SMOOTH LINES AND SIMULATING NETWORKS 17 



Part IV 

 Networks for Simulating the Impedance of Smooth Lines 



Under this heading will be described the various networks devised 

 by the writer, for simulating the characteristic impedance of smooth 

 lines, as mentioned in the latter part of the Introduction. Before 

 proceeding to the systematic description of these networks, some of 

 their practical uses will be mentioned. Foremost of these is their 

 employment for balancing purposes in connection with 22-type re- 

 peaters, already spoken of in the Introduction. Another application 

 is for properly terminating an actual telephone line in the field or an 

 artificial line in the laboratory, usually for electrical testing purposes 

 or electrical measurements on the lines. In making certain tests 

 on apparatus normally associated with a telephone line, such line 

 may be conveniently represented for impedance purposes by the ap- 

 propriate simulating network. 



Some of the networks to be shown are potentially equivalent in 

 impedance; but may differ somewhat in cost, space occupied, etc. 

 For the purpose of this paper any two networks will be called " po- 

 tentially equivalent " if, when the elements of either network are 

 assigned any arbitrary values, the other network can be so pro- 

 portioned as to have at all frequencies identically the same impedance 

 as the first network. Evidently the mathematical condition for 

 such equivalence is that the expressions for the impedances of the two 

 networks have the same functional forms when the frequency is re- 

 garded as the independent variable. The two networks will then 

 have the same number of independent parameters, or degrees of 

 freedom for adjustment; and this number is the same as the mini- 

 mum number of elements requisite for the construction of a network 

 to have identically the impedance of the given network. 



For most of the networks described, there are included design- 

 formulas for the values of the network elements (resistances and 

 capacities). But in any applications requiring the highest simulative 

 precision attainable with such networks, these formulas should be 

 regarded merely as first approximations serving to reduce the requisite 

 detailed design-work down to a relatively small amount but not 

 permitting it to be dispensed with entirely; for the best values of the 

 network elements depend somewhat on the particular frequency- 

 range involved, and on the preassigned weighting of the desired 

 simulative precision with respect to the frequency. Moreover, these 

 formulas completely ignore leakance; while actually leakance may 

 not always be quite negligible, even in the voice frequency-range. 



