Attenuation in Continuously Loaded Coaxial Cables

The development of ferrite materials having high permeability and low loss at high frequencies has raised again the question of continuous loading of coaxial cables. The question is one of many treated in a recent thorough paper 011 loading by P. M. Prache. 1,2 He considers, among other things, cables loaded with coaxial cylinders of magnetic material, and attacks the problem of minimizing the attenuation through the regulation of various free parameters. The present paper is another attempt to find the conditions under which attenuation in a loaded coaxial cable is a minimum.3 It differs from the previous attempts in several respects. First, a drastic set of changes of variable makes the problem much easier to manage mathematically. Second, the resulting simplification makes it possible to include the effect of dielectric loss in the loading material. Third, a detailed analysis of magnetic losses, such as found in Prache's paper, is ignored and losses are described in terms of Q, the ratio of peak energy stored to energy lost per radian. Special assumptions about the joint restrictions on Q and the permeability (01* dielectric constant, as the case may be) are reserved for later steps in the analysis. This paper is entirely theoretical. The results indicate that substantial reductions in attenuation are possible at frequencies of a few megacycles with magnetic materials having a pQ product (p = relative per361