Mathematical Theory of Laminated Transmission Lines - Part I

A recent theoretical paper1 by A. M. Clogston presents the very interesting discovery that under certain conditions skin effect losses in the conductors of a transmission line at elevated frequencies can be much reduced by laminating the conducting surfaces, parallel to the direction of current flow, with alternate thin layers of conducting and insulating material. The requirements are that the thickness of each conducting layer must be considerably smaller than the skin depth in the conductor, and the phase velocity of waves on the transmission line must be held very close to a certain critical value, which depends 011 the relative thicknesses and the electrical properties of the conducting and insulating layers. Under these conditions the "effective skin depth" of the laminated surface is greatly increased; in other words, the eddy currents induced by a high-frequency alternating field will penetrate much farther into such a laminated structure than into a solid conductor, with consequent marked reduction of ohmic losses in the metal. The metal losses can also be made to vary much less with frequency, over a fixed band, than the ordinary skin effect losses, which are known to be very nearly proportional to the square root of frequency. Clogston goes on to show that a laminated material composed of alternate thin conducting and insulating layers may itself be regarded as a transmission medium. For example, if the space in a coaxial cable which is ordinarily occupied by air or other dielectric be filled with a large number of coaxial cylindrical tubes which are alternately conducting and insulating, the cable will propagate various transmission modes, and under the proper circumstances some of these modes will exhibit lower attenuation constants than the transmission mode in a conventional coaxial cable of the same size at the same frequency.