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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



type cut-offs. The equalization is to be accomplished with a network 

 which has n natural modes, but no finite frequencies of infinite loss. 

 (This is simply one of the arbitrary specifications which define this 

 problem.) 



The two cut-offs may be due to circuits or devices at two different 

 points in a communication system, which may be represented schemat- 

 ically as in Fig. 5. Their effect can be described in terms of two assigned 

 natural modes. Two assigned modes are assumed, instead of only one, 

 because a single mode would make the problem too simple. Our present 

 purposes will be served well, however, if we simplify the problem by 

 requiring the two assigned modes to be identical, say at p = po . 



Fig. 5 — A system with two resistance-capacity type cut-offs. 



The two natural modes would be cancelled completely by two infinite 

 loss points at the same location in the p plane. A network with two 

 infinite loss points, however, is not physically possible unless it has also 

 at least two natural modes ; and the natural modes will have to introduce 

 distortion of their own. Thus no finite network will give perfect equali- 

 zation of unwanted natural modes. Sometimes it is desirable, in practice, 

 to use an equalizer configuration which produces no finite frequencies of 

 infinite loss, the entire equalization being accomplished by a suitable 

 choice of its n modes. Configurations of this sort are illustrated in Fig. 

 6. Thus, our simple illustrative problem, though chosen to introduce 

 principles, is also of some practical interest. 



The exclusion of finite frequencies of infinite loss simplifies the repre- 



Fig. 6 — Configurations which produce no finite frequencies of infinite loss. 



