. The Bell System technical journal . onding to K, r to E, /q to k2, and &i to g2. fi It will he noted that b is the same as already denned by (7); bi is related to b;and Fi is related to F, which has already been defined by (2). 16 BELL SYSTEM TECHNICAL JOURNAL In other respects, however, there are marked differences: K is animpedance, while w is a pure number, being the ratio of K to vR/uiC;E, though approximately proportional to the frequency, is not a purenumber (for it is not dimensionless), while r is a pure number, beingthe ratio of the general frequency to any fixed frequency; of the p
. The Bell System technical journal . onding to K, r to E, /q to k2, and &i to g2. fi It will he noted that b is the same as already denned by (7); bi is related to b;and Fi is related to F, which has already been defined by (2). 16 BELL SYSTEM TECHNICAL JOURNAL In other respects, however, there are marked differences: K is animpedance, while w is a pure number, being the ratio of K to vR/uiC;E, though approximately proportional to the frequency, is not a purenumber (for it is not dimensionless), while r is a pure number, beingthe ratio of the general frequency to any fixed frequency; of the para-meters, k2 is very different from Fi, and bi is very different from fact that (27) and (28) are of the same functional forms as (19)and (20) respectively renders formally applicable the material per-taining to equations (19) and (20) given in Appendix A. As already remarked, the effect of leakance in cables is usuallyextremely small except at very low frequencies. Hence in the graphi- mpedanceK/IKJofLeaky Cables u Fi=2. cal representation of formulas (27) and (28) it will suffice for mostpurposes to confine ourselves to the limiting case of no leakance(G = 0, and hence b = 0 and bi — 0), when these two equations reduceto the same form, namely, = VFi-i/r. (29) This has the same functional form as (21), with w corresponding toK, r to E, and F\ to k2; a circumstance rendering formally applicablethe material pertaining to equation (21) given in Appendix A. Thecurves in Fig. 4 represent the two components u and v of w as functionsof r with F\ as parameter. SMOOTH LINES AND SIMULATING NETWORKS 17 Part IVNetworks for Simulating the Impedance of Smooth Lines Under this heading will be described the various networks devisedby the writer, for simulating the characteristic impedance of smoothlines, as mentioned in the latter part of the Introduction. Beforeproceeding to the systematic description of these networks, some oftheir practical uses will be mentioned. Foremost of th
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