DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 391 



From the example given in this figure, it is seen that a ladder network is 

 transformed into another ladder network with each series branch of the 

 original network being transformed into a shunt branch in the dual network 

 and vice versa. Note also that a series combination of L and C is trans- 

 formed into a shunt combination of C and L'. The effect of a short circuit 

 between terminals 1 and 2 in the original network (which makes ci = e^) 

 is an open circuit at terminal 3 in the dual network (which makes ii = i-i). 



The Dual op an Ideal Vacuum Tube Triode 



In a previous section it was shown that transistor currents behave approxi- 

 mately like vacuum tube voltages and vice versa. In view of what has been 

 said about duality it might be assumed that, as three-terminal networks, 

 the transistor and the vacuum tube triode are approximate duals. It is the 

 purpose of this section to examine the relationships between the two devices 

 in detail and to show that they fail to be duals one of the other principally 

 because of a sign. What it amounts to is that signals transmitted through 

 the dual of a vacuum tube suffer a phase reversal while, on the other hand, 

 signals are transmitted through a transistor without change of phase. 



A convenient way of proceeding is to start with the 4-pole equations of 

 an ideal vacuum tube triode and transform them, by the methods already 

 presented, into the equations of the dual. These transformed equations will 

 then be compared with the 4-pole equations of a transistor. 



The small signal behavior of a vacuum tube triode is represented by the 

 equations, 



(13) 



where 

 and 



These equations apply when the positive directions of current and voltage 

 are as indicated in Fig. 3. The equations corresponding to the dual of the 

 ideal vacuum tube triode are found by substituting in equations (13), 



U = ^i/ry 

 ip = V2/rj 

 Vg = rii , and 

 Vp = ri2 . 



The quantities ii and v^ will then represent the current and voltage at 

 the input terminals of the dual device and ^2 and V2 will represent the cur- 



