282 



BELL SYSTEM TECHNICAL JOURNAL 



Example 1 — 104 Mil Open Wire 



To demonstrate the method we will now consider the design of a net- 

 work which simulates a 104-mil copper open-wire line with 12 in. spacing 

 and CS insulators. The impedance function for this particular facility is 

 plotted on Fig. 2. It is perhaps rather obvious that this locus can readily 

 be approximated by a semicircle whose center is on the real axis and whose 

 intercept on the real axis is not at the origin. Such a semicircle has been 

 drawn, but it is recognized that the one shown is not unique, for it would be 

 possible to draw several others which might do equally well. However, they 



3 -600 



< 



IMPEDANCE FUNCTION 

 FOR I04CU.O.W. 

 12 SPACING CS 

 INSULATORS 

 DRY WEATHER 



■IMPEDANCE FUNCTION 

 FOR NETWORK 



R|=654 

 C2-I.I 



MF=b 



R2 = 

 1600' 



200 



400 



600 



1200 



1400 



800 1000 



RESISTANCE 



Fig. 2. — Graphical design of two-terminal baiancmg network for 104-mil. copper 



open wire. 



would in general be fairly close to that shown. Having selected this semi- 

 circle, which approximates the impedance function, it is evident that a net- 

 work consisting of a resistance, Ri , in series with a parallel R2C2 combination 

 will provide a reasonable approximation above 200 cycles. The series re- 

 sistance Ri , is, of course, the left-hand intercept of the semicircle and the R 

 axis and the parallel resistance, R2 , is the diameter of the semicircle. There 

 remains, then, the problem of determining Co which obviously governs the 

 distribution of frequencies along the semicircular locus. If C2 is very small, 

 the 1000 cycle impedance will be near the right-hand end of the locus since 



