1232 THE BELL SYSTEM TECFINTIfAL JOURNAL, NOVEMBER 1952 



tionsliip between ]\ and /« is obtained: 



F, = 



r, + tie + Tb + Kb — j — 5 — j j — 5 



Tb -\- Kb + re -\- Re 



(23) 



Equation (23) is general for the given circuit; it suffers, however, in 

 difficulty in interpretation due to the numerous terms. In the regional 

 evaluation to follow, approximations will be made which bring out the 

 significant factors although decreasing the accuracy somewhat. The 

 (''c — I'c )Ico terms will be neglected. It is assumed also that large ex- 

 ternal base resistance Rb is employed. 



EVALUATION IN REGION I 



In Region I, from Fig. 10, r,„ is zero and r, is large so that r,' » 

 (rb + Rb)- Also, by assumption, rb « Rb ■ Applying these approxima- 

 tions, equation (23) becomes, 



^-■■^-:^. + ^,;y;^. (24) 



Equation (24) is the equation of a straight line, having slope r^ and 

 an intercept on the voltage axis at (VccRb)/(Rb + fc + Re)- The small- 

 signal input impedance is just the slope value or r^ . 



The short-circuit case where Re is zero is the most adverse device 

 condition in the sense that the dc term will th6n be most dependent 

 upon device parameters. When Re = 0, equation (24) becomes 



F.I ^ r'je -f -J^ (25) 



Kb + Te 

 EVALUATION IN REGION II 



In Region II all parameters are finite and the only approximations 

 which may be made are vt « Rh and r^ « Rb . Thus, 



F. 



p _ RbjRb + Tm) 

 Rb -\- Vm 



'' + ,, + t+ R. ^''^ 



If Rb is not too large, it may be approximated that (Rb + rm)/ 

 (Rb + re) = a. Taking Re = 0, thus, 



Fai ^ Rb(l - a) + -i^ (27) 



Kb -f- re 



