplishes this same 

 interchange. 



Networks in which this sort of interchange is accompHshed are known as 

 duals,^ one of the other. It has been shown in the literature that it is possible 

 to find and to realize physically the duals of most practical circuits. The total 

 number of circuit elements in a network is ordinarily preserved when the 



2 Communication Networks, E. A. Guillemin, Vol. 2, pp. 246-254, John Wiley & Sons 

 (1935) ; Network Analysis and Feedback Amplifier Design, H. W. Bode, p. 196, Van 

 Nostrand, (1945). What Bode calls inverse we have called dual. 



