152 THE BELL SYSTEM TECHNICAL JOURNAL, JANU/VUY 1951 



PART I: THE BEGINNINGS OF COIL LOADING • 

 General Theory 



For present purposes, a rigorous presentation of the mathematical theory 

 of coil loading is unnecessary/^^ A simple description and a brief statement 

 of theory is sufficient. 



The primary purpose of coil loading is to improve the transmission of 

 intelligence by substantially reducing the circuit attenuation, and by making 

 the circuit attenuation approximately uniform throughout a predetermined 

 frequency-band. These transmission benefits are obtained by serially in- 

 serting coils having uniform inductance values at regularly recurring inter- 

 vals along the circuit, but are limited to a frequency-band below the loading 

 cut-off frequency. This is an inverse function of the square root of the 

 product of the coil inductance and of the mutual capacitance of the loading 

 sections between successive coils, as determined by the coil spacing and 

 unit-length capacitance of the circuit. Above the loading cut-off frequency, 

 there is a substantial suppression of transmission. 



For more than a decade prior to Campbell's and Pupin's 1899 researches, 

 the theoretical possibility of improving transmission over telephone lines 

 by artificially increasing their inductance had become known from the 

 mathematical studies of Vaschy and Heaviside. Also there had been con- 

 siderable speculation by them"*- ^, and by others, regarding the practicability 

 of approximating the advantages of uniformly distributed inductance by 

 inserting low-resistance inductance coils along the line. Rules for spacing 

 the lumped inductances had not been worked out, however, nor had suitable 

 coils been developed. 



The requisite coil-spacing turned out to be such that there are several 

 coils per wave length at the highest frequency which should be efficiently 

 transmitted to obtain satisfactory intelligibility. Here, "several" means 

 more than two, since at the theoretical cut-off frequency there are two 

 coils per wave length. In terms of the nominal velocity of propagation of 

 the "corresponding smooth line" (a hypothetical line having the same 

 total inductance and capacitance) there are tt coils per wave length at the 

 cut-off frequency; expressed in "loads-per-second," this nominal velocity 

 is exactly w times the cut-off frequency in cycles per second. 



The attenuation improvement obtainable with loading corresponds some- 

 what to the increase in impedance that results from the increase in induct- 



^> Readers interested in the rigorous mathematical theory are referred to Bibliography 

 items (1) and (2), Campbell's treatment has been extensively used by communication 

 engineers l)ecause of its comprehensive coverage of the frequency band concept in which 

 the cut-ofT effects on propagation and impedance are emphasized. Also, his disclosures 

 include explicitly the effects of conductor resistance and ratio of coil resistance to con- 

 ductor resistance. His general formulas include the distributed inductance and leakage. 



