328 BELL SYSTEM TECHNICAL JOURNAL 



These values are to be substituted in (47) to obtain four linear equa- 

 tions. The solution of these linear equations gives 



Of) = ri — fiXibi — fi^fib-2, 

 «i = ribi — fiXib-2 + xi/fu 

 ^^ fj^ihx, -hx,){r, - r.) + (.A-V2 -/■a-0(/iVi -/2V2) ^5^^ 



, _ iMr, - r,)2 + (/,A-, - hx.Mf.x, - fuX2) 

 tH - j^ ' 



where 



D =/./.{(/iVi -/.V2)(^i - r,) + (/ixi -f-2X.y}. 



From the values of «o, fli, ^1. and b-. the network constants can be 

 computed by formulas (46). The network impedance is then given at 

 any frequency by formula (45). 



The actual impedance simulating Ki is the sum, Z/ = Zi + s; that 

 simulating K2 is the sum, Z-/ = Z2 + -. 



It should be pointed out here that the supplementary network may, 

 if desired, be given other structural forms having two resistances and 

 two capacities and having an equivalent impedance characteristic. 

 These other forms may be obtained by transformations from the 

 known one above or their elements determined from other formulas 

 corresponding to those of (46). 



Likewise, a supplementary network which has a smaller or larger 

 number of elements than the one above might be used satisfactorily 

 with the same basic networks or their equivalents. That depends upon 

 the low-frequency impedance characteristics of the given loaded line 

 and upon the closeness of simulation desired. 



4.5 Application of Results 



To illustrate the possibilities of these impedance networks, mid-load 

 and mid-section designs are given here for a 19-gauge B-88-50 loaded 

 side-circuit. The "5 " spacing is 5 = .568 mile (3000 feet). 



Data for the mid-load basic network, taken from computations of 

 A'l, are 



fa = 3000, I'a - 1324; 

 and 



fb = 5000, n = 720. 



These give from (42), R = 1564.4 ohms, and /o = 5632 cycles per 

 second. 



Data for the mid -section basic network, taken from computations 



