TRANSISTORS I.V SWITCHIXG CIRCUITS 1225 



the critical emitter current for collector \'oltaj2;e cut oft' may be obtained 

 by setting Vc = 0, as, 



/. = -- (4) 



a 



This relationship is dual to th(> gild \()ltage-plate voltage relation in 

 tubes for plate current cutoff as, 1'^ = —(Vp/^l). The criteria, for de- 

 fining the three regions are thus established as: 



Region I (Collector \'oltage Saturation): /, < (;")) 



Region II (Active): < I, < -l^ (0) 



a 



Region III (Collector Voltage Cutoff): 7^ > -- (7) 



a 



The identification of de\'ice parameters will be made for the several 

 regions by a single prime for Region I as i\ , none for Region 11 as 7\ , 

 and three primes for Region III as i\ . 



LIXEARIZATIOX OF THE CHARACTERISTICS AND APPROXIMATIONS 



The next step is to linearize the characteristics and to make suitable 

 approximations in order to obtain simple linear equations of the ter- 

 minal currents and ^'oltages. The relations which require linearization 

 are the device parameters Rn , Rr2 , R21 and R22 which are in general 

 functions of the currents as Rij = /(/i , I2). 



LINEARIZATION OF Rn AND 7?io 



In terms of the equivalent tee circuit, which has been and will be 

 employed, Rn is given as Rn = ?% + I'b . Also, Rio = Vb . It is convenient 

 to separate r^ and n and discuss each separately since Vb is fairly constant 

 and ft will have widely different regional values. 



In the R12 family of Fig. 13, it may be seen that R12 or n is fairly 

 constant in all three regions and will be so taken here. Further, in the 

 simple circuits under consideration, external base resistance Rb has 

 been inserted so that minor variations in n in the total of n + Rb are 

 inconsequential since usually Rh y> rb. The approximation that n is 

 constant is subject to review where finer detail is necessary, particularly 

 at low emitter currents where the rate of change of n is at a maximum. 



The emitter resistance r^ is approximately the resistance of a diode 

 in the forward direction. As such, r^ is high when the emitter current is 



