A METHOD OF IMPEDANCE CORRECTION 795 



This physical contrast between an ideal continuous medium and 

 an actual physical telephone circuit does not necessarily mean that the 

 application of the wave theory to circuit analysis is a difficult matter. 

 To a first approximation we can determine the response of a circuit 

 merely by adding together the propagation constants of its various 

 constituents. Unfortunately, however, the diverse components of a 

 typical circuit usually have characteristic impedances which are 

 widely different functions of frequency. Thus, for example the im- 

 pedances of the amplifiers and modulators in most telephone systems 

 are nearly constant pure resistances. Non-loaded lines approach such 

 a characteristic at high frequencies but at low frequencies their im- 

 pedance is usually large and may have a considerable reactive com- 

 ponent. Loaded lines depart from a constant resistance at high fre- 

 quencies as well. An even more complicated characteristic, consisting 

 of a varying resistance in the transmitted band, changing abruptly to a 

 pure reactance as we pass the cutoff, is exhibited by a wave filter. In 

 addition to the normal propagation constants of the circuit, therefore, 

 we must take account of reflection effects at all of the junctions between 

 these various types of characteristic impedance. In a long circuit con- 

 taining impedance irregularities at many junctions, moreover, we must 

 give consideration to an enormous variety of waves which suffer multi- 

 ple reflections from a number of junctions. This complicated system 

 of factors may make life burdensome to the man who must evaluate 

 them, but since they are seldom large enough to grossly affect the 

 transmission characteristic of a circuit, they usually play otherwise a 

 secondary role in practical transmission analyses. They do, however, 

 blur the original clarity of the wave picture and from the standpoint of 

 theoretical simplicity at least, therefore, they should be eliminated. 

 For this purpose we should have at our disposal a network whose im- 

 pedances at its two ends could be assigned arbitrarily to match the 

 impedances actually present at any junction. 



The networks which form the subject of this paper were developed to 

 eliminate reflection effects which, in addition to being a nuisance from 

 the theoretical standpoint, were attended by serious practical conse- 

 quences as well. The engineering problem involved is described in the 

 paper on "Impedance Correction of Wave Filters" by E. B. Payne 

 appearing simultaneously in this Journal. Briefly, it appears from the 

 discussion in that paper that impedance mismatches at the junctions 

 between terminal or repeater equipment of carrier systems and the line 

 give rise to reflected waves which may produce cross-talk in neighboring 

 systems. This cross-talk can be reduced as much as we like by means 

 of line transpositions but the required transposition scheme is so ex- 



