DESIGN THEORY OF JUNCTION TRANSISTORS 1289 



with it a resistance 



+ 1 



L \'*2/ j^'irW2/ 



For the proportions shown, the ratio of n^ to n^ is approximately 1.5 to 

 one. Reasonable variations in the proportions can make this ratio as 

 small as unity or as large as five. 



A common feature in these resistances is the presence of the base 

 region thickness w in the denominator. Since low values of base spreading 

 resistance are desirable, this requirement opposes directly the primary 

 requirement for a high alpha cutoff frequency — a thin base layer. 



4. 4 Base Resistance Modulation Feedback 



As was mentioned previously, the dc voltage drop between the base 

 contact and the emitter junction is modulated by the widening and 

 narrowing of the collector depletion layer which alternately increases 

 and decreases the dc base resistance. The resulting ac voltage may be 

 represented by a voltage generator in series with the base resistance, as 



r dn dw 

 dw dVc 



where h is the dc base current, Vc is the dc collector voltage, Vc is the ac 

 collector voltage, and nbcVc is the feedback voltage. 



For the structure of Fig. 2(a), the expression given earlier for n' may 

 be differentiated to obtain the dn'/dw. The calculation of dw/dVc has been 

 indicated in Section 3.0. The resulting expression for ju&c is approximately 



T r'b dw 



Hbc c^ lb- ^jj 

 W dVe 



Determination of this feedback effect for the structure of Fig. 2(b) 

 is more difficult. Only those portions of the base region adjacent to the 

 collector barrier are affected by the barrier widening, so that only the 

 first two terms in the expression for n' , given above enter into the cal- 

 culation. The value of Hbc is 



This feedback term cannot be reduced to an expression containing n' , 



