VARIABLE EQUALIZERS 



231 



where R represents this resistance, Z represents the impedance which 

 it faces, and Ys and Fo, as the equation impHes, are the transfer ad- 

 mittances obtained by short-circuiting and open-circuiting R. It is 

 evident by inspection that log Y, which represents the d of equation 

 (1), cannot be written in the form which the right-hand side of (1) 

 demands. A certain amount of distortion of the type shown by Fig. 1 

 must therefore always occur. 



24 



22 



20 



18 



16 



in 



_i 



CD '^ 



O 



Ul 



a 12 



z 

 (O 10 



V) 



O 



_J 

 6 



0.5 1.0 1.5 2.0 2.5 3.0 3-5 4.0 



OJ 



UJQ 



Fig. 1 — Characteristics of a simple variable structure. 



There still remains the possibility, however, of obtaining a network 

 in which the distortion can be kept within tolerable limits over a given 

 range. The quantities Y^, Fo, and Z, which are, of course, all functions 

 of frequency, allow us to determine the transfer admittance at three 

 values of R. The transfer admittances at other settings will then be 

 fixed. If we suppose for simplicity, that the extreme characteristics, 

 corresponding to Y^ and Fo, are set by the engineering requirements on 

 the structure, the problem reduces to that of so choosing Z in relation 

 to these quantities that the distortion is as small as possible at inter- 

 mediate settings of R. 



Of the variety of possibilities open in the selection of Z, one in par- 

 ticular commends itself by the simplicity and symmetry of the results 

 to which it leads. It is given by the condition 



