TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 



297 



(2) Amplifier must provide one net phase reversal. 



(3) Amplifier must have enough current gain to meet accuracy re- 

 quirements. 



Three possible transistor connections are available: (a) the common 

 base connection which may be considered analogous to the common 

 grid vacuum tube connection; (b) the common emitter connection 

 which is analogous to the common cathode connection; and (c) the 

 common collector connection which is analogous to the cathode follower 

 connection. These three configurations together with their approximate 

 equivalent circuits are shown in Fig. 2. It has been shown^ that for 

 most junction transistors the circuit element a is given by the expression 



a = sech 



W 



(1 + PTrn) 



1/2 



(1)^ 



where W is the thickness of the transistor base region, Lm is the diffusion 

 length and t„, the lifetime of minority charge carriers in the base region, 



Rk 



I — ^AV 



E- "J 



-^ Wvr 



Eo 



Rk A/3EL Rk ^ 



•=0" Rj (i-A/i)"^ Rj ^l 



(a) MULTIPLICATION BY A 

 CONSTANT COEFFICIENT 



E, 



R. 



E ^2 



E3 ^^ 



Rk 



I — vv\- 



Eo = E 



Rk A/bEj 



p, Rj (i-A/3) 



(b) ADDITION 



N r- . 



•RKEf: 



c 



§i — vw- 



£[Eo] 



A/3 £[el] sl[eQ 



Eo 



^N^^^^?|^-PH«[EJ 



(d) DIFFERENTIATION 



(l-A/3) pRC ~ pRC 

 (C) INTEGRATION 



note; £[Eo] = LAPLACE TRANSFORM OF OUTPUT VOLTAGE 

 £[Ei1 = LAPLACE TRANSFORM OF INPUT VOLTAGE 



p = jco 

 Fig. 1 — Summary of operational amplifiers. 



* This expression assumes that the injection factor y and the collector efficiency 

 at are both unity. This is a good approximation for all alloy junction transistors 

 and most grown junction transistors. 



