EFFECT OF FEEDBACK ON IMPEDANCE 



275 



Let us assume that we are interested in the impedance faced by the line 

 impedance Zi in Fig. 2. If the terminals 1, 1' in Fig. 3 are left open the 

 feedback is obviously zero. Let the feedback when the terminals are 

 shorted together be denoted by Fsh. If the impedances of the /x-circuit 

 and the j8-network are denoted by Z^ and Z^, respectively, then 



r'here 



Za = Zp{\ - Fah) 



Zp = Z^ -\- Zff 



(9) 



This shows the now well-known fact that series feedback may be used to 

 magnify impedance. 



Za 



Fig. 3 — Impedance faced by the line at the series feedback end of a feedback ampUfier. 



However, it should be npted that the feedback Fsh involved in (9) is not 

 now equal to the normal feedback Fn as it was when the terminals 1,1' were 

 taken as in Fig. 2. The relation between Fat and Fsh may be obtained from 

 (6) by identifying F/f with Fz, and Zi with Z. Hence 



F^ = 



Z.P 



(10) 



From (9) and (10) it follows that even with a very modest amount of normal 

 feedback the magnification of the impedance may be very large. For 

 example, if Zp = 1000 ohms, Zi = 1 megohm and Fsh = — 1000, then Za 

 is better than 1000 times as large as Zp although Fu is not quite unity in 

 magnitude. 



Similarly, the impedance faced by the line impedance Z2 in Fig. 2, as 

 shown in Fig. 4, is 



