TWO-TERMINAL BALANCING NETWORKS 285 



Tncluding G, the expression for the first approximation of the impedance 

 function may be written in the form 



Zi\) = 



= G)' 



1 + 



\2L 2C) 



^ IC 



(4) 



Following Erune's method or noting the correspondence with the impedance 

 function given in Fig. 1(c), it is apparent that the network is a resistance, 

 R\ , of 646.4 ohms in series with a parallel i?2C2 combination. Co is 1.09 

 mf as before but R2 computes as 312,000 ohms which is so large compared 

 to 1.09 mf. that the additional resistance provides negligible improvement 

 over the previous network for the voice frequency range. 



Obviously then, the analytical method requires at least a second order 

 approximation entailing considerable additional analytical work and com- 

 putation which will not be carried out here. This points out the advantages 

 of the graphical method; namely, it is rapid, requires no special skill, and 

 gives a reasonably accurate answer. 



Example 2 — Siral Four Cable — 1320 Foot Spacing — 6 Milhenry 

 Loading (SP4-1320-6) 



In order to indicate the procedure when two complete RC regenerating 

 functions are required, another example is given which covers an impedance 

 simulation of a SP4-1320-6 line. A plot of this impedance function is 

 shown on Fig. 3, and it is at once obvious that two semicircular generating 

 functions should give a reasonably good approximation to the given im- 

 pedance function. 



The method of selecting these functions may be somewhat as follows: 

 Consider first the simulation in the low-frequency range, i.e., 200 cycles to 

 500 cycles. For this region a semicircle may be selected much as in the 

 first example and the one chosen yields a network consisting of Ri = 480 

 ohms in series with the R2C2 parallel combination in which R2 — 1460 

 ohms. C2 was found by choosing an Xcj at 500 cycles close to. that of the 

 line and from which C2 was found to be 1.38 mf. 



It is evident that to provide high-frequency simulation a condenser must 

 be placed in parallel with Ri — 480 ohms. Its value is determined by the 

 intersection of the Ri and Xc^ semicircles at 10,000 cycles and Ci is found 

 to be .0161 mf. The construction lines involved in these determinations 

 are shown as light weight solid lines. 



Since there are now two impedance functions to be added in series the 

 locus will depart somewhat from the two semicircles. However, the de- 

 parture will not be great since the effect of Ci is small at low frequencies, 



