Dispersion curves for a helix in a glass tube

The dispersion equations giving the variation of velocity of propagation with frequency for a sheath helix (a thin cylinder conducting only in a helical direction) inside a dielectric tube are obtained, and, from these, dispersion curves are plotted for various ranges of the parameters (tube diameter, permittivity, wall thickness, etc.). Simple approximate formulae are derived and are used to discuss the general characteristics of the curves. A structure is given which would be non-dispersive over a very large frequency range. Its dispersion is less than ¿% for all values of ¿a above 1.2; a free-space sheath helix has 21% dispersion over the same range of frequencies. Experimental results are presented. There are considerable effects due to wire shape and size, not predicted by the sheath helix analysis. However, it appears that, from a single measurement of the velocity reduction due to thick glass, the velocity reduction due to glass of any thickness may be calculated from the formulae and curves given.