434 BELL SYSTEM TECHNICAL JOURNAL 



The effect of adding distributed inductance L to a loaded line 

 (L', C) having originally none is to replace the previous single com- 

 pound band of infinite width by an infinite number of compound 

 bands each of finite width. The larger L the narrower are the com- 

 pound /-bands, and the further to the left they are situated. Although, 

 as already noted, increasing L decreases the critical frequency, it 

 increases the relative width of each transmitting band — namely, the 

 ratio of the width of each transmitting band to the compound band of 

 which it is a constituent. Thus, when L becomes very large (so that 

 LC and X become very large) there are within even a moderate fre- 

 quency-range a very large number of compound bands whose trans- 

 mitting constituents are \-cry wide compared with the attenuating 

 constituents. 



The effect of applying lumped loading to a given smooth line (L, C) 

 is to introduce into the previous transmitting band of infinite width 

 an infinite number of attenuating bands whose upper boundary points 

 are equidistant and whose widths continually decrease toward the 

 lower frequencies. When the inductance L' of the loads is con- 

 tinually increased the attenuating bands continually increase in 

 width as a consequence of their lower boundary points moving down- 

 ward to lower frequencies, so that ultimately the attenuating bands 

 fill the entire frequency scale from zero to infinity. An alternative 

 but equivalent statement regarding the effect of applying lumped 

 loading is that the previous pure transmitting bands, each of D- 

 width equal to w/2, become compound bands whose attenuating 

 constituents continually increase in width when L' is increased. 



(The four preceding paragraphs are based on the last five para- 

 graphs of Appendix A.) 



In Fig. 6 the transmitting bands are represented as being relatively 

 narrow compared with the attenuating bands. In e.xisting loaded 

 lines this is indeed the case, but it is not an inherent relation: for any 

 number of the transmitting bands can be made wider than the associ- 

 ated attenuating bands by so designing the loading (lumped or smooth 

 or both) as to secure a sufficiently large \alue of the ratio \ = L/L'. 

 (However, for any fi.xcd loading and hence a fi.\ed value of X, there 

 is some frequency beyond which the transmitting bands are narrower 

 than the associated attenuating bands.) 



There will now be gi\'en two examples illustrating the relations rep- 

 resented in Fig. 6, and illustrating also the apjilications of certain 

 of the foregoing formulas and grai)hs. 



The first example pertains to a heavily loaded open-wire line of 

 No. 12 N. B. S. gauge, having loading coils of inductance L' = 0.241 



