744 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Importance of Cut-Off Frequency 



Basically, the general impedance-matching problem under discussion is 

 complicated by the fact that the non-loaded line is a "smooth," i.e., a 

 uniform, line, whereas the loaded cable is a "lumpy" line. On the one hand, 

 the sending-end impedance of the non-loaded line is substantially a constant 

 resistance with negligible reactance over the frequency range above about 

 1 kc. On the other hand, the high-frequency impedance of the loaded cable 

 may vary substantially in its resistance and reactance components with 

 rising frequency, depending upon the type of loading termination employed. 

 "Half-coil" and "mid-section" terminations have the important advantage 

 of substantially negligible reactance, for which reason one or the other of 

 them was used in the early applications of impedance-matching loading. ^"^^ 

 With these particular loading terminations, the resistance component of the 

 loaded cable impedance changes with rising frequency, at a rapidly ac- 

 celerating rate as the cut-off frequency is approached. The reference im- 

 pedance in these changes is the nominal impedance of the loaded cable, 

 which for optimum impedance-matching should be equal to that of the non- 

 loaded line. (Numerically, the nominal impedance in ohms is equal to the 

 square root of the ratio of the total circuit inductance, in henrys, to the 

 total mutual capacitance, in farads, per unit length.) The resistance changes 

 with rising frequency go up when mid-section termination is used, and drop 

 down when half-coil termination is used. 



The important practical significance of the foregoing is that the high- 

 frequency impedance irregularities at the open-wire cable junction become 

 progressively smaller as the loading cut-off frequency is raised (provided 

 that the nominal impedances of the line and cable are closely alike). With 

 the simple types of loading terminations above described, the requirements 

 for good impedance-matching make it desirable to have much higher cut-off 

 frequencies than those which are necessary from the standpoint of attenu- 

 ation-frequency distortion in entrance and intermediate cables. 



E28-16 Loading 



The discontinuance of the manufacture of open-wire loading coils about 

 1924, and the decreasing importance of open-wire loading, made it desirable 

 to discontinue the use of the E-spaced loading solely for entrance and inter- 

 mediate cables. Plant simplicity and flexibility requirements made it de- 

 sirable to use H-spaced loading to permit coordination with the loading 



<^^ Half-coil termination involves the use of coils having one-half of the regular "full- 

 coil" inductance at the end of the cahle, followed in regular periodic sequence by "full" 

 loading sections and "full" loading coils. In "mid-section" termination, the first full- 

 coil is located one-half of a full loading section away from the end of the cable. 



