. The Bell System technical journal . approximately, by (), Az/z0=ib/2=ia/2F. This analysis serves to account, approximately, for the nature of theeffects of small leakance, as depicted in Figs. 1 and 2 by the curves forsmall b and small a. To account for the effects of large leakance, asdepicted by the curves for large b and large a, recourse to the exactformula for Az/z0 would be necessary; but the curves for large leakancepossess hardly more than academic interest, as will be realized fromthe remarks already made under the heading The General Effect ofLeakance. SMOOTH LINES AND SIMULATIN
. The Bell System technical journal . approximately, by (), Az/z0=ib/2=ia/2F. This analysis serves to account, approximately, for the nature of theeffects of small leakance, as depicted in Figs. 1 and 2 by the curves forsmall b and small a. To account for the effects of large leakance, asdepicted by the curves for large b and large a, recourse to the exactformula for Az/z0 would be necessary; but the curves for large leakancepossess hardly more than academic interest, as will be realized fromthe remarks already made under the heading The General Effect ofLeakance. SMOOTH LINES AND SIMULATING NETWORKS When there is no leakance ((/ = (), and hence & = 0 and a = 0) equa-tions (10) and (11) reduce to the same form, namely z = \/\~i F. (12) This limiting form ot the equation for the relative impedance z israther important because it is comparatively simple and yet is a closeapproximation for the impedance of most actual lines except at verylow frequencies (since the effects of normal amounts of leakance are Relative Impedance K/k ofOpen-Wire Lines When —leakage is independentI of Frequency very small except at very low frequencies). It will therefore nowbe discussed with some fullness: For the case of no leakance the formulas for x and y are givenunder equation (12) in Appendix A; and are graphed in Fig. 1, (6 = 0),and in Fig. 2, (a=0). If the wires were devoid of resistance (i< = 0),x would be equal to unity and y would be zero. Thus the effect ofwire resistance (in a non-leaky line) is to make x greater than itslimiting value unity by the amount x — 1 (the relative excess resist-ance), and to introduce a negative value of y (the relative excessreactance, which is equal to the relative reactance). Bothx— 1 and — y increase with decreasing F; the increase being slow atlarge values of F, but more and more rapid as F is decreased, x — 1 12 BELL SYSTEM TECHNICAL JOURNAL is always smaller than — y; and is much smaller except at low valuesof F,
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