TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 301 



where Zovr is the output impedance of the amplifier measured with the 

 feedback loop opened. The expression for the output voltage is obtained 

 by combining (7), (8), (9), and (10). 



E, 



OUT 



N y 



= zL ^i 7" 



;=1 ^i 



A^ + 



3 = 1 ^1 _ 



(iir 



where 



A^ = A 



1 - 



'IN 



\Ri 



+ 



/OUT 



1 _^ ^ + ^^^ 



Rl Zovr 



IA/3 is equal to the current returned to the summing node when a unit 



Ei 



Z, 





MN 



1/3 Zk 



I IN 



Zn 



Zls 



J7 



1/5 Zk 



Equt 



NORTON EQUIVALENT CIRCUIT 



Fig. 4 — Generalized operational amplifier. 



icurrent is placed into the base of the first transistor stage (/in = 1). 

 If I A^ 1 is much greater than ] Zj^'/Zr \ and 



1 + L 



'IN 



then 



N 



Eqvt — ~ 2^ J^j nT 



(12) 



y=i 



The accuracy of the operational amplifier depends on the magnitude of 

 AjS and the precision of the components used in the input and feedback 

 networks as can be seen from (11). There is negligible interaction between 

 the input voltages because the input impedance at the summing node is 

 equal to Zin' divided by (1 — A^)? This impedance is usually negligibly 

 tsmall compared to the impedances used in the input circuit. 



* In general, E,- and Eout are the Laplace transforms of the input and output 

 fvoltages, respectively. 



