PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 549 



The matched input and output impedances are 

 Rim = (re + rt) Vl + re(rm - u)l{r, -f n){u ^U- r^) (41) 



= 619 ohms and 

 Rom = ir, + re - Trr) Vl + uir^ - re)/{r, + n){re + U - r^) (42) 



= 0.671 (10)6 ohms 



As a increases toward unity the matched input impedance increases and 

 the matched output impedance decreases. They approach the limits 



I Rim = Vin + TcKre + n) (43) 



Rom = re V{n+rc)/{re-hH) (44) 



as a — ^ 1. 



I If fm in the transistor of our numerical examples could be increased to 

 exactly the value of r^ (a = 1) then the matched impedances would be 



Rim = 59,700 ohms 



Rom= 5,800 ohms 



From this example, it is seen that the impedances vary rapidly with a 

 as a approaches unity. 



With matched impedances, the maximum available gain from the 

 grounded emitter stage is 



M.A.G. = 



v('+;)( ^--?) 

 +v''+^t:+'-?)] 



-2 



(45) 



= 2.02 {lOy or 53 db 



When a is exactly unity this expression reduces to fc/re provided r^ and n 

 are small compared with Tc . For values of a which are enough smaller than 

 unity so that 



-' « 1 - a 



re 



the expression for maximum available gain reduces to the approximate 

 expression 



M.A.G. = a(r„/r.) [,^(1 - „) 1' + j/i + (i - „) L»] ' (46) 



