392 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 



rent and voltage at the output terminals. Making these substitutions leads 

 to 



Vl = (0)ti + (0)i2 , 



(14) V2 = r^gmii + r%i2 



= r%(i2 + fJiii). 



It remains to be seen how the directions of current and voltage must be 

 assigned in Fig. 3. If the directions of ^i and ii are arbitrarily assigned as 

 indicated in the figure, then the directions of V2 and 12 can be found by an 

 argument Uke that used in connection with the passive three- terminal 

 network just discussed. The dual of making Vp = Vg by placing a short cir- 

 cuit between plate and grid is making ii = ^2 by opening terminal 3 of the 

 dual. This says that the positive direction of {2 is as shown in Fig. 3. Simi- 

 larly, the dual of making ig = —ip by opening the cathode connection to 

 the vacuum tube is making 2^1= —V2 by placing a short circuit between 

 terminals 1 and 2 of the dual. This requires that positive values of Vi and 

 V2 have opposite signs when measured with respect to terminal 3 and so fixes 

 the positive direction of V2 as shown in Fig. 3. 



The 4-pole equations for a transistor^ are 



Ve = Tnie + rnic , 



(15) Vc = r2iie + r22ic 



= r22{ic + Oiie), 



where a = ^21/^22 . 



These equations are similar in form to equations (14) which correspond 

 to the dual of an ideal vacuum tube triode. Comparing the two sets of 

 equations shows that the following transistor and vacuum tube quantities 

 correspond to each other; 



r^gm and r2i , 

 r^kp and ^22 , and 

 ju and a. 



Comparing the first of equations (14) with the first of equations (15) 

 shows that the transistor quantities rn and rn should be zero if the transistor 

 is to be an accurate dual of the vacuum tube triode. These quantities are 

 small in present day transistors and there is hope that they may be made 

 still smaller in the future. In the transistor of Fig. 1 (b) , for example, rn is 

 approximately 200 ohms. This corresponds to a grid-to-cathode leakage 

 resistance in the triode which can be computed from 



fg = r^/m . 



» Some Circuit Aspects of the Transistor, R. M. Ryder and R. J. Kircher, Bell Sys. Tech. 

 Jl., 28, 367 Quly 1949). 



