r 



DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 



393 



Since r = 6600 ohms for the transistor and vacuum tube of Fig. 1, Tq amounts 

 to 218,000 ohms. This is large compared to r^ and would not seriously impair 

 the operation of the tube for many purposes. 



What has been said indicates that transistor currents and voltages are 

 fairly accurate duals of vacuum tube voltages and currents. As a three-termi- 

 nal network, however, the transistor fails to be the dual of a vacuum tube 

 because the values of u and Vc which behave as duals of v^ and i^ are measured 

 with a convention of signs which is not consistent with Fig. 3. This can be 

 seen by comparing the directions of i^ and vi in the dual of a vacuum tube 

 (Fig. 3) with the convention of signs for the transistor indicated in Fig. 1 (b) . 

 A transistor hke present day ones in all respects except for a reversal in 

 sign of ic and Vc would be a fairly good dual for a vacuum tube triode. This 

 discrepancy in sign means, of course, that the grounded base transistor 

 fails to give the phase reversal which would be given by the dual of a vacuum 

 tube. This does not mean that the duals of vacuum tube circuits cannot be 



Fig. 3 — The right-hand figure shows the convention of signs which must be used with 

 the transformed equations (14). 



found and used to advantage with transistors. It simply means that if the 

 circuits are to be strictly dual an ideal transformer or some other means 

 must be used to supply the phase reversal. 



In finding the dual of a vacuum tube circuit there are several equally 

 satisfactory ways of proceeding. Perhaps the simplest is to begin by treating 

 the transistor as though it were a perfect dual of a vacuum tube triode. In 

 this case, the transistor is substituted for the vacuum tube — emitter for 

 grid, base for cathode, and collector for plate — and then the remaining 

 part of the vacuum tube circuit is replaced by its dual. The resulting circuit 

 fails to be a dual of the original only with respect to a phase reversal which 

 can be corrected by inserting a phase reversing ideal transformer at the 

 most convenient appropriate place. 



Another procedure, which is perhaps more straightforward but which 

 may also require more work, takes care of the phase reversal automatically. 

 The first step in this case is to write down the Kirchoff equations for the 

 vacuum tube circuit and then transform them into a new set of equations 



