1282 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



narrower because of widening of the collector depletion layer. This re- 

 duction in base thickness permits more emitter current to flow for a 

 fixed emitter to base voltage, so that both emitter and collector currents 

 are increased, thus producing output and feedback admittances. How- 

 ever, since large changes in collector potential are required to produce 

 small changes in base thickness, relatively small changes in the junction 

 currents are produced and the admittances are far smaller than those 

 associated with change of emitter potential. 



3.2 Diffusion Current Admittances 



The short circuit two terminal-pair admittances associated with the 

 diffusion of minority carriers in the structure of Fig. 1 are 



- JL[(T - T ^ (1 + io^r^;)'" tanh Wo/jDj^Tj;)''' 



+ /n. (1 + io^Tnef'^] 



„ _ _J_ \(j _ r X f d + ^'^r^)'^' tanh w,/{D^T^f'^ ^ V <JrJ\ 



1/2 



dw (1 -f i03T^ 



dVc (Dj^Tj^y^^ sinh [(1 -f- tWp)^/2^o/(Z)pTp)^/2] 



Vec — ^Tr (T\ _ MI9 -^u r/1 ; ?~ M/9-„ /fT\ vr79i -'pc 



,1/2 



dw (1 + zcjTp) J 



Wc {D^Tj^yi^ tanh [(1 + ic^Tpy''wo/{Dj,Tj,y"] ^ 



[l + ^l 

 L o-pcj 



in which Ipe , Ine , and Ipc are average hole and electron currents at the 

 emitter and collector junctions and Ipeo is the emitter reverse current 

 measured with both junctions reverse biased. Wq is the (time) average 

 base region thickness and Vc is the average collector voltage. The de- 

 pletion layer capacitances which shunt the input and output diffusion 

 admittances, yee and ycc , are discussed in Section 3.3. 



Some general features of the admittances may be noted at once. The 

 expressions are similar to those for a section of lossy transmission line, 

 but differ significantly in the ordering of the magnitudes of the terms. 

 Each of the admittances is proportional to a dc current, and in fact, 

 since Ipc is ordinarily ninety per cent or more of Ipe , approximately the 

 same dc current. This effect, which results from the exponential depend- 

 ence of emitter current on emitter potential, can be related to the 

 transmission line analogy by the argument that the increase in minority 

 carrier density in the base region which accompanies increase of dc 

 current lowers the characteristic impedance of the transmission line. 



