The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

HE 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 following: 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 propagation, 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.