TWO-TERMINAL BALANCING NETWORKS 287 



impedance of the network at frequencies from 100 cycles to 15,000 cycles 

 and, as may be seen by the comparison, a fairly good simulation exists 

 throughout the range. This fact has been verified by making return loss 

 measurements in the laboratory against the theoretical line with the results 

 indicated in the table. Return loss measurements have also been made be- 

 tween the network and an artificial line consisting of 120 sections of this 

 facility terminated in 450 ohms. These results show a fairly constant re- 

 turn loss of about 25 db throughout the frequency range. This seems to 

 indicate that the simulating network is a fairly close approximation to the 

 artificial line so far as frequency is concerned and differs from it by a con- 

 stant multiplying factor which is of the order of 1.12. It is therefore ap- 

 parent that whenever it is necessary only to simulate the impedance of this 

 particular facility, this four-element network will provide a fairly adequate 

 simulation. The analytical derivation of this network will be omitted. 



Example 3a — Non-loaded Exchange Area Cable 



Another case will be cited to show the application of the graphical 

 method. This is the simulation of non-loaded cable of which the local 

 plant is largely composed in urban areas. A first approximation of the 

 analytical method does not yield a useful network but the graphical method 

 provides a three-element network of the type discussed above which gives a 

 return of about 20 db in the 300 cycles to 3000 cycles range. The graphical 

 derivation of the three-element network is shown on Fig. 4 which also gives 

 the impedance function for 22 ga. BSA non-loaded cable. This latter func- 

 tion is virtually a straight line in the voice range whereas the network is the 

 arc of a circle. Hence it would be impossible to obtain an appreciably 

 closer approximation throughout the range with a three-element network. 

 However, the addition of elements will improve the match as will be shown 

 in example 3b. 



The network just derived can be expressed in terms of the 1000-cycle 

 impedance and applied for any gauge of non-loaded cable as follows : 



Rx = .42 K (5-a) 



i?2 = 2.8 K (5-b) 



Xc, = .9 K (5-c) 

 where K is the magnitude of the 1000-cycle impedance and 



. Table Ilia gives a comparison of the network and line impedances and the 

 computed return loss for frequencies through the 200 to 3000 cycle range. 



