TRANSM/SSIOX LINE EQUATIONS 



151 



Part II 



Transmission Lines Composed of Multi-terminal Sections 



2.1 Introductory 



Some transmission systems may be regarded as consisting of a number 

 of identical sections connected in tandem. Tlie question of determining 

 the steady state electrical behavior of such a system from a knowledge 

 of the properties of a single section will be considered here. 



Each section will have a certain number, say ;;? + 1, terminals on its 

 left end and an equal number on the right. The case in which there are 

 only two terminals (w = 1) has been completely worked out, and some 

 studies of more general cases have been made. The ones which most nearly 

 approach the point of view of the present paper are those due to S. Koizumi^. 



In the present work difference equations are used to solve the general 

 case in much the same manner as they have been used in studying the 

 two-terminal case. This approach differs from that used by Koizumi and 

 throws additional light on the problem. 



In several lists of formulas, particularly in Appendix IV, I have included 

 a number of results due to Koizumi for the sake of completeness. 



2.2 Transmission Equations for a Typical Section 



We consider the equations connecting the input and output currents and 

 voltages for the nth section which is shown in Fig. 1. The directions which 

 are assumed for positive current flow are indicated by arrows. The leads 

 marked play a special role in that all the voltages are 



l,(n + i) 



— IsCn + i) 



_.'Lm(n + 



Fig. 1 



measured with respect to them, and the currents which they carry are the 

 sum of the currents flowing into or out of the remaining terminals at the 

 end under consideration. In applications to transmission lines the terminals 

 would correspond to the ground or the cable sheath. 



The currents and voltages shown in Fig. 1 are related by a number of 



9 Archiv fur Electrotechnik, Vol. 33, pp. 171-188, 609-622 (1939). See also a paper 

 by M. G. Malti and S. E. Warschawski, Trans. A.I.E.E., Vol. 56, pp. 153-158 (1937). 



