Impedance of Loaded Lines, and Design of 

 Simulating and Compensating Networks 



By RAY S. HOYT 



Synopsis: A kn()\vk<li;e of the impedance characteristics of loaded lines 

 is of considerable iinporlance in telephone engineering, and particularly in 

 the engineering of telephone repeaters. The first half of the present paper 

 deals with the impedance of non-dissipative loaded lines as a function of the 

 frequency and the line constants, by means of description accompanied by 

 equations transformed to the most suitable forms and by graphs of those 

 equations; and it outlines qualitatively the nature of the modifications 

 produced by dissipation. The characteristics are correlated with those of 

 the corresponding smooth line. 



The somewhat complicated effects produced by the presence of dis- 

 tributcfl inductance are investigated rather fully. In the absence of 

 distributed inductance a loaded line would have only one transmitting 

 band, extending from zero frequency to the critical frequency. Actually, 

 however, every line — even a cable — has some distributed inductance; and 

 the effect of distributed inductance, besides altering the nominal impedance 

 and the critical frequency, is to introduce into the attenuating range above 

 the critical frequency a series of relatively narrow transmitting bands — 

 here termed the "minor transmitting bands" — spaced at relati\ely wide 

 intervals. The paper is concerned primarily with the impedance in the 

 first or major transmitting band; but it investigates the minor trans- 

 mitting bands sufficiently to determine how they depend on the distributed 

 inductance, and to derive general formulas and graphical methods for 

 finding their locations and widths — an investigation involving rather 

 extensive analysis. 



The latter half of the paper describes various networks devised for simu- 

 lating and for compensating the imiiedance of loaded lines; it furnishes 

 design-formulas an<l supplenientary design-methods for all of the networks 

 depicted; and outlines a considerable number of applications pertaining 

 to lines and to repeaters. 



T 



Introduction 



lliC iJicsfiU paper on periodically loaded lines (of the 

 series type) is to some extent a sequel to a previous paper 

 on smooth lines.' 



The reader may l)e reminded that the transmission of alternating 

 currents over any transmission line between specified terminal im- 

 pedances depends only on the propagation constant and the char- 

 acteristic impedance of the line. In this sense, then, the character- 

 istics of transmission lines may be classed broadly as propagation 

 characteristics and impedance characteristics. In telephony we are 

 concerned primarih- with the dependence of these characteristics on 

 the frequencN', o\er the telephonic frequency range. 



Prior to the apjilicalion of telephone repeaters to telephone lines the 

 propagation characteristics of such lines were more important than 



' " Impedance of -Smooth Lines, and Design of Simulating Networks," this Journal^ • 

 .Xpril, 1"»J3. Two t>p<)graphical errors in that article may here be noted; p. 37' 

 formula for G/C», affix an exponent ^ to the last parenthesis; p. 39, value for C,' 

 replace comma by decimal point. 



414 



