iioi.i-: ixjEcriox i\ i,i:i<\i.\\ir\[ ?,m 



cross-section of the filament. The modulation of the output current takes 

 place through the change in body conductivity due to the presence of the 

 added holes, a change which appears to be unimportant in the type-A 

 transistor. In the filamentary type, current amplification is produced by 

 the extra electrons whose presence is required to neutralize the space charge 

 of the holes. Current amplification in the type-A transistor is, probably, also 

 produced by the space charge of the holes'* but the details of the mechanism 

 are not as easily understood. 



6. Effkcts Associated with Transit Time 



Two important effects arise from the fact that a finite transit time is 

 required for holes to traverse the Re side of the filament: during this time 

 the holes recombine with electrons and the modulation effect is attenuated 

 for this reason; also the modulation of the conductivity of the filament at 

 any instant is the result of the emitter current over a previous interval and 

 for this reason there will be a loss of modulation when the period of the a-c 

 signal is comparable with the transit time or less. 



For the small signal theory, the effect of transit time is readily worked out 

 in analytic terms. We shall give a derivation based on the assumption that 

 the lifetime of a hole before it combines with an electron is Tp . According 

 to this assumption, the fraction of the holes injected at instant ti which are 

 still uncombined at time Aj is exp[— {k — /i) Vp]. This means that the effect 

 in the filament at any instant /« is the average, weighted by this factor, of 

 all the contributions prior to k back to time /j — n where Tt is the transit 

 time; holes injected prior to h — n have passed out of the filament by 

 time k • If the emitter current is represented by ieoe"^ , the effective average 

 emitter current is 



i.eff(/2) = /.c f'^' e'"''-'''--''"'^ dh/rt. (6.1) 



The term dti/rt is chosen so that a true average is obtained since the sum 

 of all the dti intervals add up to rj . The integral is readily evaluated and 

 gives 



. f,\ • iu,t. 1 — exp [— i(jjTt — {rt/Tp)] . -s 



l(j}Tt -\- [Tt/Tp) 



The result so far as the equivalent circuit is concerned is that obtained by 

 taking ae as* 



ue = t(1 + b)^, (6.3) 



* The derivation of equations (5.10) and (5.11), describing the equivalent circuit, shows 

 that hole injection enters only through the term bRJc in (5.8). This term leads only to 

 aeRcit = (1 + b)yRcit in (5.11) and should be replaced by (1 + b)yRcit cff = (1 + b)y0Rcii 

 leading to (6.3). 



