SMOOTH LINES AND SIMULATING NETWORKS 



When there is no leakance ((/ = (), and hence & = 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 is 

 rather important because it is comparatively simple and yet is a close 

 approximation for the impedance of most actual lines except at very 

 low frequencies (since the effects of normal amounts of leakance are 



16 

 1.4 

 1.2 



l.O 



Relative Impedance K/k of 

 Open-Wire Lines When — 

 leakage is independent 

 I of Frequency 



very small except at very low frequencies). It will therefore now 

 be discussed with some fullness: 



For the case of no leakance the formulas for x and y are given 

 under 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 of 

 wire resistance (in a non-leaky line) is to make x greater than its 

 limiting value unity by the amount x — 1 (the "relative excess resist- 

 ance"), and to introduce a negative value of y (the "relative excess 

 reactance," which is equal to the "relative reactance"). Both 

 x— 1 and — y increase with decreasing F; the increase being slow at 

 large values of F, but more and more rapid as F is decreased, x — 1 



