The Electromagnetic Theory of Coaxial Transmission Lines 

 and Cylindrical Shields 



By S. A. SCHELKUNOFF 



A form of circuit which is of considerable interest for the transmission 

 of high frequency currents is one consisting of a cylindrical conducting 

 tube within which a smaller conductor is coaxially placed. Such tubes 

 have found application in radio stations to connect transmitting and re- 

 ceiving apparatus to antennae. As a part of the development work on such 

 coaxial systems, it has been necessary to formulate the theory of trans- 

 mission over a coaxial circuit and of the shielding against inductive effects 

 which is afforded by the outer conductor. This paper deals generally 

 with the transmission theory of coaxial circuits and extends the theory 

 beyond the range of present application both as regards structure and 

 frequency. 



THE mathematical theory of wave propagation along a conductor 

 with an external coaxial return is very old, going back to the 

 work of Rayleigh, Heaviside and J. J. Thomson. Much important 

 work has been done in developing and extending this theory. Among 

 the problems dealt with in this development may be listed the follow- 

 ing: the extension of the theory to systems consisting of a plurality 

 of cylindrical conductors; the investigation of shielding and crosstalk 

 in coaxial systems and the effects of eccentricity; the extension of the 

 particular solution to include the complementary modes of propaga- 

 tion, etc.; and in general the adaptation of the mathematical theory 

 to engineering uses, and its translation into the concepts and language 

 of electric circuit theory. In addition to the author's contribution a 

 substantial part of this mathematical work has been done by the 

 group of engineers associated with Mr. John R. Carson, formerly of 

 the American Telephone and Telegraph Company, now of the Bell 

 Telephone Laboratories, Inc. 



The problem is ideally adapted to mathematical investigation, 

 because the conductor shape fits perfectly into the cylindrical system 

 of coordinates, thereby making it entirely feasible to carry out a 

 rigorous discussion on the basis of the electromagnetic theory, instead 

 of using ordinary circuit theory. This has obvious advantages at 

 ultra high frequencies, where the uncertainties of the circuit theory are 

 conspicuous and not easily compensated for. It also proves to be 

 of greater advantage at lower frequencies than one might at first 

 assume. Fortunately, it turns out that the final results obtained by 

 means of field theory can be expressed in a familiar language of circuit 



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