TWO-TERMINAL BALANCING NETWORKS 283 



i?2 is controlling and vice versa. The answer as to what value of C should be 

 selected depends on what frequency range we are most interested in approx- 

 imating closely. Suppose in this case that we say 1000 cycles is the fre- 

 quency at which we wish to have the best degree of approximation, d 

 will then be determined by drawing a vertical axis passing through Ri and 

 inscribing a semicircle passing through Ri and the 1000-cycle impedance 

 of the open-wire line function and having its diameter on the vertical 

 axis. The diameter of this semicircle represents Xc and therefore determines 

 the capacity, C2 -, of the parallel combination. 



Carrying out the procedure just described it will be seen by reference to 

 Fig. 2, that Xc^ = 145 ohms at 1000 cycles and therefore C2 = 1.1 mf. 

 The 3-element network thus determined is a resistance of 654 ohms in 

 series with the parallel combination of 1800 ohms and 1.1 mf. By arbitrary 

 choice the 1000-cycle impedance of the line and network are in good agree- 

 ment. It is now necessary to determine the network impedance at other 

 frequencies in order to compare them against the open-wire line impedance. 



As is well known the parallel impedance at any other frequency is the 

 intersection of the corresponding Xc and R2 semicircles. At 200 cycles Xc 

 = 725 ohms. Drawing a semicircle of diameter 725 ohms on the vertical 

 axis through 654 ohms the network impedance is located at the intersec- 

 tion of this semicircle and the R2 semicircle, i.e., at 900 — j 620. 



Thus the network impedance locus as a function of frequency may be 

 completely determined over the desired frequency range and compared with 

 the given impedance locus of the open wire. 



This may be done visually. If corresponding points on the two loci are 

 close together, the simulation will be a good one and vice versa. If it is 

 found that the simulation is too good at one frequency and not good enough 

 at other frequencies, it will be possible to alter the distribution of frequencies 

 along the locus by changing C2 or the locus may be shifted by changing R2 

 or both C2 and R2 may be changed. No specific rule can be stated for this 

 but with a little experience considerable dexterity may be acquired in this 

 sort of juggling and a locus found which will give an approximately con- 

 stant approximation over a reasonably wide frequency range. As may be 

 seen by referring to Fig. 2, it was found that a network consisting of a 654- 

 ohm resistance in series with the parallel combination of 1800 ohms and 

 1.10 mf . gives a very good simulation of a 104 rail copper open wire line over 

 the voice range. As is obvious from the graphical method, the simula- 

 tion rapidly deteriorates below 200 cycles due to departure of the network 

 locus from the impedance locus of the open wire line. If it were necessary 

 to improve this low-frequency simulation, it would be necessary to add 

 further generating functions to the design or compromise at the higher 

 frequencies. 



Since this network was intended for use as a balancing network, it was 



