3(A BELL SYSTEM TECHXICAL JOURNAL 



Although it is ciittitult to take- exact account of \bv \aiial)lc char- 

 acteristics of the loader! cable in the solution of the transient problem, 

 it is easy to take account of them in the steady state or iK-riotlic 

 analysis by means of well-known methods. If a steady sinusoidal 

 voltage, Vs, is applied at one end of the cable the resulting voltage, 

 /,, at the distant end will lie gi\-en b\- the e(|uali(in 



where / is the leiii;lli, P, the |)r()pagalion coiislaiit of tlie caljle and k, 

 a constant which depends on the terminal impedance and which is 

 unity in case the cable is terminated at the receiving end in its so- 

 called characteristic impedance. Tiie propatjation constant is gi\eii 

 by the formula, 



P=\/{R+ipL){G+ipCJ = a+ifi, 



where R is the resistance, L, the inductance, G, the leakance and C, 

 the capacity per unit length and p is 2w times the frequency. The real 

 part of the propagation constant, a, is called the attenuation constant 

 and the imaginary part, /3, the wave length constant. By separating 

 a and the amplitude and phase displacement of the received voltage 

 relative to the sent voltage may be computed for any particular 

 frequency and the behavior of a complex signal train may be worked 

 out b^■ analyzing it into its Fourier components and treating them 

 separately. The phase shift is, however, of importance mainly as 

 regards the shape of the received signals and their amplitude may, 

 in general, be obtained from the attenuation constant alone. Thus 

 if it is known that the signal shai>e can in any case be corrected by 

 terminal networks there is no need to be concerned with more than 

 the attenuation constant to compute the speed of the cable. 



In the case of a cable of the permalloy loaded type, a is gi\en with 

 an apijroximation " sufficiently close for the purposes of this discus- 

 siiiii li\' llie (-(iiKilidii. 



uu-<-P-y 



For the purpose of comi)uting R it is ciiineiiienl to sejiarate it into 

 its components, giving 



a=^yj^^(^R, + R. + R, + R,+ ^^,Ly 



' Kor accuriite cuinputation of iittenu.itloii the coiiipUtc furimila for a must be 



