EFFECT OF FEEDBACK ON IMPEDANCE 277 



if Zp = 100,000 ohms, Z2 = 100 ohms and Fop = - 1000, then Za is less 

 than 100 ohms although F^ is not quite unity in magnitude.. 



The two examples given above illustrate the use of feedback to magnify 

 or to reduce the impedance of a network. This impedance, however, will 

 be correspondingly sensitive to changes in the characteristics of the vacuum 

 tubes. A third example of the use of the relationship (3) will show that 

 feedback may also be used to make the impedance of a network less sensitive 

 to changes in the characteristics of the vacuum tubes. 



In the case of the bridge-type feedback network shown in Fig. 5 we have, 

 with respect to the terminals 1,1' 



Zp = R(l + Q) 



V — A R + Rff 

 Fsn - A j-p-^ 



Fop = ^ (1 + "l-^f'e) = (1 + Q)Fs. 



where A is the feedback designed for the condition Rp — R, and 



(Rp - R){R + R0) 



Q = 



{R + Rp)(2R + Rff) + 2RR^ 



Then, by (3) 



Za = R 



{' + r^J 



Hence, if the feedback Fop is very large the effect of bridge unbalance on 

 the impedance presented to the line will be very small. If, for example, the 

 design feedback is 40 db the output impedance cannot change more than 

 1 per cent however severely the bridge might be unbalanced by Rp being 

 larger than R. 



The feedback when the line impedance Rl is connected may be obtained 

 by identifying Rl with Z in formula (6). It is 



1 -I- 2J^ + 37?^ 

 F = A R + ^0 



whence 



a log F _ RRl Q 



d log Rl R-\- RlRl + Zp 



The effect of bridge unbalance is to make the feedback sensitive to changes 

 in the line impedance Rl- 



