The Rigorous and Approximate Theories of Electrical 

 Transmission Along Wires 



By JOHN R. CARSON 



THE theory of electrical transmission along straight parallel guiding 

 conductors is of fundamental importance to the communication 

 engineer. In its original, and largely in its present day form, it 

 involves only relatively simple concepts which go back to the early 

 work of Kelvin and Heaviside. In accordance with these concepts 

 the transmission phenomena are completely determined by the self 

 and mutual impedances of the conductors and the self and mutual 

 capacities (together with the dielectric leakage). As a consequence, 

 the phenomena are completely expressed in terms of the propagation 

 constants and corresponding characteristic impedances of the possible 

 modes of propagation deducible from these underlying concepts. 



The elementary theory sketched above is of beautiful simplicity and 

 great value. It is, however, admittedly approximate, and in two 

 respects is not altogether adequate. Its first defect is that it represents 

 the transmission phenomena correctly only at some distance from the 

 physical terminals of the system or at some distance from points of 

 discontinuity. This defect is ordinarily of small practical significance 

 when the conductors all consist of wires of small cross section. When, 

 however, conductors of large cross sections, or the ground, form part 

 of the transmission system, the elementary theory may be quite 

 inadequate. The theoretical questions here involved were briefly 

 discussed by the writer in a previous paper.^ The mathematics 

 involved in this problem are extremely complicated and the further 

 work of the writer has not as yet been carried to a point which justifies 

 publication. 



With the extension of transmission theory discussed in the preceding 

 paragraph the present paper has no concern, and it is to be expressly 

 understood that we are dealing with the transmission phenomena at a 

 sufficient distance from the physical terminals, such that the "end 

 effects" are negligible. The problems here dealt with may be stated 

 as follows: First to investigate the conditions under which the specifi- 

 cation of the system by means of its self and mutual impedances is 

 valid and secondly to provide a general method for calculating these 

 circuit parameters from the geometry and electrical constants of the 

 system. 



1 "The Guided and Radiated Energy in Wire Transmission." Trans. A. I. E. E., 

 1924. 



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