464 BELL SYSTEM TECHNICAL JOURNAL 



and hence the widths of the compaund bands, decrease in direct 

 proportion to increase of V \. The internal transition frequencies, 

 however, do not decrease so rapidly; for the ratio of transmitting 

 band width to attenuating band width increases with increasing X. 

 When X approaches infinity each compound band approaches a width 

 of zero, but the ratio of transmitting band width to compound band 

 width approaches unity; so that when X becomes infinite there are 

 within any finite frequency range an infinite number of compound 

 bands which are pure transmitting bands. On the other hand, when 

 X approaches zero the compound bands approach infinite width and 

 hence move out toward infinit>', except that the left end-point of 

 the first band is fixed at / = 0. When X has become zero the first 

 compound band has expanded to an infinite width; and its critical 

 x'alue /i of/ has become equal to the limiting \alue /'i = l/7r v L'C 

 — as can be seen from (14-A) b\- putting n = \ and then applying the 

 relation D/V\ =hwVL'C. 



When LC is fixed the /-widths and locations of the compound bands 

 are independent of X, but the widths of the constituent attenuating 

 and transmitting bands depend on X; that is, the boundary points 

 Jn-\.n and /n.n+i of the Hth compouud band are independent of X, 

 but the internal transition point /„ depends on X. With increasing 

 X the attenuating bands become continually narrower, and vanish 

 when X becomes infinite, the transmitting bands thereby coalescing to 

 form a pure transmitting band extending from zero to infinity. With 

 decreasing X the transmitting bands become continually narrower, 

 and vanish when X becomes zero, the attenuating bands thereby 

 coalescing to form a pure attenuating band extciuling from zero to 

 infinity. 



.M'PKNDIX B 



tm-loriitral b.\sf.s of the simulating networks in 

 Figs. 12 and 13 



The Impedance- Simulator in Fig. 12 



This network takes advantage of the fact, depicted in V\g. 5, that 

 the graph of the cr-section characteristic resistance of a loaded line, 

 for values of a in the neighborhood of 0.2, is nearly flat o\'er most 

 of the transmitting band and hence can be approximately simulated 

 by a mere constant resistance chosen approximately equal to the 

 nominal impedance y/ L' fC. This is the basis for the /?i-portion of 

 the network in Kig. 12. The l)asis for the LiCi-portion is the fact 

 (proved in Appendix C) that, in the transmitting band, the (r-section 



