2 BELL SYSTEM TECHNICAL JOURNAL 



21-type, impedance networks are required for closely balancing the 

 impedances of the two lines throughout the telephonic frequency 

 range. Such balancing networks are necessary also in connection 

 with the so-called four-wire repeater circuit. 1 



Smooth lines are fundamental in telephonic transmission; for any 

 telephone line is either a simple smooth line, or a compound smooth 

 line, or a periodically loaded line whose sections are themselves short 

 smooth lines. In any case the characteristic impedances of the con- 

 stituent smooth lines enter importantly into the impedance of the 

 system. Moreover, the characteristic impedance of the series type of 

 periodically loaded line, at frequencies low relatively to its critical 

 frequency, is closely the same as the characteristic impedance of the 

 corresponding smooth line. 



Parts I, II, and III of this paper aim to present in a simple yet 

 comprehensive manner the dependence of the characteristic impedance 

 of the various types of smooth lines on the frequency and on the line 

 constants, by means of description accompanied by equations 

 transformed to the most suitable forms and by graphs of such 

 equations. 



Part IV describes the principal networks devised by the writer at 

 various times within about the last ten years, for simulating the im- 

 pedance of the various types of smooth lines. Of course, the imped- 

 ance of any line could be simulated, as closely as desired, by means 

 of an artificial model constructed of many short sections each having 

 lumped constants; but such structures would be very expensive and 

 very cumbersome. Compared with them the networks described in 

 this paper are very simple non-periodic stiuctures that are relatively 

 inexpensive and are quite compact; yet the more precise of them have 

 proved to be adequate for simulating with high precision the im- 

 pedance of most types of smooth lines, while even the least precise 

 (which are the simplest) suffice for a good many applications. The 

 paper includes first approximation design-formulas and outlines a 

 supplementary semi-graphical method for arriving at the best pro- 

 portioning of the networks. A typical illustrative example is worked 

 out in Appendix E. 



It is hoped to devote a succeeding paper to the impedance char- 

 acteristics of periodically loaded lines, and to various networks de- 

 vised for simulating and compensating such impedance. 



'Regarding the broad subject of repeaters and repeater circuits, reference may 

 be made to the paper by Gherardi and Jewett: "Telephone Repeaters," A. I. E. E. 

 Trans., 1919, pp. 1287-1345. 



