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BELL SYSTEM TECHNICAL JOURNAL 



satisfy the condition expressed by equation (3). For example, any 

 structure having the general configuration of Fig. 7 will meet this con- 

 dition provided the impedances Zi, Z^ and Z3 are so related that when 

 the network is considered as a 4-terminal structure transmitting from 

 a-a' to b-h' it has a constant resistance image impedance equal to 

 i?o at a-a' . 



In contrast to the network of Fig. 3 in which both ^0 and <p are 

 merely constants, most of the networks which have been found give 

 rather complicated expressions for these two quantities. There are 

 still a number, however, the properties of which are sufficiently simple 

 to be of special interest. The first two are shown by Fig. 8. They have 



■A(^ 



Fig. 7 — Diagram to illustrate requirements on a more general 

 form of variable equalizer. 



the same design formulae, but one is terminated in a finite resistance at 

 both ends, while an open-circuit, such as the grid of a vacuum tube, 

 must be provided at one end of the other. Illustrative characteristics, 

 drawn on the assumption that the impedance Zn is a simple inductance 

 are shown at the bottom of Fig. 8. It will be seen that ip is still a con- 

 stant, so that an additional network must be added to control it, exactly 

 as in the structure of Fig. 3. The reference loss do, however, now 

 varies with frequency and can be controlled by the adjustment of Zn. 

 The design impedances have been written as Zn and Z21 in accordance 

 with the usual convention for fixed equalizers, to emphasize the fact that 

 the formula for &o is essentially similar to the standard equalizer 

 design formula 



Zu 



1 + 



R 



(9) 



