ARTIFICIAL ELECTRIC LINES WITH MUTUAL INDUCTANCE 209 



III. An Artificial Line to Simulate an Actual Smooth Line. 



Improvement as to Attenuation and Surge Impedance brought 

 ABOUT BY Proper Mutual Induction between Series Sections. 



14. Constants for Actual Smooth Line. — In the case of an 

 actual smooth line, let 



r, I, c = respectively the resistance, self-inductance, and capa- 

 city per loop unit of length; 

 a = real attenuation constant per unit of length; 

 13 = angle of lag of current per unit of length ; 

 Zi= surge impedance of the line; 



then 



a = CO 



(3 = CO 



l\ 







C /CO 



(31) 



(32) 



(33) 



These equations are the familiar expressions. See, for example 

 El. Osc. and El. Waves, pp. 329 and 330. 



15. To Design an Artificial Line with Lumped Sections that 

 Will Simulate the Smooth Line as to Surge Impedance. — For 



this purpose we shall postulate a line of the type shown in Figure 3, 

 and shall determine what value of M brings the surge impedance of 

 this line, as is given in (30), most nearly into the form of (33) in so far 

 as dependence of s,- on co is concerned. Since the real part of (30) 

 is generally much larger than the imaginary part, it is seen by inspec- 

 tion that a good approximation to this result is made by making 



M = L/4.; (34) 



which bv (13) means > 



M = Li/2. (35) 



