720 BELL SYSTEM TECHNICAL JOURNAL 



design of a reactive equalizer places a definite requirement on the behavior 

 of the transfer characteristic outside the useful frequency band. 



Although the precision of equalization as a design requirement actually 

 is inclusive in the term transmission performance as used previously, it is 

 included here as a separate requirement to emphasize its importance in this 

 problem. The specification of a flat transmission from A to B in Fig. 2 

 provides the means of assigning to the tolerance of equalization a quantita- 

 tive meaning. Hence, the tolerance per repeater section of the system may 

 be expressed as the maximum allowable db deviation from the flat trans- 

 mission characteristic, A to B, over the useful frequency band. For extremely 

 broad-band systems, such as a coaxial system for simultaneous long-distance 

 telephone and television transmission, many repeater sections appear in 

 tandem between terminals. Thus, the deviations in each of these sections 

 contribute to the system as a whole. In addition to the distances usually 

 involved, repeater spacing becomes closer as the effective transmission band 

 of these systems is increased. In order to design new systems with increas- 

 ingly better overall tolerances, at the same time that the broad-banding 

 requirements call for a greatly increased number of repeater sections per 

 system, the tolerances imposed on the mdividual sections become exceed- 

 ingly small. As a consequence, the maximum tolerance for an individual 

 section must be specified as perhaps less than ±0.05 db deviation. 



2. The Problem of Reactive Equalization 



In this section the problem of reactive equalization will be formulated in 

 terms of the special problems of input and output coupling circuit design. 

 Broadly speaking, the general characteristics of input and output coupling 

 networks, as outlined in the introduction to establish the practical basis for 

 reactive equalization, will be further developed in order to give them a 

 quantitative meaning. Because of the complexity of some derivations and 

 their extensive treatment elsewhere, detailed proofs in general will be merely 

 outlined. The method of analysis follows Bode's treatment of the problem 

 while the principal results taken from network theory are Guillemin's. 



As previously stated, the untermmated case for input and output coupling 

 circuits arises whenever the terminating resistance is infinite in comparison 

 with the other impedances of the network.® Figures 4 and 5 represent, re- 

 spectively, an output and an input couplmg network of the type illustrated 

 in Fig. 2 with infinite terminations. In each figure, Rl represents the line, N 

 is the lossless coupling network, and C„ is the parasitic shunt capacitance 



« The so-called terminated case exists when the parasitic capacitance Co or C,- in Fig. 2 

 is shunted by a finite resistance. Since no essential differences exist between the two cases 

 with respect to the approximation problem, an analysis for the unterminated case alone is 

 sufficient to clarify the more important design considerations. 



