SMOOTH LINES AND SIMULATING NETWORKS 19 



The Simplest Excess-Simulator, and Complete Network 



The simplest type of excess-simulator is a mere rapacity C\ (Fig. 6b). 

 This is adequate only for those lines whose excess characteristic 

 resistance is negligible; as, for instance, large gauge open-wire lines, 

 and even then not at very low frequencies. The capacity C\ is cap- 



(a)o — wwww — o o |f- — o(b) 



R 1 Ci 



(c) o VWWWV — o \\- o 



Fig. 6— Synthesis of the Simplest Type of Complete Network, (a). Basic Resist- 

 ance, (b). Excess-Simulator, (c). Complete Network 



able of simulating the reactance N of such a line rather closely, and 

 its proper value for that purpose is approximately 



_ 2VLC r 2VL/C m) 



although the most suitable value depends somewhat on the specific 

 frequency-range involved. The complete network (Fig. 6c) thus 

 consists merely of a resistance i?x and a capacity G in series with each 

 other, having approximately the values expressed by (30) and (31). 8 

 The simple network in Fig. 6c was devised a good many years ago. 9 

 The majority of present-day applications require such high simulative 

 precision that the excess characteristic resistance of the line is not 

 negligible, and also a mere capacity does not in all cases simulate 

 the excess characteristic reactance quite as closely as desirable. To 

 meet these needs there have been devised the much more precise, 

 yet fairly simple, excess-simulators and complete networks described 

 under several of the following headings. 



Two Precise Types of Excess-Simulators, and Their Limiting Forms 



Fig. 7 represents two potentially equivalent 10 excess-simulators 

 that in most cases admit of such proportioning as to simulate with 



8 See Appendix B for the derivation of formula (31) for t\, and incidentally formula 

 (30) for Ri\ and for a discussion of the simulative precision of this network; also 

 for the values Ri and L\' requisite for exact simulation at any preassigned single 

 frequency. 



•In 1913. U. S. Patent No. 1,167,694 of January 11, 1916. 



10 In comparing networks as to equivalence I have found very useful the general 

 theorems on equivalence given by O. J. Zobel in his paper on electric wave-filters 

 in the January Number of this Journal, pages 45-46. 



