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BELL SYSTEM TECHNICAL JOURNAL 



a unit semi-circle; in the stop ( + ) band it traverses the radius from 

 to 1, in the pass band it travels along the unit circle through 180 

 degrees to the value —1, completing the cycle from —1 to in the 

 stop ( — ) band. In this cycle there are four points of special interest, 

 corresponding to ratio values 1, 0, —1 and oo, for which the wave is 

 infinitely attenuated, unattenuated with an angular change of 0, 

 of 90, and of 180 degrees, respectively. It is at the 90 degree angle 

 that resonance of the individual section occurs; the iterative im- 

 pedance is then equal to 2\Z2\. 



Graph of the Ratio Z1/4Z2 for Fig. 14 



If we plot Z\ and 4Z2 the pass bands are shown by the points where 

 the curves become zero or infinite, and the intersections of the two 



500 Cycles 1000 



Fig. 16 — Graph for Locating the Pass and Stop Bands of the Lattice Artificial Line, 



where Z1/4Z2 = \{x\ - x^) {xl - .r^)-^ (xl - x^)! . . . , .r = cycles/100, and the 



resonant roots Xu Xz, ... are 0.650, 1, 2, 2A52,'4.U2, 5, 6, 8.476 and the double 

 anti-resonant roots Xi, .Yj. ... are 0.766, 2.301, 4.585, 7.423 



curves show the frequencies at which the attenuation becomes in- 

 finite. These intersections must be at an acute angle since each 

 branch of the two curves has a positive slope throughout its entire 

 length ; for this reason it may be desirable to plot the ratio rather than 

 the individual curves; this is especially desirable in cases where the 

 two curves do not intersect, but are tangent. Fig. 16 is for a lattice 

 network equivalent to two sections of the ladder type illustrated by 

 Fig. 7, and so cannot include a stop ( — ) band. Accordingly, the 

 ratio does not go above unity, although it reaches unity at the two 

 frequencies 300 and 400, corresponding to the infinite attenuation 

 where stop ( — ) and stop ( + ) bands meet in Fig. 7. It is also 



