272 BELL SYSTEM TECHNICAL JOURNAL 



This equation expresses the relationship between feedback and impedance. 

 To make this more apparent the physical significance of each of the factors 

 in this equation will be examined and suitable symbols will be substituted 

 for them. 



In equations (1) £2 and /i were regarded as independent variables. How- 



ever, the ratio ( — - 1 implies that £2 is adjusted to be equal to F2. 



This means that £2 is dependent upon /i. The reason for the imposition 

 of this dependence is that with Eo equal to V2 the terminals 2, 2' may be 

 connected together and the source of £2 may be removed without affecting, 

 in particular, the potential difference Vi across terminals 1,1' and the cur- 

 rent /i into these terminals. 



/fA 



Obviously, therefore, the ratio I ^r- I is the impedance which will be 



seen at the terminals 1,1' when terminals 2, 2' are connected together and 

 the only source of e.m.f. acting on the rietwork is the external circuit con- 

 nected to the terminals "1, 1'. This ratio will be symbolized by Z.4. 



The ratio I — - ) implies that no voltage is applied between the grid 



and the cathode of the tube. However, it is immaterial whether or not a 

 voltage is applied to the grid of the tube if the amplification of the tube is 

 nullified. Obviously, therefore, this ratio is the impedance which will be 

 seen at the terminals 1,1' when terminals 2, 2' are connected together and 

 the amplification of the tube is nullified. This ratio will be symbolized by 

 Zp. 



'Vo\ . /F2 



Finallv, the ratios I "zr 1 and 1 tt ) are readilv recognized from 

 £2/ri=o \£2//i=o 



the definition of feedback to be the feedback to the vacuum tube with the 

 terminals 1,1' connected together in the first case, and left open in the sec- 

 ond. These ratios will be symbolized by Fsh and Fop respectively. 

 Hence, equation (2) may be written in the more significant form 



Za _ 1 — Fsh /^\ 



Zp 1 — Fop 

 Determination or Feedback 



One of the uses to which the relationship (3) may be put is in the deter- 

 mination of feedback by impedance measurement. However, since this 

 relationship involves two feedbacks, only one of which may be identified 

 with the feedback to be determined, one of these feedbacks must be known. 



In the most common types of feedback amplifiers it is possible to choose 



