iioi.i'. i.\.n-:i r/<>\ i\ (,i:i<\i i\ii \f m,\ 



Figure 0(1)I, whidi shows the rurrciit and xoltagc relationships in a form 

 equivalent to those ust-il in coniUHtion with the type-A transistor. 



The point ./ in Im^. '•) represents a jioint in tiie lilamenl near the emiller 

 point. The current from llie emitter point will Ije determined by the differ- 

 ence l)elween its voltage I', and that of the surrounding semiconfluclor, 

 namely the voltage at ./. Thus we can write 



/. =/,(l'e - Vj). (5.1) 



l'\)r small a-c \ariations, /< , r, and v,, , this equation leads to the rela- 

 tionshij) 



/« = i'c't — Vj)fe , (5.2) 



whcre/( is the derivative oi l\ in respect to ils argument. Letting /", = \/Rf 

 this equation becomes 



t\ — v., = RJ, . (5.3) 



This relationship is correctly represented by the R^ branch of the equivalent 

 circuit. The voltage at /, under the assumed operating conditions with /« 

 positive and much less that h , will be —IbRb where Rb is the resistance 

 from the base to an imaginary equipotential surface passing through J 

 and Vh = 0, corresponding to grounded base operation. This leads to 



vj = —Rkib = +RbL + Rhic , (5.4) 



since //, + i, + /,. = 0. This relationship is obviously satisfied by the Rb 

 branch of the equivalent circuit. 



We now come to the collector branch which we have represented as a 

 resistance Re and a parallel current generator* acif . (This circuit is equivalent 

 to another in which the parallel current generator is replaced by a series 

 voltage generator acRcif ■) We must show that this part of the equivalent 

 circuit represents correctly the effect of injecting holes into the right arm 

 of the hiament. We shall suppose that there is negligible recombination so 

 that the hole current injected at the emitter point flows through the entire 

 filament. (We consider recombination in the next section.) The current /c in 

 the collector branch thus contains a component —yf( = I,, of hole current 

 (minus because of the algebraic convention that positive /c(= —lb — /«) 

 flows to the left). The added hole and electron concentrations lower the 

 resistance and Re changes to Re + 8Re , where 8Rc is negative. The current 

 voltage relationship for this branch of the filament then becomes 



Vc - I'./ = (Re + dRe)Ic . • (5.5) 



* ae in the equivalent circuit dilTers from a = — ((ilr/<^l ,)v,- by the relationship r^, = f> + 

 in — \)(K\,/R,-), equivalent to eriuation f6.8). 



